diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 438bb5ddbd..f00eb1e5a5 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -1367,7 +1367,7 @@ class Query(BaseExpression):
         # __exact is the default lookup if one isn't given.
         *transforms, lookup_name = lookups or ["exact"]
         for name in transforms:
-            lhs = self.try_transform(lhs, name)
+            lhs = self.try_transform(lhs, name, lookups)
         # First try get_lookup() so that the lookup takes precedence if the lhs
         # supports both transform and lookup for the name.
         lookup_class = lhs.get_lookup(lookup_name)
@@ -1401,7 +1401,7 @@ class Query(BaseExpression):
 
         return lookup
 
-    def try_transform(self, lhs, name):
+    def try_transform(self, lhs, name, lookups=None):
         """
         Helper method for build_lookup(). Try to fetch and initialize
         a transform for name parameter from lhs.
@@ -1418,9 +1418,14 @@ class Query(BaseExpression):
                 suggestion = ", perhaps you meant %s?" % " or ".join(suggested_lookups)
             else:
                 suggestion = "."
+            if lookups is not None:
+                name_index = lookups.index(name)
+                unsupported_lookup = LOOKUP_SEP.join(lookups[name_index:])
+            else:
+                unsupported_lookup = name
             raise FieldError(
                 "Unsupported lookup '%s' for %s or join on the field not "
-                "permitted%s" % (name, output_field.__name__, suggestion)
+                "permitted%s" % (unsupported_lookup, output_field.__name__, suggestion)
             )
 
     def build_filter(
diff --git a/tests/custom_lookups/tests.py b/tests/custom_lookups/tests.py
index f107c5320a..2f4ea0a9a0 100644
--- a/tests/custom_lookups/tests.py
+++ b/tests/custom_lookups/tests.py
@@ -614,6 +614,10 @@ class LookupTransformCallOrderTests(SimpleTestCase):
             )
             TrackCallsYearTransform.call_order = []
             # junk transform - tries transform only, then fails
+            msg = (
+                "Unsupported lookup 'junk__more_junk' for IntegerField or join"
+                " on the field not permitted."
+            )
             with self.assertRaisesMessage(FieldError, msg):
                 Author.objects.filter(birthdate__testyear__junk__more_junk=2012)
             self.assertEqual(TrackCallsYearTransform.call_order, ["transform"])
diff --git a/tests/lookup/tests.py b/tests/lookup/tests.py
index ebdaa21e3d..28acd72874 100644
--- a/tests/lookup/tests.py
+++ b/tests/lookup/tests.py
@@ -812,6 +812,34 @@ class LookupTests(TestCase):
         ):
             Article.objects.filter(pub_date__gobbledygook="blahblah")
 
+        with self.assertRaisesMessage(
+            FieldError,
+            "Unsupported lookup 'gt__foo' for DateTimeField or join on the field "
+            "not permitted, perhaps you meant gt or gte?",
+        ):
+            Article.objects.filter(pub_date__gt__foo="blahblah")
+
+        with self.assertRaisesMessage(
+            FieldError,
+            "Unsupported lookup 'gt__' for DateTimeField or join on the field "
+            "not permitted, perhaps you meant gt or gte?",
+        ):
+            Article.objects.filter(pub_date__gt__="blahblah")
+
+        with self.assertRaisesMessage(
+            FieldError,
+            "Unsupported lookup 'gt__lt' for DateTimeField or join on the field "
+            "not permitted, perhaps you meant gt or gte?",
+        ):
+            Article.objects.filter(pub_date__gt__lt="blahblah")
+
+        with self.assertRaisesMessage(
+            FieldError,
+            "Unsupported lookup 'gt__lt__foo' for DateTimeField or join"
+            " on the field not permitted, perhaps you meant gt or gte?",
+        ):
+            Article.objects.filter(pub_date__gt__lt__foo="blahblah")
+
     def test_unsupported_lookups_custom_lookups(self):
         slug_field = Article._meta.get_field("slug")
         msg = (
@@ -825,7 +853,7 @@ class LookupTests(TestCase):
     def test_relation_nested_lookup_error(self):
         # An invalid nested lookup on a related field raises a useful error.
         msg = (
-            "Unsupported lookup 'editor' for ForeignKey or join on the field not "
+            "Unsupported lookup 'editor__name' for ForeignKey or join on the field not "
             "permitted."
         )
         with self.assertRaisesMessage(FieldError, msg):
@@ -1059,6 +1087,10 @@ class LookupTests(TestCase):
         )
         with self.assertRaisesMessage(FieldError, msg):
             Article.objects.filter(headline__blahblah=99)
+        msg = (
+            "Unsupported lookup 'blahblah__exact' for CharField or join "
+            "on the field not permitted."
+        )
         with self.assertRaisesMessage(FieldError, msg):
             Article.objects.filter(headline__blahblah__exact=99)
         msg = (