Subgroups — C₁₁×#12515 #14589708

Order 2816.

398 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2246	C₂	1	4	yes	maximal, complemented
2	C₁₁×#1712	C₂	1	2	yes	maximal, complemented
3	C₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₁₆	—	2	8	no	—
5	C₁₁×#493	—	2	4	no	—
6	C₁₁×#493	C₂²	1	4	yes	—
7	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
8	C₈²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×D₈	—	2	8	no	—
10	C₂×C₁₁×D₈	—	4	8	no	—
11	C₁₁×#127	—	2	4	no	—
12	C₁₁×D₁₆	—	4	16	no	—
13	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
14	C₄×C₈×C₁₁	D₄	1	2	yes	—
15	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
16	#12515	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×D₄×C₁₁	—	4	4	no	—
18	C₂×D₄×C₁₁	—	4	8	no	—
19	C₁₁×D₈	—	4	16	no	—
20	C₁₁×D₈	—	8	16	no	—
21	C₂×C₈×C₁₁	D₈	1	4	yes	—
22	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
23	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₁₁×C₁₆	D₈	1	8	yes	complemented
25	#2246	C₂×C₁₁	1	4	yes	complemented
26	#1712	C₂×C₁₁	1	2	yes	complemented
27	C₈×C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
28	C₂³×C₁₁	—	8	4	no	—
29	D₄×C₁₁	—	8	8	no	—
30	D₄×C₁₁	—	8	16	no	—
31	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
32	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
33	C₈×C₁₁	D₁₆	1	8	yes	complemented
34	C₈×C₁₁	C₂×D₈	1	4	yes	—
35	C₂×D₁₆	—	2	8	no	—
36	#493	—	2	4	no	—
37	#493	C₂²×C₁₁	1	4	yes	—
38	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
39	C₈²	C₂²×C₁₁	1	1	yes	characteristic
40	C₂²×C₁₁	—	16	4	no	—
41	C₂²×C₁₁	—	16	8	no	—
42	C₂²×C₁₁	#493	1	1	yes	characteristic
43	C₄×C₁₁	#493	1	2	yes	—
44	C₄×C₁₁	C₂×D₁₆	1	4	yes	—
45	C₂×D₈	—	2	8	no	—
46	C₂×D₈	—	4	8	no	—
47	#127	—	2	4	no	—
48	D₁₆	—	4	16	no	—
49	C₂×C₁₆	D₄×C₁₁	1	4	yes	—
50	C₄×C₈	D₄×C₁₁	1	2	yes	—
51	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
52	C₂×C₁₁	—	32	4	no	—
53	C₂×C₁₁	#1712	1	1	yes	characteristic
54	C₂×C₁₁	#2246	1	2	yes	—
55	C₂×D₄	—	4	4	no	—
56	C₂×D₄	—	4	8	no	—
57	D₈	—	4	16	no	—
58	D₈	—	8	16	no	—
59	C₂×C₈	C₁₁×D₈	1	4	yes	—
60	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
61	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
62	C₁₆	C₁₁×D₈	1	8	yes	complemented
63	C₁₁	#12515	1	1	yes	characteristic, direct product factor, Sylow
64	C₂³	—	8	4	no	—
65	D₄	—	8	8	no	—
66	D₄	—	8	16	no	—
67	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
68	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
69	C₈	C₁₁×D₁₆	1	8	yes	complemented
70	C₈	C₂×C₁₁×D₈	1	4	yes	—
71	C₂²	—	16	4	no	—
72	C₂²	—	16	8	no	—
73	C₂²	C₁₁×#493	1	1	yes	characteristic
74	C₄	C₁₁×#493	1	2	yes	—
75	C₄	C₂×C₁₁×D₁₆	1	4	yes	—
76	C₂	—	32	4	no	—
77	C₂	C₁₁×#1712	1	1	yes	characteristic
78	C₂	C₁₁×#2246	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2246	C₂	semidirect
2. C₁₁×#1712	C₂	semidirect
3. C₈×C₁₁×C₁₆	C₂	semidirect
16. #12515	C₁₁	direct (N × H)
24. C₁₁×C₁₆	D₈	semidirect
25. #2246	C₂×C₁₁	semidirect
26. #1712	C₂×C₁₁	semidirect
27. C₈×C₁₆	C₂×C₁₁	semidirect
33. C₈×C₁₁	D₁₆	semidirect
62. C₁₆	C₁₁×D₈	semidirect
63. C₁₁	#12515	direct (N × H)
69. C₈	C₁₁×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#2246	2
C₁₁×#1712	2
C₈×C₁₁×C₁₆	2
#12515	11

Subgroups — C11×#12515 #14589708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#12515 #14589708