Subgroups — #14764205

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 382 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×#10622537	C₂	1	1	yes	maximal, characteristic
3	#13069391	C₂	1	4	yes	maximal, complemented
4	#13069389	C₂	1	4	yes	maximal, complemented
5	#13068656	C₂	1	4	yes	maximal
6	C₁₁×#2920	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×#4318	C₂²	1	2	yes	—
9	C₁₁×#432	—	2	1	no	—
10	C₁₁×#432	—	2	1	no	—
11	C₁₁×#431	—	2	1	no	—
12	C₁₁×#431	—	2	1	no	—
13	C₁₁×#423	C₂²	1	2	yes	—
14	C₁₁×#407	C₂²	1	2	yes	—
15	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
16	#10622820	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	#10622537	C₄	1	2	yes	—
23	#10622537	C₄	1	2	yes	—
24	#10622537	C₄	1	2	yes	—
25	#10622537	C₄	1	2	yes	—
26	#10622537	C₂²	1	2	yes	—
27	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
28	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
29	C₄×#4318	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	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×#4318	—	4	4	no	—
48	C₂×#4318	C₂×C₄	1	4	yes	—
49	C₂×#4318	C₂×C₄	1	4	yes	—
50	C₂×#4318	C₂³	1	4	yes	—
51	C₂²×C₁₁⋊C₈	C₂³	1	4	yes	—
52	C₁₁×C₄⋊C₈	—	2	2	no	—
53	C₁₁×C₄⋊C₈	—	2	2	no	—
54	C₁₁×C₂²⋊C₈	—	2	2	no	—
55	C₁₁×C₂²⋊C₈	—	2	2	no	—
56	C₁₁×#97	—	2	2	no	—
57	C₄×C₈×C₁₁	—	2	2	no	—
58	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
60	#66886	—	4	8	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	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
66	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
67	#66867	—	2	2	no	—
68	C₄×C₁₁⋊C₈	—	2	2	no	—
69	#21970	—	11	1	no	maximal, Sylow
70	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	—	2	2	no	—
72	C₂²×C₄×C₁₁	—	2	2	no	—
73	C₂²×C₄×C₁₁	—	4	2	no	—
74	C₂²×C₄×C₁₁	—	4	2	no	—
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	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×D₄	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	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
93	C₁₁×M₁₆	—	2	4	no	—
94	C₁₁×M₁₆	—	2	4	no	—
95	C₂×C₈×C₁₁	—	2	4	no	—
96	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×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	C₂×D₄	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	#4318	—	2	4	no	—
113	#4318	—	2	4	no	—
114	#4318	—	4	4	no	—
115	#4318	—	4	4	no	—
116	C₂×C₁₁⋊C₈	—	2	4	no	—
117	C₂×C₁₁⋊C₈	—	2	8	no	—
118	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
119	#2920	—	11	1	no	—
120	#2920	D₁₁	1	1	yes	characteristic
121	C₂×#423	—	11	1	no	—
122	#1950	—	11	4	no	—
123	#1950	—	11	4	no	—
124	#1811	—	11	4	no	—
125	C₂³×C₁₁	—	2	2	no	—
126	C₂³×C₁₁	—	4	1	no	—
127	C₂³×C₁₁	—	4	1	no	—
128	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	1	no	—
133	C₂×C₄×C₁₁	—	2	1	no	—
134	C₂×C₄×C₁₁	—	2	1	no	—
135	C₂×C₄×C₁₁	—	2	1	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	—	2	2	no	—
143	C₂×C₄×C₁₁	—	2	2	no	—
144	C₂×C₄×C₁₁	—	4	1	no	—
145	C₂×C₄×C₁₁	—	4	1	no	—
146	C₂×C₄×C₁₁	—	4	1	no	—
147	C₂×C₄×C₁₁	—	4	1	no	—
148	C₂×C₄×C₁₁	—	4	1	no	—
149	C₂×C₄×C₁₁	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
163	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
164	C₈×C₁₁	—	4	4	no	—
165	C₁₁⋊C₈	—	2	8	no	—
166	C₁₁⋊C₈	—	4	4	no	—
167	C₂²×M₁₆	—	11	2	no	—
168	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
169	#432	—	2	1	no	—
170	#432	—	2	1	no	—
171	#432	—	22	1	no	—
172	#432	—	22	1	no	—
173	#431	—	2	1	no	—
174	#431	—	2	1	no	—
175	#431	—	22	1	no	—
176	#431	—	22	1	no	—
177	C₂×#108	—	11	8	no	—
178	#423	—	11	2	no	—
179	#423	—	11	2	no	—
180	#423	—	11	2	no	—
181	#423	—	11	2	no	—
182	#423	—	11	2	no	—
183	#423	C₂×D₁₁	1	2	yes	—
184	C₂×C₄⋊C₈	—	11	2	no	—
185	C₂×C₄⋊C₈	—	11	2	no	—
186	#407	—	11	2	no	—
187	#407	C₂×D₁₁	1	2	yes	—
188	C₄×M₁₆	—	11	2	no	—
189	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
190	#341	—	11	8	no	—
191	C₂²×C₁₁	—	2	1	no	—
192	C₂²×C₁₁	—	2	1	no	—
193	C₂²×C₁₁	—	2	1	no	—
194	C₂²×C₁₁	—	2	1	no	—
195	C₂²×C₁₁	—	2	1	no	—
196	C₂²×C₁₁	—	2	1	no	—
197	C₂²×C₁₁	—	2	1	no	—
198	C₂²×C₁₁	—	2	1	no	—
199	C₂²×C₁₁	—	4	4	no	—
200	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	C₂²×C₁₁	#544	1	2	yes	—
202	C₄×C₁₁	—	2	1	no	—
203	C₄×C₁₁	—	2	1	no	—
204	C₄×C₁₁	—	2	1	no	—
205	C₄×C₁₁	—	2	1	no	—
206	C₄×C₁₁	—	2	1	no	—
207	C₄×C₁₁	—	2	1	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	—	2	1	no	—
210	C₄×C₁₁	#430	1	2	yes	—
211	C₄×C₁₁	#430	1	2	yes	—
212	C₄×C₁₁	#518	1	1	yes	characteristic
213	C₄×C₁₁	#519	1	1	yes	characteristic
214	C₄×C₁₁	#537	1	2	yes	—
215	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
216	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
218	C₂×M₁₆	—	11	4	no	—
219	C₂×M₁₆	—	11	4	no	—
220	C₂×M₁₆	—	11	4	no	—
221	C₂×M₁₆	—	44	4	no	—
222	C₂×M₁₆	C₂²×D₁₁	1	4	yes	—
223	C₂²×C₈	—	11	4	no	—
224	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
225	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
229	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
236	#108	—	44	8	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	11	4	no	—
240	C₄⋊C₈	—	11	4	no	—
241	C₄⋊C₈	—	11	4	no	—
242	C₄⋊C₈	—	11	4	no	—
243	C₄⋊C₈	—	22	2	no	—
244	C₄⋊C₈	—	22	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	22	2	no	—
248	C₂²⋊C₈	—	22	2	no	—
249	#97	—	2	2	no	—
250	#97	—	22	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	22	2	no	—
253	C₂×C₁₁	—	2	2	no	—
254	C₂×C₁₁	—	4	1	no	—
255	C₂×C₁₁	—	4	1	no	—
256	C₂×C₁₁	#2316	1	1	yes	characteristic
257	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
258	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
259	C₂⁴	C₂×Dic₂₂	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
275	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
276	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
281	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
282	M₁₆	—	2	4	no	—
283	M₁₆	—	2	4	no	—
284	M₁₆	—	22	4	no	—
285	M₁₆	—	22	4	no	—
286	M₁₆	—	44	4	no	—
287	M₁₆	—	44	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	11	8	no	—
290	C₂×C₈	—	22	8	no	—
291	C₂×C₈	—	22	4	no	—
292	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
296	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
297	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
299	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
303	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
305	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
306	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
307	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
308	C₁₁	#21970	1	1	yes	characteristic, complemented, Sylow
309	C₂³	—	2	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
313	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
314	C₂³	C₂²×Dic₂₂	1	1	yes	characteristic
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	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
345	C₂×C₄	#67042	1	2	yes	—
346	C₂×C₄	#67043	1	2	yes	—
347	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
348	C₈	—	4	4	no	—
349	C₈	—	22	8	no	—
350	C₈	—	44	4	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	4	4	no	—
360	C₂²	#10623050	1	2	yes	—
361	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	#10622737	1	2	yes	—
371	C₄	#10622737	1	2	yes	—
372	C₄	#10623047	1	1	yes	characteristic
373	C₄	#10623052	1	1	yes	characteristic
374	C₄	#10623364	1	2	yes	—
375	C₂	—	2	2	no	—
376	C₂	—	4	1	no	—
377	C₂	—	4	1	no	—
378	C₂	#13071232	1	1	yes	characteristic
379	C₂	C₂×#10622737	1	1	yes	characteristic
380	C₂	C₂×#10622737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₁₁×#2920	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#2920	D₁₁
hypocenter	C₁₁	#21970
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13069391	C₂	semidirect
4. #13069389	C₂	semidirect
308. C₁₁	#21970	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×#10622537	2
#13069391	2
#13069389	2
#13068656	2
C₁₁×#2920	2
#21970	11