Subgroups — #417×D₂₅₁ #44558873

Order 32128.

816 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊C₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631689	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631688	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631687	C₂	1	2	yes	maximal, complemented
7	#30631686	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631685	C₂	1	2	yes	maximal, complemented
9	#103×D₂₅₁	C₂	1	2	yes	maximal, complemented
10	#102×D₂₅₁	C₂	1	2	yes	maximal, complemented
11	#417×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16860811	C₂²	1	1	yes	characteristic
13	C₂×#16860810	—	2	1	no	—
14	C₂×#16860810	C₂²	1	1	yes	characteristic
15	C₂×#16860809	—	2	1	no	—
16	C₂×#16860809	C₂²	1	1	yes	characteristic
17	#41×D₂₅₁	—	2	4	no	—
18	#41×D₂₅₁	C₄	1	8	yes	complemented
19	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₂₅₁	—	2	1	no	—
21	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₂₅₁	—	2	1	no	—
23	C₂²×C₄×D₂₅₁	—	2	1	no	—
24	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
25	C₂×#16860794	C₂²	1	1	yes	characteristic, complemented
26	C₂×#16860793	C₂²	1	2	yes	complemented
27	M₁₆×D₂₅₁	—	2	4	no	—
28	C₂×C₈×D₂₅₁	C₂²	1	2	yes	—
29	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×Dic₂₅₁⋊C₄	—	2	1	no	—
31	C₄⋊C₄×D₂₅₁	—	2	1	no	—
32	C₄⋊C₄×D₂₅₁	—	2	1	no	—
33	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
34	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
35	#22548640	C₂²	1	2	yes	complemented
36	#22548639	C₂²	1	2	yes	complemented
37	#22548638	C₂²	1	2	yes	complemented
38	#22548637	C₂²	1	2	yes	complemented
39	#22548636	C₂²	1	2	yes	complemented
40	#22548635	C₂²	1	2	yes	complemented
41	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
42	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
44	#103×C₂₅₁	C₂²	1	2	yes	complemented
45	#102×C₂₅₁	C₂²	1	2	yes	complemented
46	C₂³×D₂₅₁	—	2	1	no	—
47	C₂³×D₂₅₁	D₄	1	1	yes	characteristic
48	#16860811	—	2	2	no	—
49	#16860811	C₂×C₄	1	4	yes	complemented
50	#16860810	—	2	8	no	—
51	#16860810	—	2	2	no	—
52	#16860810	C₂×C₄	1	4	yes	complemented
53	#16860809	—	2	8	no	—
54	#16860809	—	2	2	no	—
55	#16860809	C₂×C₄	1	4	yes	complemented
56	C₂×Dic₅₀₂	—	2	1	no	—
57	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
58	Q₈×D₂₅₁	—	2	2	no	—
59	Q₈×D₂₅₁	C₂×C₄	1	4	yes	complemented
60	C₂×D₁₀₀₄	—	2	1	no	—
61	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
63	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
64	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
65	D₄×D₂₅₁	—	2	8	no	—
66	D₄×D₂₅₁	—	2	2	no	—
67	D₄×D₂₅₁	C₂×C₄	1	4	yes	complemented
68	C₂²×Dic₂₅₁	—	2	1	no	—
69	C₂²×Dic₂₅₁	—	2	1	no	—
70	C₂²×Dic₂₅₁	D₄	1	1	yes	characteristic
71	C₂×C₄×D₂₅₁	—	2	1	no	—
72	C₂×C₄×D₂₅₁	—	2	1	no	—
73	C₂×C₄×D₂₅₁	—	2	8	no	—
74	C₂×C₄×D₂₅₁	—	2	2	no	—
75	C₂×C₄×D₂₅₁	—	2	2	no	—
76	C₂×C₄×D₂₅₁	—	2	1	no	—
77	C₂×C₄×D₂₅₁	—	4	4	no	—
78	C₂×C₄×D₂₅₁	C₂×C₄	1	4	yes	—
79	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
80	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
81	C₂×C₄×D₂₅₁	D₄	1	4	yes	—
82	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
84	#16860794	—	2	2	no	—
85	#16860793	—	2	4	no	—
86	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	—
87	C₈×D₂₅₁	—	2	4	no	—
88	C₄⋊Dic₂₅₁	—	2	1	no	—
89	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
90	Dic₂₅₁⋊C₄	—	2	2	no	—
91	Dic₂₅₁⋊C₄	—	2	2	no	—
92	#41×C₂₅₁	—	2	2	no	—
93	#41×C₂₅₁	C₂×C₄	1	4	yes	complemented
94	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₂₅₁	—	2	1	no	—
96	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₅₁	—	2	1	no	—
98	C₂²×C₄×C₂₅₁	—	2	1	no	—
99	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
100	M₁₆×C₂₅₁	—	2	2	no	—
101	C₂×C₈×C₂₅₁	C₂³	1	2	yes	—
102	C₄⋊C₄×C₂₅₁	—	2	1	no	—
103	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
104	C₂²×D₂₅₁	—	2	2	no	—
105	C₂²×D₂₅₁	—	2	2	no	—
106	C₂²×D₂₅₁	—	2	1	no	—
107	C₂²×D₂₅₁	—	2	4	no	—
108	C₂²×D₂₅₁	—	4	2	no	—
109	C₂²×D₂₅₁	—	4	2	no	—
110	C₂²×D₂₅₁	C₂²⋊C₄	1	4	yes	—
111	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
113	Dic₅₀₂	—	2	1	no	—
114	Dic₅₀₂	—	2	4	no	—
115	Dic₅₀₂	C₂²×C₄	1	2	yes	complemented
116	D₁₀₀₄	—	2	4	no	—
117	D₁₀₀₄	—	2	1	no	—
118	D₁₀₀₄	C₂²×C₄	1	2	yes	complemented
119	C₂²⋊D₂₅₁	—	2	4	no	—
120	C₂²⋊D₂₅₁	—	2	4	no	—
121	C₂²⋊D₂₅₁	—	2	4	no	—
122	C₂×Dic₂₅₁	—	2	1	no	—
123	C₂×Dic₂₅₁	—	2	4	no	—
124	C₂×Dic₂₅₁	—	2	2	no	—
125	C₂×Dic₂₅₁	—	4	2	no	—
126	C₂×Dic₂₅₁	C₂²⋊C₄	1	4	yes	—
127	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
128	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
129	C₄×D₂₅₁	—	2	4	no	—
130	C₄×D₂₅₁	—	2	4	no	—
131	C₄×D₂₅₁	—	2	4	no	—
132	C₄×D₂₅₁	—	4	4	no	—
133	C₄×D₂₅₁	—	4	4	no	—
134	C₄×D₂₅₁	C₂²⋊C₄	1	4	yes	—
135	C₄×D₂₅₁	C₂²⋊C₄	1	4	yes	—
136	C₄×D₂₅₁	C₂²×C₄	1	2	yes	—
137	C₄×D₂₅₁	C₂²×C₄	1	2	yes	—
138	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
139	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
140	C₂₅₁⋊C₈	—	2	2	no	—
141	C₂³×C₂₅₁	—	2	1	no	—
142	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
143	Q₈×C₂₅₁	—	2	1	no	—
144	Q₈×C₂₅₁	C₂²×C₄	1	2	yes	complemented
145	D₄×C₂₅₁	—	2	4	no	—
146	D₄×C₂₅₁	—	2	1	no	—
147	D₄×C₂₅₁	C₂²×C₄	1	2	yes	complemented
148	C₂×C₄×C₂₅₁	—	2	1	no	—
149	C₂×C₄×C₂₅₁	—	2	4	no	—
150	C₂×C₄×C₂₅₁	—	2	2	no	—
151	C₂×C₄×C₂₅₁	—	4	2	no	—
152	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
153	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
155	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
156	C₈×C₂₅₁	—	2	2	no	—
157	C₂²×C₂₅₁	—	2	1	no	—
158	C₂²×C₂₅₁	—	2	1	no	—
159	C₂²×C₂₅₁	—	2	2	no	—
160	C₂²×C₂₅₁	—	4	1	no	—
161	C₂²×C₂₅₁	—	4	1	no	—
162	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×D₂₅₁	—	2	1	no	—
165	C₂×D₂₅₁	—	2	1	no	—
166	C₂×D₂₅₁	—	2	8	no	—
167	C₂×D₂₅₁	—	2	2	no	—
168	C₂×D₂₅₁	—	4	1	no	—
169	C₂×D₂₅₁	—	4	1	no	—
170	C₂×D₂₅₁	—	4	8	no	—
171	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×D₂₅₁	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×D₂₅₁	#137	1	2	yes	—
175	C₄×C₂₅₁	—	2	2	no	—
176	C₄×C₂₅₁	—	4	2	no	—
177	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
178	C₄×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
179	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
180	Dic₂₅₁	—	2	2	no	—
181	Dic₂₅₁	—	4	2	no	—
182	Dic₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
183	Dic₂₅₁	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₂₅₁	—	2	2	no	—
185	C₂×C₂₅₁	—	4	2	no	—
186	C₂×C₂₅₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₂₅₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₂₅₁	C₂×#137	1	1	yes	characteristic
189	D₂₅₁	—	2	2	no	—
190	D₂₅₁	—	4	2	no	—
191	D₂₅₁	#417	1	4	yes	direct product factor
192	C₂₅₁	C₂×#417	1	1	yes	characteristic, complemented, Sylow
193	C₂×#417	—	251	1	no	maximal, Sylow
194	C₂²×#41	—	251	1	no	—
195	C₂²×M₁₆	—	251	1	no	—
196	C₂²×C₄⋊C₄	—	251	1	no	—
197	#417	—	251	1	no	—
198	#417	—	251	1	no	—
199	#417	—	251	1	no	—
200	#417	—	251	2	no	—
201	#417	—	251	2	no	—
202	#417	D₂₅₁	1	1	yes	characteristic, direct product factor
203	C₂×#103	—	251	2	no	—
204	C₂×#102	—	251	2	no	—
205	C₂×#41	—	502	1	no	—
206	C₂×#41	—	502	1	no	—
207	C₂×#41	—	502	4	no	—
208	C₂×#41	—	251	8	no	—
209	C₂×#41	—	251	1	no	—
210	C₂×#41	—	251	1	no	—
211	C₂×#41	—	251	1	no	—
212	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
213	C₂²×Q₈	—	251	1	no	—
214	C₂²×D₄	—	502	1	no	—
215	C₂²×D₄	—	251	1	no	—
216	C₂³×C₄	—	502	1	no	—
217	C₂³×C₄	—	502	1	no	—
218	C₂³×C₄	—	251	1	no	—
219	C₂×M₁₆	—	502	4	no	—
220	C₂×M₁₆	—	251	1	no	—
221	C₂×M₁₆	—	251	2	no	—
222	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
223	C₂²×C₈	—	251	2	no	—
224	C₂×C₄⋊C₄	—	502	1	no	—
225	C₂×C₄⋊C₄	—	502	1	no	—
226	C₂×C₄⋊C₄	—	502	1	no	—
227	C₂×C₄⋊C₄	—	251	1	no	—
228	C₂×C₄⋊C₄	—	251	2	no	—
229	C₂×C₄⋊C₄	—	251	2	no	—
230	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
231	#103	—	251	2	no	—
232	#103	—	251	2	no	—
233	#103	—	251	2	no	—
234	#103	C₂×D₂₅₁	1	2	yes	complemented
235	#102	—	251	2	no	—
236	#102	—	251	2	no	—
237	#102	—	251	2	no	—
238	#102	C₂×D₂₅₁	1	2	yes	complemented
239	C₂⁴	—	502	1	no	—
240	C₂⁴	—	251	1	no	—
241	#41	—	2	2	no	—
242	#41	—	502	8	no	—
243	#41	—	502	8	no	—
244	#41	—	502	2	no	—
245	#41	—	502	2	no	—
246	#41	—	502	2	no	—
247	#41	—	251	4	no	—
248	#41	—	251	4	no	—
249	#41	—	251	4	no	—
250	#41	C₄×D₂₅₁	1	4	yes	complemented
251	C₂×Q₈	—	502	1	no	—
252	C₂×Q₈	—	502	2	no	—
253	C₂×Q₈	—	251	4	no	—
254	C₂×Q₈	—	251	1	no	—
255	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	502	1	no	—
258	C₂×D₄	—	502	8	no	—
259	C₂×D₄	—	502	1	no	—
260	C₂×D₄	—	502	1	no	—
261	C₂×D₄	—	502	2	no	—
262	C₂×D₄	—	502	1	no	—
263	C₂×D₄	—	251	4	no	—
264	C₂×D₄	—	251	1	no	—
265	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	1004	4	no	—
269	C₂²×C₄	—	502	2	no	—
270	C₂²×C₄	—	502	2	no	—
271	C₂²×C₄	—	502	1	no	—
272	C₂²×C₄	—	502	1	no	—
273	C₂²×C₄	—	502	8	no	—
274	C₂²×C₄	—	502	1	no	—
275	C₂²×C₄	—	502	1	no	—
276	C₂²×C₄	—	502	1	no	—
277	C₂²×C₄	—	251	1	no	—
278	C₂²×C₄	—	251	4	no	—
279	C₂²×C₄	—	251	1	no	—
280	C₂²×C₄	—	251	1	no	—
281	C₂²×C₄	—	251	4	no	—
282	C₂²×C₄	—	251	1	no	—
283	C₂²×C₄	—	251	1	no	—
284	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	M₁₆	—	502	4	no	—
287	M₁₆	—	502	2	no	—
288	C₂×C₈	—	502	4	no	—
289	C₂×C₈	—	251	2	no	—
290	C₂×C₈	C₂²×D₂₅₁	1	2	yes	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	502	2	no	—
293	C₄⋊C₄	—	502	2	no	—
294	C₄⋊C₄	—	502	1	no	—
295	C₄⋊C₄	—	251	2	no	—
296	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
297	C₂³	—	2	1	no	—
298	C₂³	—	1004	2	no	—
299	C₂³	—	1004	2	no	—
300	C₂³	—	502	4	no	—
301	C₂³	—	502	2	no	—
302	C₂³	—	502	2	no	—
303	C₂³	—	502	1	no	—
304	C₂³	—	251	1	no	—
305	C₂³	—	251	4	no	—
306	C₂³	—	251	1	no	—
307	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
308	Q₈	—	2	1	no	—
309	Q₈	—	502	4	no	—
310	Q₈	—	502	1	no	—
311	Q₈	—	251	2	no	—
312	Q₈	C₂×C₄×D₂₅₁	1	2	yes	complemented
313	D₄	—	2	4	no	—
314	D₄	—	2	1	no	—
315	D₄	—	502	4	no	—
316	D₄	—	502	4	no	—
317	D₄	—	502	4	no	—
318	D₄	—	502	4	no	—
319	D₄	—	502	1	no	—
320	D₄	—	251	2	no	—
321	D₄	C₂×C₄×D₂₅₁	1	2	yes	complemented
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	1004	4	no	—
327	C₂×C₄	—	1004	4	no	—
328	C₂×C₄	—	1004	2	no	—
329	C₂×C₄	—	502	4	no	—
330	C₂×C₄	—	502	4	no	—
331	C₂×C₄	—	502	2	no	—
332	C₂×C₄	—	502	1	no	—
333	C₂×C₄	—	502	4	no	—
334	C₂×C₄	—	502	4	no	—
335	C₂×C₄	—	251	1	no	—
336	C₂×C₄	—	251	1	no	—
337	C₂×C₄	—	251	4	no	—
338	C₂×C₄	—	251	2	no	—
339	C₂×C₄	—	251	2	no	—
340	C₂×C₄	—	251	2	no	—
341	C₂×C₄	—	251	2	no	—
342	C₂×C₄	—	251	4	no	—
343	C₂×C₄	—	251	4	no	—
344	C₂×C₄	C₂×C₄×D₂₅₁	1	2	yes	—
345	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
346	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
347	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	502	2	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	1004	8	no	—
356	C₂²	—	1004	1	no	—
357	C₂²	—	1004	1	no	—
358	C₂²	—	502	8	no	—
359	C₂²	—	502	2	no	—
360	C₂²	—	502	1	no	—
361	C₂²	—	502	1	no	—
362	C₂²	—	251	2	no	—
363	C₂²	—	251	2	no	—
364	C₂²	—	251	2	no	—
365	C₂²	—	251	2	no	—
366	C₂²	C₂²⋊C₄×D₂₅₁	1	2	yes	—
367	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	1004	2	no	—
371	C₄	—	502	2	no	—
372	C₄	—	251	2	no	—
373	C₄	—	251	2	no	—
374	C₄	C₂²⋊C₄×D₂₅₁	1	2	yes	—
375	C₄	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
376	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	4	2	no	—
379	C₂	—	1004	2	no	—
380	C₂	—	502	2	no	—
381	C₂	—	251	4	no	—
382	C₂	C₂×C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
383	C₂	AGL(1,ℤ/8)×D₂₅₁	1	1	yes	characteristic
384	C₂	#137×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₅₁
commutator	C₄×C₂₅₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	#417×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
prime radical	C₂×#41×D₂₅₁	C₂
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	#417	D₂₅₁
hypocenter	C₂₅₁	C₂×#417
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #417

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×D₂₅₁	C₂	semidirect
3. C₂×C₄⋊C₄×D₂₅₁	C₂	semidirect
4. #30631689	C₂	semidirect
5. #30631688	C₂	semidirect
6. #30631687	C₂	semidirect
7. #30631686	C₂	semidirect
8. #30631685	C₂	semidirect
9. #103×D₂₅₁	C₂	semidirect
10. #102×D₂₅₁	C₂	semidirect
11. #417×C₂₅₁	C₂	semidirect
18. #41×D₂₅₁	C₄	semidirect
25. C₂×#16860794	C₂²	semidirect
26. C₂×#16860793	C₂²	semidirect
29. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
34. C₄⋊C₄×D₂₅₁	C₂²	semidirect
35. #22548640	C₂²	semidirect
36. #22548639	C₂²	semidirect
37. #22548638	C₂²	semidirect
38. #22548637	C₂²	semidirect
39. #22548636	C₂²	semidirect
40. #22548635	C₂²	semidirect
42. C₂×M₁₆×C₂₅₁	C₂²	semidirect
43. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
44. #103×C₂₅₁	C₂²	semidirect
45. #102×C₂₅₁	C₂²	semidirect
49. #16860811	C₂×C₄	semidirect
52. #16860810	C₂×C₄	semidirect
55. #16860809	C₂×C₄	semidirect
59. Q₈×D₂₅₁	C₂×C₄	semidirect
67. D₄×D₂₅₁	C₂×C₄	semidirect
93. #41×C₂₅₁	C₂×C₄	semidirect
115. Dic₅₀₂	C₂²×C₄	semidirect
118. D₁₀₀₄	C₂²×C₄	semidirect
144. Q₈×C₂₅₁	C₂²×C₄	semidirect
147. D₄×C₂₅₁	C₂²×C₄	semidirect
191. D₂₅₁	#417	direct (N × H)
192. C₂₅₁	C₂×#417	semidirect
202. #417	D₂₅₁	direct (N × H)
222. C₂×M₁₆	C₂×D₂₅₁	semidirect
230. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
234. #103	C₂×D₂₅₁	semidirect
238. #102	C₂×D₂₅₁	semidirect
250. #41	C₄×D₂₅₁	semidirect
312. Q₈	C₂×C₄×D₂₅₁	semidirect
321. D₄	C₂×C₄×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₅₁	2
C₂×M₁₆×D₂₅₁	2
C₂×C₄⋊C₄×D₂₅₁	2
#30631689	2
#30631688	2
#30631687	2
#30631686	2
#30631685	2
#103×D₂₅₁	2
#102×D₂₅₁	2
#417×C₂₅₁	2
C₂×#417	251

Subgroups — #417×D251 #44558873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #417×D₂₅₁ #44558873