diff --git a/src/cryptography/hazmat/backends/openssl/backend.py b/src/cryptography/hazmat/backends/openssl/backend.py
index 4c62146..9a89ae8 100644
--- a/src/cryptography/hazmat/backends/openssl/backend.py
+++ b/src/cryptography/hazmat/backends/openssl/backend.py
@@ -219,7 +219,7 @@
         self._cipher_registry[cipher_cls, mode_cls] = adapter
 
     def _register_default_ciphers(self):
-        for mode_cls in [CBC, CTR, ECB, OFB, CFB, CFB8]:
+        for mode_cls in [CBC, CTR, ECB, OFB, CFB, CFB8, GCM]:
             self.register_cipher_adapter(
                 AES,
                 mode_cls,
@@ -268,11 +268,6 @@
             type(None),
             GetCipherByName("rc4")
         )
-        self.register_cipher_adapter(
-            AES,
-            GCM,
-            GetCipherByName("{cipher.name}-{cipher.key_size}-{mode.name}")
-        )
 
     def create_symmetric_encryption_ctx(self, cipher, mode):
         if (isinstance(mode, CTR) and isinstance(cipher, AES) and