Subgroups — #14906977

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622753	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#66876	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070448	C₂	1	2	yes	maximal, complemented
4	#13070442	C₂	1	2	yes	maximal, complemented
5	#13070442	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
7	#13070375	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070230	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070213	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2929	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#525	C₄	1	1	yes	characteristic
15	C₁₁×#435	C₄	1	2	yes	—
16	C₁₁×#435	C₄	1	2	yes	—
17	C₈×D₄×C₁₁	C₂²	1	2	yes	—
18	C₈×D₄×C₁₁	C₂²	1	2	yes	—
19	C₁₁×#424	C₄	1	1	yes	characteristic
20	C₁₁×#408	C₄	1	1	yes	characteristic
21	C₁₁×#407	C₄	1	1	yes	characteristic
22	C₁₁×#405	C₂²	1	1	yes	characteristic
23	#10622753	—	2	4	no	—
24	C₂×#66876	—	2	4	no	—
25	C₂×#66876	C₂²	1	1	yes	characteristic
26	C₂×#66876	C₂²	1	2	yes	—
27	C₂×#66876	C₂²	1	1	yes	characteristic
28	C₂×#66876	C₂²	1	2	yes	complemented
29	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
31	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	complemented
33	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
34	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
35	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
36	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
37	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
38	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
39	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
40	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
41	#10622099	C₂²	1	2	yes	complemented
42	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	complemented
43	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₁₁×#131	—	2	2	no	—
46	C₁₁×#131	—	2	2	no	—
47	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	—	2	2	no	—
52	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×#123	C₈	1	2	yes	—
60	C₁₁×C₂²⋊Q₈	C₈	1	1	yes	characteristic
61	C₁₁×C₂²⋊Q₈	C₈	1	1	yes	characteristic
62	C₁₁×#121	C₈	1	1	yes	characteristic
63	C₁₁×#121	C₈	1	1	yes	characteristic
64	C₁₁×#120	C₈	1	2	yes	—
65	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
67	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
68	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
69	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
74	C₁₁×#97	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₁₁	C₂³	1	2	yes	—
76	#66876	—	2	2	no	—
77	#66876	—	2	4	no	—
78	#66876	—	2	4	no	—
79	#66876	D₄	1	4	yes	complemented
80	C₂×C₁₁⋊C₁₆	—	2	2	no	—
81	C₂×C₁₁⋊C₁₆	—	2	2	no	—
82	C₂×C₁₁⋊C₁₆	—	2	4	no	—
83	C₂×C₁₁⋊C₁₆	—	2	4	no	—
84	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
89	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
90	#33436	—	11	1	no	maximal, Sylow
91	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
92	C₁₁×#41	—	2	2	no	—
93	C₁₁×#41	—	2	2	no	—
94	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
96	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
97	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
98	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₁₁×M₁₆	—	2	4	no	—
109	C₁₁×M₁₆	—	2	2	no	—
110	C₁₁×M₁₆	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₁	#41	1	2	yes	—
127	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
128	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
129	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
130	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
131	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
132	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
133	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
134	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
135	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
136	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
137	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
138	C₁₁⋊C₁₆	—	2	1	no	—
139	C₁₁⋊C₁₆	—	2	1	no	—
140	C₁₁⋊C₁₆	—	2	2	no	—
141	C₁₁⋊C₁₆	—	2	1	no	—
142	C₁₁⋊C₁₆	—	2	1	no	—
143	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	—
144	C₂×#504	—	11	1	no	—
145	C₂²×M₃₂	—	11	1	no	—
146	#2929	D₁₁	1	1	yes	characteristic
147	#2169	—	11	2	no	—
148	#2168	—	11	2	no	—
149	#2168	—	11	2	no	—
150	D₄×C₁₆	—	11	2	no	—
151	#2151	—	11	1	no	—
152	#2113	—	11	1	no	—
153	C₂×C₂²⋊C₁₆	—	11	1	no	—
154	#2108	—	11	1	no	—
155	C₂³×C₁₁	—	2	2	no	—
156	C₂³×C₁₁	—	2	2	no	—
157	C₂³×C₁₁	—	4	1	no	—
158	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
159	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
160	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
161	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
162	Q₈×C₁₁	—	2	2	no	—
163	D₄×C₁₁	—	2	4	no	—
164	D₄×C₁₁	—	2	4	no	—
165	D₄×C₁₁	—	2	2	no	—
166	D₄×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₁	#131	1	2	yes	—
184	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	C₈×C₁₁	—	2	1	no	—
186	C₈×C₁₁	—	2	1	no	—
187	C₈×C₁₁	—	2	2	no	—
188	C₈×C₁₁	—	2	2	no	—
189	C₈×C₁₁	C₄×D₄	1	2	yes	—
190	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
192	C₂×#131	C₂×D₁₁	1	1	yes	characteristic
193	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
194	#525	Dic₁₁	1	1	yes	characteristic
195	#504	—	22	4	no	—
196	C₂×M₃₂	—	11	1	no	—
197	C₂×M₃₂	—	11	1	no	—
198	C₂×M₃₂	—	11	2	no	—
199	C₂×M₃₂	—	11	2	no	—
200	C₂×M₃₂	—	22	4	no	—
201	C₂²×C₁₆	—	11	1	no	—
202	C₂²×C₁₆	—	11	1	no	—
203	C₂²×C₁₆	—	11	2	no	—
204	C₂²×C₁₆	—	11	2	no	—
205	#435	Dic₁₁	1	2	yes	—
206	#435	Dic₁₁	1	2	yes	—
207	C₈×D₄	C₂×D₁₁	1	2	yes	—
208	C₈×D₄	C₂×D₁₁	1	2	yes	—
209	#424	Dic₁₁	1	1	yes	characteristic
210	#408	Dic₁₁	1	1	yes	characteristic
211	#407	Dic₁₁	1	1	yes	characteristic
212	#405	C₂×D₁₁	1	1	yes	characteristic
213	C₄⋊C₁₆	—	11	2	no	—
214	C₄⋊C₁₆	—	11	2	no	—
215	C₂²⋊C₁₆	—	11	1	no	—
216	C₂²⋊C₁₆	—	11	1	no	—
217	C₂²⋊C₁₆	—	11	1	no	—
218	C₂²⋊C₁₆	—	11	1	no	—
219	C₂²⋊C₁₆	—	11	2	no	—
220	C₂²⋊C₁₆	—	11	2	no	—
221	#346	—	11	2	no	—
222	C₄×C₁₆	—	11	2	no	—
223	C₂²×C₁₁	—	2	1	no	—
224	C₂²×C₁₁	—	2	1	no	—
225	C₂²×C₁₁	—	2	1	no	—
226	C₂²×C₁₁	—	2	1	no	—
227	C₂²×C₁₁	—	2	2	no	—
228	C₂²×C₁₁	—	2	1	no	—
229	C₂²×C₁₁	—	2	1	no	—
230	C₂²×C₁₁	—	2	2	no	—
231	C₂²×C₁₁	—	2	1	no	—
232	C₂²×C₁₁	—	2	2	no	—
233	C₂²×C₁₁	—	4	4	no	—
234	C₂²×C₁₁	C₈×D₄	1	2	yes	—
235	C₂²×C₁₁	#504	1	2	yes	complemented
236	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
237	C₄×C₁₁	—	2	2	no	—
238	C₄×C₁₁	—	2	2	no	—
239	C₄×C₁₁	—	2	1	no	—
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	2	2	no	—
242	C₄×C₁₁	C₈×D₄	1	2	yes	—
243	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
245	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
246	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
247	#131	—	2	2	no	—
248	#131	—	2	2	no	—
249	C₂×M₁₆	C₂×Dic₁₁	1	1	yes	characteristic
250	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
251	C₂×M₁₆	C₂×Dic₁₁	1	1	yes	characteristic
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
255	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
256	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
260	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
261	#123	C₁₁⋊C₈	1	2	yes	—
262	C₂²⋊Q₈	C₁₁⋊C₈	1	1	yes	characteristic
263	C₂²⋊Q₈	C₁₁⋊C₈	1	1	yes	characteristic
264	#121	C₁₁⋊C₈	1	1	yes	characteristic
265	#121	C₁₁⋊C₈	1	1	yes	characteristic
266	#120	C₁₁⋊C₈	1	2	yes	—
267	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
268	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
269	#117	C₂×Dic₁₁	1	1	yes	characteristic
270	M₃₂	—	11	4	no	—
271	M₃₂	—	22	4	no	—
272	M₃₂	—	22	4	no	—
273	M₃₂	—	22	2	no	—
274	C₂×C₁₆	—	11	2	no	—
275	C₂×C₁₆	—	11	1	no	—
276	C₂×C₁₆	—	11	1	no	—
277	C₂×C₁₆	—	11	1	no	—
278	C₂×C₁₆	—	11	1	no	—
279	C₂×C₁₆	—	11	2	no	—
280	C₂×C₁₆	—	22	4	no	—
281	C₂×C₁₆	—	22	4	no	—
282	C₂×C₁₆	—	22	2	no	—
283	C₂×C₁₆	—	22	2	no	—
284	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
285	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
286	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
287	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
288	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
289	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
290	#97	C₂×Dic₁₁	1	2	yes	—
291	C₄×C₈	C₂²×D₁₁	1	2	yes	—
292	C₂×C₁₁	—	2	2	no	—
293	C₂×C₁₁	—	2	2	no	—
294	C₂×C₁₁	—	4	2	no	—
295	C₂×C₁₁	—	4	1	no	—
296	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
297	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
298	C₂×C₁₁	#3407	1	1	yes	characteristic
299	C₂⁴	C₂×C₁₁⋊C₈	1	1	yes	characteristic
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	C₂×Q₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
303	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
304	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
305	C₂×D₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
306	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	D₄×D₁₁	1	2	yes	—
329	C₂×C₈	#4341	1	2	yes	—
330	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
331	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
332	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
333	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
334	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
335	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
336	C₄⋊C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
338	C₄⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
339	C₄⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
340	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
341	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
342	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
343	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
344	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
345	C₄²	C₂²×Dic₁₁	1	2	yes	—
346	C₁₆	—	11	4	no	—
347	C₁₆	—	22	1	no	—
348	C₁₆	—	22	2	no	—
349	C₁₆	—	22	1	no	—
350	C₁₆	—	22	1	no	—
351	C₁₆	—	22	1	no	—
352	C₁₁	#33436	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
357	C₂³	C₂²×C₁₁⋊C₈	1	2	yes	—
358	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
359	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
375	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
376	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
379	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
381	C₂×C₄	#67001	1	2	yes	—
382	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	D₄×Dic₁₁	1	2	yes	—
388	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
389	C₈	C₂×#4341	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
402	C₂²	#10622753	1	2	yes	complemented
403	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
410	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
411	C₄	C₂×#67001	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic
417	C₂	C₂×#10622753	1	1	yes	characteristic
418	C₂	#13081719	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2929	C₂
prime radical	C₁₁×#525	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2929	D₁₁
hypocenter	C₁₁	#33436
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2929

Complements

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

N	H ≅ G/N	type
1. C₂×#10622753	C₂	semidirect
2. C₂²×#66876	C₂	semidirect
3. #13070448	C₂	semidirect
4. #13070442	C₂	semidirect
5. #13070442	C₂	semidirect
6. D₄×C₁₁⋊C₁₆	C₂	semidirect
7. #13070375	C₂	semidirect
8. #13070230	C₂	semidirect
9. C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	semidirect
10. #13070213	C₂	semidirect
28. C₂×#66876	C₂²	semidirect
32. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
37. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
38. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
39. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
40. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
41. #10622099	C₂²	semidirect
42. C₄×C₁₁⋊C₁₆	C₂²	semidirect
79. #66876	D₄	semidirect
235. C₂²×C₁₁	#504	semidirect
352. C₁₁	#33436	semidirect
402. C₂²	#10622753	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622753	2
C₂²×#66876	2
#13070448	2
#13070442	2
D₄×C₁₁⋊C₁₆	2
#13070375	2
#13070230	2
C₂×C₂²⋊(C₁₁⋊C₁₆)	2
#13070213	2
C₁₁×#2929	2
#33436	11