Subgroups — #14719511

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077583	C₂	1	1	yes	maximal, characteristic
2	#13077583	C₂	1	1	yes	maximal, characteristic
3	#13066919	C₂	1	2	yes	maximal, complemented
4	#13066913	C₂	1	2	yes	maximal, complemented
5	#13066908	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066905	C₂	1	2	yes	maximal, complemented
7	C₈×#4318	C₂	1	2	yes	maximal, complemented
8	M₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	M₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10622092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#131	C₄	1	2	yes	—
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₁₁×#405	C₄	1	4	yes	—
15	C₁₁×#405	C₄	1	2	yes	—
16	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
20	#10622637	C₄	1	2	yes	—
21	#10622637	C₄	1	2	yes	—
22	#10622625	C₄	1	2	yes	—
23	#10622625	C₄	1	2	yes	—
24	#10622624	C₄	1	4	yes	—
25	#10622624	C₄	1	4	yes	—
26	#10622538	C₂²	1	1	yes	characteristic
27	#10622538	C₂²	1	1	yes	characteristic
28	#10622538	C₂²	1	2	yes	—
29	#10622538	C₂²	1	2	yes	—
30	C₄×#4318	C₂²	1	2	yes	—
31	C₄×#4318	C₂²	1	2	yes	—
32	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
34	#10622093	C₂²	1	2	yes	—
35	#10622093	C₂²	1	2	yes	—
36	#10622092	C₂²	1	1	yes	characteristic
37	#10622092	C₂²	1	1	yes	characteristic
38	#10622092	C₂²	1	1	yes	characteristic
39	#10622092	C₂²	1	1	yes	characteristic
40	#10622092	C₂²	1	2	yes	—
41	#10622092	C₂²	1	2	yes	—
42	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
43	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
44	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
45	C₁₁×#131	—	2	8	no	—
46	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
47	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
50	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₁₁×#117	C₂×C₄	1	2	yes	—
57	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
60	C₂×#4318	C₂×C₄	1	4	yes	—
61	C₂×#4318	C₂×C₄	1	4	yes	—
62	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
63	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
64	C₁₁×#97	C₂×C₄	1	4	yes	—
65	C₁₁×#97	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
68	C₄×C₈×C₁₁	C₂³	1	2	yes	—
69	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
74	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
75	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
76	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
77	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
78	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
79	#66867	C₂×C₄	1	4	yes	—
80	#66867	C₂×C₄	1	4	yes	—
81	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
82	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
83	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
86	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
87	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
88	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
89	#17337	—	11	1	no	maximal, Sylow
90	C₁₁×#41	—	2	4	no	—
91	C₂×Q₈×C₁₁	C₄²	1	1	yes	characteristic
92	C₂×D₄×C₁₁	C₄²	1	2	yes	—
93	C₂×D₄×C₁₁	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₁₁×M₁₆	—	2	8	no	—
101	C₁₁×M₁₆	M₁₆	1	8	yes	complemented
102	C₂×C₈×C₁₁	—	2	8	no	—
103	C₂×C₈×C₁₁	—	2	4	no	—
104	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
107	C₁₁×C₄⋊C₄	C₄²	1	2	yes	—
108	C₁₁×C₄⋊C₄	C₄²	1	2	yes	—
109	C₁₁×C₄⋊C₄	C₄²	1	1	yes	characteristic
110	C₁₁×C₄⋊C₄	C₄²	1	1	yes	characteristic
111	C₁₁×C₂²⋊C₄	C₄²	1	2	yes	—
112	C₁₁×C₂²⋊C₄	C₄²	1	2	yes	—
113	C₁₁×C₂²⋊C₄	C₄²	1	2	yes	—
114	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
117	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
118	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
121	#4318	—	2	8	no	—
122	#4318	—	4	4	no	—
123	C₂×C₁₁⋊C₈	—	2	4	no	—
124	C₂×C₁₁⋊C₈	—	4	2	no	—
125	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
128	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
129	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
130	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
131	#2965	—	11	1	no	—
132	#2965	—	11	1	no	—
133	C₄×#131	D₁₁	1	1	yes	characteristic
134	#1455	—	11	2	no	—
135	#1453	—	11	2	no	—
136	#1452	—	11	1	no	—
137	#1451	—	11	2	no	—
138	C₈×M₁₆	—	11	1	no	—
139	C₈×M₁₆	—	11	1	no	—
140	C₈×M₁₆	—	11	2	no	—
141	C₂×#322	—	11	1	no	—
142	C₂³×C₁₁	C₂×C₄²	1	2	yes	—
143	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
144	Q₈×C₁₁	—	2	2	no	—
145	D₄×C₁₁	—	2	4	no	—
146	D₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	4	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	4	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	4	no	—
152	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
159	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
162	C₈×C₁₁	—	2	2	no	—
163	C₈×C₁₁	—	2	2	no	—
164	C₈×C₁₁	C₂×M₁₆	1	8	yes	—
165	C₁₁⋊C₈	—	2	2	no	—
166	C₁₁⋊C₈	—	2	4	no	—
167	C₁₁⋊C₈	—	2	2	no	—
168	C₁₁⋊C₈	—	2	2	no	—
169	C₁₁⋊C₈	—	2	4	no	—
170	C₁₁⋊C₈	#131	1	4	yes	complemented
171	C₂×#131	Dic₁₁	1	2	yes	—
172	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
173	#446	—	11	2	no	—
174	#446	—	11	2	no	—
175	#436	—	11	2	no	—
176	#436	—	11	2	no	—
177	#435	—	11	4	no	—
178	#435	—	11	4	no	—
179	#431	—	11	1	no	—
180	#431	—	11	1	no	—
181	#431	—	11	2	no	—
182	#431	—	11	2	no	—
183	#405	Dic₁₁	1	4	yes	—
184	#405	Dic₁₁	1	2	yes	—
185	C₄×M₁₆	—	11	2	no	—
186	C₄×M₁₆	—	11	2	no	—
187	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
188	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
189	C₂×C₄×C₈	—	11	1	no	—
190	C₂×C₄×C₈	—	11	1	no	—
191	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
193	#322	—	11	1	no	—
194	#322	—	11	1	no	—
195	#322	—	11	1	no	—
196	#322	—	11	1	no	—
197	#322	—	11	2	no	—
198	#322	—	11	2	no	—
199	#322	—	11	2	no	—
200	#322	—	11	2	no	—
201	C₈²	—	11	2	no	—
202	C₈²	—	11	2	no	—
203	C₂²×C₁₁	—	2	1	no	—
204	C₂²×C₁₁	—	2	1	no	—
205	C₂²×C₁₁	—	2	2	no	—
206	C₂²×C₁₁	—	2	2	no	—
207	C₂²×C₁₁	—	2	2	no	—
208	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
209	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
210	C₄×C₁₁	—	2	2	no	—
211	C₄×C₁₁	—	2	1	no	—
212	C₄×C₁₁	—	2	2	no	—
213	C₄×C₁₁	—	2	1	no	—
214	C₄×C₁₁	—	2	2	no	—
215	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
216	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
217	C₄×C₁₁	C₂×#131	1	2	yes	—
218	C₄×C₁₁	#568	1	2	yes	—
219	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
220	#131	—	2	8	no	—
221	C₂×M₁₆	—	11	4	no	—
222	C₂×M₁₆	—	11	4	no	—
223	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
224	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
225	C₂²×C₈	—	11	2	no	—
226	C₂²×C₈	—	11	2	no	—
227	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
228	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
229	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
230	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
231	C₄×D₄	C₄×D₁₁	1	2	yes	—
232	C₄×D₄	C₄×D₁₁	1	2	yes	—
233	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
234	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
235	#117	C₂×Dic₁₁	1	2	yes	—
236	#117	C₂×Dic₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
238	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
239	C₄⋊C₈	—	11	4	no	—
240	C₄⋊C₈	—	11	4	no	—
241	C₄⋊C₈	—	11	2	no	—
242	C₄⋊C₈	—	11	2	no	—
243	C₂²⋊C₈	—	11	2	no	—
244	C₂²⋊C₈	—	11	2	no	—
245	C₂²⋊C₈	—	11	4	no	—
246	C₂²⋊C₈	—	11	4	no	—
247	#97	—	11	4	no	—
248	#97	—	11	4	no	—
249	#97	C₂×Dic₁₁	1	4	yes	—
250	#97	C₂×Dic₁₁	1	2	yes	—
251	C₄×C₈	—	11	2	no	—
252	C₄×C₈	—	11	2	no	—
253	C₄×C₈	—	11	1	no	—
254	C₄×C₈	—	11	1	no	—
255	C₄×C₈	—	11	2	no	—
256	C₄×C₈	—	11	2	no	—
257	C₄×C₈	—	11	1	no	—
258	C₄×C₈	—	11	1	no	—
259	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
260	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
261	C₄×C₈	C₂²×D₁₁	1	2	yes	—
262	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
263	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
264	C₂×C₁₁	—	2	2	no	—
265	C₂×C₁₁	—	4	2	no	—
266	C₂×C₁₁	C₂×C₄×M₁₆	1	1	yes	characteristic
267	C₂×C₁₁	C₄×#131	1	1	yes	characteristic
268	C₂×C₁₁	#2875	1	1	yes	characteristic
269	#41	—	2	4	no	—
270	C₂×Q₈	C₄×Dic₁₁	1	1	yes	characteristic
271	C₂×D₄	C₄×Dic₁₁	1	2	yes	—
272	C₂×D₄	C₄×Dic₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
276	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
277	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
278	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
279	M₁₆	—	2	8	no	—
280	M₁₆	—	22	8	no	—
281	M₁₆	—	44	4	no	—
282	M₁₆	#4318	1	8	yes	complemented
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	11	2	no	—
286	C₂×C₈	—	11	2	no	—
287	C₂×C₈	—	11	2	no	—
288	C₂×C₈	—	11	2	no	—
289	C₂×C₈	—	11	4	no	—
290	C₂×C₈	—	11	4	no	—
291	C₂×C₈	—	22	4	no	—
292	C₂×C₈	—	44	2	no	—
293	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
294	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
295	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
296	C₄⋊C₄	C₄×Dic₁₁	1	2	yes	—
297	C₄⋊C₄	C₄×Dic₁₁	1	2	yes	—
298	C₄⋊C₄	C₄×Dic₁₁	1	1	yes	characteristic
299	C₄⋊C₄	C₄×Dic₁₁	1	1	yes	characteristic
300	C₂²⋊C₄	C₄×Dic₁₁	1	2	yes	—
301	C₂²⋊C₄	C₄×Dic₁₁	1	2	yes	—
302	C₂²⋊C₄	C₄×Dic₁₁	1	2	yes	—
303	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
304	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
305	C₄²	C₂×C₄×D₁₁	1	2	yes	—
306	C₄²	C₂×C₄×D₁₁	1	2	yes	—
307	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
308	C₄²	C₂²×Dic₁₁	1	2	yes	—
309	C₄²	C₂³×D₁₁	1	1	yes	characteristic
310	C₁₁	#17337	1	1	yes	characteristic, complemented, Sylow
311	C₂³	C₂×C₄×Dic₁₁	1	2	yes	—
312	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
313	Q₈	—	2	2	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	C₂×#4318	1	4	yes	—
322	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
323	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
324	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
325	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
327	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
330	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
331	C₈	—	2	2	no	—
332	C₈	—	2	2	no	—
333	C₈	—	11	4	no	—
334	C₈	—	22	2	no	—
335	C₈	—	22	4	no	—
336	C₈	—	22	2	no	—
337	C₈	—	22	2	no	—
338	C₈	—	22	4	no	—
339	C₈	C₂×#4318	1	8	yes	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	C₄×#4318	1	2	yes	—
346	C₂²	C₂²×C₄×Dic₁₁	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	2	no	—
352	C₄	C₄×#4318	1	2	yes	—
353	C₄	D₁₁×#131	1	2	yes	—
354	C₄	#10623281	1	2	yes	—
355	C₄	C₂²×#4318	1	2	yes	—
356	C₂	—	2	2	no	—
357	C₂	—	4	2	no	—
358	C₂	C₂×C₄×#4318	1	1	yes	characteristic
359	C₂	#131×Dic₁₁	1	1	yes	characteristic
360	C₂	#13077042	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₄×C₁₁×#131	C₂
prime radical	C₂×C₁₁×#41	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₄×#131	D₁₁
hypocenter	C₁₁	#17337
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
3. #13066919	C₂	semidirect
4. #13066913	C₂	semidirect
5. #13066908	C₂	semidirect
6. #13066905	C₂	semidirect
7. C₈×#4318	C₂	semidirect
8. M₁₆×C₁₁⋊C₈	C₂	semidirect
9. M₁₆×C₁₁⋊C₈	C₂	semidirect
10. C₂×#10622092	C₂	semidirect
101. C₁₁×M₁₆	M₁₆	semidirect
170. C₁₁⋊C₈	#131	semidirect
282. M₁₆	#4318	semidirect
310. C₁₁	#17337	semidirect

Maximal subgroups

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

subgroup	index
#13077583	2
#13066919	2
#13066913	2
#13066908	2
#13066905	2
C₈×#4318	2
M₁₆×C₁₁⋊C₈	2
C₂×#10622092	2
C₄×C₁₁×#131	2
#17337	11