Subgroups — #44558909

Order 32128.

738 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632523	C₂	1	1	yes	maximal, characteristic
2	#30632453	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#16860810	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631704	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631703	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631702	C₂	1	4	yes	maximal, complemented
7	C₂×#22548643	C₂	1	1	yes	maximal, characteristic, complemented
8	#104×D₂₅₁	C₂	1	4	yes	maximal, complemented
9	C₂×#104×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#22548763	C₄	1	2	yes	complemented
11	#22548762	—	2	1	no	—
12	#22548762	C₄	1	2	yes	complemented
13	#22548761	—	2	1	no	—
14	#22548761	C₄	1	2	yes	complemented
15	#22548760	—	2	2	no	—
16	#22548760	C₄	1	2	yes	complemented
17	C₂×#16860810	—	2	2	no	—
18	C₂×#16860810	C₂²	1	1	yes	characteristic
19	C₂×#16860810	C₂²	1	1	yes	characteristic
20	#41×D₂₅₁	—	2	2	no	—
21	#41×D₂₅₁	C₂²	1	4	yes	—
22	#22548723	—	2	2	no	—
23	#22548721	—	2	2	no	—
24	C₂×#16860794	C₂²	1	1	yes	characteristic, complemented
25	M₁₆×D₂₅₁	C₂²	1	4	yes	complemented
26	C₄×Dic₅₀₂	—	2	1	no	—
27	C₄×D₁₀₀₄	—	2	1	no	—
28	C₄×C₂²⋊D₂₅₁	—	2	2	no	—
29	#22548674	C₂²	1	1	yes	characteristic, complemented
30	#22548672	C₂²	1	2	yes	complemented
31	C₄²×D₂₅₁	C₂²	1	2	yes	complemented
32	#22548643	C₂²	1	2	yes	complemented
33	#22548643	C₂²	1	2	yes	complemented
34	#22548642	C₂²	1	4	yes	complemented
35	#22548641	C₂²	1	4	yes	complemented
36	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
37	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
39	#104×C₂₅₁	C₂²	1	2	yes	complemented
40	#104×C₂₅₁	C₂²	1	2	yes	complemented
41	#16860811	—	2	2	no	—
42	#16860811	C₂×C₄	1	4	yes	complemented
43	#16860810	—	2	2	no	—
44	#16860810	—	2	2	no	—
45	#16860810	—	2	4	no	—
46	#16860810	—	2	4	no	—
47	#16860810	—	2	1	no	—
48	#16860810	—	2	1	no	—
49	#16860810	C₂×C₄	1	2	yes	—
50	#16860810	C₂×C₄	1	2	yes	—
51	#16860810	C₂×C₄	1	2	yes	complemented
52	#16860810	D₄	1	2	yes	—
53	#16860810	D₄	1	2	yes	—
54	#16860810	C₂³	1	2	yes	—
55	#16860809	—	2	2	no	—
56	#16860809	—	2	4	no	—
57	#16860809	—	2	4	no	—
58	#16860809	C₂×C₄	1	4	yes	complemented
59	C₂×Dic₅₀₂	—	2	2	no	—
60	C₂×Dic₅₀₂	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×Dic₅₀₂	D₄	1	1	yes	characteristic
62	Q₈×D₂₅₁	—	2	2	no	—
63	Q₈×D₂₅₁	C₂×C₄	1	4	yes	complemented
64	C₂×D₁₀₀₄	—	2	2	no	—
65	C₂×D₁₀₀₄	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×D₁₀₀₄	D₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
68	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
69	C₂×C₂²⋊D₂₅₁	D₄	1	2	yes	—
70	D₄×D₂₅₁	—	2	4	no	—
71	D₄×D₂₅₁	—	2	2	no	—
72	D₄×D₂₅₁	—	2	4	no	—
73	D₄×D₂₅₁	C₂×C₄	1	4	yes	complemented
74	C₂×C₄×D₂₅₁	—	2	4	no	—
75	C₂×C₄×D₂₅₁	—	2	2	no	—
76	C₂×C₄×D₂₅₁	—	2	1	no	—
77	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
78	#16860794	—	2	1	no	—
79	#16860794	C₂³	1	2	yes	—
80	#16860793	—	2	4	no	—
81	C₂×C₂₅₁⋊C₈	—	2	1	no	—
82	C₈×D₂₅₁	—	2	4	no	—
83	C₄⋊Dic₂₅₁	—	2	1	no	—
84	Dic₂₅₁⋊C₄	—	2	2	no	—
85	C₂²⋊Dic₂₅₁	—	2	1	no	—
86	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
87	C₄×Dic₂₅₁	—	2	2	no	—
88	C₄×Dic₂₅₁	C₂³	1	2	yes	—
89	#41×C₂₅₁	—	2	1	no	—
90	#41×C₂₅₁	—	2	1	no	—
91	#41×C₂₅₁	C₂×C₄	1	2	yes	complemented
92	#41×C₂₅₁	C₂³	1	2	yes	—
93	C₂×Q₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic, complemented
94	C₂×D₄×C₂₅₁	—	2	1	no	—
95	C₂×D₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic, complemented
96	C₂²×C₄×C₂₅₁	—	2	1	no	—
97	C₂²×C₄×C₂₅₁	—	2	1	no	—
98	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
99	M₁₆×C₂₅₁	—	2	1	no	—
100	M₁₆×C₂₅₁	C₂³	1	2	yes	—
101	C₂×C₈×C₂₅₁	—	2	1	no	—
102	C₄²×C₂₅₁	—	2	1	no	—
103	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
104	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
105	C₂²×D₂₅₁	—	2	1	no	—
106	C₂²×D₂₅₁	—	2	4	no	—
107	C₂²×D₂₅₁	C₂×D₄	1	2	yes	—
108	Dic₅₀₂	—	2	1	no	—
109	Dic₅₀₂	—	2	4	no	—
110	Dic₅₀₂	C₂²⋊C₄	1	2	yes	—
111	Dic₅₀₂	C₂²⋊C₄	1	2	yes	—
112	Dic₅₀₂	C₂²×C₄	1	2	yes	—
113	D₁₀₀₄	—	2	4	no	—
114	D₁₀₀₄	—	2	1	no	—
115	D₁₀₀₄	C₂²⋊C₄	1	2	yes	—
116	D₁₀₀₄	C₂²⋊C₄	1	2	yes	—
117	D₁₀₀₄	C₂²×C₄	1	2	yes	—
118	C₂²⋊D₂₅₁	—	2	2	no	—
119	C₂²⋊D₂₅₁	—	2	2	no	—
120	C₂²⋊D₂₅₁	—	2	4	no	—
121	C₂²⋊D₂₅₁	—	2	4	no	—
122	C₂²⋊D₂₅₁	C₂²⋊C₄	1	4	yes	—
123	C₂²⋊D₂₅₁	C₂²⋊C₄	1	4	yes	—
124	C₂×Dic₂₅₁	—	2	1	no	—
125	C₂×Dic₂₅₁	—	2	4	no	—
126	C₂×Dic₂₅₁	—	2	2	no	—
127	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
128	C₄×D₂₅₁	—	2	4	no	—
129	C₄×D₂₅₁	—	2	2	no	—
130	C₄×D₂₅₁	—	2	2	no	—
131	C₄×D₂₅₁	—	2	4	no	—
132	C₄×D₂₅₁	—	4	4	no	—
133	C₄×D₂₅₁	C₂²×C₄	1	4	yes	—
134	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
135	C₂₅₁⋊C₈	—	2	2	no	—
136	C₂³×C₂₅₁	—	2	1	no	—
137	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
138	Q₈×C₂₅₁	—	2	1	no	—
139	Q₈×C₂₅₁	C₂²×C₄	1	2	yes	—
140	D₄×C₂₅₁	—	2	2	no	—
141	D₄×C₂₅₁	—	2	2	no	—
142	D₄×C₂₅₁	—	2	1	no	—
143	D₄×C₂₅₁	C₂²×C₄	1	2	yes	—
144	C₂×C₄×C₂₅₁	—	2	1	no	—
145	C₂×C₄×C₂₅₁	—	2	1	no	—
146	C₂×C₄×C₂₅₁	—	2	2	no	—
147	C₂×C₄×C₂₅₁	—	2	2	no	—
148	C₂×C₄×C₂₅₁	—	2	1	no	—
149	C₂×C₄×C₂₅₁	—	4	2	no	—
150	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
156	C₈×C₂₅₁	—	2	2	no	—
157	C₂²×C₂₅₁	—	2	2	no	—
158	C₂²×C₂₅₁	—	4	1	no	—
159	C₂²×C₂₅₁	—	8	1	no	—
160	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×D₂₅₁	—	2	2	no	—
164	C₂×D₂₅₁	—	4	2	no	—
165	C₂×D₂₅₁	—	8	4	no	—
166	C₂×D₂₅₁	—	8	1	no	—
167	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	4	yes	—
168	C₄×C₂₅₁	—	2	2	no	—
169	C₄×C₂₅₁	—	2	2	no	—
170	C₄×C₂₅₁	—	4	1	no	—
171	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₄×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
174	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
175	Dic₂₅₁	—	2	2	no	—
176	Dic₂₅₁	—	4	2	no	—
177	Dic₂₅₁	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₂₅₁	—	2	1	no	—
179	C₂×C₂₅₁	—	2	1	no	—
180	C₂×C₂₅₁	—	2	1	no	—
181	C₂×C₂₅₁	—	4	2	no	—
182	C₂×C₂₅₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	D₂₅₁	—	2	4	no	—
184	D₂₅₁	—	4	2	no	—
185	C₂₅₁	#2901	1	1	yes	characteristic, complemented, Sylow
186	#2901	—	251	1	no	maximal, Sylow
187	#585	—	251	1	no	—
188	#568	—	251	1	no	—
189	C₄×#41	—	251	1	no	—
190	#421	—	251	1	no	—
191	#421	—	251	1	no	—
192	#421	—	251	4	no	—
193	C₂×#104	—	251	1	no	—
194	C₂×#104	—	251	4	no	—
195	C₂×#104	D₂₅₁	1	1	yes	characteristic, complemented
196	2₋¹⁺⁴	—	502	1	no	—
197	2₋¹⁺⁴	—	251	2	no	—
198	2₋¹⁺⁴	—	251	2	no	—
199	H(5,𝔽₂)	—	502	2	no	—
200	H(5,𝔽₂)	—	502	1	no	—
201	H(5,𝔽₂)	—	251	2	no	—
202	H(5,𝔽₂)	—	251	2	no	—
203	C₂×#41	—	502	2	no	—
204	C₂×#41	—	502	2	no	—
205	C₂×#41	—	251	4	no	—
206	C₂×#41	—	251	1	no	—
207	C₂×#41	—	251	1	no	—
208	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
209	#131	—	502	2	no	—
210	#131	—	502	2	no	—
211	C₂×M₁₆	—	251	1	no	—
212	C₂×M₁₆	—	251	4	no	—
213	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
214	C₄×Q₈	—	502	1	no	—
215	C₄×D₄	—	502	1	no	—
216	C₄×D₄	—	502	2	no	—
217	#117	—	251	1	no	—
218	#117	—	251	2	no	—
219	C₂×C₄²	—	251	2	no	—
220	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
221	#104	—	251	4	no	—
222	#104	—	251	4	no	—
223	#104	—	251	2	no	—
224	#104	—	251	2	no	—
225	#104	C₂×D₂₅₁	1	2	yes	complemented
226	#104	C₂×D₂₅₁	1	2	yes	complemented
227	#41	—	2	1	no	—
228	#41	—	2	1	no	—
229	#41	—	502	2	no	—
230	#41	—	502	4	no	—
231	#41	—	502	2	no	—
232	#41	—	502	4	no	—
233	#41	—	502	2	no	—
234	#41	—	502	4	no	—
235	#41	—	502	2	no	—
236	#41	—	502	4	no	—
237	#41	—	502	1	no	—
238	#41	—	502	1	no	—
239	#41	—	251	4	no	—
240	#41	—	251	4	no	—
241	#41	—	251	2	no	—
242	#41	—	251	2	no	—
243	#41	—	251	2	no	—
244	#41	—	251	2	no	—
245	#41	—	251	2	no	—
246	#41	—	251	2	no	—
247	#41	C₄×D₂₅₁	1	2	yes	complemented
248	#41	C₂²×D₂₅₁	1	2	yes	—
249	C₂×Q₈	—	502	2	no	—
250	C₂×Q₈	—	502	2	no	—
251	C₂×Q₈	—	251	4	no	—
252	C₂×Q₈	—	251	1	no	—
253	C₂×Q₈	—	251	1	no	—
254	C₂×Q₈	C₄×D₂₅₁	1	1	yes	characteristic, complemented
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	—	502	2	no	—
257	C₂×D₄	—	502	4	no	—
258	C₂×D₄	—	502	4	no	—
259	C₂×D₄	—	502	2	no	—
260	C₂×D₄	—	502	1	no	—
261	C₂×D₄	—	502	4	no	—
262	C₂×D₄	—	251	4	no	—
263	C₂×D₄	—	251	2	no	—
264	C₂×D₄	—	251	1	no	—
265	C₂×D₄	—	251	1	no	—
266	C₂×D₄	C₄×D₂₅₁	1	1	yes	characteristic, complemented
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	502	2	no	—
270	C₂²×C₄	—	502	4	no	—
271	C₂²×C₄	—	502	1	no	—
272	C₂²×C₄	—	251	2	no	—
273	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
274	M₁₆	—	2	1	no	—
275	M₁₆	—	502	4	no	—
276	M₁₆	—	502	1	no	—
277	M₁₆	—	251	2	no	—
278	M₁₆	C₂²×D₂₅₁	1	2	yes	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	502	4	no	—
281	C₂×C₈	—	502	1	no	—
282	C₄⋊C₄	—	502	2	no	—
283	C₄⋊C₄	—	502	1	no	—
284	C₂²⋊C₄	—	502	2	no	—
285	C₂²⋊C₄	—	502	1	no	—
286	C₄²	—	2	1	no	—
287	C₄²	—	502	2	no	—
288	C₄²	—	251	2	no	—
289	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
290	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
291	C₂³	—	2	1	no	—
292	C₂³	—	502	4	no	—
293	C₂³	—	502	1	no	—
294	C₂³	—	251	2	no	—
295	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
296	Q₈	—	2	1	no	—
297	Q₈	—	502	4	no	—
298	Q₈	—	502	1	no	—
299	Q₈	—	251	2	no	—
300	Q₈	—	251	2	no	—
301	Q₈	—	251	2	no	—
302	Q₈	C₂×C₄×D₂₅₁	1	2	yes	—
303	D₄	—	2	2	no	—
304	D₄	—	2	2	no	—
305	D₄	—	2	1	no	—
306	D₄	—	502	4	no	—
307	D₄	—	502	4	no	—
308	D₄	—	502	2	no	—
309	D₄	—	502	2	no	—
310	D₄	—	502	4	no	—
311	D₄	—	502	1	no	—
312	D₄	—	251	4	no	—
313	D₄	—	251	4	no	—
314	D₄	—	251	2	no	—
315	D₄	—	251	2	no	—
316	D₄	—	251	2	no	—
317	D₄	C₂×C₄×D₂₅₁	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	1004	4	no	—
325	C₂×C₄	—	502	4	no	—
326	C₂×C₄	—	502	4	no	—
327	C₂×C₄	—	502	2	no	—
328	C₂×C₄	—	502	1	no	—
329	C₂×C₄	—	502	4	no	—
330	C₂×C₄	—	502	2	no	—
331	C₂×C₄	—	502	2	no	—
332	C₂×C₄	—	251	2	no	—
333	C₂×C₄	—	251	4	no	—
334	C₂×C₄	—	251	4	no	—
335	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
337	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
338	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
339	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
341	C₈	—	2	2	no	—
342	C₈	—	502	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	8	1	no	—
346	C₂²	—	2008	1	no	—
347	C₂²	—	2008	4	no	—
348	C₂²	—	1004	2	no	—
349	C₂²	—	502	2	no	—
350	C₂²	—	251	4	no	—
351	C₂²	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
352	C₂²	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
353	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	1	no	—
357	C₄	—	1004	2	no	—
358	C₄	—	502	2	no	—
359	C₄	—	251	4	no	—
360	C₄	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
361	C₄	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
362	C₄	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
363	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
364	C₂	—	2	1	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	—	4	2	no	—
368	C₂	—	1004	2	no	—
369	C₂	—	502	4	no	—
370	C₂	C₂×C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₂₅₁
commutator	C₄×C₂₅₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	C₂×#104×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂²×C₂²⋊C₄
prime radical	#30632523	C₂
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	C₂×#104	D₂₅₁
hypocenter	C₂₅₁	#2901
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#104

Complements

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

N	H ≅ G/N	type
2. #30632453	C₂	semidirect
3. C₄×#16860810	C₂	semidirect
4. #30631704	C₂	semidirect
5. #30631703	C₂	semidirect
6. #30631702	C₂	semidirect
7. C₂×#22548643	C₂	semidirect
8. #104×D₂₅₁	C₂	semidirect
9. C₂×#104×C₂₅₁	C₂	semidirect
10. #22548763	C₄	semidirect
12. #22548762	C₄	semidirect
14. #22548761	C₄	semidirect
16. #22548760	C₄	semidirect
24. C₂×#16860794	C₂²	semidirect
25. M₁₆×D₂₅₁	C₂²	semidirect
29. #22548674	C₂²	semidirect
30. #22548672	C₂²	semidirect
31. C₄²×D₂₅₁	C₂²	semidirect
32. #22548643	C₂²	semidirect
33. #22548643	C₂²	semidirect
34. #22548642	C₂²	semidirect
35. #22548641	C₂²	semidirect
37. C₂×M₁₆×C₂₅₁	C₂²	semidirect
38. C₂×C₄²×C₂₅₁	C₂²	semidirect
39. #104×C₂₅₁	C₂²	semidirect
40. #104×C₂₅₁	C₂²	semidirect
42. #16860811	C₂×C₄	semidirect
51. #16860810	C₂×C₄	semidirect
58. #16860809	C₂×C₄	semidirect
60. C₂×Dic₅₀₂	C₂×C₄	semidirect
63. Q₈×D₂₅₁	C₂×C₄	semidirect
65. C₂×D₁₀₀₄	C₂×C₄	semidirect
73. D₄×D₂₅₁	C₂×C₄	semidirect
91. #41×C₂₅₁	C₂×C₄	semidirect
93. C₂×Q₈×C₂₅₁	C₂×C₄	semidirect
95. C₂×D₄×C₂₅₁	C₂×C₄	semidirect
185. C₂₅₁	#2901	semidirect
195. C₂×#104	D₂₅₁	semidirect
213. C₂×M₁₆	C₂×D₂₅₁	semidirect
220. C₂×C₄²	C₂×D₂₅₁	semidirect
225. #104	C₂×D₂₅₁	semidirect
226. #104	C₂×D₂₅₁	semidirect
247. #41	C₄×D₂₅₁	semidirect
254. C₂×Q₈	C₄×D₂₅₁	semidirect
266. C₂×D₄	C₄×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632523	2
#30632453	2
C₄×#16860810	2
#30631704	2
#30631703	2
#30631702	2
C₂×#22548643	2
#104×D₂₅₁	2
C₂×#104×C₂₅₁	2
#2901	251