Subgroups — #14643536

Order 2816.

610 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	C₂×#10622539	C₂	1	1	yes	maximal, characteristic
2	#13071023	C₂	1	1	yes	maximal, characteristic
3	#13066471	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#432	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66979	C₄	1	2	yes	—
7	C₁₁×#432	—	2	1	no	—
8	C₁₁×#432	—	2	1	no	—
9	C₁₁×#432	C₄	1	2	yes	complemented
10	C₁₁×#432	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
13	C₂×C₁₁×#97	C₄	1	2	yes	complemented
14	#10622825	—	2	1	no	—
15	#10622825	—	2	1	no	—
16	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
17	#10622549	—	2	1	no	—
18	#10622548	—	2	1	no	—
19	C₄×C₄⋊Dic₁₁	C₄	1	2	yes	—
20	C₄×C₄⋊Dic₁₁	C₂²	1	2	yes	—
21	#10622539	—	2	1	no	—
22	#10622539	—	2	1	no	—
23	#10622539	C₄	1	2	yes	complemented
24	#10622539	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	complemented
26	C₂×#66867	—	2	1	no	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	2	no	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
43	C₂×C₂²⋊Dic₁₁	—	2	2	no	—
44	#66979	—	4	4	no	—
45	C₂×C₄⋊Dic₁₁	—	2	2	no	—
46	C₂×C₄⋊Dic₁₁	—	2	2	no	—
47	C₂×C₄⋊Dic₁₁	—	2	2	no	—
48	C₂×C₄×Dic₁₁	C₂×C₄	1	4	yes	—
49	C₂²×C₁₁⋊C₈	—	2	2	no	—
50	C₁₁×C₄⋊C₈	—	2	2	no	—
51	C₁₁×C₄⋊C₈	—	2	2	no	—
52	C₁₁×C₂²⋊C₈	—	2	2	no	—
53	C₁₁×C₂²⋊C₈	—	2	2	no	—
54	C₁₁×#97	—	2	2	no	—
55	C₁₁×#97	C₂×C₄	1	4	yes	—
56	C₁₁⋊#95	—	2	2	no	—
57	C₁₁⋊#95	—	2	2	no	—
58	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
62	#66867	—	2	2	no	—
63	#66867	—	2	2	no	—
64	#7952	—	11	1	no	maximal, Sylow
65	C₂⁴×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	—	2	2	no	—
67	C₂²×C₄×C₁₁	—	2	2	no	—
68	C₂²×C₄×C₁₁	—	4	2	no	—
69	C₂²×C₄×C₁₁	—	4	2	no	—
70	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₁₁	—	2	4	no	—
89	C₂×C₈×C₁₁	—	2	4	no	—
90	C₂×C₈×C₁₁	—	4	4	no	—
91	C₄²×C₁₁	C₄²	1	1	yes	characteristic
92	C₄²×C₁₁	C₄²	1	1	yes	characteristic
93	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₁	C₂²⋊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	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
107	C₂²⋊Dic₁₁	—	4	4	no	—
108	C₄⋊Dic₁₁	—	4	4	no	—
109	C₄⋊Dic₁₁	—	4	4	no	—
110	C₄⋊Dic₁₁	—	4	4	no	—
111	C₄×Dic₁₁	—	4	4	no	—
112	C₂×C₁₁⋊C₈	—	2	4	no	—
113	C₂×C₁₁⋊C₈	—	4	4	no	—
114	C₂×#432	—	11	1	no	—
115	C₂×#432	D₁₁	1	1	yes	characteristic
116	#2285	—	11	1	no	—
117	#1285	—	11	4	no	—
118	C₂³×C₁₁	—	4	1	no	—
119	C₂³×C₁₁	—	4	1	no	—
120	C₂³×C₁₁	#95	1	1	yes	characteristic
121	C₂³×C₁₁	#95	1	1	yes	characteristic
122	C₂³×C₁₁	#100	1	2	yes	—
123	C₂³×C₁₁	#101	1	2	yes	—
124	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	1	no	—
130	C₂×C₄×C₁₁	—	2	1	no	—
131	C₂×C₄×C₁₁	—	2	1	no	—
132	C₂×C₄×C₁₁	—	2	1	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	—	4	1	no	—
140	C₂×C₄×C₁₁	—	4	1	no	—
141	C₂×C₄×C₁₁	—	4	1	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	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
150	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₂²⋊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×Dic₁₁	—	4	4	no	—
158	C₂×Dic₁₁	—	4	4	no	—
159	C₂×Dic₁₁	—	4	4	no	—
160	C₈×C₁₁	—	4	4	no	—
161	C₁₁⋊C₈	—	4	4	no	—
162	C₂×#117	—	11	2	no	—
163	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
164	#432	—	2	1	no	—
165	#432	—	2	1	no	—
166	#432	—	11	2	no	—
167	#432	—	11	2	no	—
168	#432	—	22	1	no	—
169	#432	—	22	1	no	—
170	#432	Dic₁₁	1	2	yes	complemented
171	#432	C₂×D₁₁	1	2	yes	—
172	C₂×C₄⋊C₈	—	2	1	no	—
173	C₂×C₄⋊C₈	—	11	2	no	—
174	C₂×C₂²⋊C₈	—	2	1	no	—
175	C₂×C₂²⋊C₈	—	22	1	no	—
176	C₂×#97	—	22	1	no	—
177	C₂×#97	Dic₁₁	1	2	yes	complemented
178	#384	—	22	1	no	—
179	#382	—	22	1	no	—
180	#380	—	22	1	no	—
181	#380	—	22	1	no	—
182	C₄×C₄⋊C₄	—	11	2	no	—
183	C₄×C₄⋊C₄	—	11	2	no	—
184	C₂²×C₁₁	—	2	1	no	—
185	C₂²×C₁₁	—	2	1	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	—	4	2	no	—
191	C₂²×C₁₁	—	4	2	no	—
192	C₂²×C₁₁	#343	1	2	yes	—
193	C₂²×C₁₁	#343	1	2	yes	—
194	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
195	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
196	C₂²×C₁₁	C₂×#101	1	1	yes	characteristic
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	—	2	1	no	—
205	C₄×C₁₁	—	2	1	no	—
206	C₄×C₁₁	—	2	1	no	—
207	C₄×C₁₁	H(3,ℤ/4)	1	2	yes	—
208	C₄×C₁₁	#421	1	2	yes	—
209	Dic₁₁	—	8	4	no	—
210	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
211	C₂³×C₄	D₄₄	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	22	2	no	—
215	#117	—	44	4	no	—
216	C₂×C₄⋊C₄	—	22	2	no	—
217	C₂×C₄⋊C₄	—	22	2	no	—
218	C₂×C₄⋊C₄	—	22	2	no	—
219	C₂×C₂²⋊C₄	—	22	2	no	—
220	C₂×C₄²	—	11	4	no	—
221	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
222	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
226	C₂×C₄²	D₄₄	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊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	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	11	4	no	—
236	C₄⋊C₈	—	22	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	22	2	no	—
240	C₂²⋊C₈	—	22	2	no	—
241	#97	—	2	2	no	—
242	#97	—	22	2	no	—
243	#97	—	22	2	no	—
244	#97	C₂×Dic₁₁	1	4	yes	—
245	#95	—	22	2	no	—
246	#95	—	22	2	no	—
247	C₂×C₁₁	—	2	1	no	—
248	C₂×C₁₁	—	2	2	no	—
249	C₂×C₁₁	—	2	2	no	—
250	C₂×C₁₁	—	2	1	no	—
251	C₂×C₁₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
252	C₂×C₁₁	#1733	1	1	yes	characteristic
253	C₂×C₁₁	C₂×#343	1	1	yes	characteristic
254	C₂⁴	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	22	4	no	—
260	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
261	C₂²×C₄	C₄×Dic₁₁	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	Dic₁₁⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₂×C₈	—	22	4	no	—
281	C₂×C₈	—	44	4	no	—
282	C₄⋊C₄	—	44	4	no	—
283	C₄⋊C₄	—	44	4	no	—
284	C₄⋊C₄	—	44	4	no	—
285	C₂²⋊C₄	—	44	4	no	—
286	C₄²	—	44	4	no	—
287	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
288	C₄²	C₄×Dic₁₁	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	Dic₁₁⋊C₄	1	1	yes	characteristic
293	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
294	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
295	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
296	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
297	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
298	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
299	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
301	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
303	C₁₁	#7952	1	1	yes	characteristic, complemented, Sylow
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	#66887	1	2	yes	—
307	C₂³	#66888	1	2	yes	—
308	C₂³	C₁₁⋊#95	1	1	yes	characteristic
309	C₂³	C₁₁⋊#95	1	1	yes	characteristic
310	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	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	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	44	4	no	—
332	C₂×C₄	—	44	4	no	—
333	C₂×C₄	—	44	4	no	—
334	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
335	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄×Dic₁₁	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×C₄⋊Dic₁₁	1	1	yes	characteristic
344	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	44	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	#10622192	1	2	yes	—
357	C₂²	#10622192	1	2	yes	—
358	C₂²	C₂×#66887	1	1	yes	characteristic
359	C₂²	C₂×#66888	1	1	yes	characteristic
360	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
361	C₄	—	2	1	no	—
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	—	2	1	no	—
371	C₄	—	88	4	no	—
372	C₄	#10622169	1	2	yes	—
373	C₄	#10622752	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	2	no	—
378	C₂	C₂×#10622169	1	1	yes	characteristic
379	C₂	#13068327	1	1	yes	characteristic
380	C₂	C₂×#10622192	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₁₁⋊#95
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#432	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#432	D₁₁
hypocenter	C₁₁	#7952
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
3. #13066471	C₂	semidirect
9. C₁₁×#432	C₄	semidirect
13. C₂×C₁₁×#97	C₄	semidirect
23. #10622539	C₄	semidirect
25. C₂×C₄⋊(C₁₁⋊C₈)	C₄	semidirect
170. #432	Dic₁₁	semidirect
177. C₂×#97	Dic₁₁	semidirect
303. C₁₁	#7952	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622539	2
#13071023	2
#13066471	2
C₂×C₁₁×#432	2
#7952	11