Subgroups — #44559021

Order 32128.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#117×D₂₅₁	C₂	1	1	yes	maximal, characteristic
2	#30631748	C₂	1	1	yes	maximal, characteristic, complemented
3	#30631745	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631745	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631743	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631742	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631739	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631738	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631712	C₂	1	1	yes	maximal, characteristic, complemented
10	#30631712	C₂	1	1	yes	maximal, characteristic, complemented
11	#30631649	C₂	1	1	yes	maximal, characteristic
12	C₂²⋊C₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic
13	#30631644	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631641	C₂	1	1	yes	maximal, characteristic, complemented
15	#433×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
17	C₂×#16860793	C₂²	1	1	yes	characteristic
18	C₂×#16860793	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₂₅₁	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₂₅₁	C₂²	1	1	yes	characteristic
21	#22548674	C₂²	1	1	yes	characteristic
22	#22548673	C₄	1	1	yes	characteristic
23	#22548673	C₄	1	1	yes	characteristic
24	#22548672	C₂²	1	1	yes	characteristic
25	#22548672	C₂²	1	1	yes	characteristic
26	#22548671	C₄	1	1	yes	characteristic
27	#22548671	C₄	1	1	yes	characteristic
28	C₄⋊C₄×D₂₅₁	C₄	1	1	yes	characteristic
29	C₄⋊C₄×D₂₅₁	C₄	1	1	yes	characteristic
30	C₂²⋊C₄×D₂₅₁	C₄	1	1	yes	characteristic
31	C₂²⋊C₄×D₂₅₁	C₄	1	1	yes	characteristic
32	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
33	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
34	C₄⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
35	C₄⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
36	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic
42	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
46	#22548626	C₂²	1	1	yes	characteristic, complemented
47	#22548625	C₂²	1	1	yes	characteristic, complemented
48	#22548625	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
52	#117×C₂₅₁	C₂²	1	1	yes	characteristic
53	C₄⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
54	C₄⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
55	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
57	#97×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₅₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×D₂₅₁	—	2	2	no	—
62	C₂×C₄×D₂₅₁	—	2	2	no	—
63	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
70	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
71	#16860793	—	2	2	no	—
72	#16860793	—	2	2	no	—
73	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
77	C₈×D₂₅₁	—	2	2	no	—
78	C₈×D₂₅₁	—	2	2	no	—
79	C₄⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
80	C₄⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
81	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
82	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
83	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
84	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
87	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
88	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
89	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
90	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
93	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
96	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
99	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
100	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
101	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
106	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
107	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
108	C₂²×D₂₅₁	—	2	2	no	—
109	C₂²×D₂₅₁	—	2	2	no	—
110	C₂²×D₂₅₁	—	4	1	no	—
111	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×Dic₂₅₁	—	2	2	no	—
114	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
120	C₄×D₂₅₁	—	2	2	no	—
121	C₄×D₂₅₁	—	2	2	no	—
122	C₄×D₂₅₁	—	2	2	no	—
123	C₄×D₂₅₁	—	2	1	no	—
124	C₄×D₂₅₁	—	2	1	no	—
125	C₄×D₂₅₁	—	2	2	no	—
126	C₄×D₂₅₁	—	4	1	no	—
127	C₄×D₂₅₁	—	4	1	no	—
128	C₄×D₂₅₁	#41	1	2	yes	—
129	C₄×D₂₅₁	#41	1	2	yes	—
130	C₂₅₁⋊C₈	—	2	1	no	—
131	C₂₅₁⋊C₈	—	2	1	no	—
132	C₂₅₁⋊C₈	—	2	1	no	—
133	C₂₅₁⋊C₈	—	2	1	no	—
134	C₂³×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₅₁	—	2	1	no	—
136	C₂×C₄×C₂₅₁	—	2	1	no	—
137	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
143	C₈×C₂₅₁	—	2	1	no	—
144	C₈×C₂₅₁	—	2	1	no	—
145	C₈×C₂₅₁	—	2	1	no	—
146	C₈×C₂₅₁	—	2	1	no	—
147	C₂²×C₂₅₁	—	2	1	no	—
148	C₂²×C₂₅₁	—	2	1	no	—
149	C₂²×C₂₅₁	—	2	1	no	—
150	C₂²×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×D₂₅₁	—	2	1	no	—
152	C₂×D₂₅₁	—	2	1	no	—
153	C₂×D₂₅₁	—	2	1	no	—
154	C₂×D₂₅₁	—	2	1	no	—
155	C₂×D₂₅₁	—	4	4	no	—
156	C₂×D₂₅₁	#117	1	2	yes	—
157	C₂×D₂₅₁	#131	1	2	yes	—
158	C₄×C₂₅₁	—	2	1	no	—
159	C₄×C₂₅₁	—	2	1	no	—
160	C₄×C₂₅₁	—	2	1	no	—
161	C₄×C₂₅₁	—	2	1	no	—
162	C₄×C₂₅₁	—	2	1	no	—
163	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
164	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
165	Dic₂₅₁	—	2	1	no	—
166	Dic₂₅₁	—	2	1	no	—
167	Dic₂₅₁	—	2	1	no	—
168	Dic₂₅₁	—	2	1	no	—
169	Dic₂₅₁	—	2	1	no	—
170	Dic₂₅₁	#117	1	2	yes	—
171	C₂×C₂₅₁	—	4	1	no	—
172	C₂×C₂₅₁	C₂×#117	1	1	yes	characteristic
173	C₂×C₂₅₁	C₂×#131	1	1	yes	characteristic
174	C₂×C₂₅₁	#568	1	1	yes	characteristic
175	D₂₅₁	—	2	2	no	—
176	D₂₅₁	—	2	2	no	—
177	C₂₅₁	#2924	1	1	yes	characteristic, complemented, Sylow
178	#2924	—	251	1	no	maximal, Sylow
179	C₂×#117	—	251	1	no	—
180	#433	—	251	1	no	—
181	#433	—	251	1	no	—
182	#433	—	251	1	no	—
183	#433	D₂₅₁	1	1	yes	characteristic, complemented
184	#432	—	251	1	no	—
185	#432	—	251	1	no	—
186	#431	—	251	1	no	—
187	#431	—	251	1	no	—
188	#424	—	251	1	no	—
189	#424	—	251	1	no	—
190	#407	—	251	1	no	—
191	C₂×C₂²⋊C₈	—	251	1	no	—
192	#405	—	251	1	no	—
193	#405	—	251	1	no	—
194	C₂³×C₄	—	251	1	no	—
195	C₂×M₁₆	—	251	1	no	—
196	C₂×M₁₆	—	251	1	no	—
197	C₂²×C₈	—	251	1	no	—
198	C₂²×C₈	—	251	1	no	—
199	#117	—	251	1	no	—
200	#117	—	251	1	no	—
201	#117	—	251	1	no	—
202	#117	—	251	1	no	—
203	#117	—	251	1	no	—
204	#117	—	251	1	no	—
205	#117	—	251	1	no	—
206	#117	C₂×D₂₅₁	1	1	yes	characteristic
207	C₂×C₄⋊C₄	—	251	1	no	—
208	C₂×C₄⋊C₄	—	251	1	no	—
209	C₂×C₂²⋊C₄	—	251	1	no	—
210	C₂×C₂²⋊C₄	—	251	1	no	—
211	C₂×C₄²	—	251	1	no	—
212	C₂×C₄²	—	251	1	no	—
213	C₄⋊C₈	—	251	1	no	—
214	C₄⋊C₈	—	251	1	no	—
215	C₄⋊C₈	—	251	1	no	—
216	C₄⋊C₈	—	251	1	no	—
217	C₄⋊C₈	—	251	1	no	—
218	C₄⋊C₈	—	251	1	no	—
219	C₄⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
220	C₄⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
221	C₂²⋊C₈	—	251	1	no	—
222	C₂²⋊C₈	—	251	1	no	—
223	C₂²⋊C₈	—	251	1	no	—
224	C₂²⋊C₈	—	251	1	no	—
225	C₂²⋊C₈	—	251	1	no	—
226	C₂²⋊C₈	—	251	1	no	—
227	C₂²⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic
228	C₂²⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic
229	#97	—	251	1	no	—
230	#97	—	251	1	no	—
231	#97	—	251	1	no	—
232	#97	C₂×D₂₅₁	1	1	yes	characteristic, complemented
233	C₄×C₈	—	251	1	no	—
234	C₄×C₈	—	251	1	no	—
235	C₄×C₈	—	251	1	no	—
236	C₄×C₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
237	C₂⁴	—	251	1	no	—
238	C₂²×C₄	—	502	2	no	—
239	C₂²×C₄	—	502	2	no	—
240	C₂²×C₄	—	251	1	no	—
241	C₂²×C₄	—	251	1	no	—
242	C₂²×C₄	—	251	1	no	—
243	C₂²×C₄	—	251	1	no	—
244	C₂²×C₄	—	251	1	no	—
245	C₂²×C₄	—	251	1	no	—
246	C₂²×C₄	—	251	1	no	—
247	C₂²×C₄	—	251	1	no	—
248	C₂²×C₄	—	251	1	no	—
249	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
250	M₁₆	—	502	2	no	—
251	M₁₆	—	502	2	no	—
252	C₂×C₈	—	502	2	no	—
253	C₂×C₈	—	502	2	no	—
254	C₂×C₈	—	251	1	no	—
255	C₂×C₈	—	251	1	no	—
256	C₂×C₈	—	251	1	no	—
257	C₂×C₈	—	251	1	no	—
258	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
259	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
260	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
261	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
262	C₄⋊C₄	—	251	1	no	—
263	C₄⋊C₄	—	251	1	no	—
264	C₄⋊C₄	—	251	1	no	—
265	C₄⋊C₄	—	251	1	no	—
266	C₄⋊C₄	—	251	1	no	—
267	C₄⋊C₄	—	251	1	no	—
268	C₄⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
269	C₄⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
270	C₂²⋊C₄	—	251	1	no	—
271	C₂²⋊C₄	—	251	1	no	—
272	C₂²⋊C₄	—	251	1	no	—
273	C₂²⋊C₄	—	251	1	no	—
274	C₂²⋊C₄	—	251	1	no	—
275	C₂²⋊C₄	—	251	1	no	—
276	C₂²⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
277	C₂²⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
278	C₄²	—	251	1	no	—
279	C₄²	—	251	1	no	—
280	C₄²	—	251	1	no	—
281	C₄²	—	251	1	no	—
282	C₄²	—	251	1	no	—
283	C₄²	—	251	1	no	—
284	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
285	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
286	C₂³	—	1004	1	no	—
287	C₂³	—	502	2	no	—
288	C₂³	—	502	2	no	—
289	C₂³	—	251	1	no	—
290	C₂³	—	251	1	no	—
291	C₂³	C₂×C₄×D₂₅₁	1	1	yes	characteristic
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	1004	1	no	—
295	C₂×C₄	—	1004	1	no	—
296	C₂×C₄	—	502	2	no	—
297	C₂×C₄	—	502	2	no	—
298	C₂×C₄	—	502	2	no	—
299	C₂×C₄	—	502	2	no	—
300	C₂×C₄	—	502	2	no	—
301	C₂×C₄	—	502	1	no	—
302	C₂×C₄	—	502	1	no	—
303	C₂×C₄	—	251	1	no	—
304	C₂×C₄	—	251	1	no	—
305	C₂×C₄	—	251	1	no	—
306	C₂×C₄	—	251	1	no	—
307	C₂×C₄	—	251	1	no	—
308	C₂×C₄	—	251	1	no	—
309	C₂×C₄	—	251	2	no	—
310	C₂×C₄	—	251	2	no	—
311	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
312	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
313	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
314	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
315	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
316	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
317	C₈	—	2	1	no	—
318	C₈	—	2	1	no	—
319	C₈	—	2	1	no	—
320	C₈	—	2	1	no	—
321	C₈	—	502	1	no	—
322	C₈	—	502	1	no	—
323	C₈	—	502	1	no	—
324	C₈	—	502	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	1004	4	no	—
329	C₂²	—	502	1	no	—
330	C₂²	—	502	1	no	—
331	C₂²	—	502	1	no	—
332	C₂²	—	502	1	no	—
333	C₂²	—	251	2	no	—
334	C₂²	—	251	2	no	—
335	C₂²	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	502	1	no	—
342	C₄	—	502	1	no	—
343	C₄	—	502	1	no	—
344	C₄	—	502	1	no	—
345	C₄	—	502	1	no	—
346	C₄	—	251	2	no	—
347	C₄	#41×D₂₅₁	1	1	yes	characteristic
348	C₄	#41×D₂₅₁	1	1	yes	characteristic
349	C₂	—	4	1	no	—
350	C₂	—	502	2	no	—
351	C₂	—	502	2	no	—
352	C₂	#117×D₂₅₁	1	1	yes	characteristic
353	C₂	#131×D₂₅₁	1	1	yes	characteristic
354	C₂	#30632452	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₅₁
commutator, socle	C₂²×C₂₅₁	C₂³×C₄
Fitting	#433×C₂₅₁	C₂
prime radical	C₂³×D₂₅₁	C₂×C₄
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	#433	D₂₅₁
hypocenter	C₂₅₁	#2924
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #30631748	C₂	semidirect
3. #30631745	C₂	semidirect
4. #30631745	C₂	semidirect
5. #30631743	C₂	semidirect
6. #30631742	C₂	semidirect
7. #30631739	C₂	semidirect
8. #30631738	C₂	semidirect
9. #30631712	C₂	semidirect
10. #30631712	C₂	semidirect
13. #30631644	C₂	semidirect
14. #30631641	C₂	semidirect
15. #433×C₂₅₁	C₂	semidirect
34. C₄⋊(C₂₅₁⋊C₈)	C₂²	semidirect
35. C₄⋊(C₂₅₁⋊C₈)	C₂²	semidirect
36. Dic₂₅₁⋊C₈	C₂²	semidirect
37. Dic₂₅₁⋊C₈	C₂²	semidirect
38. Dic₂₅₁⋊C₈	C₂²	semidirect
39. Dic₂₅₁⋊C₈	C₂²	semidirect
46. #22548626	C₂²	semidirect
47. #22548625	C₂²	semidirect
48. #22548625	C₂²	semidirect
49. C₄×C₂₅₁⋊C₈	C₂²	semidirect
50. C₈×Dic₂₅₁	C₂²	semidirect
51. C₈×Dic₂₅₁	C₂²	semidirect
53. C₄⋊C₈×C₂₅₁	C₂²	semidirect
54. C₄⋊C₈×C₂₅₁	C₂²	semidirect
57. #97×C₂₅₁	C₂²	semidirect
58. C₄×C₈×C₂₅₁	C₂²	semidirect
177. C₂₅₁	#2924	semidirect
183. #433	D₂₅₁	semidirect
219. C₄⋊C₈	C₂×D₂₅₁	semidirect
220. C₄⋊C₈	C₂×D₂₅₁	semidirect
232. #97	C₂×D₂₅₁	semidirect
236. C₄×C₈	C₂×D₂₅₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#117×D₂₅₁	2
#30631748	2
#30631745	2
#30631743	2
#30631742	2
#30631739	2
#30631738	2
#30631712	2
#30631649	2
C₂²⋊C₈×D₂₅₁	2
#30631644	2
#30631641	2
#433×C₂₅₁	2
#2924	251