Subgroups — #14674812

Order 2816.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066827	C₂	1	3	yes	maximal, complemented
2	C₂×C₁₁⋊C₆₄	C₂	1	3	yes	maximal, complemented
3	C₁₁×#2258	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#504	C₄	1	1	yes	characteristic
5	C₁₁×M₆₄	C₄	1	3	yes	—
6	C₂×C₁₁×C₃₂	C₂²	1	3	yes	—
7	C₁₁⋊C₆₄	C₂²	1	1	yes	characteristic
8	C₁₁⋊C₆₄	C₂²	1	3	yes	—
9	C₁₁×#131	C₈	1	1	yes	characteristic
10	C₁₁×M₃₂	C₈	1	3	yes	—
11	C₂×C₁₁×C₁₆	C₂×C₄	1	3	yes	—
12	C₁₁×C₃₂	C₂×C₄	1	3	yes	—
13	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
14	#13737	—	11	1	no	maximal, Sylow
15	C₁₁×#41	C₁₆	1	1	yes	characteristic
16	C₁₁×M₁₆	C₁₆	1	3	yes	—
17	C₂×C₈×C₁₁	C₂×C₈	1	3	yes	—
18	C₁₁×C₁₆	C₂×C₈	1	3	yes	—
19	C₁₁×C₁₆	C₂²×C₄	1	1	yes	characteristic
20	#2258	D₁₁	1	1	yes	characteristic
21	M₁₂₈	—	11	3	no	—
22	C₂×C₆₄	—	11	3	no	—
23	Q₈×C₁₁	C₃₂	1	1	yes	characteristic
24	D₄×C₁₁	C₃₂	1	3	yes	—
25	C₂×C₄×C₁₁	C₂×C₁₆	1	3	yes	—
26	C₈×C₁₁	C₂×C₁₆	1	3	yes	—
27	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
28	#504	Dic₁₁	1	1	yes	characteristic
29	M₆₄	Dic₁₁	1	3	yes	—
30	C₂×C₃₂	C₂×D₁₁	1	3	yes	—
31	C₆₄	—	11	1	no	—
32	C₆₄	—	11	3	no	—
33	C₂²×C₁₁	C₂×C₃₂	1	3	yes	—
34	C₄×C₁₁	C₂×C₃₂	1	3	yes	—
35	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
36	#131	C₁₁⋊C₈	1	1	yes	characteristic
37	M₃₂	C₁₁⋊C₈	1	3	yes	—
38	C₂×C₁₆	C₂×Dic₁₁	1	3	yes	—
39	C₃₂	C₂×Dic₁₁	1	3	yes	—
40	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
41	C₂×C₁₁	—	2	3	no	—
42	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
43	#41	C₁₁⋊C₁₆	1	1	yes	characteristic
44	M₁₆	C₁₁⋊C₁₆	1	3	yes	—
45	C₂×C₈	C₂×C₁₁⋊C₈	1	3	yes	—
46	C₁₆	C₂×C₁₁⋊C₈	1	3	yes	—
47	C₁₆	C₂²×Dic₁₁	1	1	yes	characteristic
48	C₁₁	#13737	1	1	yes	characteristic, complemented, Sylow
49	Q₈	C₁₁⋊C₃₂	1	1	yes	characteristic
50	D₄	C₁₁⋊C₃₂	1	3	yes	—
51	C₂×C₄	C₂×C₁₁⋊C₁₆	1	3	yes	—
52	C₈	C₂×C₁₁⋊C₁₆	1	3	yes	—
53	C₈	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
54	C₂²	C₂×C₁₁⋊C₃₂	1	3	yes	—
55	C₄	C₂×C₁₁⋊C₃₂	1	3	yes	—
56	C₄	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×C₁₁⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃₂	C₂²×D₁₁
commutator, socle	C₂×C₁₁	C₂²×C₃₂
Fitting	C₁₁×#2258	C₂
prime radical	C₁₁×#41	C₁₆
cosocle	C₁₁×C₃₂	C₂³
hypercenter	#2258	D₁₁
hypocenter	C₁₁	#13737
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₃₂ ◁ #2258

Complements

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

N	H ≅ G/N	type
1. #13066827	C₂	semidirect
2. C₂×C₁₁⋊C₆₄	C₂	semidirect
48. C₁₁	#13737	semidirect

Maximal subgroups

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

subgroup	index
#13066827	2
C₂×C₁₁⋊C₆₄	2
C₁₁×#2258	2
#13737	11