Subgroups — C₂×C₁₁×#2150 #14610588

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×M₃₂	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2150	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₁×C₄⋊C₁₆	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₁₁	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄²×C₁₁	C₄	1	1	yes	characteristic
8	C₂×C₁₁×M₃₂	—	2	8	no	—
9	C₂×C₁₁×M₃₂	C₂²	1	8	yes	—
10	C₂²×C₁₁×C₁₆	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
15	C₁₁×C₄⋊C₁₆	C₂²	1	16	yes	complemented
16	C₂³×C₄×C₁₁	C₈	1	2	yes	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	—	2	4	no	—
19	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
20	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	D₄	1	4	yes	—
24	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	C₈	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	C₈	1	4	yes	—
29	C₂×C₄²×C₁₁	C₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
32	C₁₁×M₃₂	—	2	16	no	—
33	C₂×C₁₁×C₁₆	—	2	8	no	—
34	C₂×C₁₁×C₁₆	C₂³	1	8	yes	—
35	C₄×C₈×C₁₁	C₂×C₄	1	8	yes	—
36	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
37	C₄×C₈×C₁₁	C₂³	1	4	yes	—
38	C₂×#2150	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	—	2	8	no	—
41	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
42	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂×C₈	1	8	yes	—
44	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
45	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
47	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
48	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	—	2	8	no	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	C₄⋊C₄	1	8	yes	—
53	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
55	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
59	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
60	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
61	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
62	C₄²×C₁₁	C₂×C₈	1	4	yes	—
63	C₄²×C₁₁	C₂×C₈	1	4	yes	—
64	C₄²×C₁₁	C₂×C₈	1	4	yes	—
65	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
66	C₁₁×C₁₆	—	2	8	no	—
67	C₂²×M₃₂	C₂×C₁₁	1	2	yes	—
68	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
69	#2150	C₂×C₁₁	1	8	yes	direct product factor
70	C₂×C₄⋊C₁₆	C₂×C₁₁	1	4	yes	complemented
71	C₂³×C₁₁	—	2	4	no	—
72	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
73	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
74	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₁	—	2	4	no	—
76	C₂×C₄×C₁₁	—	2	16	no	—
77	C₂×C₄×C₁₁	C₄⋊C₈	1	8	yes	—
78	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
79	C₂×C₄×C₁₁	M₃₂	1	8	yes	complemented
80	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
81	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
82	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
83	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
84	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
86	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
87	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
88	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
89	C₈×C₁₁	—	2	4	no	—
90	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
91	C₈×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
92	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
93	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
94	C₂³×C₈	C₄×C₁₁	1	1	yes	characteristic
95	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
96	C₂²×C₄²	C₄×C₁₁	1	1	yes	characteristic
97	C₂×M₃₂	—	2	8	no	—
98	C₂×M₃₂	C₂²×C₁₁	1	8	yes	—
99	C₂²×C₁₆	C₂²×C₁₁	1	4	yes	—
100	C₂×C₄×C₈	C₄×C₁₁	1	4	yes	—
101	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
102	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
103	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
104	C₄⋊C₁₆	C₂²×C₁₁	1	16	yes	complemented
105	C₂²×C₁₁	—	2	4	no	—
106	C₂²×C₁₁	—	2	8	no	—
107	C₂²×C₁₁	C₂×C₄⋊C₈	1	4	yes	—
108	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
109	C₂²×C₁₁	C₂×M₃₂	1	4	yes	—
110	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
111	C₄×C₁₁	—	2	4	no	—
112	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
113	C₄×C₁₁	C₂×C₄⋊C₈	1	4	yes	—
114	C₄×C₁₁	C₂×M₃₂	1	8	yes	complemented
115	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
116	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
117	C₂³×C₄	C₈×C₁₁	1	2	yes	—
118	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
119	C₂²×C₈	—	2	4	no	—
120	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
121	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
122	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
123	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
124	C₂²×C₈	D₄×C₁₁	1	4	yes	—
125	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
126	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
127	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
128	C₂×C₄²	C₈×C₁₁	1	1	yes	characteristic
129	C₂×C₄²	C₈×C₁₁	1	4	yes	—
130	C₂×C₄²	C₈×C₁₁	1	1	yes	characteristic
131	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
132	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
133	M₃₂	—	2	16	no	—
134	C₂×C₁₆	—	2	8	no	—
135	C₂×C₁₆	C₂³×C₁₁	1	8	yes	—
136	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
137	C₄×C₈	C₂×C₄×C₁₁	1	8	yes	—
138	C₄×C₈	C₂³×C₁₁	1	4	yes	—
139	C₂×C₁₁	—	2	4	no	—
140	C₂×C₁₁	#2150	1	4	yes	direct product factor
141	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
142	C₂×C₁₁	C₂²×M₃₂	1	2	yes	—
143	C₂⁴	C₂×C₈×C₁₁	1	1	yes	characteristic
144	C₂²×C₄	—	2	8	no	—
145	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
146	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
147	C₂²×C₄	C₂×C₈×C₁₁	1	8	yes	—
148	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
149	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
151	C₂²×C₄	C₁₁×M₁₆	1	4	yes	—
152	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
153	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
154	C₂×C₈	—	2	8	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	C₁₁×C₄⋊C₄	1	8	yes	—
157	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
158	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
159	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
160	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
161	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
162	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
163	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
164	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
165	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
166	C₄²	C₂×C₈×C₁₁	1	4	yes	—
167	C₄²	C₂×C₈×C₁₁	1	4	yes	—
168	C₄²	C₂×C₈×C₁₁	1	4	yes	—
169	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
170	C₁₆	—	2	8	no	—
171	C₁₁	C₂×#2150	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	—	2	4	no	—
173	C₂³	C₁₁×C₄⋊C₈	1	4	yes	—
174	C₂³	C₂²×C₈×C₁₁	1	2	yes	—
175	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	16	no	—
178	C₂×C₄	C₁₁×C₄⋊C₈	1	8	yes	—
179	C₂×C₄	C₁₁×C₄⋊C₈	1	4	yes	—
180	C₂×C₄	C₁₁×M₃₂	1	8	yes	complemented
181	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
182	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
183	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
184	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
185	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
186	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
187	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
188	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
189	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
190	C₈	—	2	4	no	—
191	C₈	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
192	C₈	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
193	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
194	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
195	C₂²	—	2	4	no	—
196	C₂²	—	2	8	no	—
197	C₂²	C₂×C₁₁×C₄⋊C₈	1	4	yes	—
198	C₂²	C₂×C₁₁×C₄⋊C₈	1	2	yes	—
199	C₂²	C₂×C₁₁×M₃₂	1	4	yes	—
200	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
201	C₄	—	2	4	no	—
202	C₄	C₂×C₁₁×C₄⋊C₈	1	2	yes	—
203	C₄	C₂×C₁₁×C₄⋊C₈	1	4	yes	—
204	C₄	C₂×C₁₁×M₃₂	1	8	yes	complemented
205	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
206	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
207	C₂	—	2	4	no	—
208	C₂	C₁₁×#2150	1	4	yes	direct product factor
209	C₂	C₂²×C₁₁×C₄⋊C₈	1	1	yes	characteristic
210	C₂	C₂²×C₁₁×M₃₂	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2150	C₂	direct (N × H)
4. C₂×C₁₁×C₄⋊C₁₆	C₂	semidirect
15. C₁₁×C₄⋊C₁₆	C₂²	semidirect
38. C₂×#2150	C₁₁	direct (N × H)
69. #2150	C₂×C₁₁	direct (N × H)
70. C₂×C₄⋊C₁₆	C₂×C₁₁	semidirect
79. C₂×C₄×C₁₁	M₃₂	semidirect
104. C₄⋊C₁₆	C₂²×C₁₁	semidirect
114. C₄×C₁₁	C₂×M₃₂	semidirect
140. C₂×C₁₁	#2150	direct (N × H)
171. C₁₁	C₂×#2150	direct (N × H)
180. C₂×C₄	C₁₁×M₃₂	semidirect
204. C₄	C₂×C₁₁×M₃₂	semidirect
208. C₂	C₁₁×#2150	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×C₁₁×M₃₂	2
C₂²×C₄×C₈×C₁₁	2
C₁₁×#2150	2
C₂×C₁₁×C₄⋊C₁₆	2
C₂×#2150	11

Subgroups — C2×C11×#2150 #14610588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2150 #14610588