Subgroups — C₁₁×#1275 #13064113

Order 1408.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#431	C₂	1	2	yes	maximal
2	C₂×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₁	C₄	1	2	yes	—
4	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
5	C₁₁×C₄⋊C₈	—	2	2	no	—
6	C₁₁×C₂²⋊C₈	—	2	2	no	—
7	C₁₁×#97	—	2	2	no	—
8	C₄×C₈×C₁₁	C₄	1	4	yes	—
9	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₁	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₁₁	—	2	2	no	—
13	C₂×C₈×C₁₁	—	2	4	no	—
14	C₂×C₈×C₁₁	—	2	2	no	—
15	C₂×C₈×C₁₁	C₈	1	4	yes	complemented
16	C₄²×C₁₁	C₂×C₄	1	2	yes	—
17	C₄²×C₁₁	D₄	1	2	yes	—
18	#1275	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₁₁	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₁	—	4	1	no	—
21	C₂×C₄×C₁₁	—	4	1	no	—
22	C₂×C₄×C₁₁	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₁	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₁	M₁₆	1	2	yes	—
28	C₈×C₁₁	—	2	4	no	—
29	C₈×C₁₁	—	4	4	no	—
30	#431	C₂×C₁₁	1	2	yes	—
31	C₂×#97	C₂×C₁₁	1	1	yes	characteristic
32	C₂²×C₁₁	—	2	1	no	—
33	C₂²×C₁₁	—	2	1	no	—
34	C₂²×C₁₁	#95	1	1	yes	characteristic
35	C₂²×C₁₁	C₄⋊C₈	1	2	yes	—
36	C₄×C₁₁	—	2	2	no	—
37	C₄×C₁₁	—	2	2	no	—
38	C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
39	C₄×C₁₁	#97	1	1	yes	characteristic
40	C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
41	C₂²×C₈	C₄×C₁₁	1	2	yes	—
42	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
43	C₄⋊C₈	—	2	2	no	—
44	C₂²⋊C₈	—	2	2	no	—
45	#97	—	2	2	no	—
46	C₄×C₈	C₄×C₁₁	1	4	yes	—
47	C₂×C₁₁	—	2	2	no	—
48	C₂×C₁₁	#336	1	1	yes	characteristic
49	C₂×C₁₁	H(3,ℤ/4)	1	1	yes	characteristic
50	C₂×C₁₁	#338	1	1	yes	characteristic
51	C₂²×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
52	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
53	C₂²×C₄	Q₈×C₁₁	1	1	yes	characteristic
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	2	4	no	—
57	C₂×C₈	C₈×C₁₁	1	4	yes	complemented
58	C₄²	C₂×C₄×C₁₁	1	2	yes	—
59	C₄²	D₄×C₁₁	1	2	yes	—
60	C₁₁	#1275	1	1	yes	characteristic, direct product factor, Sylow
61	C₂³	C₁₁×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄	—	4	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄²×C₁₁	1	1	yes	characteristic
65	C₂×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
66	C₂×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
68	C₂×C₄	C₂×C₈×C₁₁	1	2	yes	—
69	C₂×C₄	C₁₁×M₁₆	1	2	yes	—
70	C₈	—	2	4	no	—
71	C₈	—	4	4	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	C₁₁×#95	1	1	yes	characteristic
75	C₂²	C₁₁×C₄⋊C₈	1	2	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	2	2	no	—
78	C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
79	C₄	C₁₁×#97	1	1	yes	characteristic
80	C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
81	C₂	—	2	2	no	—
82	C₂	C₁₁×#336	1	1	yes	characteristic
83	C₂	C₁₁×H(3,ℤ/4)	1	1	yes	characteristic
84	C₂	C₁₁×#338	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₄²
commutator	C₄	C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄²	C₂²×C₁₁
socle	C₂²×C₁₁	#95
prime radical	C₂³×C₁₁	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₂×C₈×C₁₁	C₈	semidirect
18. #1275	C₁₁	direct (N × H)
57. C₂×C₈	C₈×C₁₁	semidirect
60. C₁₁	#1275	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#431	2
C₂×C₁₁×#97	2
#1275	11

Subgroups — C11×#1275 #13064113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1275 #13064113