Subgroups — #14906991

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 568 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×#10622514	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077323	C₂	1	1	yes	maximal, characteristic
4	#13070446	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070445	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070443	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070442	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070440	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
10	(C₂²⋊D₁₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#13070228	C₂	1	1	yes	maximal, characteristic, complemented
13	#13070228	C₂	1	1	yes	maximal, characteristic, complemented
14	#13070209	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#66954	C₂²	1	1	yes	characteristic
17	C₂×#66954	C₂²	1	1	yes	characteristic
18	#10623079	C₄	1	1	yes	characteristic
19	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
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
26	#10622625	C₄	1	1	yes	characteristic
27	#10622520	—	2	4	no	—
28	#10622514	—	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×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
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
37	#10622451	C₄	1	1	yes	characteristic
38	#10622450	C₄	1	1	yes	characteristic
39	#10622342	C₄	1	1	yes	characteristic
40	#10622342	C₄	1	1	yes	characteristic
41	#10622340	C₄	1	1	yes	characteristic
42	#10622340	C₄	1	1	yes	characteristic
43	C₈×D₄₄	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
45	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
47	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
48	C₁₁×#346	C₂²	1	1	yes	characteristic
49	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
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
54	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
55	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
56	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
58	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
59	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
60	#10622099	C₂²	1	1	yes	characteristic
61	C₂×#4339	C₂×C₄	1	1	yes	characteristic
62	C₂×#4339	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	#66993	C₈	1	1	yes	characteristic
67	#66991	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	C₂×#4318	C₂×C₄	1	1	yes	characteristic
72	#66954	—	2	2	no	—
73	#66954	—	2	2	no	—
74	#66954	—	2	2	no	—
75	#66954	—	2	2	no	—
76	C₂×#4313	C₂×C₄	1	1	yes	characteristic
77	C₂×#4313	C₂×C₄	1	1	yes	characteristic
78	C₂×#4313	C₂×C₄	1	1	yes	characteristic
79	C₂×#4313	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	#66948	C₈	1	1	yes	characteristic
85	#66941	C₈	1	1	yes	characteristic
86	#66938	C₈	1	1	yes	characteristic
87	#66938	C₈	1	1	yes	characteristic
88	#66937	C₈	1	1	yes	characteristic
89	#66937	C₈	1	1	yes	characteristic
90	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
92	C₁₁×M₃₂	—	2	2	no	—
93	C₂×C₁₁×C₁₆	—	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	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
109	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₁₁	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	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
120	#66862	—	2	2	no	—
121	#66862	—	2	2	no	—
122	#66862	—	2	2	no	—
123	#66862	D₄	1	4	yes	complemented
124	C₁₆×D₁₁	—	2	2	no	—
125	C₁₆×D₁₁	—	2	2	no	—
126	C₁₆×D₁₁	—	2	2	no	—
127	C₁₆×D₁₁	—	2	2	no	—
128	#33438	—	11	1	no	maximal, Sylow
129	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₁	C₂×C₈	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	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
138	#4339	—	2	2	no	—
139	#4339	—	2	2	no	—
140	#4339	—	2	2	no	—
141	#4339	—	2	2	no	—
142	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
143	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
144	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂×C₈	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×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
151	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
152	C₂×C₈×C₁₁	—	2	1	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	—	2	1	no	—
155	C₂×C₈×C₁₁	—	2	1	no	—
156	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
160	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
161	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
162	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
163	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
164	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
165	C₂²⋊Dic₁₁	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	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
176	#4318	—	2	2	no	—
177	#4318	—	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	#4313	—	2	2	no	—
186	C₈×D₁₁	—	2	2	no	—
187	C₈×D₁₁	—	2	1	no	—
188	C₈×D₁₁	—	2	1	no	—
189	C₈×D₁₁	—	2	1	no	—
190	C₈×D₁₁	—	2	1	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	C₂×#504	—	11	1	no	—
203	#2931	—	11	1	no	—
204	#2169	—	11	1	no	—
205	#2169	—	11	1	no	—
206	#2168	—	11	1	no	—
207	#2168	—	11	1	no	—
208	#2168	—	11	1	no	—
209	#2168	D₁₁	1	1	yes	characteristic, complemented
210	D₄×C₁₆	—	11	1	no	—
211	D₄×C₁₆	—	11	1	no	—
212	C₂×C₄⋊C₁₆	—	11	1	no	—
213	#2113	—	11	1	no	—
214	#2113	—	11	1	no	—
215	C₄×M₃₂	—	11	1	no	—
216	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
217	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
218	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
219	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
220	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
221	D₄×C₁₁	—	4	1	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	1	no	—
225	C₂×C₄×C₁₁	—	2	1	no	—
226	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
227	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
228	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
231	C₂²⋊D₁₁	—	2	2	no	—
232	C₂²⋊D₁₁	—	2	2	no	—
233	C₂²⋊D₁₁	—	2	2	no	—
234	C₂²⋊D₁₁	—	2	2	no	—
235	C₂²⋊D₁₁	—	2	2	no	—
236	C₂²⋊D₁₁	—	2	2	no	—
237	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
238	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
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	D₄₄	—	2	2	no	—
243	D₄₄	—	2	2	no	—
244	D₄₄	—	4	1	no	—
245	C₄×D₁₁	—	2	1	no	—
246	C₄×D₁₁	—	2	1	no	—
247	C₄×D₁₁	—	2	1	no	—
248	C₄×D₁₁	—	2	1	no	—
249	C₄×D₁₁	—	2	2	no	—
250	C₄×D₁₁	—	4	1	no	—
251	C₄×D₁₁	C₄×D₄	1	2	yes	—
252	C₄×D₁₁	#131	1	2	yes	—
253	Dic₂₂	—	2	2	no	—
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	C₂×#131	—	11	1	no	—
266	#532	—	11	1	no	—
267	#504	—	22	4	no	—
268	#504	—	22	4	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	C₂×D₁₁	1	1	yes	characteristic
275	C₂²×C₁₆	—	11	1	no	—
276	C₂²×C₁₆	—	11	1	no	—
277	C₂²×C₁₆	—	11	1	no	—
278	C₂²×C₁₆	—	11	1	no	—
279	C₂²×C₁₆	—	11	1	no	—
280	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
281	#436	—	11	1	no	—
282	#436	—	11	1	no	—
283	#436	—	11	1	no	—
284	#436	—	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	#423	—	11	1	no	—
290	#408	—	11	1	no	—
291	#408	—	11	1	no	—
292	C₂×C₄×C₈	—	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
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
305	#346	—	11	1	no	—
306	#346	C₂×D₁₁	1	1	yes	characteristic
307	C₄×C₁₆	—	11	1	no	—
308	C₄×C₁₆	—	11	1	no	—
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	C₈×D₄	1	2	yes	—
325	C₄×C₁₁	—	2	1	no	—
326	C₄×C₁₁	—	2	1	no	—
327	C₄×C₁₁	—	2	1	no	—
328	C₄×C₁₁	—	2	1	no	—
329	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
330	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
331	Dic₁₁	—	2	1	no	—
332	Dic₁₁	—	2	1	no	—
333	Dic₁₁	—	2	1	no	—
334	Dic₁₁	C₈×D₄	1	2	yes	—
335	Dic₁₁	#504	1	2	yes	complemented
336	C₂×#41	—	11	1	no	—
337	C₂×#41	—	11	1	no	—
338	#131	—	22	2	no	—
339	#131	—	22	2	no	—
340	#131	—	22	2	no	—
341	#131	—	22	2	no	—
342	C₂×M₁₆	—	11	1	no	—
343	C₂×M₁₆	—	11	1	no	—
344	C₂×M₁₆	—	11	1	no	—
345	C₂×M₁₆	—	11	1	no	—
346	C₂×M₁₆	—	11	1	no	—
347	C₂×M₁₆	—	11	1	no	—
348	C₂²×C₈	—	11	1	no	—
349	C₂²×C₈	—	11	1	no	—
350	C₂²×C₈	—	11	1	no	—
351	C₂²×C₈	—	11	1	no	—
352	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
354	C₄⋊Q₈	—	11	1	no	—
355	#127	—	11	1	no	—
356	#124	—	11	1	no	—
357	#124	—	11	1	no	—
358	#121	—	11	1	no	—
359	#121	—	11	1	no	—
360	#121	—	11	1	no	—
361	#121	—	11	1	no	—
362	C₄×D₄	—	11	1	no	—
363	C₄×D₄	—	11	1	no	—
364	C₄×D₄	—	11	1	no	—
365	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
366	C₂×C₄²	—	11	1	no	—
367	M₃₂	—	2	2	no	—
368	M₃₂	—	11	4	no	—
369	M₃₂	—	22	2	no	—
370	M₃₂	—	22	2	no	—
371	M₃₂	—	22	2	no	—
372	M₃₂	—	22	2	no	—
373	C₂×C₁₆	—	2	2	no	—
374	C₂×C₁₆	—	11	1	no	—
375	C₂×C₁₆	—	11	1	no	—
376	C₂×C₁₆	—	11	1	no	—
377	C₂×C₁₆	—	11	1	no	—
378	C₂×C₁₆	—	22	2	no	—
379	C₂×C₁₆	—	22	2	no	—
380	C₂×C₁₆	—	22	2	no	—
381	C₂×C₁₆	—	22	2	no	—
382	C₂×C₁₆	—	22	2	no	—
383	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
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	C₄⋊C₈	—	11	1	no	—
388	C₄⋊C₈	—	11	1	no	—
389	C₄⋊C₈	—	11	1	no	—
390	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
391	C₂²⋊C₈	—	11	1	no	—
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	C₄×D₁₁	1	1	yes	characteristic
398	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
399	C₄×C₈	—	11	1	no	—
400	C₄×C₈	—	11	1	no	—
401	C₄×C₈	—	11	1	no	—
402	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
403	C₂×C₁₁	—	4	1	no	—
404	C₂×C₁₁	—	4	1	no	—
405	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
406	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
407	C₂×C₁₁	#3407	1	1	yes	characteristic
408	D₁₁	—	2	2	no	—
409	D₁₁	—	4	1	no	—
410	D₁₁	—	4	1	no	—
411	#41	—	22	2	no	—
412	#41	—	22	2	no	—
413	#41	—	22	2	no	—
414	#41	—	22	2	no	—
415	C₂×Q₈	—	11	1	no	—
416	C₂×Q₈	—	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	—	11	1	no	—
423	C₂×D₄	—	11	1	no	—
424	C₂×D₄	—	11	1	no	—
425	C₂×D₄	—	11	1	no	—
426	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
427	C₂²×C₄	—	11	1	no	—
428	C₂²×C₄	—	11	1	no	—
429	C₂²×C₄	—	11	1	no	—
430	C₂²×C₄	—	11	1	no	—
431	C₂²×C₄	—	11	1	no	—
432	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
434	M₁₆	—	22	2	no	—
435	M₁₆	—	22	2	no	—
436	M₁₆	—	22	2	no	—
437	M₁₆	—	22	2	no	—
438	M₁₆	—	22	2	no	—
439	M₁₆	—	22	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	11	1	no	—
445	C₂×C₈	—	11	2	no	—
446	C₂×C₈	—	11	2	no	—
447	C₂×C₈	—	11	1	no	—
448	C₂×C₈	—	11	1	no	—
449	C₂×C₈	—	11	1	no	—
450	C₂×C₈	—	22	2	no	—
451	C₂×C₈	—	22	1	no	—
452	C₂×C₈	—	22	1	no	—
453	C₂×C₈	—	22	1	no	—
454	C₂×C₈	—	22	1	no	—
455	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
457	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
458	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
459	C₄⋊C₄	—	11	1	no	—
460	C₄⋊C₄	—	11	1	no	—
461	C₄⋊C₄	—	11	1	no	—
462	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
463	C₂²⋊C₄	—	11	1	no	—
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	C₈×D₁₁	1	1	yes	characteristic
470	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
471	C₄²	—	11	1	no	—
472	C₄²	—	11	1	no	—
473	C₄²	—	11	1	no	—
474	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
475	C₁₆	—	2	1	no	—
476	C₁₆	—	2	1	no	—
477	C₁₆	—	2	1	no	—
478	C₁₆	—	11	2	no	—
479	C₁₆	—	22	1	no	—
480	C₁₆	—	22	1	no	—
481	C₁₆	—	22	1	no	—
482	C₁₆	D₄×D₁₁	1	2	yes	—
483	C₁₁	#33438	1	1	yes	characteristic, complemented, Sylow
484	C₂³	—	11	1	no	—
485	C₂³	—	11	1	no	—
486	C₂³	—	11	1	no	—
487	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
488	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
489	Q₈	—	22	2	no	—
490	Q₈	—	22	2	no	—
491	D₄	—	4	1	no	—
492	D₄	—	22	2	no	—
493	D₄	—	22	2	no	—
494	D₄	—	22	2	no	—
495	D₄	—	22	2	no	—
496	D₄	—	22	2	no	—
497	D₄	—	22	2	no	—
498	D₄	—	22	2	no	—
499	D₄	—	22	2	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	1	no	—
507	C₂×C₄	—	11	2	no	—
508	C₂×C₄	—	11	2	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	1	no	—
514	C₂×C₄	—	22	1	no	—
515	C₂×C₄	—	22	1	no	—
516	C₂×C₄	—	22	1	no	—
517	C₂×C₄	—	44	1	no	—
518	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
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	C₂²×C₄×D₁₁	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	11	2	no	—
527	C₈	—	22	1	no	—
528	C₈	—	22	1	no	—
529	C₈	—	22	1	no	—
530	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
531	C₈	#41×D₁₁	1	1	yes	characteristic
532	C₂²	—	2	1	no	—
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	—	11	2	no	—
539	C₂²	—	22	1	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	C₂²×C₈×D₁₁	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	11	2	no	—
553	C₄	—	11	2	no	—
554	C₄	—	22	1	no	—
555	C₄	—	22	1	no	—
556	C₄	—	22	1	no	—
557	C₄	C₄×D₄×D₁₁	1	1	yes	characteristic
558	C₄	D₁₁×#131	1	1	yes	characteristic
559	C₂	—	4	1	no	—
560	C₂	—	4	1	no	—
561	C₂	—	22	2	no	—
562	C₂	—	44	1	no	—
563	C₂	—	44	1	no	—
564	C₂	C₈×D₄×D₁₁	1	1	yes	characteristic
565	C₂	D₁₁×#504	1	1	yes	characteristic
566	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2168	C₂
prime radical	#10623079	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2168	D₁₁
hypocenter	C₁₁	#33438
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×#10622520	C₂	semidirect
2. C₂×#10622514	C₂	semidirect
4. #13070446	C₂	semidirect
5. #13070445	C₂	semidirect
6. #13070443	C₂	semidirect
7. #13070442	C₂	semidirect
8. #13070440	C₂	semidirect
9. C₁₆×C₂²⋊D₁₁	C₂	semidirect
10. (C₂²⋊D₁₁)⋊C₁₆	C₂	semidirect
11. D₁₁×C₄⋊C₁₆	C₂	semidirect
12. #13070228	C₂	semidirect
13. #13070228	C₂	semidirect
14. #13070209	C₂	semidirect
15. C₁₁×#2168	C₂	semidirect
123. #66862	D₄	semidirect
209. #2168	D₁₁	semidirect
335. Dic₁₁	#504	semidirect
483. C₁₁	#33438	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×#10622514	2
#13077323	2
#13070446	2
#13070445	2
#13070443	2
#13070442	2
#13070440	2
C₁₆×C₂²⋊D₁₁	2
(C₂²⋊D₁₁)⋊C₁₆	2
D₁₁×C₄⋊C₁₆	2
#13070228	2
#13070209	2
C₁₁×#2168	2
#33438	11