Subgroups — #14723255

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077727	C₂	1	2	yes	maximal, complemented
2	SD₁₆⋊(C₁₁⋊C₈)	C₂	1	4	yes	maximal, complemented
3	Q₁₆×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
4	D₈×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×#10622096	C₂	1	1	yes	maximal, characteristic, complemented
6	#13067003	C₂	1	2	yes	maximal, complemented
7	#13066899	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
10	C₄×C₁₁×#41	C₂²	1	2	yes	—
11	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
12	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×SD₁₆	C₄	1	2	yes	—
14	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
16	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
17	C₁₁×#427	C₄	1	1	yes	characteristic
18	C₁₁×#416	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	Q₈×C₁₁⋊C₈	C₂²	1	4	yes	—
21	D₄×C₁₁⋊C₈	—	2	4	no	—
22	D₄×C₁₁⋊C₈	C₂²	1	4	yes	—
23	#10622538	—	2	2	no	—
24	#10622538	C₂²	1	1	yes	characteristic
25	#10622538	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
27	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
28	Q₈⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
29	D₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
30	#10622096	C₂²	1	2	yes	—
31	#10622096	C₂²	1	2	yes	—
32	#10622093	C₂²	1	2	yes	—
33	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
35	C₁₁×#135	C₈	1	8	yes	complemented
36	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
38	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
42	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₄×D₄×C₁₁	—	2	2	no	—
44	C₄×D₄×C₁₁	—	2	2	no	—
45	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₁₁	C₂³	1	2	yes	—
47	C₁₁×#117	—	2	2	no	—
48	C₁₁×#117	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₁	—	2	2	no	—
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₁₁⋊C₈	—	2	2	no	—
52	C₂²×C₁₁⋊C₈	—	2	4	no	—
53	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
54	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#106	C₂×C₄	1	2	yes	—
56	C₁₁×#103	C₂×C₄	1	2	yes	—
57	C₁₁×#103	C₂×C₄	1	2	yes	—
58	C₁₁×#102	C₂×C₄	1	2	yes	—
59	C₁₁×#102	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
66	C₂²⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
67	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
68	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
70	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
71	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
72	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
73	C₄×C₁₁⋊C₈	—	2	4	no	—
74	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
75	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
76	#17857	—	11	1	no	maximal, Sylow
77	C₁₁×#41	—	2	4	no	—
78	C₁₁×#41	C₂×C₈	1	8	yes	complemented
79	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂×D₄×C₁₁	—	2	2	no	—
81	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
88	C₁₁×Q₁₆	C₂×C₈	1	4	yes	complemented
89	C₁₁×SD₁₆	C₂×C₈	1	8	yes	complemented
90	C₁₁×D₈	C₂×C₈	1	4	yes	complemented
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	complemented
93	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₁₁×C₄⋊C₄	—	2	2	no	—
98	C₁₁×C₄⋊C₄	—	2	2	no	—
99	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
100	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
101	C₁₁×C₂²⋊C₄	—	2	2	no	—
102	C₁₁×C₂²⋊C₄	—	2	2	no	—
103	C₁₁×C₂²⋊C₄	—	2	2	no	—
104	C₄²×C₁₁	—	2	2	no	—
105	C₄²×C₁₁	—	2	2	no	—
106	C₄²×C₁₁	—	2	2	no	—
107	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₁	#41	1	1	yes	characteristic
110	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
111	C₂×C₁₁⋊C₈	—	2	4	no	—
112	C₂×C₁₁⋊C₈	—	2	2	no	—
113	C₂×C₁₁⋊C₈	—	8	2	no	—
114	C₂×C₁₁⋊C₈	—	8	4	no	—
115	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
116	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
117	#2988	—	11	2	no	—
118	C₄×#135	D₁₁	1	1	yes	characteristic
119	SD₁₆⋊C₈	—	11	4	no	—
120	C₈×Q₁₆	—	11	2	no	—
121	C₈×D₈	—	11	2	no	—
122	C₂×#335	—	11	1	no	—
123	#1477	—	11	2	no	—
124	#1450	—	11	1	no	—
125	C₂³×C₁₁	—	2	2	no	—
126	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
127	Q₈×C₁₁	—	2	2	no	—
128	Q₈×C₁₁	C₂²×C₈	1	4	yes	—
129	D₄×C₁₁	—	2	8	no	—
130	D₄×C₁₁	—	2	2	no	—
131	D₄×C₁₁	C₂²×C₈	1	4	yes	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	1	no	—
134	C₂×C₄×C₁₁	—	2	1	no	—
135	C₂×C₄×C₁₁	—	2	8	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	4	1	no	—
139	C₂×C₄×C₁₁	—	4	2	no	—
140	C₂×C₄×C₁₁	—	4	2	no	—
141	C₂×C₄×C₁₁	—	8	2	no	—
142	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
146	C₂×C₄×C₁₁	#131	1	2	yes	—
147	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
150	C₈×C₁₁	—	2	1	no	—
151	C₈×C₁₁	—	2	1	no	—
152	C₈×C₁₁	C₂²×C₈	1	2	yes	—
153	C₈×C₁₁	C₂²×C₈	1	2	yes	—
154	C₁₁⋊C₈	—	2	2	no	—
155	C₁₁⋊C₈	—	2	2	no	—
156	C₁₁⋊C₈	—	4	2	no	—
157	C₁₁⋊C₈	—	4	4	no	—
158	C₂×#135	Dic₁₁	1	1	yes	characteristic
159	C₄×#41	C₂×D₁₁	1	2	yes	—
160	C₈×Q₈	—	11	4	no	—
161	C₄×Q₁₆	Dic₁₁	1	1	yes	characteristic
162	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
163	C₄×SD₁₆	Dic₁₁	1	2	yes	—
164	C₄×SD₁₆	C₂×D₁₁	1	2	yes	—
165	C₄×D₈	Dic₁₁	1	1	yes	characteristic
166	C₄×D₈	C₂×D₁₁	1	1	yes	characteristic
167	C₈×D₄	—	11	4	no	—
168	C₈×D₄	—	22	4	no	—
169	#431	—	11	1	no	—
170	#431	—	11	1	no	—
171	#431	—	22	2	no	—
172	#427	Dic₁₁	1	1	yes	characteristic
173	C₂×C₄⋊C₈	—	11	2	no	—
174	C₂×C₄⋊C₈	—	22	2	no	—
175	#416	Dic₁₁	1	2	yes	—
176	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
177	#335	—	11	2	no	—
178	#335	—	11	2	no	—
179	Q₈⋊C₈	—	11	4	no	—
180	D₄⋊C₈	—	11	4	no	—
181	#322	—	11	2	no	—
182	C₈²	—	11	2	no	—
183	C₂²×C₁₁	—	2	1	no	—
184	C₂²×C₁₁	—	2	1	no	—
185	C₂²×C₁₁	—	2	4	no	—
186	C₂²×C₁₁	—	4	2	no	—
187	C₂²×C₁₁	—	4	2	no	—
188	C₂²×C₁₁	C₈×D₄	1	2	yes	—
189	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₁₁	—	2	4	no	—
191	C₄×C₁₁	—	2	1	no	—
192	C₄×C₁₁	—	2	1	no	—
193	C₄×C₁₁	—	2	1	no	—
194	C₄×C₁₁	—	4	2	no	—
195	C₄×C₁₁	—	4	2	no	—
196	C₄×C₁₁	C₈×D₄	1	2	yes	—
197	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
198	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
199	C₄×C₁₁	#576	1	1	yes	characteristic
200	C₄×C₁₁	#578	1	1	yes	characteristic
201	C₂×#41	C₂×Dic₁₁	1	2	yes	—
202	#135	C₁₁⋊C₈	1	8	yes	complemented
203	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic
204	C₂×SD₁₆	C₂×Dic₁₁	1	2	yes	—
205	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic
206	C₂²×C₈	—	22	4	no	—
207	C₂²×C₈	—	22	2	no	—
208	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
209	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
210	C₄×Q₈	C₂×Dic₁₁	1	2	yes	—
211	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
212	C₄×D₄	—	2	2	no	—
213	C₄×D₄	—	2	2	no	—
214	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
215	C₄×D₄	C₂²×D₁₁	1	2	yes	—
216	#117	—	2	2	no	—
217	#117	C₂×Dic₁₁	1	2	yes	—
218	C₂×C₄²	—	2	2	no	—
219	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
220	#107	C₂×Dic₁₁	1	1	yes	characteristic
221	#107	C₂×Dic₁₁	1	1	yes	characteristic
222	#106	C₂×Dic₁₁	1	2	yes	—
223	C₄⋊C₈	—	11	1	no	—
224	C₄⋊C₈	—	11	1	no	—
225	C₄⋊C₈	—	11	4	no	—
226	C₄⋊C₈	—	22	4	no	—
227	C₄⋊C₈	—	22	2	no	—
228	C₄⋊C₈	—	22	1	no	—
229	#103	C₂×Dic₁₁	1	2	yes	—
230	#103	C₂×Dic₁₁	1	2	yes	—
231	#102	C₂×Dic₁₁	1	2	yes	—
232	#102	C₂×Dic₁₁	1	2	yes	—
233	C₂²⋊C₈	—	11	2	no	—
234	C₂²⋊C₈	—	22	4	no	—
235	C₂²⋊C₈	—	22	1	no	—
236	C₄×C₈	—	11	2	no	—
237	C₄×C₈	—	11	2	no	—
238	C₄×C₈	—	22	4	no	—
239	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
240	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
241	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
242	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
243	C₂×C₁₁	—	2	2	no	—
244	C₂×C₁₁	—	4	4	no	—
245	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
246	C₂×C₁₁	#2951	1	1	yes	characteristic
247	C₂×C₁₁	#2957	1	1	yes	characteristic
248	#41	—	2	4	no	—
249	#41	C₂×C₁₁⋊C₈	1	8	yes	complemented
250	C₂×Q₈	C₂²×Dic₁₁	1	2	yes	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	C₂²×Dic₁₁	1	2	yes	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
257	C₂²×C₄	#4341	1	1	yes	characteristic
258	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
259	Q₁₆	C₂×C₁₁⋊C₈	1	4	yes	complemented
260	SD₁₆	C₂×C₁₁⋊C₈	1	8	yes	complemented
261	D₈	C₂×C₁₁⋊C₈	1	4	yes	complemented
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	11	2	no	—
264	C₂×C₈	—	11	2	no	—
265	C₂×C₈	—	22	4	no	—
266	C₂×C₈	—	22	2	no	—
267	C₂×C₈	—	88	4	no	—
268	C₂×C₈	—	88	2	no	—
269	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	complemented
270	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
271	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
272	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
273	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
277	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	D₄×D₁₁	1	1	yes	characteristic
285	C₄²	#4341	1	1	yes	characteristic
286	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
287	C₄²	C₂³×D₁₁	1	1	yes	characteristic
288	C₁₁	#17857	1	1	yes	characteristic, complemented, Sylow
289	C₂³	—	2	2	no	—
290	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
291	Q₈	—	2	2	no	—
292	Q₈	C₂²×C₁₁⋊C₈	1	4	yes	—
293	D₄	—	2	8	no	—
294	D₄	—	2	2	no	—
295	D₄	C₂²×C₁₁⋊C₈	1	4	yes	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	8	2	no	—
306	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
307	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
308	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
309	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
310	C₂×C₄	#67001	1	2	yes	—
311	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
312	C₂×C₄	C₂×#4341	1	1	yes	characteristic
313	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
314	C₈	—	2	1	no	—
315	C₈	—	2	1	no	—
316	C₈	—	22	2	no	—
317	C₈	—	22	2	no	—
318	C₈	—	44	2	no	—
319	C₈	—	44	4	no	—
320	C₈	C₂²×C₁₁⋊C₈	1	2	yes	—
321	C₈	C₂²×C₁₁⋊C₈	1	2	yes	—
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
328	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
329	C₄	—	2	1	no	—
330	C₄	—	2	1	no	—
331	C₄	—	2	4	no	—
332	C₄	—	2	1	no	—
333	C₄	—	4	2	no	—
334	C₄	—	4	2	no	—
335	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
336	C₄	#10623300	1	1	yes	characteristic
337	C₄	#10623302	1	1	yes	characteristic
338	C₄	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
339	C₄	C₂×#67001	1	1	yes	characteristic
340	C₂	—	2	2	no	—
341	C₂	—	4	4	no	—
342	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic
343	C₂	#13077492	1	1	yes	characteristic
344	C₂	#13077533	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₄×C₁₁×#135	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₄×#135	D₁₁
hypocenter	C₁₁	#17857
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13077727	C₂	semidirect
2. SD₁₆⋊(C₁₁⋊C₈)	C₂	semidirect
3. Q₁₆×C₁₁⋊C₈	C₂	semidirect
4. D₈×C₁₁⋊C₈	C₂	semidirect
5. C₂×#10622096	C₂	semidirect
6. #13067003	C₂	semidirect
7. #13066899	C₂	semidirect
35. C₁₁×#135	C₈	semidirect
78. C₁₁×#41	C₂×C₈	semidirect
88. C₁₁×Q₁₆	C₂×C₈	semidirect
89. C₁₁×SD₁₆	C₂×C₈	semidirect
90. C₁₁×D₈	C₂×C₈	semidirect
92. C₂×C₈×C₁₁	C₂×C₈	semidirect
202. #135	C₁₁⋊C₈	semidirect
249. #41	C₂×C₁₁⋊C₈	semidirect
259. Q₁₆	C₂×C₁₁⋊C₈	semidirect
260. SD₁₆	C₂×C₁₁⋊C₈	semidirect
261. D₈	C₂×C₁₁⋊C₈	semidirect
269. C₂×C₈	C₂×C₁₁⋊C₈	semidirect
288. C₁₁	#17857	semidirect

Maximal subgroups

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

subgroup	index
#13077727	2
SD₁₆⋊(C₁₁⋊C₈)	2
Q₁₆×C₁₁⋊C₈	2
D₈×C₁₁⋊C₈	2
C₂×#10622096	2
#13067003	2
#13066899	2
C₄×C₁₁×#135	2
#17857	11