Subgroups — #14719422

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622538	C₂	1	1	yes	maximal, characteristic
3	#13066916	C₂	1	4	yes	maximal, complemented
4	#13066909	C₂	1	2	yes	maximal, complemented
5	#13066905	C₂	1	2	yes	maximal, complemented
6	#13066900	C₂	1	2	yes	maximal, complemented
7	C₈×#4318	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×#431	C₄	1	2	yes	—
11	C₁₁×#431	C₄	1	2	yes	—
12	C₁₁×#431	C₂²	1	1	yes	characteristic
13	C₁₁×#431	C₂²	1	1	yes	characteristic
14	C₁₁×#431	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
16	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
18	#10622820	C₄	1	2	yes	—
19	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
20	#10622539	C₄	1	2	yes	—
21	#10622539	C₄	1	2	yes	—
22	#10622538	C₄	1	2	yes	—
23	#10622538	C₄	1	2	yes	—
24	#10622538	C₂²	1	2	yes	—
25	#10622538	C₂²	1	2	yes	—
26	#10622538	C₂²	1	1	yes	characteristic
27	#10622538	C₂²	1	1	yes	characteristic
28	#10622538	C₂²	1	2	yes	—
29	#10622537	C₄	1	2	yes	—
30	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
31	C₄×#4318	C₂²	1	2	yes	—
32	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
33	#10622093	C₂²	1	4	yes	complemented
34	#10622092	C₂²	1	4	yes	complemented
35	#10622092	C₂²	1	4	yes	complemented
36	C₈×C₁₁⋊C₈	C₂²	1	4	yes	complemented
37	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×#4318	C₂×C₄	1	4	yes	—
54	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
56	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₁₁	C₂³	1	2	yes	—
63	C₄×C₈×C₁₁	C₂³	1	2	yes	—
64	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
65	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
67	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
68	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
69	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
70	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
71	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
72	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
73	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
74	#66867	C₂×C₄	1	4	yes	—
75	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
76	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
77	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
78	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
79	#17326	—	11	1	no	maximal, Sylow
80	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	—	2	4	no	—
82	C₂²×C₄×C₁₁	—	2	4	no	—
83	C₂²×C₄×C₁₁	—	4	2	no	—
84	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₂²×C₄	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	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	—	4	4	no	—
103	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
104	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
105	C₄²×C₁₁	C₄²	1	1	yes	characteristic
106	C₄²×C₁₁	C₄²	1	1	yes	characteristic
107	C₄²×C₁₁	C₄²	1	1	yes	characteristic
108	C₄²×C₁₁	C₄²	1	1	yes	characteristic
109	C₄²×C₁₁	C₄²	1	1	yes	characteristic
110	C₄²×C₁₁	C₄²	1	1	yes	characteristic
111	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
121	#4318	—	2	8	no	—
122	C₂×C₁₁⋊C₈	—	2	8	no	—
123	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
124	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
125	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
126	#2920	—	11	1	no	—
127	C₂×#431	—	11	1	no	—
128	C₂×#431	D₁₁	1	1	yes	characteristic
129	#1454	—	11	4	no	—
130	#1452	—	11	2	no	—
131	#1451	—	11	2	no	—
132	#1450	—	11	2	no	—
133	C₈×M₁₆	—	11	2	no	—
134	C₂³×C₁₁	—	2	2	no	—
135	C₂³×C₁₁	—	2	2	no	—
136	C₂³×C₁₁	—	4	1	no	—
137	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
138	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
139	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	2	2	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	4	1	no	—
154	C₂×C₄×C₁₁	—	4	1	no	—
155	C₂×C₄×C₁₁	—	4	1	no	—
156	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₁	#131	1	4	yes	—
166	C₂×C₄×C₁₁	#131	1	4	yes	—
167	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
170	C₈×C₁₁	—	2	4	no	—
171	C₈×C₁₁	—	2	4	no	—
172	C₁₁⋊C₈	—	2	4	no	—
173	C₁₁⋊C₈	—	2	4	no	—
174	C₁₁⋊C₈	—	2	8	no	—
175	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
176	#432	—	11	2	no	—
177	#432	—	11	2	no	—
178	#431	—	11	1	no	—
179	#431	—	11	1	no	—
180	#431	—	11	2	no	—
181	#431	—	11	2	no	—
182	#431	—	11	2	no	—
183	#431	—	11	2	no	—
184	#431	—	11	2	no	—
185	#431	Dic₁₁	1	2	yes	—
186	#431	Dic₁₁	1	2	yes	—
187	#431	C₂×D₁₁	1	1	yes	characteristic
188	#431	C₂×D₁₁	1	1	yes	characteristic
189	#431	C₂×D₁₁	1	2	yes	—
190	#423	—	11	2	no	—
191	C₂×C₄⋊C₈	—	11	2	no	—
192	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
193	#407	—	11	2	no	—
194	C₂×C₂²⋊C₈	—	11	2	no	—
195	C₂×C₂²⋊C₈	Dic₁₁	1	2	yes	—
196	C₄×M₁₆	—	11	2	no	—
197	C₂×C₄×C₈	—	11	2	no	—
198	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
199	#322	—	11	4	no	—
200	#322	—	11	4	no	—
201	#322	—	11	4	no	—
202	C₈²	—	11	4	no	—
203	C₂²×C₁₁	—	2	1	no	—
204	C₂²×C₁₁	—	2	1	no	—
205	C₂²×C₁₁	—	2	1	no	—
206	C₂²×C₁₁	—	2	1	no	—
207	C₂²×C₁₁	—	2	1	no	—
208	C₂²×C₁₁	—	2	1	no	—
209	C₂²×C₁₁	—	2	1	no	—
210	C₂²×C₁₁	—	4	4	no	—
211	C₂²×C₁₁	#405	1	2	yes	—
212	C₂²×C₁₁	#405	1	2	yes	—
213	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	—	2	1	no	—
217	C₄×C₁₁	—	2	1	no	—
218	C₄×C₁₁	—	2	1	no	—
219	C₄×C₁₁	—	2	1	no	—
220	C₄×C₁₁	—	2	1	no	—
221	C₄×C₁₁	#405	1	2	yes	—
222	C₄×C₁₁	#405	1	2	yes	—
223	C₄×C₁₁	C₂×#131	1	2	yes	—
224	C₄×C₁₁	C₂×#131	1	2	yes	—
225	C₄×C₁₁	#568	1	2	yes	—
226	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
227	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
228	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
229	C₂×M₁₆	—	11	4	no	—
230	C₂²×C₈	—	11	4	no	—
231	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
232	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
239	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
244	C₄⋊C₈	—	11	2	no	—
245	C₄⋊C₈	—	11	2	no	—
246	C₄⋊C₈	—	11	4	no	—
247	C₄⋊C₈	—	11	4	no	—
248	C₄⋊C₈	—	11	4	no	—
249	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
250	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
251	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
252	C₂²⋊C₈	—	11	2	no	—
253	C₂²⋊C₈	—	11	2	no	—
254	C₂²⋊C₈	—	11	4	no	—
255	C₂²⋊C₈	—	11	4	no	—
256	C₂²⋊C₈	—	11	4	no	—
257	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
258	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
259	C₂²⋊C₈	C₂×Dic₁₁	1	4	yes	—
260	#97	—	11	4	no	—
261	C₄×C₈	—	11	4	no	—
262	C₄×C₈	—	11	2	no	—
263	C₄×C₈	—	11	4	no	—
264	C₄×C₈	—	11	2	no	—
265	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
266	C₄×C₈	C₂²×D₁₁	1	2	yes	—
267	C₄×C₈	C₂²×D₁₁	1	2	yes	—
268	C₂×C₁₁	—	2	2	no	—
269	C₂×C₁₁	—	2	2	no	—
270	C₂×C₁₁	—	4	1	no	—
271	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
272	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
273	C₂×C₁₁	#2873	1	1	yes	characteristic
274	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
281	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
282	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
283	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
286	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
295	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
296	M₁₆	—	22	8	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	—	11	4	no	—
299	C₂×C₈	—	11	4	no	—
300	C₂×C₈	—	11	8	no	—
301	C₂×C₈	—	22	8	no	—
302	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
303	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
304	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
305	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
306	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
307	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
308	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
309	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
310	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
311	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
312	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
313	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
316	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
317	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
318	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
319	C₄²	C₂³×D₁₁	1	1	yes	characteristic
320	C₁₁	#17326	1	1	yes	characteristic, complemented, Sylow
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
325	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
326	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	#66954	1	4	yes	—
344	C₂×C₄	#66960	1	4	yes	—
345	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
356	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	2	4	no	—
359	C₈	—	22	4	no	—
360	C₈	—	22	4	no	—
361	C₈	—	22	8	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	#10622714	1	2	yes	—
371	C₂²	#10622735	1	2	yes	—
372	C₂²	C₂²×C₄×Dic₁₁	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	#10622714	1	2	yes	—
381	C₄	#10622735	1	2	yes	—
382	C₄	C₂×#66954	1	2	yes	—
383	C₄	C₂×#66960	1	2	yes	—
384	C₄	#10623350	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	C₂×#10622714	1	1	yes	characteristic
389	C₂	C₂×#10622735	1	1	yes	characteristic
390	C₂	#13077035	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₂×C₁₁×#431	C₂
prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	#17326
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13066916	C₂	semidirect
4. #13066909	C₂	semidirect
5. #13066905	C₂	semidirect
6. #13066900	C₂	semidirect
7. C₈×#4318	C₂	semidirect
33. #10622093	C₂²	semidirect
34. #10622092	C₂²	semidirect
35. #10622092	C₂²	semidirect
36. C₈×C₁₁⋊C₈	C₂²	semidirect
320. C₁₁	#17326	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
C₂×#10622538	2
#13066916	2
#13066909	2
#13066905	2
#13066900	2
C₈×#4318	2
C₂×C₁₁×#431	2
#17326	11