Subgroups — #44565138

Order 32128.

1424 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632523	C₂	1	2	yes	maximal, complemented
2	#30632503	C₂	1	4	yes	maximal, complemented
3	#30632497	C₂	1	4	yes	maximal, complemented
4	#30632496	C₂	1	4	yes	maximal, complemented
5	#30632491	C₂	1	4	yes	maximal, complemented
6	#30632487	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632484	C₂	1	4	yes	maximal, complemented
8	C₂×#22548735	C₂	1	2	yes	maximal, complemented
9	#135×D₂₅₁	C₂	1	4	yes	maximal, complemented
10	C₂×#22548723	C₂	1	1	yes	maximal, characteristic, complemented
11	#575×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#22548763	C₂²	1	4	yes	complemented
13	#22548762	—	2	2	no	—
14	#22548762	C₂²	1	4	yes	complemented
15	#22548761	—	2	2	no	—
16	#22548761	C₂²	1	4	yes	complemented
17	#22548760	—	2	4	no	—
18	#22548760	C₂²	1	4	yes	complemented
19	C₂×#16860810	—	2	4	no	—
20	C₂×#16860810	C₂²	1	1	yes	characteristic
21	C₂×#16860810	C₂²	1	2	yes	complemented
22	#41×D₂₅₁	—	2	4	no	—
23	#41×D₂₅₁	C₂²	1	8	yes	complemented
24	#22548748	C₂²	1	4	yes	complemented
25	#22548747	C₂²	1	8	yes	complemented
26	#22548744	C₂²	1	8	yes	complemented
27	#22548743	C₂²	1	4	yes	complemented
28	#22548742	C₂²	1	8	yes	complemented
29	#22548739	C₂²	1	8	yes	complemented
30	#22548738	C₂²	1	4	yes	complemented
31	#22548737	C₂²	1	4	yes	complemented
32	#22548736	C₂²	1	8	yes	complemented
33	#22548735	C₂²	1	4	yes	complemented
34	#22548735	C₂²	1	4	yes	complemented
35	#22548735	C₂²	1	4	yes	complemented
36	#22548735	C₂²	1	4	yes	complemented
37	#22548734	C₂²	1	4	yes	complemented
38	C₂×#16860800	C₂²	1	2	yes	complemented
39	Q₁₆×D₂₅₁	C₂²	1	4	yes	complemented
40	C₂×#16860798	C₂²	1	2	yes	complemented
41	C₂×#16860797	C₂²	1	2	yes	complemented
42	SD₁₆×D₂₅₁	C₂²	1	8	yes	complemented
43	C₂×#16860795	C₂²	1	2	yes	complemented
44	D₈×D₂₅₁	C₂²	1	4	yes	complemented
45	#22548723	C₂²	1	4	yes	complemented
46	#22548723	C₂²	1	4	yes	complemented
47	C₂×#16860793	C₂²	1	2	yes	complemented
48	C₂²×C₂₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₈×D₂₅₁	C₂²	1	2	yes	complemented
50	C₂×#41×C₂₅₁	C₂²	1	2	yes	complemented
51	#137×C₂₅₁	C₂²	1	4	yes	complemented
52	AGL(1,ℤ/8)×C₂₅₁	C₂²	1	4	yes	complemented
53	#135×C₂₅₁	C₂²	1	4	yes	complemented
54	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
55	#16860811	—	2	4	no	—
56	#16860811	C₂³	1	8	yes	—
57	#16860810	—	2	4	no	—
58	#16860810	—	2	4	no	—
59	#16860810	—	2	8	no	—
60	#16860810	—	2	8	no	—
61	#16860810	—	2	2	no	—
62	#16860810	—	2	2	no	—
63	#16860810	D₄	1	4	yes	—
64	#16860810	C₂³	1	4	yes	—
65	#16860810	C₂³	1	4	yes	—
66	#16860810	C₂³	1	4	yes	—
67	#16860809	—	2	4	no	—
68	#16860809	—	2	8	no	—
69	#16860809	—	2	8	no	—
70	#16860809	C₂³	1	8	yes	—
71	C₂×Dic₅₀₂	—	2	4	no	—
72	C₂×Dic₅₀₂	D₄	1	1	yes	characteristic
73	C₂×Dic₅₀₂	C₂³	1	2	yes	—
74	Q₈×D₂₅₁	—	2	4	no	—
75	Q₈×D₂₅₁	C₂³	1	8	yes	—
76	C₂×D₁₀₀₄	—	2	4	no	—
77	C₂×D₁₀₀₄	D₄	1	1	yes	characteristic
78	C₂×D₁₀₀₄	C₂³	1	2	yes	—
79	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
80	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
81	C₂×C₂²⋊D₂₅₁	D₄	1	2	yes	—
82	D₄×D₂₅₁	—	2	8	no	—
83	D₄×D₂₅₁	—	2	4	no	—
84	D₄×D₂₅₁	—	2	8	no	—
85	D₄×D₂₅₁	C₂³	1	8	yes	—
86	C₂×C₄×D₂₅₁	—	2	8	no	—
87	C₂×C₄×D₂₅₁	—	2	2	no	—
88	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
89	Dic₁₀₀₄	C₂³	1	4	yes	—
90	#16860800	C₂³	1	4	yes	—
91	#16860800	C₂³	1	4	yes	—
92	#16860799	C₂³	1	8	yes	—
93	#16860798	C₂³	1	4	yes	—
94	#16860798	C₂³	1	4	yes	—
95	#16860797	C₂³	1	4	yes	—
96	#16860797	C₂³	1	4	yes	—
97	D₂₀₀₈	C₂³	1	4	yes	—
98	#16860795	C₂³	1	4	yes	—
99	#16860795	C₂³	1	4	yes	—
100	#16860793	C₂³	1	8	yes	—
101	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	—
104	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	—
105	C₈×D₂₅₁	C₂³	1	4	yes	—
106	C₈×D₂₅₁	C₂³	1	4	yes	—
107	#41×C₂₅₁	—	2	2	no	—
108	#41×C₂₅₁	—	2	2	no	—
109	#41×C₂₅₁	C₂³	1	4	yes	—
110	#41×C₂₅₁	C₂³	1	4	yes	—
111	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
112	C₂×D₄×C₂₅₁	—	2	2	no	—
113	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
114	C₂²×C₄×C₂₅₁	—	2	2	no	—
115	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
116	Q₁₆×C₂₅₁	C₂³	1	4	yes	—
117	SD₁₆×C₂₅₁	C₂³	1	8	yes	—
118	D₈×C₂₅₁	C₂³	1	4	yes	—
119	M₁₆×C₂₅₁	C₂³	1	4	yes	—
120	C₂×C₈×C₂₅₁	C₂³	1	2	yes	—
121	C₂²×D₂₅₁	—	2	2	no	—
122	C₂²×D₂₅₁	—	2	8	no	—
123	C₂²×D₂₅₁	C₂×D₄	1	2	yes	—
124	Dic₅₀₂	—	2	2	no	—
125	Dic₅₀₂	—	2	8	no	—
126	Dic₅₀₂	C₂×D₄	1	4	yes	—
127	Dic₅₀₂	C₂⁴	1	4	yes	—
128	D₁₀₀₄	—	2	8	no	—
129	D₁₀₀₄	—	2	2	no	—
130	D₁₀₀₄	C₂×D₄	1	4	yes	—
131	D₁₀₀₄	C₂⁴	1	4	yes	—
132	C₂²⋊D₂₅₁	—	2	4	no	—
133	C₂²⋊D₂₅₁	—	2	4	no	—
134	C₂²⋊D₂₅₁	—	2	8	no	—
135	C₂²⋊D₂₅₁	—	2	8	no	—
136	C₂²⋊D₂₅₁	C₂×D₄	1	8	yes	—
137	C₂×Dic₂₅₁	—	2	2	no	—
138	C₂×Dic₂₅₁	—	2	8	no	—
139	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
140	C₄×D₂₅₁	—	2	8	no	—
141	C₄×D₂₅₁	—	2	4	no	—
142	C₄×D₂₅₁	—	2	4	no	—
143	C₄×D₂₅₁	—	2	8	no	—
144	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
145	C₄×D₂₅₁	C₂⁴	1	4	yes	—
146	C₂₅₁⋊C₈	C₂⁴	1	1	yes	characteristic
147	C₂₅₁⋊C₈	C₂⁴	1	1	yes	characteristic
148	C₂₅₁⋊C₈	C₂⁴	1	2	yes	—
149	C₂³×C₂₅₁	—	2	2	no	—
150	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
151	Q₈×C₂₅₁	—	2	2	no	—
152	Q₈×C₂₅₁	C₂⁴	1	4	yes	—
153	D₄×C₂₅₁	—	2	4	no	—
154	D₄×C₂₅₁	—	2	4	no	—
155	D₄×C₂₅₁	—	2	2	no	—
156	D₄×C₂₅₁	C₂⁴	1	4	yes	—
157	C₂×C₄×C₂₅₁	—	2	2	no	—
158	C₂×C₄×C₂₅₁	—	2	4	no	—
159	C₂×C₄×C₂₅₁	—	2	4	no	—
160	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
164	C₈×C₂₅₁	C₂⁴	1	4	yes	—
165	C₂²×C₂₅₁	—	2	4	no	—
166	C₂²×C₂₅₁	—	4	1	no	—
167	C₂²×C₂₅₁	—	8	2	no	—
168	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
169	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×D₂₅₁	—	2	4	no	—
171	C₂×D₂₅₁	—	4	2	no	—
172	C₂×D₂₅₁	—	8	8	no	—
173	C₂×D₂₅₁	—	8	2	no	—
174	C₂×D₂₅₁	C₂²×D₄	1	4	yes	—
175	C₄×C₂₅₁	—	2	4	no	—
176	C₄×C₂₅₁	C₂²×D₄	1	2	yes	—
177	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
178	C₄×C₂₅₁	C₂⁵	1	1	yes	characteristic
179	Dic₂₅₁	—	2	4	no	—
180	Dic₂₅₁	C₂²×D₄	1	4	yes	—
181	C₂×C₂₅₁	—	2	1	no	—
182	C₂×C₂₅₁	—	2	2	no	—
183	C₂×C₂₅₁	—	4	4	no	—
184	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
185	D₂₅₁	—	2	4	no	—
186	D₂₅₁	—	4	4	no	—
187	C₂₅₁	#3584	1	1	yes	characteristic, complemented, Sylow
188	#3584	—	251	1	no	maximal, Sylow
189	#585	—	251	2	no	—
190	#578	—	251	4	no	—
191	#577	—	251	4	no	—
192	#577	—	251	4	no	—
193	#576	—	251	4	no	—
194	#575	—	251	4	no	—
195	#575	—	251	1	no	—
196	#575	D₂₅₁	1	1	yes	characteristic, complemented
197	C₂×#135	—	251	2	no	—
198	C₂×#135	—	251	4	no	—
199	C₂×#131	—	251	1	no	—
200	2₋¹⁺⁴	—	502	2	no	—
201	2₋¹⁺⁴	—	251	4	no	—
202	2₋¹⁺⁴	—	251	4	no	—
203	H(5,𝔽₂)	—	502	4	no	—
204	H(5,𝔽₂)	—	502	2	no	—
205	H(5,𝔽₂)	—	251	4	no	—
206	H(5,𝔽₂)	—	251	4	no	—
207	C₂×#41	—	502	4	no	—
208	C₂×#41	—	502	4	no	—
209	C₂×#41	—	251	8	no	—
210	C₂×#41	—	251	2	no	—
211	C₂×#41	—	251	1	no	—
212	C₂×#41	C₂×D₂₅₁	1	2	yes	complemented
213	#137	—	251	8	no	—
214	#137	—	251	8	no	—
215	#137	—	251	4	no	—
216	#137	C₂×D₂₅₁	1	4	yes	complemented
217	AGL(1,ℤ/8)	—	251	8	no	—
218	AGL(1,ℤ/8)	—	251	8	no	—
219	AGL(1,ℤ/8)	—	251	4	no	—
220	AGL(1,ℤ/8)	C₂×D₂₅₁	1	4	yes	complemented
221	#135	—	251	4	no	—
222	#135	—	251	4	no	—
223	#135	—	251	4	no	—
224	#135	—	251	4	no	—
225	#135	—	251	4	no	—
226	#135	—	251	8	no	—
227	#135	—	251	4	no	—
228	#135	—	251	4	no	—
229	#135	C₂×D₂₅₁	1	4	yes	complemented
230	C₂×Q₁₆	—	251	2	no	—
231	C₂×Q₁₆	—	251	4	no	—
232	C₂×SD₁₆	—	251	2	no	—
233	C₂×SD₁₆	—	251	2	no	—
234	C₂×SD₁₆	—	251	8	no	—
235	C₂×D₈	—	251	2	no	—
236	C₂×D₈	—	251	4	no	—
237	#131	—	251	4	no	—
238	#131	—	251	4	no	—
239	C₂×M₁₆	—	251	2	no	—
240	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
241	C₂²×C₈	—	251	1	no	—
242	C₂²×C₈	—	251	2	no	—
243	#41	—	2	2	no	—
244	#41	—	2	2	no	—
245	#41	—	502	4	no	—
246	#41	—	502	8	no	—
247	#41	—	502	4	no	—
248	#41	—	502	8	no	—
249	#41	—	502	4	no	—
250	#41	—	502	8	no	—
251	#41	—	502	4	no	—
252	#41	—	502	8	no	—
253	#41	—	502	2	no	—
254	#41	—	502	2	no	—
255	#41	—	251	8	no	—
256	#41	—	251	8	no	—
257	#41	—	251	4	no	—
258	#41	—	251	4	no	—
259	#41	—	251	4	no	—
260	#41	—	251	4	no	—
261	#41	C₂²×D₂₅₁	1	4	yes	—
262	#41	C₂²×D₂₅₁	1	4	yes	—
263	C₂×Q₈	—	502	4	no	—
264	C₂×Q₈	—	502	4	no	—
265	C₂×Q₈	—	251	8	no	—
266	C₂×Q₈	—	251	2	no	—
267	C₂×Q₈	—	251	1	no	—
268	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	502	4	no	—
271	C₂×D₄	—	502	8	no	—
272	C₂×D₄	—	502	8	no	—
273	C₂×D₄	—	502	4	no	—
274	C₂×D₄	—	502	2	no	—
275	C₂×D₄	—	502	8	no	—
276	C₂×D₄	—	251	8	no	—
277	C₂×D₄	—	251	2	no	—
278	C₂×D₄	—	251	1	no	—
279	C₂×D₄	—	251	2	no	—
280	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	502	8	no	—
283	C₂²×C₄	—	502	2	no	—
284	C₂²×C₄	—	251	2	no	—
285	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
286	Q₁₆	—	251	4	no	—
287	Q₁₆	—	251	4	no	—
288	Q₁₆	—	251	4	no	—
289	Q₁₆	C₂²×D₂₅₁	1	4	yes	—
290	SD₁₆	—	251	4	no	—
291	SD₁₆	—	251	4	no	—
292	SD₁₆	—	251	4	no	—
293	SD₁₆	—	251	4	no	—
294	SD₁₆	—	251	8	no	—
295	SD₁₆	C₂²×D₂₅₁	1	8	yes	—
296	D₈	—	251	4	no	—
297	D₈	—	251	4	no	—
298	D₈	—	251	4	no	—
299	D₈	C₂²×D₂₅₁	1	4	yes	—
300	M₁₆	—	251	8	no	—
301	M₁₆	C₂²×D₂₅₁	1	4	yes	—
302	C₂×C₈	—	251	1	no	—
303	C₂×C₈	—	251	1	no	—
304	C₂×C₈	—	251	2	no	—
305	C₂×C₈	—	251	2	no	—
306	C₂×C₈	—	251	4	no	—
307	C₂×C₈	—	251	4	no	—
308	C₂×C₈	C₂²×D₂₅₁	1	2	yes	—
309	C₂³	—	2	2	no	—
310	C₂³	—	502	8	no	—
311	C₂³	—	502	2	no	—
312	C₂³	—	251	2	no	—
313	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
314	Q₈	—	2	2	no	—
315	Q₈	—	502	8	no	—
316	Q₈	—	502	2	no	—
317	Q₈	—	251	4	no	—
318	Q₈	—	251	4	no	—
319	Q₈	C₂³×D₂₅₁	1	4	yes	—
320	D₄	—	2	4	no	—
321	D₄	—	2	4	no	—
322	D₄	—	2	2	no	—
323	D₄	—	502	8	no	—
324	D₄	—	502	8	no	—
325	D₄	—	502	4	no	—
326	D₄	—	502	4	no	—
327	D₄	—	502	8	no	—
328	D₄	—	502	2	no	—
329	D₄	—	251	8	no	—
330	D₄	—	251	4	no	—
331	D₄	—	251	4	no	—
332	D₄	C₂³×D₂₅₁	1	4	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	502	8	no	—
337	C₂×C₄	—	502	8	no	—
338	C₂×C₄	—	502	2	no	—
339	C₂×C₄	—	502	8	no	—
340	C₂×C₄	—	502	4	no	—
341	C₂×C₄	—	502	4	no	—
342	C₂×C₄	—	251	2	no	—
343	C₂×C₄	—	251	4	no	—
344	C₂×C₄	—	251	4	no	—
345	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
346	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
347	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
348	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
349	C₈	—	251	1	no	—
350	C₈	—	251	1	no	—
351	C₈	—	251	2	no	—
352	C₈	C₂³×D₂₅₁	1	4	yes	—
353	C₂²	—	2	4	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	2008	2	no	—
357	C₂²	—	2008	8	no	—
358	C₂²	—	1004	2	no	—
359	C₂²	—	502	4	no	—
360	C₂²	—	251	4	no	—
361	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
362	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	502	4	no	—
365	C₄	—	251	4	no	—
366	C₄	C₂×D₄×D₂₅₁	1	2	yes	—
367	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
368	C₄	C₂⁴×D₂₅₁	1	1	yes	characteristic
369	C₂	—	2	2	no	—
370	C₂	—	2	1	no	—
371	C₂	—	4	4	no	—
372	C₂	—	1004	4	no	—
373	C₂	—	502	4	no	—
374	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₂₅₁
commutator, cosocle	C₄×C₂₅₁	C₂⁵
Frattini	C₄	C₂⁴×D₂₅₁
Fitting	#575×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂³×D₄
hypercenter	#575	D₂₅₁
hypocenter	C₂₅₁	#3584
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. #30632523	C₂	semidirect
2. #30632503	C₂	semidirect
3. #30632497	C₂	semidirect
4. #30632496	C₂	semidirect
5. #30632491	C₂	semidirect
6. #30632487	C₂	semidirect
7. #30632484	C₂	semidirect
8. C₂×#22548735	C₂	semidirect
9. #135×D₂₅₁	C₂	semidirect
10. C₂×#22548723	C₂	semidirect
11. #575×C₂₅₁	C₂	semidirect
12. #22548763	C₂²	semidirect
14. #22548762	C₂²	semidirect
16. #22548761	C₂²	semidirect
18. #22548760	C₂²	semidirect
21. C₂×#16860810	C₂²	semidirect
23. #41×D₂₅₁	C₂²	semidirect
24. #22548748	C₂²	semidirect
25. #22548747	C₂²	semidirect
26. #22548744	C₂²	semidirect
27. #22548743	C₂²	semidirect
28. #22548742	C₂²	semidirect
29. #22548739	C₂²	semidirect
30. #22548738	C₂²	semidirect
31. #22548737	C₂²	semidirect
32. #22548736	C₂²	semidirect
33. #22548735	C₂²	semidirect
34. #22548735	C₂²	semidirect
35. #22548735	C₂²	semidirect
36. #22548735	C₂²	semidirect
37. #22548734	C₂²	semidirect
38. C₂×#16860800	C₂²	semidirect
39. Q₁₆×D₂₅₁	C₂²	semidirect
40. C₂×#16860798	C₂²	semidirect
41. C₂×#16860797	C₂²	semidirect
42. SD₁₆×D₂₅₁	C₂²	semidirect
43. C₂×#16860795	C₂²	semidirect
44. D₈×D₂₅₁	C₂²	semidirect
45. #22548723	C₂²	semidirect
46. #22548723	C₂²	semidirect
47. C₂×#16860793	C₂²	semidirect
48. C₂²×C₂₅₁⋊C₈	C₂²	semidirect
49. C₂×C₈×D₂₅₁	C₂²	semidirect
50. C₂×#41×C₂₅₁	C₂²	semidirect
51. #137×C₂₅₁	C₂²	semidirect
52. AGL(1,ℤ/8)×C₂₅₁	C₂²	semidirect
53. #135×C₂₅₁	C₂²	semidirect
54. C₂×M₁₆×C₂₅₁	C₂²	semidirect
187. C₂₅₁	#3584	semidirect
196. #575	D₂₅₁	semidirect
212. C₂×#41	C₂×D₂₅₁	semidirect
216. #137	C₂×D₂₅₁	semidirect
220. AGL(1,ℤ/8)	C₂×D₂₅₁	semidirect
229. #135	C₂×D₂₅₁	semidirect
240. C₂×M₁₆	C₂×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
#30632503	2
#30632497	2
#30632496	2
#30632491	2
#30632487	2
#30632484	2
C₂×#22548735	2
#135×D₂₅₁	2
C₂×#22548723	2
#575×C₂₅₁	2
#3584	251