Subgroups — M₃₂×C₂²⋊D₁₁ #14906984

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 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	1	yes	maximal, characteristic, complemented
2	C₂×C₈×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic
3	#13070446	C₂	1	2	yes	maximal, complemented
4	#13070441	C₂	1	2	yes	maximal, complemented
5	#13070439	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₁₁	C₂	1	2	yes	maximal, complemented
7	#13070371	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070227	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070226	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×M₃₂	—	2	4	no	—
16	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×M₃₂	C₂²	1	2	yes	complemented
19	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₁₁)⋊C₈	C₄	1	1	yes	characteristic
30	C₂×Dic₁₁⋊C₈	C₄	1	1	yes	characteristic
31	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
32	C₂×#66876	C₂²	1	1	yes	characteristic
33	C₂×#66876	C₂²	1	1	yes	characteristic
34	D₁₁×M₃₂	—	2	4	no	—
35	C₂×#66862	C₂²	1	2	yes	complemented
36	C₂×C₁₆×D₁₁	C₂²	1	2	yes	complemented
37	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
38	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
39	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
40	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
41	#10622140	C₂²	1	2	yes	complemented
42	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
43	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
44	C₁₆×Dic₁₁	C₂²	1	2	yes	complemented
45	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
47	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	—	2	2	no	—
49	C₂²×C₈×C₁₁	—	2	2	no	—
50	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₂²⋊Dic₁₁	C₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂×(C₂×D₁₁)⋊C₄	C₈	1	1	yes	characteristic
66	C₂×Dic₁₁⋊C₄	C₈	1	1	yes	characteristic
67	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₁	—	2	2	no	—
71	C₂×C₈×D₁₁	—	2	2	no	—
72	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×M₃₂	—	2	2	no	—
77	C₁₁×M₃₂	—	2	4	no	—
78	C₁₁×M₃₂	D₄	1	4	yes	complemented
79	C₂×C₁₁×C₁₆	—	2	4	no	—
80	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
81	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
82	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
86	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
87	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
88	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
89	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
90	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
97	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
98	#66876	—	2	2	no	—
99	#66876	—	2	2	no	—
100	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
101	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
102	#66862	—	2	4	no	—
103	C₁₆×D₁₁	—	2	4	no	—
104	D₄×M₃₂	—	11	1	no	maximal, Sylow
105	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
106	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₁	—	2	4	no	—
116	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₁₁	—	2	2	no	—
124	C₂×C₄×D₁₁	—	2	2	no	—
125	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
127	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	2	2	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₁	#41	1	2	yes	—
141	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
142	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
145	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
146	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
147	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
148	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
149	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
150	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
151	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
152	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
153	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₁₁⋊C₈	—	2	2	no	—
159	C₂×C₁₁⋊C₈	—	2	2	no	—
160	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₁₁	—	2	2	no	—
165	C₈×D₁₁	—	2	2	no	—
166	C₈×D₁₁	—	2	1	no	—
167	C₈×D₁₁	—	2	1	no	—
168	C₈×D₁₁	—	2	1	no	—
169	C₈×D₁₁	—	2	1	no	—
170	C₁₁×C₁₆	—	2	2	no	—
171	C₁₁×C₁₆	C₂×D₄	1	4	yes	complemented
172	C₁₁⋊C₁₆	—	2	2	no	—
173	C₁₁⋊C₁₆	—	2	2	no	—
174	C₂²×M₃₂	—	11	1	no	—
175	C₂²×M₃₂	D₁₁	1	1	yes	characteristic, complemented
176	C₂×C₈×D₄	—	11	1	no	—
177	#2169	—	11	2	no	—
178	#2168	—	11	2	no	—
179	#2168	—	11	2	no	—
180	D₄×C₁₆	—	11	2	no	—
181	#2150	—	11	1	no	—
182	#2112	—	11	1	no	—
183	#2112	—	11	1	no	—
184	C₄×M₃₂	—	11	1	no	—
185	C₂³×C₁₁	—	2	2	no	—
186	C₂³×C₁₁	—	2	2	no	—
187	C₂³×C₁₁	—	4	1	no	—
188	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
189	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
190	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
191	C₂²×D₁₁	—	2	2	no	—
192	C₂²×D₁₁	—	2	2	no	—
193	C₂²×D₁₁	—	4	1	no	—
194	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
195	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
207	C₂×C₄×C₁₁	#131	1	2	yes	—
208	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
209	C₂²⋊D₁₁	—	2	2	no	—
210	C₂²⋊D₁₁	—	2	2	no	—
211	C₂²⋊D₁₁	—	2	2	no	—
212	C₂²⋊D₁₁	M₃₂	1	4	yes	direct product factor
213	C₂×Dic₁₁	—	2	2	no	—
214	C₂×Dic₁₁	—	2	2	no	—
215	C₂×Dic₁₁	—	4	1	no	—
216	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
217	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
219	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
220	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
221	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
222	C₄×D₁₁	—	2	1	no	—
223	C₄×D₁₁	—	2	1	no	—
224	C₄×D₁₁	—	2	1	no	—
225	C₄×D₁₁	—	2	1	no	—
226	C₄×D₁₁	—	2	2	no	—
227	C₄×D₁₁	—	2	2	no	—
228	C₈×C₁₁	—	2	1	no	—
229	C₈×C₁₁	—	2	1	no	—
230	C₈×C₁₁	C₄×D₄	1	2	yes	—
231	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
233	C₁₁⋊C₈	—	2	1	no	—
234	C₁₁⋊C₈	—	2	1	no	—
235	C₁₁⋊C₈	—	2	1	no	—
236	C₁₁⋊C₈	—	2	1	no	—
237	C₂³×C₈	—	11	1	no	—
238	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
239	C₂×C₄×D₄	—	11	1	no	—
240	C₂×M₃₂	—	2	4	no	—
241	C₂×M₃₂	—	11	1	no	—
242	C₂×M₃₂	—	11	1	no	—
243	C₂×M₃₂	—	11	2	no	—
244	C₂×M₃₂	—	22	4	no	—
245	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
246	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
247	C₂×M₃₂	C₂×D₁₁	1	2	yes	complemented
248	C₂²×C₁₆	—	11	2	no	—
249	C₂²×C₁₆	C₂×D₁₁	1	2	yes	complemented
250	C₈×D₄	—	11	1	no	—
251	C₈×D₄	—	11	1	no	—
252	C₈×D₄	—	11	1	no	—
253	C₈×D₄	—	11	1	no	—
254	C₈×D₄	—	11	1	no	—
255	C₈×D₄	—	11	1	no	—
256	C₈×D₄	—	11	1	no	—
257	C₈×D₄	—	11	1	no	—
258	C₂×C₄⋊C₈	—	11	1	no	—
259	C₂×C₂²⋊C₈	—	11	1	no	—
260	C₂×C₂²⋊C₈	—	11	1	no	—
261	C₂×C₄×C₈	—	11	1	no	—
262	C₄⋊C₁₆	—	11	2	no	—
263	C₄⋊C₁₆	—	11	2	no	—
264	C₂²⋊C₁₆	—	11	2	no	—
265	C₂²⋊C₁₆	—	11	2	no	—
266	C₂²⋊C₁₆	—	11	2	no	—
267	C₂²⋊C₁₆	—	11	2	no	—
268	#346	—	11	2	no	—
269	C₄×C₁₆	—	11	2	no	—
270	C₂²×C₁₁	—	2	1	no	—
271	C₂²×C₁₁	—	2	1	no	—
272	C₂²×C₁₁	—	2	1	no	—
273	C₂²×C₁₁	—	2	1	no	—
274	C₂²×C₁₁	—	2	1	no	—
275	C₂²×C₁₁	—	2	1	no	—
276	C₂²×C₁₁	—	2	1	no	—
277	C₂²×C₁₁	—	4	4	no	—
278	C₂²×C₁₁	C₈×D₄	1	2	yes	—
279	C₂²×C₁₁	C₂×M₃₂	1	2	yes	complemented
280	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
281	C₂×D₁₁	—	2	1	no	—
282	C₂×D₁₁	—	2	1	no	—
283	C₂×D₁₁	—	2	1	no	—
284	C₂×D₁₁	—	2	1	no	—
285	C₂×D₁₁	—	2	1	no	—
286	C₂×D₁₁	—	4	4	no	—
287	C₂×D₁₁	C₂×M₃₂	1	2	yes	complemented
288	C₄×C₁₁	—	2	1	no	—
289	C₄×C₁₁	—	2	1	no	—
290	C₄×C₁₁	C₈×D₄	1	2	yes	—
291	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
293	Dic₁₁	—	2	1	no	—
294	Dic₁₁	—	2	1	no	—
295	Dic₁₁	—	2	1	no	—
296	Dic₁₁	—	2	1	no	—
297	Dic₁₁	—	2	1	no	—
298	Dic₁₁	C₂×M₃₂	1	2	yes	complemented
299	C₂²×D₄	—	11	1	no	—
300	C₂³×C₄	—	11	1	no	—
301	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	11	1	no	—
305	C₂²×C₈	—	11	1	no	—
306	C₂²×C₈	—	11	1	no	—
307	C₂²×C₈	—	11	1	no	—
308	C₂²×C₈	—	11	1	no	—
309	C₂²×C₈	—	11	1	no	—
310	C₂²×C₈	—	22	2	no	—
311	C₂²×C₈	—	22	2	no	—
312	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
313	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
314	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
315	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
316	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
318	C₄×D₄	—	11	1	no	—
319	C₄×D₄	—	11	1	no	—
320	C₄×D₄	—	11	1	no	—
321	C₄×D₄	—	11	1	no	—
322	C₄×D₄	—	11	1	no	—
323	C₄×D₄	—	11	1	no	—
324	C₄×D₄	—	11	1	no	—
325	C₄×D₄	—	11	1	no	—
326	C₂×C₄⋊C₄	—	11	1	no	—
327	C₂×C₂²⋊C₄	—	11	1	no	—
328	C₂×C₂²⋊C₄	—	11	1	no	—
329	C₂×C₄²	—	11	1	no	—
330	M₃₂	—	2	2	no	—
331	M₃₂	—	2	4	no	—
332	M₃₂	—	22	2	no	—
333	M₃₂	—	22	2	no	—
334	M₃₂	—	22	4	no	—
335	M₃₂	C₂²⋊D₁₁	1	4	yes	direct product factor
336	C₂×C₁₆	—	2	4	no	—
337	C₂×C₁₆	—	11	2	no	—
338	C₂×C₁₆	—	11	2	no	—
339	C₂×C₁₆	—	22	4	no	—
340	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
341	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
342	C₄⋊C₈	—	11	1	no	—
343	C₄⋊C₈	—	11	1	no	—
344	C₄⋊C₈	—	11	1	no	—
345	C₄⋊C₈	—	11	1	no	—
346	C₂²⋊C₈	—	11	1	no	—
347	C₂²⋊C₈	—	11	1	no	—
348	C₂²⋊C₈	—	11	1	no	—
349	C₂²⋊C₈	—	11	1	no	—
350	C₂²⋊C₈	—	11	1	no	—
351	C₂²⋊C₈	—	11	1	no	—
352	C₂²⋊C₈	—	11	1	no	—
353	C₂²⋊C₈	—	11	1	no	—
354	C₄×C₈	—	11	1	no	—
355	C₄×C₈	—	11	1	no	—
356	C₄×C₈	—	11	1	no	—
357	C₄×C₈	—	11	1	no	—
358	C₂×C₁₁	—	2	2	no	—
359	C₂×C₁₁	—	2	2	no	—
360	C₂×C₁₁	—	4	1	no	—
361	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
362	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
363	C₂×C₁₁	#3407	1	1	yes	characteristic
364	D₁₁	—	2	2	no	—
365	D₁₁	—	4	1	no	—
366	C₂⁴	—	11	1	no	—
367	C₂⁴	C₈×D₁₁	1	1	yes	characteristic
368	C₂×D₄	—	11	1	no	—
369	C₂×D₄	—	11	1	no	—
370	C₂×D₄	—	11	1	no	—
371	C₂×D₄	—	11	1	no	—
372	C₂×D₄	—	22	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	11	1	no	—
376	C₂²×C₄	—	11	1	no	—
377	C₂²×C₄	—	11	1	no	—
378	C₂²×C₄	—	11	1	no	—
379	C₂²×C₄	—	11	1	no	—
380	C₂²×C₄	—	11	1	no	—
381	C₂²×C₄	—	11	1	no	—
382	C₂²×C₄	—	22	2	no	—
383	C₂²×C₄	—	22	2	no	—
384	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
385	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
386	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	11	1	no	—
398	C₂×C₈	—	11	1	no	—
399	C₂×C₈	—	11	1	no	—
400	C₂×C₈	—	11	1	no	—
401	C₂×C₈	—	22	2	no	—
402	C₂×C₈	—	22	2	no	—
403	C₂×C₈	—	22	2	no	—
404	C₂×C₈	—	22	2	no	—
405	C₂×C₈	—	22	1	no	—
406	C₂×C₈	—	22	1	no	—
407	C₂×C₈	—	22	1	no	—
408	C₂×C₈	—	22	1	no	—
409	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
410	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
411	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
412	C₂×C₈	#4339	1	2	yes	—
413	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
414	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
415	C₄⋊C₄	—	11	1	no	—
416	C₄⋊C₄	—	11	1	no	—
417	C₄⋊C₄	—	11	1	no	—
418	C₄⋊C₄	—	11	1	no	—
419	C₂²⋊C₄	—	11	1	no	—
420	C₂²⋊C₄	—	11	1	no	—
421	C₂²⋊C₄	—	11	1	no	—
422	C₂²⋊C₄	—	11	1	no	—
423	C₂²⋊C₄	—	11	1	no	—
424	C₂²⋊C₄	—	11	1	no	—
425	C₂²⋊C₄	—	11	1	no	—
426	C₂²⋊C₄	—	11	1	no	—
427	C₄²	—	11	1	no	—
428	C₄²	—	11	1	no	—
429	C₄²	—	11	1	no	—
430	C₄²	—	11	1	no	—
431	C₁₆	—	2	2	no	—
432	C₁₆	—	22	2	no	—
433	C₁₆	—	22	2	no	—
434	C₁₆	C₂×C₂²⋊D₁₁	1	4	yes	complemented
435	C₁₁	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	11	1	no	—
440	C₂³	—	11	1	no	—
441	C₂³	—	22	2	no	—
442	C₂³	—	22	2	no	—
443	C₂³	—	44	1	no	—
444	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
445	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
446	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
447	D₄	—	11	4	no	—
448	D₄	—	22	2	no	—
449	D₄	—	22	2	no	—
450	D₄	—	22	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	11	1	no	—
459	C₂×C₄	—	11	1	no	—
460	C₂×C₄	—	11	1	no	—
461	C₂×C₄	—	11	1	no	—
462	C₂×C₄	—	11	1	no	—
463	C₂×C₄	—	11	1	no	—
464	C₂×C₄	—	22	2	no	—
465	C₂×C₄	—	22	2	no	—
466	C₂×C₄	—	22	2	no	—
467	C₂×C₄	—	22	2	no	—
468	C₂×C₄	—	22	1	no	—
469	C₂×C₄	—	22	1	no	—
470	C₂×C₄	—	22	1	no	—
471	C₂×C₄	—	22	1	no	—
472	C₂×C₄	—	44	1	no	—
473	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
474	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
475	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
476	C₂×C₄	#66954	1	2	yes	—
477	C₂×C₄	C₄×C₂²⋊D₁₁	1	2	yes	—
478	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	22	1	no	—
482	C₈	—	22	1	no	—
483	C₈	—	22	1	no	—
484	C₈	—	22	1	no	—
485	C₈	C₄×C₂²⋊D₁₁	1	2	yes	—
486	C₈	C₂×#4339	1	1	yes	characteristic
487	C₈	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	11	2	no	—
497	C₂²	—	22	1	no	—
498	C₂²	—	22	1	no	—
499	C₂²	—	22	1	no	—
500	C₂²	—	22	1	no	—
501	C₂²	—	22	1	no	—
502	C₂²	—	44	4	no	—
503	C₂²	D₁₁×M₃₂	1	2	yes	complemented
504	C₂²	C₈×C₂²⋊D₁₁	1	2	yes	—
505	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	11	2	no	—
509	C₄	—	22	1	no	—
510	C₄	—	22	1	no	—
511	C₄	—	22	1	no	—
512	C₄	—	22	1	no	—
513	C₄	—	22	1	no	—
514	C₄	C₈×C₂²⋊D₁₁	1	2	yes	—
515	C₄	C₂×#66954	1	1	yes	characteristic
516	C₄	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	22	2	no	—
521	C₂	—	44	1	no	—
522	C₂	C₂×C₈×C₂²⋊D₁₁	1	1	yes	characteristic
523	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
524	C₂	#13081718	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₁×M₃₂	C₂	semidirect
3. #13070446	C₂	semidirect
4. #13070441	C₂	semidirect
5. #13070439	C₂	semidirect
6. C₁₆×C₂²⋊D₁₁	C₂	semidirect
7. #13070371	C₂	semidirect
8. #13070227	C₂	semidirect
9. #13070226	C₂	semidirect
10. M₃₂×Dic₁₁	C₂	semidirect
11. C₂²×C₁₁×M₃₂	C₂	semidirect
18. C₂×C₁₁×M₃₂	C₂²	semidirect
19. C₂²×C₁₁×C₁₆	C₂²	semidirect
35. C₂×#66862	C₂²	semidirect
36. C₂×C₁₆×D₁₁	C₂²	semidirect
37. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
38. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
39. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
40. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
41. #10622140	C₂²	semidirect
42. Dic₁₁⋊C₁₆	C₂²	semidirect
43. Dic₁₁⋊C₁₆	C₂²	semidirect
44. C₁₆×Dic₁₁	C₂²	semidirect
78. C₁₁×M₃₂	D₄	semidirect
171. C₁₁×C₁₆	C₂×D₄	semidirect
175. C₂²×M₃₂	D₁₁	semidirect
212. C₂²⋊D₁₁	M₃₂	direct (N × H)
247. C₂×M₃₂	C₂×D₁₁	semidirect
249. C₂²×C₁₆	C₂×D₁₁	semidirect
279. C₂²×C₁₁	C₂×M₃₂	semidirect
287. C₂×D₁₁	C₂×M₃₂	semidirect
298. Dic₁₁	C₂×M₃₂	semidirect
335. M₃₂	C₂²⋊D₁₁	direct (N × H)
434. C₁₆	C₂×C₂²⋊D₁₁	semidirect
435. C₁₁	D₄×M₃₂	semidirect
503. C₂²	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
C₂×C₈×C₂²⋊D₁₁	2
#13070446	2
#13070441	2
#13070439	2
C₁₆×C₂²⋊D₁₁	2
#13070371	2
#13070227	2
#13070226	2
M₃₂×Dic₁₁	2
C₂²×C₁₁×M₃₂	2
D₄×M₃₂	11

Subgroups — M32×C22⋊D11 #14906984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×C₂²⋊D₁₁ #14906984