Subgroups — #44564722

Order 32128.

1060 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632437	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632431	C₂	1	2	yes	maximal, complemented
3	#30632429	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632399	C₂	1	2	yes	maximal, complemented
5	#30632367	C₂	1	2	yes	maximal, complemented
6	#30632363	C₂	1	4	yes	maximal, complemented
7	#30632327	C₂	1	4	yes	maximal, complemented
8	#30632301	C₂	1	4	yes	maximal, complemented
9	#30632271	C₂	1	4	yes	maximal, complemented
10	#30632261	C₂	1	2	yes	maximal, complemented
11	#30632246	C₂	1	2	yes	maximal, complemented
12	#30632221	C₂	1	2	yes	maximal, complemented
13	C₂×#124×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16860810	C₂²	1	2	yes	—
15	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
16	#22548713	C₂²	1	2	yes	complemented
17	#22548713	C₂²	1	2	yes	complemented
18	#22548709	C₂²	1	4	yes	complemented
19	#22548708	C₂²	1	4	yes	complemented
20	#22548708	C₂²	1	4	yes	complemented
21	#22548707	C₂²	1	2	yes	complemented
22	#22548704	C₂²	1	2	yes	complemented
23	#22548704	C₂²	1	2	yes	complemented
24	#22548703	C₂²	1	2	yes	complemented
25	#22548701	C₂²	1	4	yes	complemented
26	#22548701	C₂²	1	4	yes	complemented
27	#22548699	C₂²	1	4	yes	complemented
28	#22548698	C₂²	1	4	yes	complemented
29	#22548698	C₂²	1	4	yes	complemented
30	#22548697	C₂²	1	4	yes	complemented
31	#22548697	C₂²	1	4	yes	complemented
32	#22548696	C₂²	1	2	yes	—
33	#22548696	C₂²	1	2	yes	complemented
34	#22548694	C₂²	1	2	yes	complemented
35	#22548692	C₂²	1	4	yes	complemented
36	#22548692	C₂²	1	4	yes	complemented
37	#22548691	C₂²	1	4	yes	complemented
38	#22548691	C₂²	1	4	yes	complemented
39	#22548689	C₂²	1	2	yes	—
40	#22548688	C₂²	1	4	yes	complemented
41	#22548688	C₂²	1	4	yes	complemented
42	#22548687	C₂²	1	4	yes	—
43	#22548687	C₂²	1	4	yes	complemented
44	#22548685	C₂²	1	4	yes	complemented
45	#22548684	C₂²	1	4	yes	—
46	#22548683	C₂²	1	2	yes	—
47	#22548683	C₂²	1	2	yes	complemented
48	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
49	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₂₅₁	C₂²	1	4	yes	complemented
51	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
52	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
53	#22548674	C₂²	1	2	yes	complemented
54	#22548672	C₂²	1	4	yes	complemented
55	#22548671	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
57	C₂²⋊C₄×D₂₅₁	C₂²	1	4	yes	complemented
58	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
60	#124×C₂₅₁	C₂²	1	1	yes	characteristic
61	#124×C₂₅₁	C₂²	1	1	yes	characteristic
62	#124×C₂₅₁	C₂²	1	4	yes	complemented
63	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
64	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	4	yes	complemented
66	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₂₅₁	C₂³	1	2	yes	—
68	#16860810	—	4	4	no	—
69	C₂×Dic₅₀₂	C₂³	1	2	yes	—
70	C₂×Dic₅₀₂	C₂³	1	2	yes	—
71	C₂×D₁₀₀₄	C₂³	1	2	yes	—
72	C₂×D₁₀₀₄	C₂³	1	2	yes	—
73	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
74	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
78	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
79	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
80	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
81	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
82	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
83	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
84	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
85	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
86	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
87	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
88	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
89	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
90	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
91	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
92	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
93	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
94	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
95	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
96	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
97	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
98	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
99	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
100	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
101	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
102	C₄×Dic₂₅₁	C₂³	1	2	yes	—
103	C₄×Dic₂₅₁	C₂³	1	4	yes	—
104	C₄×Dic₂₅₁	C₂³	1	2	yes	—
105	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
106	C₂×Q₈×C₂₅₁	—	4	2	no	—
107	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
110	C₂×D₄×C₂₅₁	—	4	2	no	—
111	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
113	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
115	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
120	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
121	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
122	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
123	C₄²×C₂₅₁	C₂³	1	2	yes	—
124	C₂²×D₂₅₁	—	4	2	no	—
125	C₂²×D₂₅₁	—	4	4	no	—
126	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
127	Dic₅₀₂	—	4	2	no	—
128	Dic₅₀₂	—	4	2	no	—
129	D₁₀₀₄	—	4	2	no	—
130	D₁₀₀₄	—	4	2	no	—
131	C₂²⋊D₂₅₁	—	2	8	no	—
132	C₂²⋊D₂₅₁	—	4	4	no	—
133	C₂²⋊D₂₅₁	—	4	4	no	—
134	C₂²⋊D₂₅₁	—	4	4	no	—
135	C₂×Dic₂₅₁	—	4	4	no	—
136	C₂×Dic₂₅₁	—	4	2	no	—
137	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
138	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
139	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
140	C₄×D₂₅₁	—	4	4	no	—
141	C₄×D₂₅₁	—	4	4	no	—
142	C₂³×C₂₅₁	—	2	4	no	—
143	C₂³×C₂₅₁	—	4	4	no	—
144	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
145	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
146	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
147	Q₈×C₂₅₁	—	4	1	no	—
148	Q₈×C₂₅₁	—	4	2	no	—
149	Q₈×C₂₅₁	—	4	1	no	—
150	D₄×C₂₅₁	—	4	1	no	—
151	D₄×C₂₅₁	—	4	2	no	—
152	D₄×C₂₅₁	—	4	1	no	—
153	C₂×C₄×C₂₅₁	—	2	2	no	—
154	C₂×C₄×C₂₅₁	—	2	4	no	—
155	C₂×C₄×C₂₅₁	—	4	2	no	—
156	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
157	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
158	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
161	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
162	C₂²×C₂₅₁	—	2	2	no	—
163	C₂²×C₂₅₁	—	2	2	no	—
164	C₂²×C₂₅₁	—	2	2	no	—
165	C₂²×C₂₅₁	—	2	4	no	—
166	C₂²×C₂₅₁	—	2	4	no	—
167	C₂²×C₂₅₁	—	8	4	no	—
168	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
169	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
170	C₂×D₂₅₁	—	2	4	no	—
171	C₂×D₂₅₁	—	2	4	no	—
172	C₂×D₂₅₁	—	2	4	no	—
173	C₂×D₂₅₁	—	8	4	no	—
174	C₄×C₂₅₁	—	2	1	no	—
175	C₄×C₂₅₁	—	2	1	no	—
176	C₄×C₂₅₁	—	2	2	no	—
177	C₄×C₂₅₁	—	2	2	no	—
178	C₄×C₂₅₁	—	2	2	no	—
179	C₄×C₂₅₁	—	2	2	no	—
180	Dic₂₅₁	—	2	4	no	—
181	Dic₂₅₁	—	2	4	no	—
182	Dic₂₅₁	—	2	4	no	—
183	C₂×C₂₅₁	—	2	2	no	—
184	C₂×C₂₅₁	—	4	2	no	—
185	C₂×C₂₅₁	—	4	2	no	—
186	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₂₅₁	#585	1	2	yes	—
188	D₂₅₁	—	4	4	no	—
189	C₂₅₁	#3545	1	1	yes	characteristic, complemented, Sylow
190	#3545	—	251	1	no	maximal, Sylow
191	#563	—	251	1	no	—
192	#562	—	251	2	no	—
193	H(3,𝔽₄)	—	251	1	no	—
194	#555	—	251	2	no	—
195	#551	—	251	2	no	—
196	#551	—	251	4	no	—
197	#546	—	251	4	no	—
198	#542	—	251	4	no	—
199	#538	—	251	4	no	—
200	#536	—	251	2	no	—
201	#534	—	251	2	no	—
202	#529	—	251	2	no	—
203	C₂×#124	D₂₅₁	1	1	yes	characteristic, complemented
204	C₂×#41	—	251	2	no	—
205	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
206	C₂²×D₄	—	251	2	no	—
207	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
208	C₄⋊Q₈	—	251	2	no	—
209	C₄⋊Q₈	—	251	2	no	—
210	#126	—	251	4	no	—
211	#126	—	251	4	no	—
212	#126	—	251	4	no	—
213	#125	—	251	2	no	—
214	#124	—	251	2	no	—
215	#124	—	251	2	no	—
216	#124	—	251	4	no	—
217	#124	—	251	4	no	—
218	#124	—	251	2	no	—
219	#124	C₂×D₂₅₁	1	1	yes	characteristic
220	#124	C₂×D₂₅₁	1	1	yes	characteristic
221	#124	C₂×D₂₅₁	1	4	yes	complemented
222	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
223	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
224	#123	—	251	2	no	—
225	#123	—	251	2	no	—
226	#123	—	251	4	no	—
227	#123	—	251	4	no	—
228	#123	—	251	4	no	—
229	#123	—	251	4	no	—
230	#123	—	251	4	no	—
231	C₂²⋊Q₈	—	251	4	no	—
232	C₂²⋊Q₈	—	251	4	no	—
233	C₂²⋊Q₈	—	251	2	no	—
234	C₂²⋊Q₈	—	251	4	no	—
235	C₂²⋊Q₈	—	251	4	no	—
236	#121	—	251	4	no	—
237	#121	—	251	4	no	—
238	#121	—	251	2	no	—
239	#121	—	251	4	no	—
240	#121	—	251	4	no	—
241	#120	—	251	4	no	—
242	#120	—	251	2	no	—
243	#120	—	251	2	no	—
244	#120	—	251	4	no	—
245	C₄×Q₈	—	251	2	no	—
246	C₄×D₄	—	251	4	no	—
247	C₄×D₄	—	251	4	no	—
248	C₄×D₄	—	251	4	no	—
249	C₄×D₄	—	251	2	no	—
250	#117	—	251	2	no	—
251	#117	—	251	4	no	—
252	#117	—	251	4	no	—
253	C₂×C₂²⋊C₄	—	251	2	no	—
254	C₂×C₂²⋊C₄	—	251	4	no	—
255	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	4	yes	complemented
256	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
257	C₂⁴	—	251	2	no	—
258	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
259	#41	—	1004	4	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	251	2	no	—
262	C₂×Q₈	—	251	2	no	—
263	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
264	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
265	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	1004	4	no	—
268	C₂×D₄	—	251	4	no	—
269	C₂×D₄	—	251	4	no	—
270	C₂×D₄	—	251	4	no	—
271	C₂×D₄	—	251	4	no	—
272	C₂×D₄	—	251	2	no	—
273	C₂×D₄	—	251	2	no	—
274	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
275	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
276	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
277	C₂²×C₄	—	251	4	no	—
278	C₂²×C₄	—	251	2	no	—
279	C₂²×C₄	—	251	4	no	—
280	C₂²×C₄	—	251	4	no	—
281	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
283	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
284	C₄⋊C₄	—	251	4	no	—
285	C₄⋊C₄	—	251	4	no	—
286	C₄⋊C₄	—	251	4	no	—
287	C₄⋊C₄	—	251	4	no	—
288	C₄⋊C₄	—	251	4	no	—
289	C₄⋊C₄	—	251	4	no	—
290	C₄⋊C₄	—	251	4	no	—
291	C₄⋊C₄	—	251	2	no	—
292	C₄⋊C₄	—	251	2	no	—
293	C₂²⋊C₄	—	251	4	no	—
294	C₂²⋊C₄	—	251	4	no	—
295	C₂²⋊C₄	—	251	2	no	—
296	C₂²⋊C₄	—	251	2	no	—
297	C₂²⋊C₄	—	251	4	no	—
298	C₂²⋊C₄	—	251	4	no	—
299	C₂²⋊C₄	—	251	4	no	—
300	C₂²⋊C₄	—	251	4	no	—
301	C₂²⋊C₄	—	251	4	no	—
302	C₂²⋊C₄	—	251	4	no	—
303	C₂²⋊C₄	—	251	4	no	—
304	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
305	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
306	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
307	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
308	C₄²	—	251	2	no	—
309	C₄²	—	251	4	no	—
310	C₄²	—	251	2	no	—
311	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
312	C₄²	C₂²×D₂₅₁	1	2	yes	—
313	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
314	C₂³	—	2	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	1004	2	no	—
317	C₂³	—	1004	4	no	—
318	C₂³	—	251	4	no	—
319	C₂³	C₂³×D₂₅₁	1	2	yes	—
320	C₂³	C₂³×D₂₅₁	1	2	yes	—
321	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	1004	2	no	—
326	Q₈	—	1004	2	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	1	no	—
330	D₄	—	1004	2	no	—
331	D₄	—	1004	2	no	—
332	D₄	—	1004	4	no	—
333	D₄	—	1004	4	no	—
334	D₄	—	1004	4	no	—
335	D₄	—	502	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	1004	4	no	—
340	C₂×C₄	—	1004	4	no	—
341	C₂×C₄	—	1004	2	no	—
342	C₂×C₄	—	1004	4	no	—
343	C₂×C₄	—	251	4	no	—
344	C₂×C₄	—	251	4	no	—
345	C₂×C₄	—	251	4	no	—
346	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
347	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
348	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
349	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
350	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
351	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	2008	4	no	—
359	C₂²	—	502	4	no	—
360	C₂²	—	502	4	no	—
361	C₂²	—	502	4	no	—
362	C₂²	#22548760	1	2	yes	—
363	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	502	4	no	—
371	C₄	—	502	4	no	—
372	C₄	—	502	4	no	—
373	C₂	—	2	2	no	—
374	C₂	—	4	2	no	—
375	C₂	—	4	2	no	—
376	C₂	—	1004	4	no	—
377	C₂	C₂×#22548760	1	1	yes	characteristic
378	C₂	#30632523	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	C₂×#124×C₂₅₁	C₂
hypercenter	C₂×#124	D₂₅₁
hypocenter	C₂₅₁	#3545
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. #30632437	C₂	semidirect
2. #30632431	C₂	semidirect
3. #30632429	C₂	semidirect
4. #30632399	C₂	semidirect
5. #30632367	C₂	semidirect
6. #30632363	C₂	semidirect
7. #30632327	C₂	semidirect
8. #30632301	C₂	semidirect
9. #30632271	C₂	semidirect
10. #30632261	C₂	semidirect
11. #30632246	C₂	semidirect
12. #30632221	C₂	semidirect
13. C₂×#124×C₂₅₁	C₂	semidirect
15. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
16. #22548713	C₂²	semidirect
17. #22548713	C₂²	semidirect
18. #22548709	C₂²	semidirect
19. #22548708	C₂²	semidirect
20. #22548708	C₂²	semidirect
21. #22548707	C₂²	semidirect
22. #22548704	C₂²	semidirect
23. #22548704	C₂²	semidirect
24. #22548703	C₂²	semidirect
25. #22548701	C₂²	semidirect
26. #22548701	C₂²	semidirect
27. #22548699	C₂²	semidirect
28. #22548698	C₂²	semidirect
29. #22548698	C₂²	semidirect
30. #22548697	C₂²	semidirect
31. #22548697	C₂²	semidirect
33. #22548696	C₂²	semidirect
34. #22548694	C₂²	semidirect
35. #22548692	C₂²	semidirect
36. #22548692	C₂²	semidirect
37. #22548691	C₂²	semidirect
38. #22548691	C₂²	semidirect
40. #22548688	C₂²	semidirect
41. #22548688	C₂²	semidirect
43. #22548687	C₂²	semidirect
44. #22548685	C₂²	semidirect
47. #22548683	C₂²	semidirect
48. C₄×Dic₅₀₂	C₂²	semidirect
49. C₄×D₁₀₀₄	C₂²	semidirect
50. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
51. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
52. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
53. #22548674	C₂²	semidirect
54. #22548672	C₂²	semidirect
55. #22548671	C₂²	semidirect
56. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
57. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
58. C₂²×Q₈×C₂₅₁	C₂²	semidirect
62. #124×C₂₅₁	C₂²	semidirect
63. #124×C₂₅₁	C₂²	semidirect
64. #124×C₂₅₁	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
66. C₂×C₄²×C₂₅₁	C₂²	semidirect
189. C₂₅₁	#3545	semidirect
203. C₂×#124	D₂₅₁	semidirect
205. C₂²×Q₈	C₂×D₂₅₁	semidirect
221. #124	C₂×D₂₅₁	semidirect
222. #124	C₂×D₂₅₁	semidirect
223. #124	C₂×D₂₅₁	semidirect
255. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
256. C₂×C₄²	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632437	2
#30632431	2
#30632429	2
#30632399	2
#30632367	2
#30632363	2
#30632327	2
#30632301	2
#30632271	2
#30632261	2
#30632246	2
#30632221	2
C₂×#124×C₂₅₁	2
#3545	251