diff -r c2f3b7c56dff Lib/sre_parse.py
--- a/Lib/sre_parse.py	Sat Oct 15 15:41:05 2016 +0900
+++ b/Lib/sre_parse.py	Thu Oct 20 21:28:45 2016 +0200
@@ -725,7 +725,7 @@
                             raise source.error("bad group number",
                                                len(condname) + 1)
                         if condgroup >= MAXGROUPS:
-                            raise source.error("invalid group reference",
+                            raise source.error("invalid group reference %r" % condgroup,
                                                len(condname) + 1)
                     state.checklookbehindgroup(condgroup, source)
                 elif char in FLAGS or char == "-":
@@ -884,6 +884,8 @@
     literal = []
     lappend = literal.append
     def addgroup(index):
+        if index > pattern.groups:
+            raise s.error("invalid group reference %r" % index)
         if literal:
             literals.append(''.join(literal))
             del literal[:]
@@ -916,7 +918,7 @@
                         raise s.error("bad character in group name %r" % name,
                                       len(name) + 1) from None
                     if index >= MAXGROUPS:
-                        raise s.error("invalid group reference",
+                        raise s.error("invalid group reference %r" % index,
                                       len(name) + 1)
                 addgroup(index)
             elif c == "0":
@@ -966,5 +968,5 @@
         for index, group in groups:
             literals[index] = g(group) or empty
     except IndexError:
-        raise error("invalid group reference")
+        raise error("invalid group reference %r" % index)
     return empty.join(literals)
diff -r c2f3b7c56dff Lib/test/test_re.py
--- a/Lib/test/test_re.py	Sat Oct 15 15:41:05 2016 +0900
+++ b/Lib/test/test_re.py	Thu Oct 20 21:28:45 2016 +0200
@@ -186,18 +186,20 @@
                                 r'octal escape value \777 outside of '
                                 r'range 0-0o377', 0)
 
-        self.checkTemplateError('x', r'\1', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\8', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\9', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\11', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\18', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\1a', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\90', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\99', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\118', 'x', 'invalid group reference') # r'\11' + '8'
-        self.checkTemplateError('x', r'\11a', 'x', 'invalid group reference')
-        self.checkTemplateError('x', r'\181', 'x', 'invalid group reference') # r'\18' + '1'
-        self.checkTemplateError('x', r'\800', 'x', 'invalid group reference') # r'\80' + '0'
+        self.checkTemplateError('x', r'\1', 'x', 'invalid group reference 1')
+        self.checkTemplateError('x', r'\8', 'x', 'invalid group reference 8')
+        self.checkTemplateError('x', r'\9', 'x', 'invalid group reference 9')
+        self.checkTemplateError('x', r'\11', 'x', 'invalid group reference 11')
+        self.checkTemplateError('x', r'\18', 'x', 'invalid group reference 18')
+        self.checkTemplateError('x', r'\1a', 'x', 'invalid group reference 1')
+        self.checkTemplateError('x', r'\90', 'x', 'invalid group reference 90')
+        self.checkTemplateError('x', r'\99', 'x', 'invalid group reference 99')
+        self.checkTemplateError('x', r'\118', 'x', 'invalid group reference 11') # r'\11' + '8'
+        self.checkTemplateError('x', r'\11a', 'x', 'invalid group reference 11')
+        self.checkTemplateError('x', r'\181', 'x', 'invalid group reference 18') # r'\18' + '1'
+        self.checkTemplateError('x', r'\800', 'x', 'invalid group reference 80') # r'\80' + '0'
+        with self.assertRaisesRegex(re.error, 'invalid group reference 8 at position 2'):
+            re.sub('x', r'\8', '')
 
         # in python2.3 (etc), these loop endlessly in sre_parser.py
         self.assertEqual(re.sub('(((((((((((x)))))))))))', r'\11', 'x'), 'x')
@@ -271,9 +273,9 @@
         self.checkTemplateError('(?P<a>x)', r'\g<1a1>', 'xx',
                                 "bad character in group name '1a1'", 3)
         self.checkTemplateError('(?P<a>x)', r'\g<2>', 'xx',
-                                'invalid group reference')
+                                'invalid group reference 2')
         self.checkTemplateError('(?P<a>x)', r'\2', 'xx',
-                                'invalid group reference')
+                                'invalid group reference 2')
         with self.assertRaisesRegex(IndexError, "unknown group name 'ab'"):
             re.sub('(?P<a>x)', r'\g<ab>', 'xx')
         self.assertEqual(re.sub('(?P<a>x)|(?P<b>y)', r'\g<b>', 'xx'), '')
@@ -559,9 +561,9 @@
 
     def test_re_groupref_overflow(self):
         self.checkTemplateError('()', r'\g<%s>' % sre_constants.MAXGROUPS, 'xx',
-                                'invalid group reference', 3)
+                                'invalid group reference %d' % sre_constants.MAXGROUPS, 3)
         self.checkPatternError(r'(?P<a>)(?(%d))' % sre_constants.MAXGROUPS,
-                               'invalid group reference', 10)
+                               'invalid group reference %d' % sre_constants.MAXGROUPS, 10)
 
     def test_re_groupref(self):
         self.assertEqual(re.match(r'^(\|)?([^()]+)\1$', '|a|').groups(),