Subgroups — #14906950

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077305	C₂	1	1	yes	maximal, characteristic
4	#13070449	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070446	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070446	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070444	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070442	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070440	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070438	C₂	1	1	yes	maximal, characteristic, complemented
11	#13070373	C₂	1	1	yes	maximal, characteristic, complemented
12	#13070228	C₂	1	1	yes	maximal, characteristic, complemented
13	#13070225	C₂	1	1	yes	maximal, characteristic, complemented
14	#13070211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#66954	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
18	#10623078	C₄	1	1	yes	characteristic
19	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
24	C₂×#66876	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
26	#10622624	C₄	1	1	yes	characteristic
27	#10622520	—	2	4	no	—
28	D₁₁×M₃₂	—	2	4	no	—
29	C₂×#66862	C₂²	1	1	yes	characteristic
30	C₂×#66862	C₂²	1	1	yes	characteristic
31	C₂×#66862	C₂²	1	1	yes	characteristic
32	C₂×#66862	C₂²	1	1	yes	characteristic
33	C₂×#66862	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
35	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
36	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic, complemented
37	#10622452	C₄	1	1	yes	characteristic
38	#10622449	C₄	1	1	yes	characteristic
39	#10622343	C₄	1	1	yes	characteristic
40	#10622341	C₄	1	1	yes	characteristic
41	#10622340	C₄	1	1	yes	characteristic
42	#10622339	C₄	1	1	yes	characteristic
43	#10622302	C₂²	1	1	yes	characteristic
44	C₈×D₄₄	C₂²	1	1	yes	characteristic
45	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
47	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
52	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
53	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
55	#10622140	C₂²	1	1	yes	characteristic, complemented
56	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
60	#10622099	C₂²	1	1	yes	characteristic, complemented
61	C₂×#4339	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
66	#66992	C₈	1	1	yes	characteristic
67	#66990	C₈	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂×#4318	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
72	#66954	—	2	2	no	—
73	#66954	—	2	2	no	—
74	C₂×#4313	C₂×C₄	1	1	yes	characteristic
75	C₂×#4313	C₂×C₄	1	1	yes	characteristic
76	C₂×#4313	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₁	—	2	2	no	—
78	C₂×C₈×D₁₁	—	2	2	no	—
79	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
84	#66949	C₈	1	1	yes	characteristic
85	#66947	C₈	1	1	yes	characteristic
86	#66937	C₈	1	1	yes	characteristic
87	#66936	C₈	1	1	yes	characteristic
88	#66935	C₈	1	1	yes	characteristic
89	#66931	C₈	1	1	yes	characteristic
90	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
91	#66925	C₂×C₄	1	1	yes	characteristic
92	C₁₁×M₃₂	—	2	2	no	—
93	C₁₁×M₃₂	—	2	2	no	—
94	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
98	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
102	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
104	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
105	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
106	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
107	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
108	#66879	C₂×C₄	1	1	yes	characteristic
109	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
110	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
112	#66876	—	2	2	no	—
113	C₂×C₁₁⋊C₁₆	—	2	2	no	—
114	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
118	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
119	#66867	C₂×C₄	1	1	yes	characteristic
120	#66862	—	2	2	no	—
121	#66862	—	2	2	no	—
122	#66862	—	2	2	no	—
123	#66862	—	2	2	no	—
124	#66862	—	2	2	no	—
125	C₁₆×D₁₁	—	2	2	no	—
126	C₁₆×D₁₁	—	2	2	no	—
127	C₁₆×D₁₁	D₄	1	4	yes	complemented
128	#33433	—	11	1	no	maximal, Sylow
129	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
130	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
137	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
138	#4339	—	2	2	no	—
139	#4339	—	2	2	no	—
140	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
141	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₁₁	—	2	2	no	—
143	C₂×C₄×D₁₁	—	2	2	no	—
144	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
150	C₂×C₈×C₁₁	—	2	1	no	—
151	C₂×C₈×C₁₁	—	2	1	no	—
152	C₂×C₈×C₁₁	—	2	1	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
158	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
159	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
160	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
161	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
163	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
164	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
165	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
166	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
167	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
168	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
169	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
171	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
172	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
173	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
174	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
176	#4318	—	2	2	no	—
177	C₂×C₁₁⋊C₈	—	2	2	no	—
178	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	#4313	—	2	2	no	—
183	#4313	—	2	2	no	—
184	#4313	—	2	2	no	—
185	C₈×D₁₁	—	2	2	no	—
186	C₈×D₁₁	—	2	1	no	—
187	C₈×D₁₁	—	2	1	no	—
188	C₈×D₁₁	—	2	1	no	—
189	C₈×D₁₁	—	2	1	no	—
190	C₈×D₁₁	—	2	2	no	—
191	C₈×D₁₁	C₂×D₄	1	2	yes	—
192	C₈×D₁₁	#41	1	2	yes	—
193	C₁₁×C₁₆	—	2	1	no	—
194	C₁₁×C₁₆	—	2	1	no	—
195	C₁₁×C₁₆	—	2	1	no	—
196	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
197	C₁₁⋊C₁₆	—	2	1	no	—
198	C₁₁⋊C₁₆	—	2	1	no	—
199	C₁₁⋊C₁₆	—	2	1	no	—
200	C₁₁⋊C₁₆	C₂×D₄	1	2	yes	—
201	C₂×#504	—	11	1	no	—
202	C₂²×M₃₂	—	11	1	no	—
203	#2929	—	11	1	no	—
204	#2169	—	11	1	no	—
205	#2169	—	11	1	no	—
206	#2169	—	11	1	no	—
207	#2169	D₁₁	1	1	yes	characteristic, complemented
208	#2168	—	11	1	no	—
209	#2168	—	11	1	no	—
210	#2168	—	11	1	no	—
211	#2168	—	11	1	no	—
212	#2151	—	11	1	no	—
213	#2113	—	11	1	no	—
214	#2112	—	11	1	no	—
215	#2108	—	11	1	no	—
216	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
217	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
218	C₂²×D₁₁	—	2	2	no	—
219	C₂²×D₁₁	—	4	1	no	—
220	C₂²×D₁₁	—	4	1	no	—
221	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
222	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
223	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
224	D₄×C₁₁	—	4	1	no	—
225	C₂×C₄×C₁₁	—	2	1	no	—
226	C₂×C₄×C₁₁	—	2	1	no	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	—	2	1	no	—
229	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
233	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
234	C₂²⋊D₁₁	—	2	2	no	—
235	C₂²⋊D₁₁	—	2	2	no	—
236	C₂²⋊D₁₁	—	4	1	no	—
237	C₂²⋊D₁₁	—	4	1	no	—
238	C₂×Dic₁₁	—	2	2	no	—
239	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
240	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
241	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
242	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
243	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
244	D₄₄	—	2	2	no	—
245	D₄₄	—	4	1	no	—
246	C₄×D₁₁	—	2	2	no	—
247	C₄×D₁₁	—	2	1	no	—
248	C₄×D₁₁	—	2	1	no	—
249	C₄×D₁₁	—	2	1	no	—
250	C₄×D₁₁	—	2	1	no	—
251	C₄×D₁₁	—	2	2	no	—
252	C₄×D₁₁	C₄×D₄	1	2	yes	—
253	C₄×D₁₁	#131	1	2	yes	—
254	Dic₂₂	—	2	2	no	—
255	C₈×C₁₁	—	2	1	no	—
256	C₈×C₁₁	—	2	1	no	—
257	C₈×C₁₁	—	2	1	no	—
258	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
260	C₁₁⋊C₈	—	2	1	no	—
261	C₁₁⋊C₈	—	2	1	no	—
262	C₁₁⋊C₈	—	2	1	no	—
263	C₁₁⋊C₈	C₄×D₄	1	2	yes	—
264	C₂×#131	—	11	1	no	—
265	C₂³×C₈	—	11	1	no	—
266	#525	—	11	1	no	—
267	#504	—	22	4	no	—
268	C₂×M₃₂	—	11	1	no	—
269	C₂×M₃₂	—	11	1	no	—
270	C₂×M₃₂	—	11	1	no	—
271	C₂×M₃₂	—	11	1	no	—
272	C₂×M₃₂	—	11	1	no	—
273	C₂×M₃₂	—	11	1	no	—
274	C₂×M₃₂	—	22	4	no	—
275	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
276	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic, complemented
277	C₂²×C₁₆	—	11	1	no	—
278	C₂²×C₁₆	—	11	1	no	—
279	C₂²×C₁₆	—	11	1	no	—
280	C₂²×C₁₆	—	11	1	no	—
281	#435	—	11	1	no	—
282	#435	—	11	1	no	—
283	#435	—	11	1	no	—
284	#435	—	11	1	no	—
285	C₈×D₄	—	11	1	no	—
286	C₈×D₄	—	11	1	no	—
287	C₈×D₄	—	11	1	no	—
288	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
289	#424	—	11	1	no	—
290	#408	—	11	1	no	—
291	#407	—	11	1	no	—
292	#405	—	11	1	no	—
293	C₄⋊C₁₆	—	11	1	no	—
294	C₄⋊C₁₆	—	11	1	no	—
295	C₄⋊C₁₆	—	11	1	no	—
296	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
297	C₂²⋊C₁₆	—	11	1	no	—
298	C₂²⋊C₁₆	—	11	1	no	—
299	C₂²⋊C₁₆	—	11	1	no	—
300	C₂²⋊C₁₆	—	11	1	no	—
301	C₂²⋊C₁₆	—	11	1	no	—
302	C₂²⋊C₁₆	—	11	1	no	—
303	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
304	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
305	#346	—	11	1	no	—
306	#346	—	11	1	no	—
307	C₄×C₁₆	—	11	1	no	—
308	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
309	C₂²×C₁₁	—	2	1	no	—
310	C₂²×C₁₁	—	2	1	no	—
311	C₂²×C₁₁	—	2	1	no	—
312	C₂²×C₁₁	—	2	1	no	—
313	C₂²×C₁₁	—	2	1	no	—
314	C₂²×C₁₁	—	2	1	no	—
315	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
316	C₂×D₁₁	—	2	1	no	—
317	C₂×D₁₁	—	2	1	no	—
318	C₂×D₁₁	—	2	1	no	—
319	C₂×D₁₁	—	2	1	no	—
320	C₂×D₁₁	—	2	1	no	—
321	C₂×D₁₁	—	2	1	no	—
322	C₂×D₁₁	—	2	1	no	—
323	C₂×D₁₁	—	2	1	no	—
324	C₂×D₁₁	—	4	4	no	—
325	C₂×D₁₁	C₈×D₄	1	2	yes	—
326	C₄×C₁₁	—	2	1	no	—
327	C₄×C₁₁	—	2	1	no	—
328	C₄×C₁₁	—	2	1	no	—
329	C₄×C₁₁	—	2	1	no	—
330	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
331	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
332	Dic₁₁	—	2	1	no	—
333	Dic₁₁	—	2	1	no	—
334	Dic₁₁	—	2	1	no	—
335	Dic₁₁	—	2	1	no	—
336	Dic₁₁	C₈×D₄	1	2	yes	—
337	C₂×#41	—	11	1	no	—
338	C₂³×C₄	—	11	1	no	—
339	#131	—	22	2	no	—
340	#131	—	22	2	no	—
341	C₂×M₁₆	—	11	1	no	—
342	C₂×M₁₆	—	11	1	no	—
343	C₂×M₁₆	—	11	1	no	—
344	C₂×M₁₆	—	11	1	no	—
345	C₂²×C₈	—	11	1	no	—
346	C₂²×C₈	—	11	1	no	—
347	C₂²×C₈	—	11	1	no	—
348	C₂²×C₈	—	11	1	no	—
349	C₂²×C₈	—	11	1	no	—
350	C₂²×C₈	—	11	1	no	—
351	C₂²×C₈	—	22	2	no	—
352	C₂²×C₈	—	22	2	no	—
353	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
355	#123	—	11	1	no	—
356	#123	—	11	1	no	—
357	C₂²⋊Q₈	—	11	1	no	—
358	C₂²⋊Q₈	—	11	1	no	—
359	#121	—	11	1	no	—
360	#121	—	11	1	no	—
361	#120	—	11	1	no	—
362	#120	—	11	1	no	—
363	C₄×D₄	—	11	1	no	—
364	C₄×D₄	—	11	1	no	—
365	C₄×D₄	—	11	1	no	—
366	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
367	#117	—	11	1	no	—
368	M₃₂	—	2	2	no	—
369	M₃₂	—	2	2	no	—
370	M₃₂	—	22	2	no	—
371	M₃₂	—	22	2	no	—
372	M₃₂	—	22	2	no	—
373	M₃₂	—	22	2	no	—
374	M₃₂	—	22	2	no	—
375	M₃₂	—	22	2	no	—
376	C₂×C₁₆	—	11	1	no	—
377	C₂×C₁₆	—	11	4	no	—
378	C₂×C₁₆	—	11	1	no	—
379	C₂×C₁₆	—	11	1	no	—
380	C₂×C₁₆	—	11	1	no	—
381	C₂×C₁₆	—	22	2	no	—
382	C₂×C₁₆	—	22	2	no	—
383	C₂×C₁₆	—	22	2	no	—
384	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
385	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
386	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
387	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
388	C₄⋊C₈	—	11	1	no	—
389	C₄⋊C₈	—	11	1	no	—
390	C₄⋊C₈	—	11	1	no	—
391	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
392	C₂²⋊C₈	—	11	1	no	—
393	C₂²⋊C₈	—	11	1	no	—
394	C₂²⋊C₈	—	11	1	no	—
395	C₂²⋊C₈	—	11	1	no	—
396	C₂²⋊C₈	—	11	1	no	—
397	C₂²⋊C₈	—	11	1	no	—
398	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
399	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
400	#97	—	11	1	no	—
401	#97	—	11	1	no	—
402	C₄×C₈	—	11	1	no	—
403	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
404	C₂×C₁₁	—	4	1	no	—
405	C₂×C₁₁	—	4	1	no	—
406	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
407	C₂×C₁₁	#3407	1	1	yes	characteristic
408	C₂×C₁₁	#3407	1	1	yes	characteristic
409	D₁₁	—	2	2	no	—
410	D₁₁	—	4	1	no	—
411	D₁₁	—	4	1	no	—
412	C₂⁴	—	11	1	no	—
413	#41	—	22	2	no	—
414	#41	—	22	2	no	—
415	C₂×Q₈	—	11	1	no	—
416	C₂×D₄	—	11	1	no	—
417	C₂×D₄	—	11	1	no	—
418	C₂×D₄	—	11	1	no	—
419	C₂×D₄	—	11	1	no	—
420	C₂×D₄	—	11	1	no	—
421	C₂×D₄	—	11	1	no	—
422	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
423	C₂²×C₄	—	11	1	no	—
424	C₂²×C₄	—	11	1	no	—
425	C₂²×C₄	—	11	1	no	—
426	C₂²×C₄	—	11	1	no	—
427	C₂²×C₄	—	11	1	no	—
428	C₂²×C₄	—	11	1	no	—
429	C₂²×C₄	—	22	2	no	—
430	C₂²×C₄	—	22	2	no	—
431	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
433	M₁₆	—	22	2	no	—
434	M₁₆	—	22	2	no	—
435	M₁₆	—	22	2	no	—
436	M₁₆	—	22	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	11	1	no	—
442	C₂×C₈	—	11	2	no	—
443	C₂×C₈	—	11	2	no	—
444	C₂×C₈	—	11	1	no	—
445	C₂×C₈	—	11	1	no	—
446	C₂×C₈	—	11	1	no	—
447	C₂×C₈	—	22	2	no	—
448	C₂×C₈	—	22	2	no	—
449	C₂×C₈	—	22	2	no	—
450	C₂×C₈	—	22	1	no	—
451	C₂×C₈	—	22	1	no	—
452	C₂×C₈	—	22	1	no	—
453	C₂×C₈	—	22	1	no	—
454	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
455	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
457	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
458	C₄⋊C₄	—	11	1	no	—
459	C₄⋊C₄	—	11	1	no	—
460	C₄⋊C₄	—	11	1	no	—
461	C₄⋊C₄	—	11	1	no	—
462	C₄⋊C₄	—	11	1	no	—
463	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
464	C₂²⋊C₄	—	11	1	no	—
465	C₂²⋊C₄	—	11	1	no	—
466	C₂²⋊C₄	—	11	1	no	—
467	C₂²⋊C₄	—	11	1	no	—
468	C₂²⋊C₄	—	11	1	no	—
469	C₂²⋊C₄	—	11	1	no	—
470	C₂²⋊C₄	—	11	1	no	—
471	C₂²⋊C₄	—	11	1	no	—
472	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
473	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
474	C₄²	—	11	1	no	—
475	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
476	C₁₆	—	2	1	no	—
477	C₁₆	—	2	1	no	—
478	C₁₆	—	2	1	no	—
479	C₁₆	—	11	2	no	—
480	C₁₆	—	22	1	no	—
481	C₁₆	—	22	1	no	—
482	C₁₆	—	22	1	no	—
483	C₁₆	D₄×D₁₁	1	2	yes	—
484	C₁₁	#33433	1	1	yes	characteristic, complemented, Sylow
485	C₂³	—	11	1	no	—
486	C₂³	—	11	1	no	—
487	C₂³	—	11	1	no	—
488	C₂³	—	22	2	no	—
489	C₂³	—	44	1	no	—
490	C₂³	—	44	1	no	—
491	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
492	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
493	Q₈	—	22	2	no	—
494	D₄	—	4	1	no	—
495	D₄	—	22	2	no	—
496	D₄	—	22	2	no	—
497	D₄	—	22	2	no	—
498	D₄	—	44	1	no	—
499	D₄	—	44	1	no	—
500	D₄	—	44	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	11	1	no	—
506	C₂×C₄	—	11	2	no	—
507	C₂×C₄	—	11	2	no	—
508	C₂×C₄	—	11	1	no	—
509	C₂×C₄	—	11	1	no	—
510	C₂×C₄	—	11	1	no	—
511	C₂×C₄	—	11	1	no	—
512	C₂×C₄	—	22	2	no	—
513	C₂×C₄	—	22	2	no	—
514	C₂×C₄	—	22	2	no	—
515	C₂×C₄	—	22	1	no	—
516	C₂×C₄	—	22	1	no	—
517	C₂×C₄	—	22	1	no	—
518	C₂×C₄	—	22	1	no	—
519	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
520	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
521	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
522	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	11	2	no	—
528	C₈	—	22	1	no	—
529	C₈	—	22	1	no	—
530	C₈	—	22	1	no	—
531	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
532	C₈	#41×D₁₁	1	1	yes	characteristic
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	11	2	no	—
540	C₂²	—	22	1	no	—
541	C₂²	—	22	1	no	—
542	C₂²	—	22	1	no	—
543	C₂²	—	22	1	no	—
544	C₂²	—	22	1	no	—
545	C₂²	—	22	1	no	—
546	C₂²	—	22	1	no	—
547	C₂²	—	22	1	no	—
548	C₂²	—	44	4	no	—
549	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	11	2	no	—
555	C₄	—	22	1	no	—
556	C₄	—	22	1	no	—
557	C₄	—	22	1	no	—
558	C₄	—	22	1	no	—
559	C₄	C₄×D₄×D₁₁	1	1	yes	characteristic
560	C₄	D₁₁×#131	1	1	yes	characteristic
561	C₂	—	4	1	no	—
562	C₂	—	4	1	no	—
563	C₂	—	22	2	no	—
564	C₂	—	44	1	no	—
565	C₂	—	44	1	no	—
566	C₂	C₈×D₄×D₁₁	1	1	yes	characteristic
567	C₂	#13081717	1	1	yes	characteristic
568	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2169	C₂
prime radical	#10623078	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2169	D₁₁
hypocenter	C₁₁	#33433
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2169

Complements

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

N	H ≅ G/N	type
1. C₂×#10622520	C₂	semidirect
2. C₂×D₁₁×M₃₂	C₂	semidirect
4. #13070449	C₂	semidirect
5. #13070446	C₂	semidirect
6. #13070446	C₂	semidirect
7. #13070444	C₂	semidirect
8. #13070442	C₂	semidirect
9. #13070440	C₂	semidirect
10. #13070438	C₂	semidirect
11. #13070373	C₂	semidirect
12. #13070228	C₂	semidirect
13. #13070225	C₂	semidirect
14. #13070211	C₂	semidirect
15. C₁₁×#2169	C₂	semidirect
20. C₂×C₁₁×M₃₂	C₂²	semidirect
25. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
33. C₂×#66862	C₂²	semidirect
36. C₂×C₁₆×D₁₁	C₂²	semidirect
45. C₁₁×C₄⋊C₁₆	C₂²	semidirect
47. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
48. C₄×C₁₁×C₁₆	C₂²	semidirect
50. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
53. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
54. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
55. #10622140	C₂²	semidirect
56. Dic₁₁⋊C₁₆	C₂²	semidirect
57. Dic₁₁⋊C₁₆	C₂²	semidirect
58. C₁₆×Dic₁₁	C₂²	semidirect
59. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
60. #10622099	C₂²	semidirect
127. C₁₆×D₁₁	D₄	semidirect
207. #2169	D₁₁	semidirect
276. C₂×M₃₂	C₂×D₁₁	semidirect
296. C₄⋊C₁₆	C₂×D₁₁	semidirect
304. C₂²⋊C₁₆	C₂×D₁₁	semidirect
308. C₄×C₁₆	C₂×D₁₁	semidirect
484. C₁₁	#33433	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622520	2
C₂×D₁₁×M₃₂	2
#13077305	2
#13070449	2
#13070446	2
#13070444	2
#13070442	2
#13070440	2
#13070438	2
#13070373	2
#13070228	2
#13070225	2
#13070211	2
C₁₁×#2169	2
#33433	11