Subgroups — #44559170

Order 32128.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22548742	C₂	1	1	yes	maximal, characteristic
2	C₄×#16860811	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631800	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631797	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631785	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631772	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631769	C₂	1	1	yes	maximal, characteristic, complemented
10	#30631767	C₂	1	1	yes	maximal, characteristic, complemented
11	#30631728	C₂	1	1	yes	maximal, characteristic, complemented
12	#30631690	C₂	1	1	yes	maximal, characteristic, complemented
13	#30631687	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631639	C₂	1	1	yes	maximal, characteristic, complemented
15	#440×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860811	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₅₁	—	2	1	no	—
19	#22548742	C₄	1	8	yes	complemented
20	C₂×#16860797	C₂²	1	1	yes	characteristic
21	C₂×D₂₀₀₈	C₂²	1	1	yes	characteristic
22	C₂×#16860795	C₂²	1	1	yes	characteristic
23	C₂×#16860793	C₂²	1	1	yes	characteristic
24	C₂×#16860793	C₂²	1	1	yes	characteristic
25	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₁₀₀₄	—	2	1	no	—
27	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
28	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
29	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
30	#22548677	—	2	1	no	—
31	#22548677	C₂²	1	1	yes	characteristic
32	#22548677	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₂²⋊D₂₅₁	—	2	1	no	—
34	(C₂²⋊D₂₅₁)⋊C₄	—	2	1	no	—
35	#22548673	—	2	1	no	—
36	#22548673	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₂₅₁	—	2	1	no	—
39	C₄²×D₂₅₁	—	2	1	no	—
40	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
41	#22548648	C₂²	1	1	yes	characteristic, complemented
42	#22548647	C₂²	1	1	yes	characteristic, complemented
43	#22548646	C₂²	1	1	yes	characteristic, complemented
44	#22548639	C₂²	1	1	yes	characteristic, complemented
45	#22548637	C₂²	1	1	yes	characteristic
46	#22548637	C₂²	1	1	yes	characteristic, complemented
47	#22548636	C₂²	1	1	yes	characteristic
48	#22548635	C₂²	1	1	yes	characteristic
49	#22548635	C₂²	1	1	yes	characteristic, complemented
50	#22548626	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
56	#107×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
57	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
58	#102×C₂₅₁	C₂²	1	1	yes	characteristic
59	#97×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₂₅₁	—	2	1	no	—
61	#16860811	—	2	2	no	—
62	#16860811	C₂×C₄	1	4	yes	complemented
63	C₂×D₁₀₀₄	—	2	1	no	—
64	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
65	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
67	D₄×D₂₅₁	—	2	2	no	—
68	D₄×D₂₅₁	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₂₅₁	—	2	1	no	—
70	C₂×C₄×D₂₅₁	—	2	1	no	—
71	C₂×C₄×D₂₅₁	—	2	1	no	—
72	C₂×C₄×D₂₅₁	—	2	1	no	—
73	C₂×C₄×D₂₅₁	—	2	1	no	—
74	C₂×C₄×D₂₅₁	—	2	1	no	—
75	C₂×C₄×D₂₅₁	—	2	1	no	—
76	C₂×C₄×D₂₅₁	—	4	4	no	—
77	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
78	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
79	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
80	#16860797	C₂×C₄	1	4	yes	complemented
81	D₂₀₀₈	C₂×C₄	1	4	yes	complemented
82	#16860795	C₂×C₄	1	4	yes	complemented
83	#16860793	—	2	2	no	—
84	#16860793	C₂×C₄	1	4	yes	complemented
85	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₂₅₁	—	2	1	no	—
88	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
90	Dic₂₅₁⋊C₄	—	2	1	no	—
91	C₂²⋊Dic₂₅₁	—	2	1	no	—
92	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
93	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
94	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
95	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
96	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
97	C₄×Dic₂₅₁	—	2	1	no	—
98	C₄×Dic₂₅₁	—	2	1	no	—
99	C₄×Dic₂₅₁	D₄	1	1	yes	characteristic
100	C₄×Dic₂₅₁	D₄	1	1	yes	characteristic
101	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₂₅₁	—	2	1	no	—
105	SD₁₆×C₂₅₁	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₂₅₁	—	2	1	no	—
109	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
112	C₄²×C₂₅₁	—	2	1	no	—
113	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
114	C₂²×D₂₅₁	—	2	1	no	—
115	C₂²×D₂₅₁	—	2	1	no	—
116	C₂²×D₂₅₁	—	2	4	no	—
117	C₂²×D₂₅₁	—	4	2	no	—
118	C₂²×D₂₅₁	—	4	2	no	—
119	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
120	D₁₀₀₄	—	2	4	no	—
121	D₁₀₀₄	—	2	1	no	—
122	D₁₀₀₄	—	2	1	no	—
123	D₁₀₀₄	C₂²×C₄	1	2	yes	—
124	D₁₀₀₄	C₂²×C₄	1	2	yes	complemented
125	C₂²⋊D₂₅₁	—	2	4	no	—
126	C₂×Dic₂₅₁	—	2	1	no	—
127	C₂×Dic₂₅₁	—	2	1	no	—
128	C₂×Dic₂₅₁	—	4	2	no	—
129	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
132	C₄×D₂₅₁	—	2	4	no	—
133	C₄×D₂₅₁	—	2	2	no	—
134	C₄×D₂₅₁	—	4	1	no	—
135	C₄×D₂₅₁	—	4	2	no	—
136	C₄×D₂₅₁	—	4	2	no	—
137	C₄×D₂₅₁	—	4	2	no	—
138	C₄×D₂₅₁	—	4	2	no	—
139	C₄×D₂₅₁	—	4	2	no	—
140	C₄×D₂₅₁	C₂²×C₄	1	2	yes	—
141	C₄×D₂₅₁	#41	1	2	yes	—
142	C₂₅₁⋊C₈	—	2	1	no	—
143	C₂₅₁⋊C₈	C₂²×C₄	1	2	yes	complemented
144	C₂³×C₂₅₁	—	2	1	no	—
145	Q₈×C₂₅₁	—	2	1	no	—
146	Q₈×C₂₅₁	C₂²×C₄	1	2	yes	complemented
147	D₄×C₂₅₁	—	2	1	no	—
148	D₄×C₂₅₁	C₂²×C₄	1	2	yes	—
149	C₂×C₄×C₂₅₁	—	2	1	no	—
150	C₂×C₄×C₂₅₁	—	2	1	no	—
151	C₂×C₄×C₂₅₁	—	2	1	no	—
152	C₂×C₄×C₂₅₁	—	4	2	no	—
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	1	no	—
157	C₈×C₂₅₁	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₂₅₁	—	2	2	no	—
159	C₂²×C₂₅₁	—	4	1	no	—
160	C₂²×C₂₅₁	—	4	1	no	—
161	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₂₅₁	—	2	1	no	—
163	C₂×D₂₅₁	—	2	1	no	—
164	C₂×D₂₅₁	—	2	2	no	—
165	C₂×D₂₅₁	—	2	2	no	—
166	C₂×D₂₅₁	—	4	8	no	—
167	C₂×D₂₅₁	—	4	1	no	—
168	C₂×D₂₅₁	—	4	1	no	—
169	C₂×D₂₅₁	—	4	1	no	—
170	C₂×D₂₅₁	—	4	1	no	—
171	C₂×D₂₅₁	C₄×D₄	1	2	yes	—
172	C₄×C₂₅₁	—	2	2	no	—
173	C₄×C₂₅₁	—	2	1	no	—
174	C₄×C₂₅₁	—	2	1	no	—
175	C₄×C₂₅₁	—	4	1	no	—
176	C₄×C₂₅₁	—	4	1	no	—
177	C₄×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
178	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
179	Dic₂₅₁	—	2	1	no	—
180	Dic₂₅₁	—	4	1	no	—
181	Dic₂₅₁	—	4	1	no	—
182	Dic₂₅₁	C₄×D₄	1	2	yes	—
183	Dic₂₅₁	AGL(1,ℤ/8)	1	2	yes	complemented
184	C₂×C₂₅₁	—	4	2	no	—
185	C₂×C₂₅₁	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×C₂₅₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₂₅₁	#575	1	1	yes	characteristic
188	D₂₅₁	—	2	2	no	—
189	D₂₅₁	—	4	2	no	—
190	D₂₅₁	—	4	2	no	—
191	C₂₅₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
192	C₄×AGL(1,ℤ/8)	—	251	1	no	maximal, Sylow
193	C₂×AGL(1,ℤ/8)	—	251	1	no	—
194	C₄×#41	—	251	1	no	—
195	C₂×C₄×D₄	—	251	1	no	—
196	#442	—	251	1	no	—
197	#442	—	251	1	no	—
198	#440	—	251	1	no	—
199	#440	D₂₅₁	1	1	yes	characteristic, complemented
200	C₄×SD₁₆	—	251	1	no	—
201	C₄×SD₁₆	—	251	1	no	—
202	C₄×D₈	—	251	1	no	—
203	C₄×D₈	—	251	1	no	—
204	#428	—	251	1	no	—
205	#418	—	251	1	no	—
206	#417	—	251	1	no	—
207	C₄×M₁₆	—	251	1	no	—
208	C₂×#41	—	251	1	no	—
209	C₂²×D₄	—	251	1	no	—
210	C₂³×C₄	—	502	1	no	—
211	AGL(1,ℤ/8)	—	251	8	no	—
212	C₂×SD₁₆	—	251	1	no	—
213	C₂×SD₁₆	C₂×D₂₅₁	1	1	yes	characteristic
214	C₂×D₈	—	251	1	no	—
215	C₂×D₈	—	251	1	no	—
216	C₂×M₁₆	—	251	1	no	—
217	C₂×M₁₆	—	251	1	no	—
218	C₄×Q₈	—	251	1	no	—
219	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
220	C₄×D₄	—	502	1	no	—
221	C₄×D₄	—	502	1	no	—
222	C₄×D₄	—	502	1	no	—
223	C₄×D₄	—	502	1	no	—
224	C₄×D₄	—	251	1	no	—
225	C₄×D₄	—	251	1	no	—
226	C₄×D₄	—	251	1	no	—
227	C₄×D₄	—	251	1	no	—
228	C₄×D₄	—	251	1	no	—
229	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
230	#117	—	502	1	no	—
231	#117	—	251	1	no	—
232	C₂×C₄⋊C₄	—	251	1	no	—
233	C₂×C₂²⋊C₄	—	502	1	no	—
234	C₂×C₄²	—	502	1	no	—
235	C₂×C₄²	—	251	1	no	—
236	#107	—	251	1	no	—
237	#107	C₂×D₂₅₁	1	1	yes	characteristic, complemented
238	#106	—	251	1	no	—
239	#106	—	251	1	no	—
240	#103	—	251	1	no	—
241	#103	C₂×D₂₅₁	1	1	yes	characteristic, complemented
242	#102	—	251	1	no	—
243	#102	—	251	1	no	—
244	#102	—	251	1	no	—
245	#102	—	251	1	no	—
246	#102	—	251	1	no	—
247	#102	C₂×D₂₅₁	1	1	yes	characteristic
248	#97	—	251	1	no	—
249	#97	C₂×D₂₅₁	1	1	yes	characteristic, complemented
250	C₄×C₈	—	251	1	no	—
251	C₄×C₈	—	251	1	no	—
252	C₂⁴	—	502	1	no	—
253	#41	—	502	2	no	—
254	#41	—	251	4	no	—
255	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
256	C₂×D₄	—	502	1	no	—
257	C₂×D₄	—	502	2	no	—
258	C₂×D₄	—	502	1	no	—
259	C₂×D₄	—	251	4	no	—
260	C₂×D₄	—	251	1	no	—
261	C₂×D₄	—	251	1	no	—
262	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	1004	4	no	—
265	C₂²×C₄	—	502	1	no	—
266	C₂²×C₄	—	502	1	no	—
267	C₂²×C₄	—	502	1	no	—
268	C₂²×C₄	—	502	1	no	—
269	C₂²×C₄	—	502	1	no	—
270	C₂²×C₄	—	502	1	no	—
271	C₂²×C₄	—	502	1	no	—
272	C₂²×C₄	—	251	1	no	—
273	C₂²×C₄	—	251	1	no	—
274	C₂²×C₄	—	251	1	no	—
275	SD₁₆	—	251	4	no	—
276	SD₁₆	C₄×D₂₅₁	1	4	yes	complemented
277	D₈	—	251	4	no	—
278	D₈	—	251	4	no	—
279	M₁₆	—	502	2	no	—
280	M₁₆	—	251	4	no	—
281	C₂×C₈	—	251	1	no	—
282	C₂×C₈	—	251	1	no	—
283	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	502	1	no	—
287	C₄⋊C₄	—	502	1	no	—
288	C₄⋊C₄	—	251	1	no	—
289	C₄⋊C₄	—	251	1	no	—
290	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	502	1	no	—
294	C₂²⋊C₄	—	502	1	no	—
295	C₂²⋊C₄	—	502	1	no	—
296	C₂²⋊C₄	—	502	1	no	—
297	C₂²⋊C₄	—	502	1	no	—
298	C₂²⋊C₄	—	502	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	502	1	no	—
301	C₄²	—	502	1	no	—
302	C₄²	—	251	1	no	—
303	C₄²	—	251	1	no	—
304	C₄²	—	251	1	no	—
305	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	1004	2	no	—
308	C₂³	—	1004	2	no	—
309	C₂³	—	502	4	no	—
310	C₂³	—	502	1	no	—
311	C₂³	—	502	1	no	—
312	C₂³	—	251	1	no	—
313	Q₈	—	2	1	no	—
314	Q₈	C₂×C₄×D₂₅₁	1	2	yes	complemented
315	D₄	—	2	1	no	—
316	D₄	—	502	4	no	—
317	D₄	—	502	4	no	—
318	D₄	—	502	1	no	—
319	D₄	—	502	1	no	—
320	D₄	—	251	2	no	—
321	D₄	—	251	2	no	—
322	D₄	C₂×C₄×D₂₅₁	1	2	yes	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	1004	2	no	—
328	C₂×C₄	—	1004	2	no	—
329	C₂×C₄	—	1004	1	no	—
330	C₂×C₄	—	1004	2	no	—
331	C₂×C₄	—	1004	2	no	—
332	C₂×C₄	—	1004	2	no	—
333	C₂×C₄	—	1004	2	no	—
334	C₂×C₄	—	502	2	no	—
335	C₂×C₄	—	502	4	no	—
336	C₂×C₄	—	502	1	no	—
337	C₂×C₄	—	502	1	no	—
338	C₂×C₄	—	251	1	no	—
339	C₂×C₄	—	251	1	no	—
340	C₂×C₄	—	251	1	no	—
341	C₂×C₄	—	251	2	no	—
342	C₂×C₄	—	251	2	no	—
343	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
344	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	502	1	no	—
348	C₈	—	251	2	no	—
349	C₈	C₂×C₄×D₂₅₁	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	1004	8	no	—
354	C₂²	—	1004	1	no	—
355	C₂²	—	1004	1	no	—
356	C₂²	—	1004	1	no	—
357	C₂²	—	1004	1	no	—
358	C₂²	—	502	2	no	—
359	C₂²	—	502	2	no	—
360	C₂²	—	502	1	no	—
361	C₂²	—	502	1	no	—
362	C₂²	—	251	2	no	—
363	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	1004	1	no	—
370	C₄	—	1004	1	no	—
371	C₄	—	502	1	no	—
372	C₄	—	251	2	no	—
373	C₄	—	251	2	no	—
374	C₄	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
375	C₄	#41×D₂₅₁	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	1004	2	no	—
378	C₂	—	1004	2	no	—
379	C₂	—	502	2	no	—
380	C₂	C₄×D₄×D₂₅₁	1	1	yes	characteristic
381	C₂	AGL(1,ℤ/8)×D₂₅₁	1	1	yes	characteristic
382	C₂	#30632486	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₅₁
commutator	C₄×C₂₅₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	#440×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
prime radical	C₂×#22548742	C₂
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	#440	D₂₅₁
hypocenter	C₂₅₁	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
2. C₄×#16860811	C₂	semidirect
3. C₄×D₄×D₂₅₁	C₂	semidirect
4. #30631800	C₂	semidirect
5. #30631797	C₂	semidirect
6. #30631785	C₂	semidirect
7. SD₁₆×Dic₂₅₁	C₂	semidirect
8. #30631772	C₂	semidirect
9. #30631769	C₂	semidirect
10. #30631767	C₂	semidirect
11. #30631728	C₂	semidirect
12. #30631690	C₂	semidirect
13. #30631687	C₂	semidirect
14. #30631639	C₂	semidirect
15. #440×C₂₅₁	C₂	semidirect
19. #22548742	C₄	semidirect
25. Q₈×Dic₂₅₁	C₂²	semidirect
28. C₄×D₁₀₀₄	C₂²	semidirect
32. #22548677	C₂²	semidirect
41. #22548648	C₂²	semidirect
42. #22548647	C₂²	semidirect
43. #22548646	C₂²	semidirect
44. #22548639	C₂²	semidirect
46. #22548637	C₂²	semidirect
49. #22548635	C₂²	semidirect
50. #22548626	C₂²	semidirect
51. C₈×Dic₂₅₁	C₂²	semidirect
52. C₈×Dic₂₅₁	C₂²	semidirect
54. C₄×Q₈×C₂₅₁	C₂²	semidirect
56. #107×C₂₅₁	C₂²	semidirect
57. #103×C₂₅₁	C₂²	semidirect
59. #97×C₂₅₁	C₂²	semidirect
62. #16860811	C₂×C₄	semidirect
68. D₄×D₂₅₁	C₂×C₄	semidirect
80. #16860797	C₂×C₄	semidirect
81. D₂₀₀₈	C₂×C₄	semidirect
82. #16860795	C₂×C₄	semidirect
84. #16860793	C₂×C₄	semidirect
105. SD₁₆×C₂₅₁	C₂×C₄	semidirect
124. D₁₀₀₄	C₂²×C₄	semidirect
143. C₂₅₁⋊C₈	C₂²×C₄	semidirect
146. Q₈×C₂₅₁	C₂²×C₄	semidirect
157. C₈×C₂₅₁	C₂²×C₄	semidirect
183. Dic₂₅₁	AGL(1,ℤ/8)	semidirect
191. C₂₅₁	C₄×AGL(1,ℤ/8)	semidirect
199. #440	D₂₅₁	semidirect
219. C₄×Q₈	C₂×D₂₅₁	semidirect
237. #107	C₂×D₂₅₁	semidirect
241. #103	C₂×D₂₅₁	semidirect
249. #97	C₂×D₂₅₁	semidirect
276. SD₁₆	C₄×D₂₅₁	semidirect
314. Q₈	C₂×C₄×D₂₅₁	semidirect
349. C₈	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×#22548742	2
C₄×#16860811	2
C₄×D₄×D₂₅₁	2
#30631800	2
#30631797	2
#30631785	2
SD₁₆×Dic₂₅₁	2
#30631772	2
#30631769	2
#30631767	2
#30631728	2
#30631690	2
#30631687	2
#30631639	2
#440×C₂₅₁	2
C₄×AGL(1,ℤ/8)	251