diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index cb56f7b8d535b..61a04431f99cb 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -11,6 +11,8 @@ class providing the base-class of operations.
 from contextlib import contextmanager
 import datetime
 from functools import partial, wraps
+import inspect
+import re
 import types
 from typing import FrozenSet, List, Optional, Tuple, Type, Union
 
@@ -613,23 +615,21 @@ def _make_wrapper(self, name):
             return self.apply(lambda self: getattr(self, name))
 
         f = getattr(type(self._selected_obj), name)
+        sig = inspect.signature(f)
 
         def wrapper(*args, **kwargs):
             # a little trickery for aggregation functions that need an axis
             # argument
-            kwargs_with_axis = kwargs.copy()
-            if "axis" not in kwargs_with_axis or kwargs_with_axis["axis"] is None:
-                kwargs_with_axis["axis"] = self.axis
-
-            def curried_with_axis(x):
-                return f(x, *args, **kwargs_with_axis)
+            if "axis" in sig.parameters:
+                if kwargs.get("axis", None) is None:
+                    kwargs["axis"] = self.axis
 
             def curried(x):
                 return f(x, *args, **kwargs)
 
             # preserve the name so we can detect it when calling plot methods,
             # to avoid duplicates
-            curried.__name__ = curried_with_axis.__name__ = name
+            curried.__name__ = name
 
             # special case otherwise extra plots are created when catching the
             # exception below
@@ -637,24 +637,31 @@ def curried(x):
                 return self.apply(curried)
 
             try:
-                return self.apply(curried_with_axis)
-            except Exception:
-                try:
-                    return self.apply(curried)
-                except Exception:
-
-                    # related to : GH3688
-                    # try item-by-item
-                    # this can be called recursively, so need to raise
-                    # ValueError
-                    # if we don't have this method to indicated to aggregate to
-                    # mark this column as an error
-                    try:
-                        return self._aggregate_item_by_item(name, *args, **kwargs)
-                    except AttributeError:
-                        # e.g. SparseArray has no flags attr
-                        raise ValueError
-
+                return self.apply(curried)
+            except TypeError as err:
+                if not re.search(
+                    "reduction operation '.*' not allowed for this dtype", str(err)
+                ):
+                    # We don't have a cython implementation
+                    # TODO: is the above comment accurate?
+                    raise
+
+            # related to : GH3688
+            # try item-by-item
+            # this can be called recursively, so need to raise
+            # ValueError
+            # if we don't have this method to indicated to aggregate to
+            # mark this column as an error
+            try:
+                return self._aggregate_item_by_item(name, *args, **kwargs)
+            except AttributeError:
+                # e.g. SparseArray has no flags attr
+                # FIXME: 'SeriesGroupBy' has no attribute '_aggregate_item_by_item'
+                #  occurs in idxmax() case
+                #  in tests.groupby.test_function.test_non_cython_api
+                raise ValueError
+
+        wrapper.__name__ = name
         return wrapper
 
     def get_group(self, name, obj=None):