Subgroups — #576×D₂₅₁ #44565113

Order 32128.

1512 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×D₂₅₁	C₂	1	2	yes	maximal, complemented
2	#30632492	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632491	C₂	1	6	yes	maximal, complemented
4	#30632490	C₂	1	2	yes	maximal, complemented
5	#30632489	C₂	1	3	yes	maximal, complemented
6	#30632488	C₂	1	3	yes	maximal, complemented
7	AGL(1,ℤ/8)×D₂₅₁	C₂	1	6	yes	maximal, complemented
8	#135×D₂₅₁	C₂	1	3	yes	maximal, complemented
9	C₂×D₈×D₂₅₁	C₂	1	3	yes	maximal, complemented
10	#131×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#576×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#22548761	—	2	2	no	—
13	#22548761	C₂²	1	2	yes	complemented
14	#22548761	C₂²	1	6	yes	complemented
15	#22548760	—	2	6	no	—
16	#22548760	C₂²	1	6	yes	complemented
17	#41×D₂₅₁	—	2	2	no	—
18	#41×D₂₅₁	C₂²	1	1	yes	characteristic
19	#41×D₂₅₁	C₂²	1	6	yes	complemented
20	C₂×D₄×D₂₅₁	—	2	6	no	—
21	C₂×D₄×D₂₅₁	C₂²	1	6	yes	complemented
22	#22548743	C₂²	1	6	yes	complemented
23	#22548742	C₂²	1	12	yes	complemented
24	#22548741	C₂²	1	6	yes	complemented
25	#22548740	C₂²	1	6	yes	complemented
26	#22548739	C₂²	1	12	yes	complemented
27	#22548738	C₂²	1	3	yes	complemented
28	#22548737	C₂²	1	3	yes	complemented
29	#22548736	C₂²	1	6	yes	complemented
30	#22548735	C₂²	1	6	yes	complemented
31	#22548734	C₂²	1	3	yes	complemented
32	Q₁₆×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
33	SD₁₆×D₂₅₁	C₂²	1	6	yes	complemented
34	C₂×D₂₀₀₈	C₂²	1	3	yes	complemented
35	C₂×#16860795	C₂²	1	6	yes	complemented
36	D₈×D₂₅₁	C₂²	1	3	yes	complemented
37	D₈×D₂₅₁	C₂²	1	6	yes	complemented
38	D₈×D₂₅₁	C₂²	1	6	yes	complemented
39	D₈×D₂₅₁	C₂²	1	6	yes	complemented
40	#22548723	C₂²	1	3	yes	complemented
41	#22548722	C₂²	1	1	yes	characteristic, complemented
42	#22548721	C₂²	1	3	yes	complemented
43	M₁₆×D₂₅₁	C₂²	1	3	yes	complemented
44	C₂×C₈×D₂₅₁	C₂²	1	3	yes	complemented
45	H(5,𝔽₂)×C₂₅₁	C₂²	1	2	yes	complemented
46	AGL(1,ℤ/8)×C₂₅₁	C₂²	1	6	yes	complemented
47	#135×C₂₅₁	C₂²	1	3	yes	complemented
48	C₂×D₈×C₂₅₁	C₂²	1	3	yes	complemented
49	#131×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
50	C₂³×D₂₅₁	—	2	6	no	—
51	#16860811	—	2	2	no	—
52	#16860811	D₄	1	1	yes	characteristic
53	#16860811	C₂³	1	6	yes	complemented
54	#16860810	—	2	6	no	—
55	#16860810	—	2	6	no	—
56	#16860810	C₂³	1	3	yes	—
57	#16860810	C₂³	1	6	yes	complemented
58	#16860809	—	2	6	no	—
59	#16860809	—	2	6	no	—
60	#16860809	D₄	1	3	yes	—
61	#16860809	C₂³	1	6	yes	complemented
62	Q₈×D₂₅₁	D₄	1	1	yes	characteristic
63	Q₈×D₂₅₁	C₂³	1	2	yes	—
64	C₂×D₁₀₀₄	—	2	6	no	—
65	C₂×D₁₀₀₄	C₂³	1	6	yes	complemented
66	C₂×C₂²⋊D₂₅₁	—	2	12	no	—
67	C₂×C₂²⋊D₂₅₁	—	2	6	no	—
68	D₄×D₂₅₁	—	2	6	no	—
69	D₄×D₂₅₁	—	2	6	no	—
70	D₄×D₂₅₁	—	2	12	no	—
71	D₄×D₂₅₁	—	2	6	no	—
72	D₄×D₂₅₁	—	2	6	no	—
73	D₄×D₂₅₁	—	2	6	no	—
74	D₄×D₂₅₁	D₄	1	3	yes	—
75	D₄×D₂₅₁	C₂³	1	6	yes	—
76	D₄×D₂₅₁	C₂³	1	12	yes	complemented
77	C₂×C₄×D₂₅₁	—	2	6	no	—
78	C₂×C₄×D₂₅₁	C₂³	1	3	yes	—
79	Dic₁₀₀₄	C₂³	1	1	yes	characteristic, complemented
80	#16860800	C₂³	1	2	yes	complemented
81	#16860799	C₂³	1	6	yes	complemented
82	#16860798	C₂³	1	6	yes	complemented
83	#16860797	C₂³	1	6	yes	complemented
84	D₂₀₀₈	C₂³	1	3	yes	complemented
85	D₂₀₀₈	C₂³	1	6	yes	complemented
86	#16860795	C₂³	1	6	yes	complemented
87	#16860795	C₂³	1	12	yes	complemented
88	#16860794	C₂³	1	3	yes	complemented
89	#16860793	C₂³	1	6	yes	complemented
90	C₂×C₂₅₁⋊C₈	C₂³	1	3	yes	complemented
91	C₈×D₂₅₁	C₂³	1	1	yes	characteristic
92	C₈×D₂₅₁	C₂³	1	3	yes	—
93	C₈×D₂₅₁	C₂³	1	3	yes	complemented
94	C₈×D₂₅₁	C₂³	1	3	yes	complemented
95	#41×C₂₅₁	—	2	2	no	—
96	#41×C₂₅₁	C₂³	1	1	yes	characteristic
97	#41×C₂₅₁	C₂³	1	6	yes	complemented
98	C₂×D₄×C₂₅₁	—	2	6	no	—
99	C₂×D₄×C₂₅₁	C₂³	1	6	yes	complemented
100	Q₁₆×C₂₅₁	C₂³	1	1	yes	characteristic, complemented
101	SD₁₆×C₂₅₁	C₂³	1	6	yes	complemented
102	D₈×C₂₅₁	C₂³	1	6	yes	complemented
103	D₈×C₂₅₁	C₂³	1	3	yes	complemented
104	M₁₆×C₂₅₁	C₂³	1	3	yes	complemented
105	C₂×C₈×C₂₅₁	C₂³	1	3	yes	complemented
106	C₂²×D₂₅₁	—	2	6	no	—
107	C₂²×D₂₅₁	—	2	6	no	—
108	C₂²×D₂₅₁	—	2	12	no	—
109	C₂²×D₂₅₁	—	8	12	no	—
110	C₂²×D₂₅₁	C₂×D₄	1	3	yes	—
111	Dic₅₀₂	—	2	2	no	—
112	Dic₅₀₂	C₂×D₄	1	3	yes	—
113	Dic₅₀₂	C₂⁴	1	2	yes	—
114	D₁₀₀₄	—	2	6	no	—
115	D₁₀₀₄	—	2	6	no	—
116	D₁₀₀₄	C₂×D₄	1	3	yes	—
117	D₁₀₀₄	C₂⁴	1	6	yes	—
118	C₂²⋊D₂₅₁	—	2	6	no	—
119	C₂²⋊D₂₅₁	—	2	6	no	—
120	C₂²⋊D₂₅₁	—	2	6	no	—
121	C₂²⋊D₂₅₁	—	2	12	no	—
122	C₂²⋊D₂₅₁	C₂×D₄	1	6	yes	—
123	C₂×Dic₂₅₁	—	2	6	no	—
124	C₂×Dic₂₅₁	C₂×D₄	1	3	yes	—
125	C₄×D₂₅₁	—	2	2	no	—
126	C₄×D₂₅₁	—	2	6	no	—
127	C₄×D₂₅₁	—	2	6	no	—
128	C₄×D₂₅₁	C₂×D₄	1	3	yes	—
129	C₄×D₂₅₁	C₂×D₄	1	3	yes	—
130	C₄×D₂₅₁	C₂⁴	1	1	yes	characteristic
131	C₄×D₂₅₁	C₂⁴	1	3	yes	—
132	C₂₅₁⋊C₈	C₂⁴	1	1	yes	characteristic
133	C₂₅₁⋊C₈	C₂⁴	1	3	yes	—
134	C₂³×C₂₅₁	—	2	6	no	—
135	Q₈×C₂₅₁	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₂₅₁	C₂⁴	1	2	yes	—
137	D₄×C₂₅₁	—	2	6	no	—
138	D₄×C₂₅₁	—	2	6	no	—
139	D₄×C₂₅₁	C₂×D₄	1	3	yes	—
140	D₄×C₂₅₁	C₂⁴	1	6	yes	—
141	C₂×C₄×C₂₅₁	—	2	6	no	—
142	C₂×C₄×C₂₅₁	C₂⁴	1	3	yes	—
143	C₈×C₂₅₁	C₂⁴	1	1	yes	characteristic
144	C₈×C₂₅₁	C₂⁴	1	3	yes	—
145	C₂²×C₂₅₁	—	2	6	no	—
146	C₂²×C₂₅₁	—	8	6	no	—
147	C₂²×C₂₅₁	C₂²×D₄	1	3	yes	—
148	C₂×D₂₅₁	—	2	6	no	—
149	C₂×D₂₅₁	—	2	6	no	—
150	C₂×D₂₅₁	—	4	12	no	—
151	C₂×D₂₅₁	—	8	12	no	—
152	C₂×D₂₅₁	—	8	6	no	—
153	C₂×D₂₅₁	C₂²×D₄	1	3	yes	—
154	C₂×D₂₅₁	C₂²×D₄	1	1	yes	characteristic
155	C₄×C₂₅₁	—	2	2	no	—
156	C₄×C₂₅₁	C₂²×D₄	1	3	yes	—
157	C₄×C₂₅₁	C₂⁵	1	1	yes	characteristic
158	Dic₂₅₁	—	2	2	no	—
159	Dic₂₅₁	C₂²×D₄	1	3	yes	—
160	Dic₂₅₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₂₅₁	—	2	3	no	—
162	C₂×C₂₅₁	—	4	6	no	—
163	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
164	D₂₅₁	—	2	3	no	—
165	D₂₅₁	—	4	6	no	—
166	D₂₅₁	#576	1	2	yes	direct product factor
167	C₂₅₁	C₂×#576	1	1	yes	characteristic, complemented, Sylow
168	C₂×#576	—	251	1	no	maximal, Sylow
169	C₂×H(5,𝔽₂)	—	251	2	no	—
170	#576	—	251	2	no	—
171	#576	—	251	6	no	—
172	#576	—	251	3	no	—
173	#576	—	251	3	no	—
174	#576	—	251	1	no	—
175	#576	D₂₅₁	1	1	yes	characteristic, direct product factor
176	C₂×AGL(1,ℤ/8)	—	251	6	no	—
177	C₂×#135	—	251	3	no	—
178	C₂²×D₈	—	251	3	no	—
179	C₂×#131	—	251	1	no	—
180	H(5,𝔽₂)	—	502	6	no	—
181	H(5,𝔽₂)	—	502	2	no	—
182	H(5,𝔽₂)	—	251	2	no	—
183	H(5,𝔽₂)	—	251	6	no	—
184	H(5,𝔽₂)	—	251	6	no	—
185	H(5,𝔽₂)	C₂×D₂₅₁	1	2	yes	complemented
186	C₂×#41	—	502	2	no	—
187	C₂×#41	—	251	6	no	—
188	C₂×#41	—	251	1	no	—
189	C₂²×D₄	—	502	6	no	—
190	C₂²×D₄	—	251	6	no	—
191	AGL(1,ℤ/8)	—	251	6	no	—
192	AGL(1,ℤ/8)	—	251	6	no	—
193	AGL(1,ℤ/8)	—	251	12	no	—
194	AGL(1,ℤ/8)	—	251	12	no	—
195	AGL(1,ℤ/8)	—	251	6	no	—
196	AGL(1,ℤ/8)	C₂×D₂₅₁	1	6	yes	complemented
197	#135	—	251	6	no	—
198	#135	—	251	3	no	—
199	#135	—	251	6	no	—
200	#135	—	251	3	no	—
201	#135	—	251	3	no	—
202	#135	C₂×D₂₅₁	1	3	yes	complemented
203	C₂×Q₁₆	—	251	1	no	—
204	C₂×SD₁₆	—	251	6	no	—
205	C₂×D₈	—	251	6	no	—
206	C₂×D₈	—	251	3	no	—
207	C₂×D₈	—	251	6	no	—
208	C₂×D₈	—	251	6	no	—
209	C₂×D₈	—	251	6	no	—
210	C₂×D₈	—	251	3	no	—
211	C₂×D₈	C₂×D₂₅₁	1	3	yes	complemented
212	#131	—	251	1	no	—
213	#131	—	251	3	no	—
214	#131	—	251	3	no	—
215	#131	C₂×D₂₅₁	1	1	yes	characteristic, complemented
216	C₂×M₁₆	—	251	3	no	—
217	C₂²×C₈	—	251	3	no	—
218	C₂⁴	—	502	6	no	—
219	#41	—	2	2	no	—
220	#41	—	502	6	no	—
221	#41	—	502	6	no	—
222	#41	—	502	6	no	—
223	#41	—	502	2	no	—
224	#41	—	502	6	no	—
225	#41	—	251	6	no	—
226	#41	—	251	6	no	—
227	#41	—	251	6	no	—
228	#41	—	251	1	no	—
229	#41	—	251	3	no	—
230	#41	—	251	3	no	—
231	#41	C₂²×D₂₅₁	1	1	yes	characteristic
232	#41	C₂²×D₂₅₁	1	6	yes	complemented
233	C₂×Q₈	—	251	2	no	—
234	C₂×Q₈	—	251	1	no	—
235	C₂×D₄	—	2	6	no	—
236	C₂×D₄	—	502	6	no	—
237	C₂×D₄	—	502	6	no	—
238	C₂×D₄	—	502	12	no	—
239	C₂×D₄	—	502	6	no	—
240	C₂×D₄	—	502	12	no	—
241	C₂×D₄	—	502	6	no	—
242	C₂×D₄	—	502	6	no	—
243	C₂×D₄	—	502	6	no	—
244	C₂×D₄	—	502	6	no	—
245	C₂×D₄	—	251	6	no	—
246	C₂×D₄	—	251	12	no	—
247	C₂×D₄	—	251	3	no	—
248	C₂×D₄	—	251	6	no	—
249	C₂×D₄	C₂²×D₂₅₁	1	6	yes	complemented
250	C₂²×C₄	—	502	6	no	—
251	C₂²×C₄	—	251	3	no	—
252	Q₁₆	—	251	2	no	—
253	Q₁₆	—	251	1	no	—
254	Q₁₆	C₂²×D₂₅₁	1	1	yes	characteristic, complemented
255	SD₁₆	—	251	6	no	—
256	SD₁₆	—	251	6	no	—
257	SD₁₆	—	251	6	no	—
258	SD₁₆	C₂²×D₂₅₁	1	6	yes	complemented
259	D₈	—	251	6	no	—
260	D₈	—	251	12	no	—
261	D₈	—	251	3	no	—
262	D₈	—	251	6	no	—
263	D₈	C₂²×D₂₅₁	1	3	yes	complemented
264	D₈	C₂²×D₂₅₁	1	6	yes	complemented
265	M₁₆	—	251	3	no	—
266	M₁₆	—	251	6	no	—
267	M₁₆	C₂²×D₂₅₁	1	3	yes	complemented
268	C₂×C₈	—	251	3	no	—
269	C₂×C₈	—	251	1	no	—
270	C₂×C₈	—	251	3	no	—
271	C₂×C₈	—	251	3	no	—
272	C₂×C₈	—	251	3	no	—
273	C₂×C₈	C₂²×D₂₅₁	1	3	yes	complemented
274	C₂³	—	2	6	no	—
275	C₂³	—	2008	12	no	—
276	C₂³	—	502	12	no	—
277	C₂³	—	502	6	no	—
278	C₂³	—	502	6	no	—
279	C₂³	—	251	3	no	—
280	Q₈	—	502	2	no	—
281	Q₈	—	251	2	no	—
282	Q₈	—	251	3	no	—
283	Q₈	D₄×D₂₅₁	1	1	yes	characteristic
284	Q₈	C₂³×D₂₅₁	1	2	yes	—
285	D₄	—	2	6	no	—
286	D₄	—	2	6	no	—
287	D₄	—	502	6	no	—
288	D₄	—	502	6	no	—
289	D₄	—	502	6	no	—
290	D₄	—	502	12	no	—
291	D₄	—	502	6	no	—
292	D₄	—	502	6	no	—
293	D₄	—	251	6	no	—
294	D₄	—	251	3	no	—
295	D₄	—	251	6	no	—
296	D₄	D₄×D₂₅₁	1	3	yes	—
297	D₄	C₂³×D₂₅₁	1	6	yes	—
298	C₂×C₄	—	2	6	no	—
299	C₂×C₄	—	502	2	no	—
300	C₂×C₄	—	502	6	no	—
301	C₂×C₄	—	502	6	no	—
302	C₂×C₄	—	502	6	no	—
303	C₂×C₄	—	251	3	no	—
304	C₂×C₄	—	251	3	no	—
305	C₂×C₄	—	251	3	no	—
306	C₂×C₄	—	251	1	no	—
307	C₂×C₄	—	251	3	no	—
308	C₂×C₄	C₂³×D₂₅₁	1	3	yes	—
309	C₈	—	251	1	no	—
310	C₈	—	251	3	no	—
311	C₈	C₂³×D₂₅₁	1	1	yes	characteristic
312	C₈	C₂³×D₂₅₁	1	3	yes	—
313	C₂²	—	2	6	no	—
314	C₂²	—	8	6	no	—
315	C₂²	—	2008	6	no	—
316	C₂²	—	2008	12	no	—
317	C₂²	—	1004	12	no	—
318	C₂²	—	502	6	no	—
319	C₂²	—	502	6	no	—
320	C₂²	—	251	3	no	—
321	C₂²	—	251	1	no	—
322	C₂²	C₂×D₄×D₂₅₁	1	3	yes	—
323	C₄	—	2	2	no	—
324	C₄	—	502	2	no	—
325	C₄	—	251	3	no	—
326	C₄	—	251	1	no	—
327	C₄	C₂×D₄×D₂₅₁	1	3	yes	—
328	C₄	C₂⁴×D₂₅₁	1	1	yes	characteristic
329	C₂	—	2	3	no	—
330	C₂	—	4	6	no	—
331	C₂	—	1004	6	no	—
332	C₂	—	502	3	no	—
333	C₂	—	251	2	no	—
334	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₂₅₁
commutator, cosocle	C₄×C₂₅₁	C₂⁵
Frattini	C₄	C₂⁴×D₂₅₁
Fitting	#576×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂³×D₄
hypercenter	#576	D₂₅₁
hypocenter	C₂₅₁	C₂×#576
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×D₂₅₁	C₂	semidirect
2. #30632492	C₂	semidirect
3. #30632491	C₂	semidirect
4. #30632490	C₂	semidirect
5. #30632489	C₂	semidirect
6. #30632488	C₂	semidirect
7. AGL(1,ℤ/8)×D₂₅₁	C₂	semidirect
8. #135×D₂₅₁	C₂	semidirect
9. C₂×D₈×D₂₅₁	C₂	semidirect
10. #131×D₂₅₁	C₂	semidirect
11. #576×C₂₅₁	C₂	semidirect
13. #22548761	C₂²	semidirect
14. #22548761	C₂²	semidirect
16. #22548760	C₂²	semidirect
19. #41×D₂₅₁	C₂²	semidirect
21. C₂×D₄×D₂₅₁	C₂²	semidirect
22. #22548743	C₂²	semidirect
23. #22548742	C₂²	semidirect
24. #22548741	C₂²	semidirect
25. #22548740	C₂²	semidirect
26. #22548739	C₂²	semidirect
27. #22548738	C₂²	semidirect
28. #22548737	C₂²	semidirect
29. #22548736	C₂²	semidirect
30. #22548735	C₂²	semidirect
31. #22548734	C₂²	semidirect
32. Q₁₆×D₂₅₁	C₂²	semidirect
33. SD₁₆×D₂₅₁	C₂²	semidirect
34. C₂×D₂₀₀₈	C₂²	semidirect
35. C₂×#16860795	C₂²	semidirect
36. D₈×D₂₅₁	C₂²	semidirect
37. D₈×D₂₅₁	C₂²	semidirect
38. D₈×D₂₅₁	C₂²	semidirect
39. D₈×D₂₅₁	C₂²	semidirect
40. #22548723	C₂²	semidirect
41. #22548722	C₂²	semidirect
42. #22548721	C₂²	semidirect
43. M₁₆×D₂₅₁	C₂²	semidirect
44. C₂×C₈×D₂₅₁	C₂²	semidirect
45. H(5,𝔽₂)×C₂₅₁	C₂²	semidirect
46. AGL(1,ℤ/8)×C₂₅₁	C₂²	semidirect
47. #135×C₂₅₁	C₂²	semidirect
48. C₂×D₈×C₂₅₁	C₂²	semidirect
49. #131×C₂₅₁	C₂²	semidirect
53. #16860811	C₂³	semidirect
57. #16860810	C₂³	semidirect
61. #16860809	C₂³	semidirect
65. C₂×D₁₀₀₄	C₂³	semidirect
76. D₄×D₂₅₁	C₂³	semidirect
79. Dic₁₀₀₄	C₂³	semidirect
80. #16860800	C₂³	semidirect
81. #16860799	C₂³	semidirect
82. #16860798	C₂³	semidirect
83. #16860797	C₂³	semidirect
84. D₂₀₀₈	C₂³	semidirect
85. D₂₀₀₈	C₂³	semidirect
86. #16860795	C₂³	semidirect
87. #16860795	C₂³	semidirect
88. #16860794	C₂³	semidirect
89. #16860793	C₂³	semidirect
90. C₂×C₂₅₁⋊C₈	C₂³	semidirect
93. C₈×D₂₅₁	C₂³	semidirect
94. C₈×D₂₅₁	C₂³	semidirect
97. #41×C₂₅₁	C₂³	semidirect
99. C₂×D₄×C₂₅₁	C₂³	semidirect
100. Q₁₆×C₂₅₁	C₂³	semidirect
101. SD₁₆×C₂₅₁	C₂³	semidirect
102. D₈×C₂₅₁	C₂³	semidirect
103. D₈×C₂₅₁	C₂³	semidirect
104. M₁₆×C₂₅₁	C₂³	semidirect
105. C₂×C₈×C₂₅₁	C₂³	semidirect
166. D₂₅₁	#576	direct (N × H)
167. C₂₅₁	C₂×#576	semidirect
175. #576	D₂₅₁	direct (N × H)
185. H(5,𝔽₂)	C₂×D₂₅₁	semidirect
196. AGL(1,ℤ/8)	C₂×D₂₅₁	semidirect
202. #135	C₂×D₂₅₁	semidirect
211. C₂×D₈	C₂×D₂₅₁	semidirect
215. #131	C₂×D₂₅₁	semidirect
232. #41	C₂²×D₂₅₁	semidirect
249. C₂×D₄	C₂²×D₂₅₁	semidirect
254. Q₁₆	C₂²×D₂₅₁	semidirect
258. SD₁₆	C₂²×D₂₅₁	semidirect
263. D₈	C₂²×D₂₅₁	semidirect
264. D₈	C₂²×D₂₅₁	semidirect
267. M₁₆	C₂²×D₂₅₁	semidirect
273. C₂×C₈	C₂²×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
H(5,𝔽₂)×D₂₅₁	2
#30632492	2
#30632491	2
#30632490	2
#30632489	2
#30632488	2
AGL(1,ℤ/8)×D₂₅₁	2
#135×D₂₅₁	2
C₂×D₈×D₂₅₁	2
#131×D₂₅₁	2
#576×C₂₅₁	2
C₂×#576	251

Subgroups — #576×D251 #44565113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #576×D₂₅₁ #44565113