Subgroups — #72254622

Order 3520.

524 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#4339⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#67004⋊C₅	C₂	1	2	yes	maximal, complemented
4	#67003⋊C₅	C₂	1	4	yes	maximal, complemented
5	#67002⋊C₅	C₂	1	2	yes	maximal, complemented
6	#66995⋊C₅	C₂	1	2	yes	maximal, complemented
7	#66985⋊C₅	C₂	1	2	yes	maximal, complemented
8	C₂×#4318⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
9	#41×C₁₁⋊C₅	—	2	1	no	—
10	#41×C₁₁⋊C₅	—	2	1	no	—
11	#41×C₁₁⋊C₅	C₂²	1	2	yes	—
12	#41×C₁₁⋊C₅	C₂²	1	2	yes	complemented
13	C₂×Q₈×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₄×C₁₁⋊C₅	—	2	1	no	—
15	C₂×D₄×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄×C₁₁⋊C₅	—	2	1	no	—
17	C₂²×C₄×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊AGL(1,𝔽₁₁)	—	2	1	no	—
19	#4339⋊C₅	—	2	1	no	—
20	#4339⋊C₅	—	2	1	no	—
21	#4339⋊C₅	C₂²	1	2	yes	—
22	#4339⋊C₅	C₂²	1	2	yes	complemented
23	C₂×C₄⋊AGL(1,𝔽₁₁)	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×AGL(1,𝔽₁₁)	—	2	1	no	—
25	C₂×(C₁₁⋊C₅)⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	#4326⋊C₅	C₂²	1	4	yes	complemented
27	#4325⋊C₅	C₂²	1	4	yes	complemented
28	#4324⋊C₅	C₂²	1	4	yes	complemented
29	#4323⋊C₅	C₂²	1	4	yes	complemented
30	#4318⋊C₅	C₂²	1	2	yes	complemented
31	#4318⋊C₅	C₂²	1	2	yes	complemented
32	C₂×(C₁₁⋊C₅)⋊C₈	C₂²	1	2	yes	complemented
33	#10623353	C₅	1	1	yes	maximal, characteristic, complemented, Hall
34	C₂³×C₁₁⋊C₅	—	2	1	no	—
35	C₂³×C₁₁⋊C₅	D₄	1	1	yes	characteristic
36	C₂²×AGL(1,𝔽₁₁)	—	2	1	no	—
37	Q₈×C₁₁⋊C₅	—	2	1	no	—
38	Q₈×C₁₁⋊C₅	C₂³	1	2	yes	—
39	D₄×C₁₁⋊C₅	—	2	2	no	—
40	D₄×C₁₁⋊C₅	—	2	2	no	—
41	D₄×C₁₁⋊C₅	—	2	1	no	—
42	D₄×C₁₁⋊C₅	C₂³	1	2	yes	—
43	C₂×C₄×C₁₁⋊C₅	—	2	1	no	—
44	C₂×C₄×C₁₁⋊C₅	—	2	2	no	—
45	C₂×C₄×C₁₁⋊C₅	—	2	2	no	—
46	C₂×C₄×C₁₁⋊C₅	D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₁⋊C₅	D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₁⋊C₅	D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
50	C₂×C₄×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
51	C₂×C₄×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
52	C₂²⋊AGL(1,𝔽₁₁)	—	2	2	no	—
53	C₂²⋊AGL(1,𝔽₁₁)	—	2	2	no	—
54	C₂×Dic₁₁⋊C₅	—	2	1	no	—
55	C₄⋊AGL(1,𝔽₁₁)	—	2	1	no	—
56	C₄⋊AGL(1,𝔽₁₁)	C₂³	1	2	yes	—
57	C₄×AGL(1,𝔽₁₁)	—	2	2	no	—
58	C₄×AGL(1,𝔽₁₁)	—	2	2	no	—
59	(C₁₁⋊C₅)⋊Q₈	—	2	1	no	—
60	(C₁₁⋊C₅)⋊Q₈	C₂³	1	2	yes	—
61	(C₁₁⋊C₅)⋊C₈	C₂³	1	4	yes	—
62	C₂×C₁₁×#41	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#4339	C₂×C₅	1	1	yes	characteristic, complemented
64	#67004	C₂×C₅	1	2	yes	complemented
65	#67003	C₂×C₅	1	4	yes	complemented
66	#67002	C₂×C₅	1	2	yes	complemented
67	#66995	C₂×C₅	1	2	yes	complemented
68	#66985	C₂×C₅	1	2	yes	complemented
69	C₂×#4318	C₂×C₅	1	1	yes	characteristic, complemented
70	C₅×#575	—	11	1	no	maximal, Hall
71	C₂²×C₁₁⋊C₅	—	2	2	no	—
72	C₂²×C₁₁⋊C₅	—	4	1	no	—
73	C₂²×C₁₁⋊C₅	—	4	2	no	—
74	C₂²×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
77	C₂×AGL(1,𝔽₁₁)	—	2	2	no	—
78	C₂×AGL(1,𝔽₁₁)	—	4	2	no	—
79	C₄×C₁₁⋊C₅	—	2	2	no	—
80	C₄×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
81	C₄×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
82	C₄×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
83	C₄×C₁₁⋊C₅	C₂⁴	1	1	yes	characteristic
84	Dic₁₁⋊C₅	—	2	2	no	—
85	C₁₁×#41	—	2	1	no	—
86	C₁₁×#41	—	2	1	no	—
87	C₁₁×#41	C₂²×C₅	1	2	yes	—
88	C₁₁×#41	C₂²×C₅	1	2	yes	complemented
89	C₂×Q₈×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
90	C₂×D₄×C₁₁	—	2	1	no	—
91	C₂×D₄×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
92	C₂²×C₄×C₁₁	—	2	1	no	—
93	C₂²×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₂²⋊D₁₁	—	2	1	no	—
95	#4339	—	2	1	no	—
96	#4339	—	2	1	no	—
97	#4339	C₂²×C₅	1	2	yes	—
98	#4339	C₂²×C₅	1	2	yes	complemented
99	C₂×D₄₄	C₂²×C₅	1	1	yes	characteristic, complemented
100	C₂×C₄×D₁₁	—	2	1	no	—
101	C₂×Dic₂₂	C₂²×C₅	1	1	yes	characteristic, complemented
102	#4326	C₂²×C₅	1	4	yes	complemented
103	#4325	C₂²×C₅	1	4	yes	complemented
104	#4324	C₂²×C₅	1	4	yes	complemented
105	#4323	C₂²×C₅	1	4	yes	complemented
106	#4318	C₂²×C₅	1	2	yes	complemented
107	#4318	C₂²×C₅	1	2	yes	complemented
108	C₂×C₁₁⋊C₈	C₂²×C₅	1	2	yes	complemented
109	C₂×C₅×#41	—	11	1	no	—
110	C₂×C₅×#41	—	22	1	no	—
111	C₅×#137	—	11	2	no	—
112	C₅×#137	—	11	2	no	—
113	C₅×AGL(1,ℤ/8)	—	11	2	no	—
114	C₅×AGL(1,ℤ/8)	—	11	2	no	—
115	C₅×#135	—	11	4	no	—
116	C₂×C₅×M₁₆	—	11	1	no	—
117	C₂×C₁₁⋊C₅	—	2	1	no	—
118	C₂×C₁₁⋊C₅	—	2	1	no	—
119	C₂×C₁₁⋊C₅	—	2	1	no	—
120	C₂×C₁₁⋊C₅	—	4	2	no	—
121	C₂×C₁₁⋊C₅	C₂²×D₄	1	1	yes	characteristic
122	AGL(1,𝔽₁₁)	—	4	2	no	—
123	C₂³×C₁₁	—	2	1	no	—
124	C₂³×C₁₁	C₅×D₄	1	1	yes	characteristic
125	C₂²×D₁₁	—	2	1	no	—
126	Q₈×C₁₁	—	2	1	no	—
127	Q₈×C₁₁	C₂³×C₅	1	2	yes	—
128	D₄×C₁₁	—	2	2	no	—
129	D₄×C₁₁	—	2	2	no	—
130	D₄×C₁₁	—	2	1	no	—
131	D₄×C₁₁	C₂³×C₅	1	2	yes	—
132	C₂×C₄×C₁₁	—	2	1	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	C₅×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₁	C₅×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₅×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
141	C₂²⋊D₁₁	—	2	2	no	—
142	C₂²⋊D₁₁	—	2	2	no	—
143	C₂×Dic₁₁	—	2	1	no	—
144	D₄₄	—	2	1	no	—
145	D₄₄	C₂³×C₅	1	2	yes	—
146	C₄×D₁₁	—	2	2	no	—
147	C₄×D₁₁	—	2	2	no	—
148	Dic₂₂	—	2	1	no	—
149	Dic₂₂	C₂³×C₅	1	2	yes	—
150	C₁₁⋊C₈	C₂³×C₅	1	4	yes	—
151	C₅×#41	—	11	2	no	—
152	C₅×#41	—	11	2	no	—
153	C₅×#41	—	22	1	no	—
154	C₅×#41	—	22	1	no	—
155	C₅×#41	—	22	1	no	—
156	C₅×#41	—	22	1	no	—
157	C₅×#41	—	22	2	no	—
158	C₅×#41	—	22	2	no	—
159	C₂×C₅×Q₈	—	11	1	no	—
160	C₂×C₅×Q₈	—	22	1	no	—
161	C₂×C₅×D₄	—	11	1	no	—
162	C₂×C₅×D₄	—	22	1	no	—
163	C₂×C₅×D₄	—	22	1	no	—
164	C₂×C₅×D₄	—	22	1	no	—
165	C₂²×C₄×C₅	—	22	1	no	—
166	C₂²×C₄×C₅	—	22	1	no	—
167	C₂²×C₄×C₅	—	22	1	no	—
168	C₅×Q₁₆	—	11	4	no	—
169	C₅×SD₁₆	—	11	4	no	—
170	C₅×SD₁₆	—	11	4	no	—
171	C₅×D₈	—	11	4	no	—
172	C₅×M₁₆	—	11	2	no	—
173	C₅×M₁₆	—	11	2	no	—
174	C₂×C₅×C₈	—	11	2	no	—
175	#575	—	11	1	no	Sylow
176	C₁₁⋊C₅	#575	1	1	yes	characteristic, complemented, Hall
177	C₂²×C₁₁	—	2	2	no	—
178	C₂²×C₁₁	—	4	1	no	—
179	C₂²×C₁₁	—	4	2	no	—
180	C₂²×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
181	C₂²×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
182	C₂²×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
183	C₂×D₁₁	—	2	2	no	—
184	C₂×D₁₁	—	4	2	no	—
185	C₄×C₁₁	—	2	2	no	—
186	C₄×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
187	C₄×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
188	C₄×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
189	C₄×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
190	Dic₁₁	—	2	2	no	—
191	C₂³×C₅	—	22	1	no	—
192	C₂³×C₅	—	22	1	no	—
193	C₂³×C₅	—	22	1	no	—
194	C₅×Q₈	—	11	2	no	—
195	C₅×Q₈	—	22	1	no	—
196	C₅×Q₈	—	22	1	no	—
197	C₅×Q₈	—	22	2	no	—
198	C₅×D₄	—	11	2	no	—
199	C₅×D₄	—	22	2	no	—
200	C₅×D₄	—	22	2	no	—
201	C₅×D₄	—	22	1	no	—
202	C₅×D₄	—	22	1	no	—
203	C₅×D₄	—	22	2	no	—
204	C₅×D₄	—	22	2	no	—
205	C₅×D₄	—	22	2	no	—
206	C₂×C₄×C₅	—	22	1	no	—
207	C₂×C₄×C₅	—	22	2	no	—
208	C₂×C₄×C₅	—	22	2	no	—
209	C₂×C₄×C₅	—	22	2	no	—
210	C₂×C₄×C₅	—	22	2	no	—
211	C₂×C₄×C₅	—	22	1	no	—
212	C₂×C₄×C₅	—	22	1	no	—
213	C₂×C₄×C₅	—	22	1	no	—
214	C₂×C₄×C₅	—	22	1	no	—
215	C₂×C₄×C₅	—	22	1	no	—
216	C₂×C₄×C₅	—	22	1	no	—
217	C₂×C₄×C₅	—	22	1	no	—
218	C₅×C₈	—	11	4	no	—
219	C₂×#41	—	11	1	no	—
220	C₂×#41	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
221	#137	—	11	2	no	—
222	#137	—	11	2	no	—
223	AGL(1,ℤ/8)	—	11	2	no	—
224	AGL(1,ℤ/8)	—	11	2	no	—
225	#135	—	11	4	no	—
226	C₂×M₁₆	—	11	1	no	—
227	C₂×C₁₁	—	2	1	no	—
228	C₂×C₁₁	—	2	1	no	—
229	C₂×C₁₁	—	2	1	no	—
230	C₂×C₁₁	—	4	2	no	—
231	C₂×C₁₁	C₂²×C₅×D₄	1	1	yes	characteristic
232	D₁₁	—	4	2	no	—
233	C₂²×C₅	—	22	2	no	—
234	C₂²×C₅	—	22	2	no	—
235	C₂²×C₅	—	22	1	no	—
236	C₂²×C₅	—	22	1	no	—
237	C₂²×C₅	—	22	1	no	—
238	C₂²×C₅	—	44	1	no	—
239	C₂²×C₅	—	44	2	no	—
240	C₂²×C₅	—	44	2	no	—
241	C₄×C₅	—	22	2	no	—
242	C₄×C₅	—	22	2	no	—
243	C₄×C₅	—	22	1	no	—
244	C₄×C₅	—	22	1	no	—
245	C₄×C₅	—	22	1	no	—
246	C₄×C₅	—	22	1	no	—
247	#41	—	2	1	no	—
248	#41	—	2	1	no	—
249	#41	—	11	2	no	—
250	#41	—	11	2	no	—
251	#41	—	22	1	no	—
252	#41	—	22	1	no	—
253	#41	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
254	#41	C₂×AGL(1,𝔽₁₁)	1	2	yes	complemented
255	C₂×Q₈	—	11	1	no	—
256	C₂×Q₈	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	11	1	no	—
259	C₂×D₄	—	22	1	no	—
260	C₂×D₄	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	22	1	no	—
263	C₂²×C₄	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
264	Q₁₆	—	11	4	no	—
265	SD₁₆	—	11	4	no	—
266	SD₁₆	—	11	4	no	—
267	D₈	—	11	4	no	—
268	M₁₆	—	11	2	no	—
269	M₁₆	—	11	2	no	—
270	C₂×C₈	—	11	2	no	—
271	C₁₁	C₅×#575	1	1	yes	characteristic, complemented, Sylow
272	C₂×C₅	—	22	1	no	—
273	C₂×C₅	—	22	1	no	—
274	C₂×C₅	—	44	1	no	—
275	C₂×C₅	—	44	1	no	—
276	C₂×C₅	—	44	2	no	—
277	C₂×C₅	—	44	2	no	—
278	C₂³	—	2	1	no	—
279	C₂³	—	22	1	no	—
280	C₂³	C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
281	Q₈	—	2	1	no	—
282	Q₈	—	11	2	no	—
283	Q₈	—	22	1	no	—
284	Q₈	C₂²×AGL(1,𝔽₁₁)	1	2	yes	—
285	D₄	—	2	2	no	—
286	D₄	—	2	2	no	—
287	D₄	—	2	1	no	—
288	D₄	—	11	2	no	—
289	D₄	—	22	2	no	—
290	D₄	—	22	2	no	—
291	D₄	—	22	1	no	—
292	D₄	C₂²×AGL(1,𝔽₁₁)	1	2	yes	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	22	1	no	—
297	C₂×C₄	—	22	2	no	—
298	C₂×C₄	—	22	2	no	—
299	C₂×C₄	C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
300	C₂×C₄	C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
301	C₂×C₄	C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
302	C₂×C₄	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
303	C₂×C₄	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
304	C₂×C₄	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
305	C₈	—	11	4	no	—
306	C₅	—	22	1	no	Sylow
307	C₂²	—	2	2	no	—
308	C₂²	—	4	1	no	—
309	C₂²	—	4	2	no	—
310	C₂²	—	22	2	no	—
311	C₂²	—	44	2	no	—
312	C₂²	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
313	C₂²	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
314	C₂²	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
315	C₄	—	2	2	no	—
316	C₄	—	22	2	no	—
317	C₄	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
318	C₄	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
319	C₄	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
320	C₄	C₂³×AGL(1,𝔽₁₁)	1	1	yes	characteristic
321	C₂	—	2	1	no	—
322	C₂	—	2	1	no	—
323	C₂	—	2	1	no	—
324	C₂	—	4	2	no	—
325	C₂	—	44	2	no	—
326	C₂	C₂²×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊AGL(1,𝔽₁₁)
commutator, cosocle	C₄×C₁₁	C₂⁴×C₅
Frattini	C₄	C₂³×AGL(1,𝔽₁₁)
Fitting	C₂×C₁₁×#41	C₂×C₅
socle	C₂×C₁₁	C₂²×C₅×D₄
hypercenter	C₂×#41	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₅×#575
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×C₁₁⋊C₅	C₂	semidirect
2. C₂×#4339⋊C₅	C₂	semidirect
3. #67004⋊C₅	C₂	semidirect
4. #67003⋊C₅	C₂	semidirect
5. #67002⋊C₅	C₂	semidirect
6. #66995⋊C₅	C₂	semidirect
7. #66985⋊C₅	C₂	semidirect
8. C₂×#4318⋊C₅	C₂	semidirect
12. #41×C₁₁⋊C₅	C₂²	semidirect
13. C₂×Q₈×C₁₁⋊C₅	C₂²	semidirect
15. C₂×D₄×C₁₁⋊C₅	C₂²	semidirect
22. #4339⋊C₅	C₂²	semidirect
23. C₂×C₄⋊AGL(1,𝔽₁₁)	C₂²	semidirect
25. C₂×(C₁₁⋊C₅)⋊Q₈	C₂²	semidirect
26. #4326⋊C₅	C₂²	semidirect
27. #4325⋊C₅	C₂²	semidirect
28. #4324⋊C₅	C₂²	semidirect
29. #4323⋊C₅	C₂²	semidirect
30. #4318⋊C₅	C₂²	semidirect
31. #4318⋊C₅	C₂²	semidirect
32. C₂×(C₁₁⋊C₅)⋊C₈	C₂²	semidirect
33. #10623353	C₅	semidirect
62. C₂×C₁₁×#41	C₂×C₅	semidirect
63. C₂×#4339	C₂×C₅	semidirect
64. #67004	C₂×C₅	semidirect
65. #67003	C₂×C₅	semidirect
66. #67002	C₂×C₅	semidirect
67. #66995	C₂×C₅	semidirect
68. #66985	C₂×C₅	semidirect
69. C₂×#4318	C₂×C₅	semidirect
88. C₁₁×#41	C₂²×C₅	semidirect
89. C₂×Q₈×C₁₁	C₂²×C₅	semidirect
91. C₂×D₄×C₁₁	C₂²×C₅	semidirect
98. #4339	C₂²×C₅	semidirect
99. C₂×D₄₄	C₂²×C₅	semidirect
101. C₂×Dic₂₂	C₂²×C₅	semidirect
102. #4326	C₂²×C₅	semidirect
103. #4325	C₂²×C₅	semidirect
104. #4324	C₂²×C₅	semidirect
105. #4323	C₂²×C₅	semidirect
106. #4318	C₂²×C₅	semidirect
107. #4318	C₂²×C₅	semidirect
108. C₂×C₁₁⋊C₈	C₂²×C₅	semidirect
176. C₁₁⋊C₅	#575	semidirect
220. C₂×#41	AGL(1,𝔽₁₁)	semidirect
254. #41	C₂×AGL(1,𝔽₁₁)	semidirect
256. C₂×Q₈	C₂×AGL(1,𝔽₁₁)	semidirect
260. C₂×D₄	C₂×AGL(1,𝔽₁₁)	semidirect
271. C₁₁	C₅×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×C₁₁⋊C₅	2
C₂×#4339⋊C₅	2
#67004⋊C₅	2
#67003⋊C₅	2
#67002⋊C₅	2
#66995⋊C₅	2
#66985⋊C₅	2
C₂×#4318⋊C₅	2
#10623353	5
C₅×#575	11