Subgroups — C₃²⋊(C₃₁⋊C₈₁) #36379695

Order 22599.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁⋊C₈₁	C₃	1	3	yes	maximal, complemented
2	C₃²×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃₁⋊C₈₁	—	3	3	no	—
4	C₃²×C₉×C₃₁	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₃₁	—	3	1	no	—
6	C₃×C₂₇×C₃₁	—	3	2	no	—
7	C₃×C₂₇×C₃₁	C₉	1	2	yes	—
8	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
9	C₃³×C₃₁	C₂₇	1	1	yes	characteristic
10	C₃×C₉×C₃₁	—	3	1	no	—
11	C₃×C₉×C₃₁	—	3	2	no	—
12	C₃×C₉×C₃₁	C₂₇	1	2	yes	—
13	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
14	C₂₇×C₃₁	—	3	2	no	—
15	C₂₇×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
16	C₂₇×C₃₁	3₋¹⁺²	1	2	yes	—
17	C₃²⋊C₈₁	—	31	1	no	maximal, Sylow
18	C₃²×C₃₁	—	3	1	no	—
19	C₃²×C₃₁	—	3	2	no	—
20	C₃²×C₃₁	C₈₁	1	3	yes	complemented
21	C₃²×C₃₁	C₃×C₂₇	1	1	yes	characteristic
22	C₉×C₃₁	—	3	2	no	—
23	C₉×C₃₁	C₃²⋊C₉	1	1	yes	characteristic
24	C₉×C₃₁	C₂₇⋊C₃	1	2	yes	—
25	C₃²×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic
26	C₃×C₈₁	—	31	3	no	—
27	C₃×C₃₁	—	3	3	no	—
28	C₃×C₃₁	C₃²⋊C₂₇	1	1	yes	characteristic
29	C₃×C₃₁	C₃×C₈₁	1	1	yes	characteristic
30	C₃×C₃₁	C₈₁⋊C₃	1	2	yes	—
31	C₃²×C₉	C₃₁⋊C₉	1	1	yes	characteristic
32	C₃×C₂₇	—	3	2	no	—
33	C₃×C₂₇	—	3	1	no	—
34	C₃×C₂₇	C₃₁⋊C₉	1	2	yes	—
35	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
36	C₈₁	—	93	3	no	—
37	C₃₁	C₃²⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
38	C₃³	C₃₁⋊C₂₇	1	1	yes	characteristic
39	C₃×C₉	—	3	1	no	—
40	C₃×C₉	—	3	2	no	—
41	C₃×C₉	C₃₁⋊C₂₇	1	2	yes	—
42	C₃×C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
43	C₂₇	—	3	2	no	—
44	C₂₇	#11719689	1	2	yes	—
45	C₂₇	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
46	C₃²	—	3	1	no	—
47	C₃²	—	3	2	no	—
48	C₃²	C₃₁⋊C₈₁	1	3	yes	complemented
49	C₃²	C₃×C₃₁⋊C₂₇	1	1	yes	characteristic
50	C₉	—	3	2	no	—
51	C₉	C₃²⋊(C₃₁⋊C₉)	1	1	yes	characteristic
52	C₉	#14578892	1	2	yes	—
53	C₃	—	3	3	no	—
54	C₃	C₃²⋊(C₃₁⋊C₂₇)	1	1	yes	characteristic
55	C₃	C₃×C₃₁⋊C₈₁	1	1	yes	characteristic
56	C₃	#21419258	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₂₇	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃×C₈₁
Fitting	C₃²×C₂₇×C₃₁	C₃
socle	C₃²×C₃₁	C₃×C₂₇
prime radical	C₃³×C₃₁	C₂₇
cosocle	C₃×C₂₇×C₃₁	C₃²
hypercenter	C₃²×C₂₇	C₃₁⋊C₃
hypocenter	C₃₁	C₃²⋊C₈₁
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁⋊C₈₁	C₃	semidirect
20. C₃²×C₃₁	C₈₁	semidirect
37. C₃₁	C₃²⋊C₈₁	semidirect
48. C₃²	C₃₁⋊C₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₁⋊C₈₁	3
C₃²×C₂₇×C₃₁	3
C₃²⋊C₈₁	31

Subgroups — C32⋊(C31⋊C81) #36379695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²⋊(C₃₁⋊C₈₁) #36379695