Subgroups — #14906986

Order 2816.

734 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	C₂×D₁₁×M₃₂	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic
3	#13070448	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070444	C₂	1	2	yes	maximal, complemented
5	#13070439	C₂	1	2	yes	maximal, complemented
6	C₁₆×D₄₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070435	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070370	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070225	C₂	1	2	yes	maximal, complemented
10	C₄×#66862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₁₁	C₂²	1	2	yes	—
13	C₄×D₄×D₁₁	C₄	1	1	yes	characteristic
14	C₂×C₁₁×M₃₂	C₂²	1	2	yes	complemented
15	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₈×C₂²⋊D₁₁	C₂²	1	2	yes	—
17	C₂×#66876	C₂²	1	2	yes	complemented
18	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
19	D₁₁×M₃₂	—	2	8	no	—
20	C₂×#66862	C₂²	1	2	yes	—
21	C₂×#66862	C₂²	1	1	yes	characteristic
22	C₂×#66862	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₁₁	C₂²	1	2	yes	complemented
24	C₂×C₁₆×D₁₁	C₂²	1	2	yes	complemented
25	#10622447	C₄	1	1	yes	characteristic
26	D₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
27	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
28	D₁₁×C₂²⋊C₈	C₄	1	2	yes	—
29	C₈×D₄₄	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
35	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
36	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
37	#10622140	C₂²	1	1	yes	characteristic, complemented
38	#10622140	C₂²	1	1	yes	characteristic, complemented
39	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₁	C₈	1	1	yes	characteristic
43	C₂²×C₄×D₁₁	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
46	D₄×Dic₁₁	C₈	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
48	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₁₁	—	2	4	no	—
50	C₂×C₈×D₁₁	—	2	4	no	—
51	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₁	C₂³	1	2	yes	—
55	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
56	#66946	C₈	1	1	yes	characteristic
57	C₄⋊C₄×D₁₁	C₈	1	1	yes	characteristic
58	(C₂²⋊D₁₁)⋊C₄	C₈	1	2	yes	—
59	C₂²⋊C₄×D₁₁	C₈	1	2	yes	—
60	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₁₁×M₃₂	—	2	4	no	—
63	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
70	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
71	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
72	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
73	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
75	#66876	—	2	4	no	—
76	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
77	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
79	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
81	#66862	—	2	4	no	—
82	#66862	—	2	2	no	—
83	#66862	D₄	1	4	yes	complemented
84	C₁₆×D₁₁	—	2	4	no	—
85	C₁₆×D₁₁	—	2	4	no	—
86	D₄×M₃₂	—	11	1	no	maximal, Sylow
87	C₂³×D₁₁	C₂×C₈	1	2	yes	—
88	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
90	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
91	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
92	D₄×D₁₁	—	2	4	no	—
93	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₁₁	—	2	4	no	—
95	C₂×C₄×D₁₁	—	2	4	no	—
96	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
99	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	—	2	2	no	—
104	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
107	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
108	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
109	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
111	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
112	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
113	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
114	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
115	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
117	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₁₁⋊C₈	—	2	4	no	—
119	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₁₁	—	2	4	no	—
123	C₈×D₁₁	—	2	2	no	—
124	C₈×D₁₁	—	2	2	no	—
125	C₈×D₁₁	—	2	2	no	—
126	C₈×D₁₁	—	2	4	no	—
127	C₈×D₁₁	C₂×D₄	1	2	yes	—
128	C₈×D₁₁	#41	1	2	yes	—
129	C₁₁×C₁₆	—	2	2	no	—
130	C₁₁×C₁₆	—	2	1	no	—
131	C₁₁×C₁₆	C₂×D₄	1	2	yes	complemented
132	C₁₁⋊C₁₆	—	2	2	no	—
133	C₁₁⋊C₁₆	—	2	1	no	—
134	C₁₁⋊C₁₆	C₂×D₄	1	2	yes	complemented
135	C₂²×M₃₂	—	11	2	no	—
136	C₂×C₈×D₄	—	11	1	no	—
137	#2169	—	11	1	no	—
138	#2169	D₁₁	1	1	yes	characteristic, complemented
139	#2168	—	11	2	no	—
140	#2168	—	11	2	no	—
141	D₄×C₁₆	—	11	1	no	—
142	D₄×C₁₆	—	11	1	no	—
143	#2150	—	11	1	no	—
144	#2112	—	11	2	no	—
145	C₄×M₃₂	—	11	1	no	—
146	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
147	C₂²×D₁₁	—	2	4	no	—
148	C₂²×D₁₁	—	2	4	no	—
149	C₂²×D₁₁	—	4	2	no	—
150	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
151	C₂²×D₁₁	C₂²×C₈	1	2	yes	—
152	D₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
159	C₂²⋊D₁₁	—	2	4	no	—
160	C₂×Dic₁₁	—	2	4	no	—
161	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
162	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
164	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
165	D₄₄	M₃₂	1	4	yes	complemented
166	C₄×D₁₁	—	2	4	no	—
167	C₄×D₁₁	—	2	2	no	—
168	C₄×D₁₁	—	2	2	no	—
169	C₄×D₁₁	—	2	2	no	—
170	C₄×D₁₁	—	2	4	no	—
171	C₄×D₁₁	—	4	1	no	—
172	C₄×D₁₁	C₄×D₄	1	2	yes	—
173	C₄×D₁₁	#131	1	2	yes	—
174	C₈×C₁₁	—	2	2	no	—
175	C₈×C₁₁	—	2	1	no	—
176	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
178	C₁₁⋊C₈	—	2	2	no	—
179	C₁₁⋊C₈	—	2	1	no	—
180	C₁₁⋊C₈	C₄×D₄	1	2	yes	—
181	C₂³×C₈	—	11	2	no	—
182	C₂×C₄×D₄	—	11	1	no	—
183	C₂×M₃₂	—	11	2	no	—
184	C₂×M₃₂	—	11	1	no	—
185	C₂×M₃₂	—	11	1	no	—
186	C₂×M₃₂	—	11	2	no	—
187	C₂×M₃₂	—	22	8	no	—
188	C₂×M₃₂	C₂×D₁₁	1	2	yes	complemented
189	C₂²×C₁₆	—	11	2	no	—
190	C₂²×C₁₆	—	11	2	no	—
191	C₈×D₄	—	11	2	no	—
192	C₈×D₄	—	11	1	no	—
193	C₈×D₄	—	11	1	no	—
194	C₈×D₄	—	11	2	no	—
195	C₈×D₄	—	11	1	no	—
196	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
197	C₂×C₄⋊C₈	—	11	1	no	—
198	C₂×C₂²⋊C₈	—	11	2	no	—
199	C₂×C₄×C₈	—	11	1	no	—
200	C₄⋊C₁₆	—	11	2	no	—
201	C₄⋊C₁₆	—	11	1	no	—
202	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
203	C₂²⋊C₁₆	—	11	2	no	—
204	C₂²⋊C₁₆	—	11	2	no	—
205	C₂²⋊C₁₆	—	11	2	no	—
206	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	complemented
207	#346	—	11	1	no	—
208	#346	—	11	1	no	—
209	C₄×C₁₆	—	11	1	no	—
210	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
211	C₂²×C₁₁	—	2	2	no	—
212	C₂²×C₁₁	—	2	2	no	—
213	C₂²×C₁₁	—	2	2	no	—
214	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
215	C₂×D₁₁	—	2	1	no	—
216	C₂×D₁₁	—	2	1	no	—
217	C₂×D₁₁	—	2	2	no	—
218	C₂×D₁₁	—	2	2	no	—
219	C₂×D₁₁	—	4	8	no	—
220	C₂×D₁₁	C₈×D₄	1	2	yes	—
221	C₂×D₁₁	C₂×M₃₂	1	4	yes	complemented
222	C₄×C₁₁	—	2	1	no	—
223	C₄×C₁₁	—	2	2	no	—
224	C₄×C₁₁	C₂×M₃₂	1	2	yes	complemented
225	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
227	Dic₁₁	—	2	1	no	—
228	Dic₁₁	—	2	1	no	—
229	Dic₁₁	—	2	2	no	—
230	Dic₁₁	C₈×D₄	1	2	yes	—
231	C₂²×D₄	—	11	1	no	—
232	C₂³×C₄	—	11	2	no	—
233	C₂²×C₈	—	11	1	no	—
234	C₂²×C₈	—	11	2	no	—
235	C₂²×C₈	—	11	2	no	—
236	C₂²×C₈	—	11	2	no	—
237	C₂²×C₈	—	11	1	no	—
238	C₂²×C₈	—	11	2	no	—
239	C₂²×C₈	—	22	4	no	—
240	C₂²×C₈	—	22	4	no	—
241	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
242	C₄×D₄	—	11	1	no	—
243	C₄×D₄	—	11	2	no	—
244	C₄×D₄	—	11	1	no	—
245	C₄×D₄	—	11	2	no	—
246	C₄×D₄	—	11	1	no	—
247	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
248	C₂×C₄⋊C₄	—	11	1	no	—
249	C₂×C₂²⋊C₄	—	11	2	no	—
250	C₂×C₄²	—	11	1	no	—
251	M₃₂	—	2	4	no	—
252	M₃₂	—	11	4	no	—
253	M₃₂	—	22	2	no	—
254	M₃₂	—	22	4	no	—
255	M₃₂	—	22	4	no	—
256	C₂×C₁₆	—	11	1	no	—
257	C₂×C₁₆	—	11	1	no	—
258	C₂×C₁₆	—	11	2	no	—
259	C₂×C₁₆	—	22	4	no	—
260	C₂×C₁₆	—	22	4	no	—
261	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
263	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
264	C₄⋊C₈	—	11	2	no	—
265	C₄⋊C₈	—	11	1	no	—
266	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
267	C₂²⋊C₈	—	11	2	no	—
268	C₂²⋊C₈	—	11	2	no	—
269	C₂²⋊C₈	—	11	2	no	—
270	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
271	C₄×C₈	—	11	1	no	—
272	C₄×C₈	—	11	1	no	—
273	C₄×C₈	—	11	1	no	—
274	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
275	C₂×C₁₁	—	4	2	no	—
276	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
277	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
278	C₂×C₁₁	#3407	1	1	yes	characteristic
279	D₁₁	—	2	2	no	—
280	D₁₁	—	2	4	no	—
281	C₂⁴	—	11	2	no	—
282	C₂×D₄	—	11	2	no	—
283	C₂×D₄	—	11	1	no	—
284	C₂×D₄	—	22	4	no	—
285	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
286	C₂²×C₄	—	11	1	no	—
287	C₂²×C₄	—	11	2	no	—
288	C₂²×C₄	—	11	1	no	—
289	C₂²×C₄	—	11	2	no	—
290	C₂²×C₄	—	11	2	no	—
291	C₂²×C₄	—	11	2	no	—
292	C₂²×C₄	—	11	1	no	—
293	C₂²×C₄	—	22	4	no	—
294	C₂²×C₄	—	22	4	no	—
295	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	11	1	no	—
299	C₂×C₈	—	11	2	no	—
300	C₂×C₈	—	11	2	no	—
301	C₂×C₈	—	11	1	no	—
302	C₂×C₈	—	11	2	no	—
303	C₂×C₈	—	22	4	no	—
304	C₂×C₈	—	22	4	no	—
305	C₂×C₈	—	22	2	no	—
306	C₂×C₈	—	22	4	no	—
307	C₂×C₈	—	22	2	no	—
308	C₂×C₈	—	22	2	no	—
309	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
310	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
311	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
312	C₄⋊C₄	—	11	2	no	—
313	C₄⋊C₄	—	11	1	no	—
314	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
315	C₂²⋊C₄	—	11	2	no	—
316	C₂²⋊C₄	—	11	2	no	—
317	C₂²⋊C₄	—	11	2	no	—
318	C₂²⋊C₄	C₈×D₁₁	1	2	yes	—
319	C₄²	—	11	1	no	—
320	C₄²	—	11	1	no	—
321	C₄²	—	11	1	no	—
322	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
323	C₁₆	—	2	2	no	—
324	C₁₆	—	2	1	no	—
325	C₁₆	—	11	2	no	—
326	C₁₆	—	22	2	no	—
327	C₁₆	—	22	1	no	—
328	C₁₆	D₄×D₁₁	1	2	yes	complemented
329	C₁₁	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	11	2	no	—
331	C₂³	—	11	1	no	—
332	C₂³	—	22	4	no	—
333	C₂³	—	22	4	no	—
334	C₂³	—	44	2	no	—
335	C₂³	C₂×C₈×D₁₁	1	2	yes	—
336	D₄	—	2	2	no	—
337	D₄	—	11	4	no	—
338	D₄	—	22	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	11	1	no	—
342	C₂×C₄	—	11	2	no	—
343	C₂×C₄	—	11	2	no	—
344	C₂×C₄	—	11	1	no	—
345	C₂×C₄	—	11	1	no	—
346	C₂×C₄	—	11	2	no	—
347	C₂×C₄	—	22	4	no	—
348	C₂×C₄	—	22	4	no	—
349	C₂×C₄	—	22	4	no	—
350	C₂×C₄	—	22	2	no	—
351	C₂×C₄	—	22	2	no	—
352	C₂×C₄	—	22	2	no	—
353	C₂×C₄	—	44	1	no	—
354	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	2	no	—
360	C₈	—	11	2	no	—
361	C₈	—	22	1	no	—
362	C₈	—	22	2	no	—
363	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
364	C₈	#41×D₁₁	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	11	2	no	—
369	C₂²	—	11	4	no	—
370	C₂²	—	22	2	no	—
371	C₂²	—	22	1	no	—
372	C₂²	—	22	1	no	—
373	C₂²	—	22	2	no	—
374	C₂²	—	44	8	no	—
375	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	1	no	—
378	C₄	—	11	2	no	—
379	C₄	—	22	2	no	—
380	C₄	—	22	1	no	—
381	C₄	—	22	1	no	—
382	C₄	D₁₁×M₃₂	1	2	yes	complemented
383	C₄	C₄×D₄×D₁₁	1	1	yes	characteristic
384	C₄	D₁₁×#131	1	1	yes	characteristic
385	C₂	—	4	2	no	—
386	C₂	—	22	2	no	—
387	C₂	—	22	4	no	—
388	C₂	C₈×D₄×D₁₁	1	1	yes	characteristic
389	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
390	C₂	#13081717	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2169	C₂
prime radical	C₂×D₄×D₁₁	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2169	D₁₁
hypocenter	C₁₁	D₄×M₃₂
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2169

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₁×M₃₂	C₂	semidirect
3. #13070448	C₂	semidirect
4. #13070444	C₂	semidirect
5. #13070439	C₂	semidirect
6. C₁₆×D₄₄	C₂	semidirect
7. #13070435	C₂	semidirect
8. #13070370	C₂	semidirect
9. #13070225	C₂	semidirect
10. C₄×#66862	C₂	semidirect
11. C₁₁×#2169	C₂	semidirect
14. C₂×C₁₁×M₃₂	C₂²	semidirect
17. C₂×#66876	C₂²	semidirect
23. C₂×C₁₆×D₁₁	C₂²	semidirect
24. C₂×C₁₆×D₁₁	C₂²	semidirect
31. C₁₁×C₄⋊C₁₆	C₂²	semidirect
32. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
33. C₄×C₁₁×C₁₆	C₂²	semidirect
34. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
35. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
36. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
37. #10622140	C₂²	semidirect
38. #10622140	C₂²	semidirect
39. Dic₁₁⋊C₁₆	C₂²	semidirect
40. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
41. C₄×C₁₁⋊C₁₆	C₂²	semidirect
83. #66862	D₄	semidirect
131. C₁₁×C₁₆	C₂×D₄	semidirect
134. C₁₁⋊C₁₆	C₂×D₄	semidirect
138. #2169	D₁₁	semidirect
165. D₄₄	M₃₂	semidirect
188. C₂×M₃₂	C₂×D₁₁	semidirect
202. C₄⋊C₁₆	C₂×D₁₁	semidirect
206. C₂²⋊C₁₆	C₂×D₁₁	semidirect
210. C₄×C₁₆	C₂×D₁₁	semidirect
221. C₂×D₁₁	C₂×M₃₂	semidirect
224. C₄×C₁₁	C₂×M₃₂	semidirect
328. C₁₆	D₄×D₁₁	semidirect
329. C₁₁	D₄×M₃₂	semidirect
382. C₄	D₁₁×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₁×M₃₂	2
C₈×D₄×D₁₁	2
#13070448	2
#13070444	2
#13070439	2
C₁₆×D₄₄	2
#13070435	2
#13070370	2
#13070225	2
C₄×#66862	2
C₁₁×#2169	2
D₄×M₃₂	11