Subgroups — #14641586

Order 2816.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066827	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2258	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#504	C₄	1	1	yes	characteristic
5	C₁₁×M₆₄	—	2	1	no	—
6	C₁₁×M₆₄	C₄	1	1	yes	characteristic
7	C₂×C₁₁×C₃₂	—	2	1	no	—
8	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
9	C₁₁⋊C₆₄	—	2	1	no	—
10	C₁₁⋊C₆₄	—	2	1	no	—
11	C₁₁×#131	C₈	1	1	yes	characteristic
12	C₁₁×M₃₂	—	2	1	no	—
13	C₁₁×M₃₂	C₈	1	1	yes	characteristic
14	C₂×C₁₁×C₁₆	—	2	1	no	—
15	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₃₂	—	2	1	no	—
17	C₁₁×C₃₂	D₄	1	1	yes	characteristic
18	C₁₁×C₃₂	D₄	1	1	yes	characteristic
19	#7514	—	11	1	no	maximal, Sylow
20	C₁₁×#41	C₁₆	1	1	yes	characteristic
21	C₁₁×M₁₆	—	2	1	no	—
22	C₁₁×M₁₆	C₁₆	1	1	yes	characteristic
23	C₂×C₈×C₁₁	—	2	1	no	—
24	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
25	C₁₁×C₁₆	—	2	1	no	—
26	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
28	#2258	D₁₁	1	1	yes	characteristic
29	M₁₂₈	—	11	1	no	—
30	C₂×C₆₄	—	11	1	no	—
31	Q₈×C₁₁	C₃₂	1	1	yes	characteristic
32	D₄×C₁₁	—	2	1	no	—
33	D₄×C₁₁	C₃₂	1	1	yes	characteristic
34	C₂×C₄×C₁₁	—	2	1	no	—
35	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
36	C₈×C₁₁	—	2	1	no	—
37	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
38	C₈×C₁₁	M₃₂	1	1	yes	characteristic
39	#504	Dic₁₁	1	1	yes	characteristic
40	M₆₄	—	2	1	no	—
41	M₆₄	Dic₁₁	1	1	yes	characteristic
42	C₂×C₃₂	—	2	1	no	—
43	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
44	C₆₄	—	22	1	no	—
45	C₆₄	—	22	1	no	—
46	C₂²×C₁₁	—	2	1	no	—
47	C₂²×C₁₁	M₆₄	1	1	yes	characteristic
48	C₄×C₁₁	—	2	1	no	—
49	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
50	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
51	#131	C₁₁⋊C₈	1	1	yes	characteristic
52	M₃₂	—	2	1	no	—
53	M₃₂	C₁₁⋊C₈	1	1	yes	characteristic
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
56	C₃₂	—	2	1	no	—
57	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	—	4	1	no	—
61	C₂×C₁₁	C₂²⋊C₃₂	1	1	yes	characteristic
62	#41	C₁₁⋊C₁₆	1	1	yes	characteristic
63	M₁₆	—	2	1	no	—
64	M₁₆	C₁₁⋊C₁₆	1	1	yes	characteristic
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
67	C₁₆	—	2	1	no	—
68	C₁₆	#4318	1	1	yes	characteristic
69	C₁₆	C₂²⋊Dic₁₁	1	1	yes	characteristic
70	C₁₁	#7514	1	1	yes	characteristic, complemented, Sylow
71	Q₈	C₁₁⋊C₃₂	1	1	yes	characteristic
72	D₄	—	2	1	no	—
73	D₄	C₁₁⋊C₃₂	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	#66876	1	1	yes	characteristic
78	C₈	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
79	C₂²	—	2	1	no	—
80	C₂²	#10622137	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic
83	C₄	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	4	1	no	—
86	C₂	C₂²⋊(C₁₁⋊C₃₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×#2258	C₂
socle	C₂×C₁₁	C₂²⋊C₃₂
prime radical	C₁₁×#41	C₁₆
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	#2258	D₁₁
hypocenter	C₁₁	#7514
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₃₂ ◁ C₂×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
70. C₁₁	#7514	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
#7514	11