Subgroups — C₂×C₁₁×#2162 #14610608

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2162	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₁₁×C₄⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₁×C₂²⋊C₁₆	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₁×C₁₆	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₁₁	C₄	1	1	yes	characteristic
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₁	C₄	1	1	yes	characteristic
9	C₂²×C₁₁×C₁₆	C₂²	1	4	yes	—
10	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×C₄⋊C₁₆	C₂²	1	8	yes	complemented
17	C₁₁×C₂²⋊C₁₆	C₂²	1	8	yes	—
18	C₄×C₁₁×C₁₆	C₂²	1	8	yes	complemented
19	C₂³×C₄×C₁₁	C₈	1	1	yes	characteristic
20	C₂³×C₄×C₁₁	C₈	1	1	yes	characteristic
21	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	—	2	4	no	—
23	C₂²×C₈×C₁₁	—	2	4	no	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
30	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₈	1	4	yes	—
33	C₂×C₄²×C₁₁	C₈	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₁×C₁₆	—	2	8	no	—
38	C₂×C₁₁×C₁₆	C₂³	1	8	yes	—
39	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
40	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₁	C₂³	1	2	yes	—
44	C₄×C₈×C₁₁	C₂³	1	2	yes	—
45	C₂×#2162	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	—	2	4	no	—
48	C₂²×C₄×C₁₁	—	2	2	no	—
49	C₂²×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₄×C₁₁	C₁₆	1	8	yes	complemented
51	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
55	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
58	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	8	no	—
63	C₂×C₈×C₁₁	—	2	4	no	—
64	C₂×C₈×C₁₁	—	2	2	no	—
65	C₂×C₈×C₁₁	—	2	2	no	—
66	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
67	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
69	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
71	C₂×C₈×C₁₁	#41	1	4	yes	—
72	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×C₈	1	4	yes	—
74	C₄²×C₁₁	C₂×C₈	1	4	yes	—
75	C₄²×C₁₁	C₂×C₈	1	2	yes	—
76	C₄²×C₁₁	C₂×C₈	1	2	yes	—
77	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
78	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
79	C₁₁×C₁₆	—	2	8	no	—
80	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
81	#2162	C₂×C₁₁	1	8	yes	direct product factor
82	C₂×C₄⋊C₁₆	C₂×C₁₁	1	2	yes	complemented
83	C₂×C₂²⋊C₁₆	C₂×C₁₁	1	2	yes	—
84	C₂×C₄×C₁₆	C₂×C₁₁	1	2	yes	complemented
85	C₂³×C₁₁	—	2	2	no	—
86	C₂³×C₁₁	—	2	2	no	—
87	C₂³×C₁₁	C₂×C₁₆	1	4	yes	—
88	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
89	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	2	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	4	no	—
95	C₂×C₄×C₁₁	—	2	8	no	—
96	C₂×C₄×C₁₁	C₂×C₁₆	1	4	yes	—
97	C₂×C₄×C₁₁	C₂×C₁₆	1	4	yes	—
98	C₂×C₄×C₁₁	C₂×C₁₆	1	16	yes	complemented
99	C₂×C₄×C₁₁	M₃₂	1	4	yes	—
100	C₂×C₄×C₁₁	#117	1	2	yes	—
101	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
102	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
103	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
105	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
106	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
107	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
108	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
109	C₈×C₁₁	—	2	2	no	—
110	C₈×C₁₁	—	2	2	no	—
111	C₈×C₁₁	#117	1	2	yes	—
112	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
113	C₈×C₁₁	C₂×#41	1	2	yes	—
114	C₂³×C₈	C₄×C₁₁	1	1	yes	characteristic
115	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
116	C₂²×C₄²	C₄×C₁₁	1	1	yes	characteristic
117	C₂²×C₁₆	C₂²×C₁₁	1	4	yes	—
118	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
119	C₂×C₄×C₈	C₄×C₁₁	1	4	yes	—
120	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
121	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
124	C₄⋊C₁₆	C₂²×C₁₁	1	8	yes	complemented
125	C₂²⋊C₁₆	C₂²×C₁₁	1	8	yes	—
126	C₄×C₁₆	C₂²×C₁₁	1	8	yes	complemented
127	C₂²×C₁₁	—	2	2	no	—
128	C₂²×C₁₁	—	2	2	no	—
129	C₂²×C₁₁	—	2	8	no	—
130	C₂²×C₁₁	#431	1	2	yes	—
131	C₂²×C₁₁	C₂²×C₁₆	1	4	yes	—
132	C₂²×C₁₁	C₂²×C₁₆	1	2	yes	—
133	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
134	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	—	2	2	no	—
137	C₄×C₁₁	#431	1	2	yes	—
138	C₄×C₁₁	C₂²×C₁₆	1	4	yes	—
139	C₄×C₁₁	C₂²×C₁₆	1	4	yes	—
140	C₄×C₁₁	C₂×M₃₂	1	4	yes	—
141	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
142	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
143	C₂³×C₄	C₈×C₁₁	1	1	yes	characteristic
144	C₂³×C₄	C₈×C₁₁	1	1	yes	characteristic
145	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
146	C₂²×C₈	—	2	4	no	—
147	C₂²×C₈	—	2	4	no	—
148	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
149	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
150	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
151	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
152	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
153	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
154	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
155	C₂×C₄²	C₈×C₁₁	1	1	yes	characteristic
156	C₂×C₄²	C₈×C₁₁	1	4	yes	—
157	C₂×C₄²	C₈×C₁₁	1	1	yes	characteristic
158	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
159	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
160	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
161	C₂×C₁₆	—	2	8	no	—
162	C₂×C₁₆	C₂³×C₁₁	1	8	yes	—
163	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
164	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
165	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
166	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
167	C₄×C₈	C₂³×C₁₁	1	2	yes	—
168	C₄×C₈	C₂³×C₁₁	1	2	yes	—
169	C₂×C₁₁	—	2	4	no	—
170	C₂×C₁₁	#2162	1	4	yes	direct product factor
171	C₂×C₁₁	C₂×#431	1	1	yes	characteristic
172	C₂×C₁₁	C₂³×C₁₆	1	1	yes	characteristic
173	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
174	C₂⁴	C₂×C₈×C₁₁	1	1	yes	characteristic
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	C₁₁×C₁₆	1	8	yes	complemented
179	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₈×C₁₁	1	4	yes	—
181	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
183	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
184	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₈×C₁₁	1	4	yes	—
186	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
187	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
188	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	2	8	no	—
193	C₂×C₈	—	2	4	no	—
194	C₂×C₈	C₁₁×M₁₆	1	4	yes	—
195	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
196	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
197	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
198	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
199	C₂×C₈	C₁₁×#41	1	4	yes	—
200	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
201	C₄²	C₂×C₈×C₁₁	1	4	yes	—
202	C₄²	C₂×C₈×C₁₁	1	4	yes	—
203	C₄²	C₂×C₈×C₁₁	1	2	yes	—
204	C₄²	C₂×C₈×C₁₁	1	2	yes	—
205	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
206	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
207	C₁₆	—	2	8	no	—
208	C₁₁	C₂×#2162	1	1	yes	characteristic, direct product factor, Sylow
209	C₂³	—	2	2	no	—
210	C₂³	—	2	2	no	—
211	C₂³	C₂×C₁₁×C₁₆	1	4	yes	—
212	C₂³	C₂²×C₈×C₁₁	1	2	yes	—
213	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	8	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	C₂×C₁₁×C₁₆	1	4	yes	—
221	C₂×C₄	C₂×C₁₁×C₁₆	1	4	yes	—
222	C₂×C₄	C₂×C₁₁×C₁₆	1	16	yes	complemented
223	C₂×C₄	C₁₁×M₃₂	1	4	yes	—
224	C₂×C₄	C₁₁×#117	1	2	yes	—
225	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
226	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
227	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
228	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
229	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
230	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
231	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
232	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
233	C₈	—	2	2	no	—
234	C₈	—	2	2	no	—
235	C₈	C₁₁×#117	1	2	yes	—
236	C₈	C₂×C₁₁×M₁₆	1	4	yes	—
237	C₈	C₂×C₁₁×#41	1	2	yes	—
238	C₂²	—	2	2	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	2	8	no	—
241	C₂²	C₁₁×#431	1	2	yes	—
242	C₂²	C₂²×C₁₁×C₁₆	1	4	yes	—
243	C₂²	C₂²×C₁₁×C₁₆	1	2	yes	—
244	C₂²	C₂×C₁₁×M₃₂	1	2	yes	—
245	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	C₁₁×#431	1	2	yes	—
249	C₄	C₂²×C₁₁×C₁₆	1	4	yes	—
250	C₄	C₂²×C₁₁×C₁₆	1	4	yes	—
251	C₄	C₂×C₁₁×M₃₂	1	4	yes	—
252	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
253	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
254	C₂	—	2	4	no	—
255	C₂	C₁₁×#2162	1	4	yes	direct product factor
256	C₂	C₂×C₁₁×#431	1	1	yes	characteristic
257	C₂	C₂³×C₁₁×C₁₆	1	1	yes	characteristic
258	C₂	C₂²×C₁₁×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈×C₁₁	C₂²
commutator	C₂	C₂³×C₁₁×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂²×C₈
prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2162	C₂	direct (N × H)
3. C₂×C₁₁×C₄⋊C₁₆	C₂	semidirect
5. C₂×C₄×C₁₁×C₁₆	C₂	semidirect
16. C₁₁×C₄⋊C₁₆	C₂²	semidirect
18. C₄×C₁₁×C₁₆	C₂²	semidirect
45. C₂×#2162	C₁₁	direct (N × H)
50. C₂²×C₄×C₁₁	C₁₆	semidirect
81. #2162	C₂×C₁₁	direct (N × H)
82. C₂×C₄⋊C₁₆	C₂×C₁₁	semidirect
84. C₂×C₄×C₁₆	C₂×C₁₁	semidirect
98. C₂×C₄×C₁₁	C₂×C₁₆	semidirect
124. C₄⋊C₁₆	C₂²×C₁₁	semidirect
126. C₄×C₁₆	C₂²×C₁₁	semidirect
170. C₂×C₁₁	#2162	direct (N × H)
178. C₂²×C₄	C₁₁×C₁₆	semidirect
208. C₁₁	C₂×#2162	direct (N × H)
222. C₂×C₄	C₂×C₁₁×C₁₆	semidirect
255. C₂	C₁₁×#2162	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈×C₁₁	2
C₁₁×#2162	2
C₂×C₁₁×C₄⋊C₁₆	2
C₂×C₁₁×C₂²⋊C₁₆	2
C₂×C₄×C₁₁×C₁₆	2
C₂×#2162	11

Subgroups — C2×C11×#2162 #14610608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2162 #14610608