Subgroups — #14643530

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 390 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×C₄×C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	#13066473	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊Dic₁₁	—	2	1	no	—
7	C₂²×C₄×Dic₁₁	C₄	1	2	yes	—
8	C₁₁×#432	—	2	1	no	—
9	C₁₁×#432	C₂²	1	2	yes	—
10	C₁₁×#431	—	2	1	no	—
11	C₁₁×#431	C₄	1	2	yes	complemented
12	C₁₁×#423	C₄	1	2	yes	complemented
13	C₁₁×#407	—	2	1	no	—
14	C₄×C₁₁×M₁₆	—	2	1	no	—
15	C₂×C₁₁⋊#95	—	2	1	no	—
16	#10622820	—	2	1	no	—
17	C₄×C₄⋊Dic₁₁	—	2	1	no	—
18	C₄×C₄⋊Dic₁₁	—	2	1	no	—
19	C₄×C₄⋊Dic₁₁	C₄	1	2	yes	—
20	C₄×C₄⋊Dic₁₁	C₂²	1	2	yes	—
21	#10622539	C₄	1	2	yes	complemented
22	#10622539	C₂²	1	2	yes	—
23	#10622538	—	2	1	no	—
24	#10622538	—	2	1	no	—
25	#10622537	—	2	1	no	—
26	C₄×#4318	C₄	1	2	yes	complemented
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	C₂³×Dic₁₁	—	2	2	no	—
31	C₂×C₁₁×M₁₆	—	2	2	no	—
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	C₂×C₄	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	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊Dic₁₁	—	2	8	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	—	4	4	no	—
49	C₂×C₄×Dic₁₁	C₂×C₄	1	4	yes	—
50	C₂×#4318	—	2	2	no	—
51	C₁₁×C₄⋊C₈	—	2	2	no	—
52	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
53	C₁₁×C₂²⋊C₈	—	2	2	no	—
54	C₁₁×C₂²⋊C₈	—	2	2	no	—
55	C₁₁×#97	—	2	2	no	—
56	C₄×C₈×C₁₁	—	2	2	no	—
57	C₁₁⋊#95	—	2	2	no	—
58	C₁₁⋊#95	—	2	2	no	—
59	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
63	#66867	C₂×C₄	1	4	yes	complemented
64	C₄×C₁₁⋊C₈	—	2	2	no	—
65	#7950	—	11	1	no	maximal, Sylow
66	C₂⁴×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	—	2	2	no	—
68	C₂²×C₄×C₁₁	—	2	2	no	—
69	C₂²×C₄×C₁₁	—	2	4	no	—
70	C₂²×C₄×C₁₁	—	4	2	no	—
71	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₄²	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	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₁₁	—	2	8	no	—
90	C₂²×Dic₁₁	—	2	4	no	—
91	C₂²×Dic₁₁	—	4	4	no	—
92	C₂²×Dic₁₁	—	4	4	no	—
93	C₁₁×M₁₆	—	4	4	no	—
94	C₂×C₈×C₁₁	—	2	4	no	—
95	C₄²×C₁₁	C₄²	1	1	yes	characteristic
96	C₄²×C₁₁	C₄²	1	1	yes	characteristic
97	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₄⋊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×Q₈	1	1	yes	characteristic
111	C₄⋊Dic₁₁	—	2	8	no	—
112	C₄⋊Dic₁₁	—	2	8	no	—
113	C₄×Dic₁₁	—	4	4	no	—
114	C₄×Dic₁₁	—	4	4	no	—
115	#4318	—	4	4	no	—
116	C₂×C₁₁⋊C₈	—	2	4	no	—
117	#2920	—	11	1	no	—
118	#2920	D₁₁	1	1	yes	characteristic
119	C₂×C₄×C₄⋊C₄	—	11	1	no	—
120	#1285	—	11	4	no	—
121	C₂³×C₁₁	—	2	2	no	—
122	C₂³×C₁₁	—	2	2	no	—
123	C₂³×C₁₁	—	2	1	no	—
124	C₂³×C₁₁	—	2	1	no	—
125	C₂³×C₁₁	#95	1	1	yes	characteristic
126	C₂³×C₁₁	#95	1	1	yes	characteristic
127	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	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	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	2	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	#100	1	2	yes	—
152	C₂×C₄×C₁₁	#101	1	2	yes	—
153	C₂×C₄×C₁₁	#104	1	4	yes	—
154	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂×C₂²⋊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×Dic₁₁	—	2	8	no	—
161	C₂×Dic₁₁	—	4	16	no	—
162	C₂×Dic₁₁	—	4	4	no	—
163	C₂×Dic₁₁	—	4	4	no	—
164	C₈×C₁₁	—	4	4	no	—
165	C₁₁⋊C₈	—	4	4	no	—
166	C₂²×C₄⋊C₄	—	22	1	no	—
167	C₂²×C₄²	—	11	2	no	—
168	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
169	#432	—	2	1	no	—
170	#432	—	11	2	no	—
171	#432	—	11	2	no	—
172	#432	C₂×D₁₁	1	2	yes	—
173	#431	—	2	1	no	—
174	#431	—	22	1	no	—
175	#431	—	22	1	no	—
176	#431	Dic₁₁	1	2	yes	complemented
177	#423	—	22	1	no	—
178	#423	Dic₁₁	1	2	yes	complemented
179	#407	—	2	1	no	—
180	#407	—	22	1	no	—
181	C₄×M₁₆	—	2	1	no	—
182	C₄×M₁₆	—	11	2	no	—
183	C₄×C₄⋊C₄	—	11	2	no	—
184	C₄×C₄⋊C₄	—	11	2	no	—
185	C₄×C₄⋊C₄	—	22	1	no	—
186	C₄×C₄⋊C₄	—	22	1	no	—
187	C₂×#95	—	22	1	no	—
188	C₂²×C₁₁	—	2	4	no	—
189	C₂²×C₁₁	—	2	4	no	—
190	C₂²×C₁₁	—	2	1	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	H(3,ℤ/4)	1	2	yes	—
197	C₂²×C₁₁	#339	1	2	yes	—
198	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
199	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
200	C₂²×C₁₁	C₂×#101	1	1	yes	characteristic
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	—	2	1	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	#339	1	2	yes	—
210	C₄×C₁₁	#343	1	2	yes	—
211	C₄×C₁₁	#343	1	2	yes	—
212	C₄×C₁₁	C₂×#104	1	2	yes	—
213	Dic₁₁	—	4	8	no	—
214	C₂³×C₄	—	22	2	no	—
215	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
216	C₂³×C₄	D₄₄	1	1	yes	characteristic
217	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	22	2	no	—
220	C₂×C₄⋊C₄	—	22	8	no	—
221	C₂×C₄⋊C₄	—	22	2	no	—
222	C₂×C₄⋊C₄	—	22	2	no	—
223	C₂×C₄²	—	11	4	no	—
224	C₂×C₄²	—	22	2	no	—
225	C₂×C₄²	—	44	4	no	—
226	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
227	C₂×C₄²	Dic₂₂	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	C₄×D₁₁	1	1	yes	characteristic
231	C₂×C₄²	D₄₄	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
236	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	22	2	no	—
240	C₄⋊C₈	—	22	2	no	—
241	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	complemented
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	22	2	no	—
245	C₂²⋊C₈	—	22	2	no	—
246	#97	—	2	2	no	—
247	#97	—	11	4	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	22	2	no	—
250	#95	—	22	2	no	—
251	#95	—	22	2	no	—
252	C₂×C₁₁	—	2	1	no	—
253	C₂×C₁₁	—	2	2	no	—
254	C₂×C₁₁	—	2	2	no	—
255	C₂×C₁₁	—	2	1	no	—
256	C₂×C₁₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
257	C₂×C₁₁	C₂×#339	1	1	yes	characteristic
258	C₂×C₁₁	C₂×#343	1	1	yes	characteristic
259	C₂⁴	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	22	8	no	—
265	C₂²×C₄	—	22	4	no	—
266	C₂²×C₄	—	44	4	no	—
267	C₂²×C₄	—	44	4	no	—
268	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₄×Dic₁₁	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	Dic₁₁⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
286	M₁₆	—	4	4	no	—
287	M₁₆	—	44	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	22	4	no	—
290	C₄⋊C₄	—	22	8	no	—
291	C₄⋊C₄	—	22	8	no	—
292	C₄²	—	44	4	no	—
293	C₄²	—	44	4	no	—
294	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
295	C₄²	C₄×Dic₁₁	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	C₄⋊Dic₁₁	1	1	yes	characteristic
301	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
302	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
303	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
304	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
305	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
306	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
307	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
308	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
309	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
310	C₁₁	#7950	1	1	yes	characteristic, complemented, Sylow
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	C₁₁⋊#95	1	1	yes	characteristic
316	C₂³	C₁₁⋊#95	1	1	yes	characteristic
317	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	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	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
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	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	22	8	no	—
336	C₂×C₄	—	44	16	no	—
337	C₂×C₄	—	44	4	no	—
338	C₂×C₄	—	44	4	no	—
339	C₂×C₄	#66887	1	2	yes	—
340	C₂×C₄	#66888	1	2	yes	—
341	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
346	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
347	C₂×C₄	#66901	1	4	yes	—
348	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
352	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
354	C₈	—	4	4	no	—
355	C₈	—	44	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	#10622170	1	2	yes	—
365	C₂²	#10622195	1	2	yes	—
366	C₂²	C₂×#66887	1	1	yes	characteristic
367	C₂²	C₂×#66888	1	1	yes	characteristic
368	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	44	8	no	—
378	C₄	#10622170	1	2	yes	—
379	C₄	#10622192	1	2	yes	—
380	C₄	#10622192	1	2	yes	—
381	C₄	C₂×#66901	1	2	yes	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	2	no	—
385	C₂	—	2	2	no	—
386	C₂	C₂×#10622195	1	1	yes	characteristic
387	C₂	C₂×#10622170	1	1	yes	characteristic
388	C₂	C₂×#10622192	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₁₁⋊#95
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2920	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2920	D₁₁
hypocenter	C₁₁	#7950
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. #13066473	C₂	semidirect
11. C₁₁×#431	C₄	semidirect
12. C₁₁×#423	C₄	semidirect
21. #10622539	C₄	semidirect
26. C₄×#4318	C₄	semidirect
52. C₁₁×C₄⋊C₈	C₂×C₄	semidirect
63. #66867	C₂×C₄	semidirect
176. #431	Dic₁₁	semidirect
178. #423	Dic₁₁	semidirect
241. C₄⋊C₈	C₂×Dic₁₁	semidirect
310. C₁₁	#7950	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×C₄×C₄⋊Dic₁₁	2
#13066473	2
C₁₁×#2920	2
#7950	11