Subgroups — #14758710

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 370 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	#13069391	C₂	1	4	yes	maximal, complemented
4	#13068821	C₂	1	4	yes	maximal
5	C₄×#66886	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₄×C₁₁×M₁₆	—	2	1	no	—
10	C₄×C₁₁×M₁₆	—	2	1	no	—
11	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
12	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
13	C₂×C₁₁×#97	—	2	1	no	—
14	C₂×C₄×C₈×C₁₁	—	2	1	no	—
15	#10622820	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
17	C₂×#66886	C₂²	1	8	yes	—
18	#10622539	—	2	1	no	—
19	#10622539	—	2	1	no	—
20	#10622538	—	2	1	no	—
21	#10622538	—	2	1	no	—
22	#10622538	C₄	1	2	yes	—
23	#10622538	C₄	1	2	yes	—
24	#10622538	C₄	1	2	yes	—
25	#10622538	C₄	1	2	yes	—
26	#10622537	C₂²	1	2	yes	—
27	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
28	C₄×#4318	C₂²	1	2	yes	—
29	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
30	#10622196	C₂²	1	8	yes	—
31	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
34	C₂×C₁₁×M₁₆	—	2	2	no	—
35	C₂×C₁₁×M₁₆	—	2	8	no	—
36	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
37	C₂²×C₈×C₁₁	—	2	2	no	—
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
50	C₂×#4318	C₂³	1	4	yes	—
51	C₂²×C₁₁⋊C₈	C₂³	1	4	yes	—
52	C₁₁×#97	—	2	2	no	—
53	C₁₁×#97	—	2	2	no	—
54	C₄×C₈×C₁₁	—	2	2	no	—
55	C₄×C₈×C₁₁	—	2	2	no	—
56	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
59	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
60	#66886	—	2	16	no	—
61	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
63	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
64	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
65	#66867	—	2	2	no	—
66	C₄×C₁₁⋊C₈	—	2	2	no	—
67	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
68	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
69	#21370	—	11	1	no	maximal, Sylow
70	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	—	2	4	no	—
72	C₂²×C₄×C₁₁	—	2	4	no	—
73	C₂²×C₄×C₁₁	—	4	2	no	—
74	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
92	C₁₁×M₁₆	—	2	8	no	—
93	C₁₁×M₁₆	—	2	4	no	—
94	C₁₁×M₁₆	#41	1	8	yes	—
95	C₂×C₈×C₁₁	—	2	8	no	—
96	C₂×C₈×C₁₁	—	2	4	no	—
97	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
113	#4318	—	2	8	no	—
114	C₂×C₁₁⋊C₈	—	2	4	no	—
115	C₂×C₁₁⋊C₈	—	2	8	no	—
116	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
117	#2920	—	11	1	no	—
118	C₂×#431	—	11	1	no	—
119	C₂×C₄×M₁₆	D₁₁	1	1	yes	characteristic
120	#1950	—	11	4	no	—
121	#1855	—	11	4	no	—
122	C₄×#108	—	11	4	no	—
123	C₂³×C₁₁	—	2	2	no	—
124	C₂³×C₁₁	—	2	2	no	—
125	C₂³×C₁₁	—	4	1	no	—
126	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	4	1	no	—
143	C₂×C₄×C₁₁	—	4	1	no	—
144	C₂×C₄×C₁₁	—	4	1	no	—
145	C₂×C₄×C₁₁	#108	1	4	yes	complemented
146	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
159	C₈×C₁₁	—	2	8	no	—
160	C₁₁⋊C₈	—	2	8	no	—
161	C₁₁⋊C₈	—	4	4	no	—
162	C₂²×M₁₆	C₂×D₁₁	1	2	yes	—
163	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
164	#432	—	22	1	no	—
165	#432	—	22	1	no	—
166	#431	—	11	2	no	—
167	#431	—	11	2	no	—
168	#431	—	11	2	no	—
169	#431	—	11	2	no	—
170	#431	—	22	1	no	—
171	#431	—	22	1	no	—
172	C₂×#108	—	11	8	no	—
173	#423	—	11	2	no	—
174	C₂×C₄⋊C₈	—	11	2	no	—
175	#407	—	11	2	no	—
176	C₂×C₂²⋊C₈	—	11	2	no	—
177	C₄×M₁₆	—	2	1	no	—
178	C₄×M₁₆	—	2	1	no	—
179	C₄×M₁₆	—	11	2	no	—
180	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
181	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
182	C₂×#97	—	2	1	no	—
183	C₂×C₄×C₈	—	2	1	no	—
184	C₂×C₄×C₈	—	11	2	no	—
185	#341	—	11	8	no	—
186	C₂²×C₁₁	—	2	1	no	—
187	C₂²×C₁₁	—	2	1	no	—
188	C₂²×C₁₁	—	2	1	no	—
189	C₂²×C₁₁	—	2	1	no	—
190	C₂²×C₁₁	—	2	1	no	—
191	C₂²×C₁₁	—	2	1	no	—
192	C₂²×C₁₁	—	2	1	no	—
193	C₂²×C₁₁	—	4	4	no	—
194	C₂²×C₁₁	C₂×#108	1	2	yes	—
195	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
196	C₂²×C₁₁	#533	1	2	yes	—
197	C₄×C₁₁	—	2	1	no	—
198	C₄×C₁₁	—	2	1	no	—
199	C₄×C₁₁	—	2	1	no	—
200	C₄×C₁₁	—	2	1	no	—
201	C₄×C₁₁	—	2	1	no	—
202	C₄×C₁₁	—	2	1	no	—
203	C₄×C₁₁	—	2	1	no	—
204	C₄×C₁₁	C₂×#108	1	2	yes	—
205	C₄×C₁₁	C₂×#108	1	2	yes	—
206	C₄×C₁₁	#430	1	2	yes	—
207	C₄×C₁₁	C₄×#41	1	2	yes	—
208	C₄×C₁₁	#525	1	2	yes	—
209	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
210	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
211	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	8	no	—
214	C₂×M₁₆	—	11	4	no	—
215	C₂×M₁₆	C₂²×D₁₁	1	4	yes	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	11	4	no	—
218	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
219	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
220	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
221	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
225	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
226	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
227	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
228	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
229	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
230	#108	—	22	16	no	—
231	C₄⋊C₈	—	11	4	no	—
232	C₄⋊C₈	—	11	4	no	—
233	C₄⋊C₈	—	22	2	no	—
234	C₄⋊C₈	—	22	2	no	—
235	C₂²⋊C₈	—	11	4	no	—
236	C₂²⋊C₈	—	11	4	no	—
237	C₂²⋊C₈	—	22	2	no	—
238	C₂²⋊C₈	—	22	2	no	—
239	#97	—	2	2	no	—
240	#97	—	2	2	no	—
241	#97	—	22	2	no	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	11	4	no	—
245	C₄×C₈	—	11	4	no	—
246	C₄×C₈	—	22	2	no	—
247	C₂×C₁₁	—	2	2	no	—
248	C₂×C₁₁	—	2	2	no	—
249	C₂×C₁₁	—	4	1	no	—
250	C₂×C₁₁	#2296	1	1	yes	characteristic
251	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
252	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
253	C₂⁴	C₂×Dic₂₂	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
268	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
269	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
275	M₁₆	—	2	8	no	—
276	M₁₆	—	2	4	no	—
277	M₁₆	—	22	8	no	—
278	M₁₆	#4339	1	8	yes	—
279	C₂×C₈	—	2	8	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	11	8	no	—
282	C₂×C₈	—	22	8	no	—
283	C₂×C₈	—	22	4	no	—
284	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
287	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
288	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
289	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
290	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
292	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
294	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
295	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
296	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
297	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
298	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
299	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
300	C₁₁	#21370	1	1	yes	characteristic, complemented, Sylow
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	1	no	—
304	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
305	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
306	C₂³	C₂²×Dic₂₂	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	#66886	1	4	yes	complemented
324	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#4339	1	4	yes	—
336	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	22	8	no	—
339	C₈	—	44	4	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	C₂×#66886	1	2	yes	—
349	C₂²	#10623001	1	2	yes	—
350	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	C₂×#66886	1	2	yes	—
359	C₄	C₂×#66886	1	2	yes	—
360	C₄	#10622737	1	2	yes	—
361	C₄	C₄×#4339	1	2	yes	—
362	C₄	#10623322	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	4	1	no	—
366	C₂	#13071099	1	1	yes	characteristic
367	C₂	C₂²×#66886	1	1	yes	characteristic
368	C₂	C₂×#10622737	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₂×C₄×C₁₁×M₁₆	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₁
hypocenter	C₁₁	#21370
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13069391	C₂	semidirect
5. C₄×#66886	C₂	semidirect
145. C₂×C₄×C₁₁	#108	semidirect
300. C₁₁	#21370	semidirect
323. C₂×C₄	#66886	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
#13069391	2
#13068821	2
C₄×#66886	2
C₂×C₄×C₁₁×M₁₆	2
#21370	11