diff --git a/build/pkgs/nauty/checksums.ini b/build/pkgs/nauty/checksums.ini
index 644f4b75146..a9dd1246e91 100644
--- a/build/pkgs/nauty/checksums.ini
+++ b/build/pkgs/nauty/checksums.ini
@@ -1,5 +1,5 @@
 tarball=nautyVERSION.tar.gz
-sha1=c9fd2b4c99b8c624e430f3f4e1492a4219e3495e
-md5=2ead635a417e20a18b3aabee83fac1ef
-cksum=718823455
-upstream_url=http://pallini.di.uniroma1.it/nauty27r1.tar.gz
+sha1=10c39117c55c69c18c6a107110e7c08f3d873652
+md5=7a82f4209f5d552da3078c67e5af872e
+cksum=2164796643
+upstream_url=https://pallini.di.uniroma1.it/nauty2_8_6.tar.gz
diff --git a/build/pkgs/nauty/package-version.txt b/build/pkgs/nauty/package-version.txt
index 9a8067baa68..b6b3dcc5aa0 100644
--- a/build/pkgs/nauty/package-version.txt
+++ b/build/pkgs/nauty/package-version.txt
@@ -1 +1 @@
-27r1.p1
+2.8.6.p0
diff --git a/build/pkgs/nauty/patches/nauty-2.8.6-gentreeg-gentourng.patch b/build/pkgs/nauty/patches/nauty-2.8.6-gentreeg-gentourng.patch
new file mode 100644
index 00000000000..322b25326ee
--- /dev/null
+++ b/build/pkgs/nauty/patches/nauty-2.8.6-gentreeg-gentourng.patch
@@ -0,0 +1,144 @@
+From edb0474a4db8e69f971e4eebe18716309f5a7bb3 Mon Sep 17 00:00:00 2001
+From: Michael Orlitzky <michael@orlitzky.com>
+Date: Tue, 17 Jan 2023 19:44:49 -0500
+Subject: [PATCH 1/1] Upstream fixes for gentreeg and gentourng.
+
+https://mailman.anu.edu.au/pipermail/nauty/2023-January/000903.html
+---
+ gentourng.c |  2 +-
+ gentreeg.c  | 95 ++++++++++++++++++++++++++++-------------------------
+ 2 files changed, 51 insertions(+), 46 deletions(-)
+
+diff --git a/gentourng.c b/gentourng.c
+index 634e5e8..5c7ffff 100644
+--- a/gentourng.c
++++ b/gentourng.c
+@@ -1408,7 +1408,7 @@ PLUGIN_INIT
+                 (*outproc)(outfile,g,1);
+             }
+         }
+-        else
++        else if (!connec || maxn != 2)
+         {
+             makeleveldata();
+ 
+diff --git a/gentreeg.c b/gentreeg.c
+index 946d5f8..15bf87b 100644
+--- a/gentreeg.c
++++ b/gentreeg.c
+@@ -1,4 +1,4 @@
+-/* gentree version 1.3; Brendan McKay Oct 2022 */
++/* gentree version 1.4; Brendan McKay Dec 2022 */
+ /* This program is a wrapper for the program FreeTrees.c written
+  * by Gang Li & Frank Ruskey.  See below for their original
+  * comments. */
+@@ -32,49 +32,54 @@ Counts for n=1..45:
+  1: 1
+  2: 1
+  3: 1
+- 4: 1
+- 5: 2
+- 6: 3
+- 7: 6
+- 8: 11
+- 9: 23
+-10: 47
+-11: 106
+-12: 235
+-13: 551
+-14: 1301
+-15: 3159
+-16: 7741
+-17: 19320
+-18: 48629
+-19: 123867
+-20: 317955
+-21: 823065
+-22: 2144505
+-23: 5623756
+-24: 14828074
+-25: 39299897
+-26: 104636890
+-27: 279793450
+-28: 751065460
+-29: 2023443032
+-30: 5469566585
+-31: 14830871802
+-32: 40330829030
+-33: 109972410221
+-34: 300628862480
+-35: 823779631721
+-36: 2262366343746
+-37: 6226306037178
+-38: 17169677490714
+-39: 47436313524262
+-40: 131290543779126
+-41: 363990257783343
+-42: 1010748076717151
+-43: 2810986483493475
+-44: 7828986221515605
+-45: 21835027912963086
+-********************************/
++ 4: 2
++ 5: 3
++ 6: 6
++ 7: 11
++ 8: 23
++ 9: 47
++10: 106
++11: 235
++12: 551
++13: 1301
++14: 3159
++15: 7741
++16: 19320
++17: 48629
++18: 123867
++19: 317955
++20: 823065
++21: 2144505
++22: 5623756
++23: 14828074
++24: 39299897
++25: 104636890
++26: 279793450
++27: 751065460
++28: 2023443032
++29: 5469566585
++30: 14830871802
++31: 40330829030
++32: 109972410221
++33: 300628862480
++34: 823779631721
++35: 2262366343746
++36: 6226306037178
++37: 17169677490714
++38: 47436313524262
++39: 131290543779126
++40: 363990257783343
++41: 1010748076717151
++42: 2810986483493475
++43: 7828986221515605
++44: 21835027912963086
++45: 60978390985918906
++46: 170508699155987862
++47: 477355090753926460
++48: 1337946100045842285
++49: 3754194185716399992
++50: 10545233702911509534
++*******************************/
+ 
+ /* Comments on original program by original authors */
+ /*==============================================================*/
+@@ -676,7 +681,7 @@ PLUGIN_INIT
+         }
+         else if (nv == 2)
+         {
+-            if (res == 0 && maxdeg >= 1 && mindiam <= 1 && maxdiam >= 2)
++            if (res == 0 && maxdeg >= 1 && mindiam <= 1 && maxdiam >= 1)
+             {
+                 par[1] = 0;
+                 par[2] = 1;
+-- 
+2.38.2
+
diff --git a/build/pkgs/nauty/spkg-configure.m4 b/build/pkgs/nauty/spkg-configure.m4
index d986105f2e3..4d5bbcf2091 100644
--- a/build/pkgs/nauty/spkg-configure.m4
+++ b/build/pkgs/nauty/spkg-configure.m4
@@ -1,8 +1,12 @@
 # We don't use the "converseg" program, but we need to ensure that we
 # only detect nauty >= 2.6 because we use the digraph6 format from
 # that version -- and converseg was added in nauty-2.6.
+#
+# We also don't use the "genposetg" program (added in nauty 2.8) yet.
+# We require it here to prepare Sage for the use of the major new features
+# added in 2.7 and 2.8 (https://pallini.di.uniroma1.it/changes24-28.txt).
 AC_DEFUN([SAGE_TEST_NAUTY_PROGS], [
-    m4_foreach([nautyprog], [directg, gentourng, geng, genbg, gentreeg, converseg], [
+    m4_foreach([nautyprog], [directg, gentourng, geng, genbg, gentreeg, converseg, genposetg], [
       AC_PATH_PROG([$2]nautyprog, [[$1]nautyprog])
       AS_IF([test x$[$2]nautyprog = x], [sage_spkg_install_nauty=yes])
     ])
diff --git a/build/pkgs/nauty/spkg-install.in b/build/pkgs/nauty/spkg-install.in
index 6b25ac9d2ea..cf685ba5370 100644
--- a/build/pkgs/nauty/spkg-install.in
+++ b/build/pkgs/nauty/spkg-install.in
@@ -7,10 +7,10 @@ sdh_make
 
 # No install target so we resort to manual copy
 PROGRAMS="
-addedgeg amtog biplabg catg complg converseg copyg countg cubhamg deledgeg
-delptg directg dreadnaut dretodot dretog genbg genbgL geng genquarticg genrang
-genspecialg gentourng gentreeg hamheuristic labelg linegraphg listg multig
-newedgeg pickg planarg ranlabg shortg showg subdivideg twohamg vcolg
+addedgeg addptg amtog ancestorg assembleg biplabg catg complg converseg copyg countg cubhamg deledgeg
+delptg dimacs2g directg dreadnaut dretodot dretog edgetransg genbg genbgL geng gengL genposetg genquarticg genrang
+genspecialg gentourng gentreeg hamheuristic labelg linegraphg listg multig nbrhoodg
+newedgeg pickg planarg productg ranlabg shortg showg subdivideg twohamg underlyingg vcolg
 watercluster2 NRswitchg"
 sdh_install $PROGRAMS "$SAGE_LOCAL/bin"