Subgroups — (C₄₃⋊C₉)⋊C₈₁ #44532197

Order 31347.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃⋊C₈₁	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄₃⋊C₈₁	C₃	1	1	yes	maximal, characteristic
3	C₂₇×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃×C₈₁	C₃	1	1	yes	maximal, characteristic
5	C₃×C₄₃⋊C₂₇	C₉	1	1	yes	characteristic
6	C₃×C₄₃⋊C₂₇	C₉	1	1	yes	characteristic
7	C₉×C₄₃⋊C₉	C₉	1	1	yes	characteristic
8	C₄₃⋊C₈₁	—	3	1	no	—
9	C₄₃⋊C₈₁	—	3	1	no	—
10	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
11	C₄₃×C₈₁	—	3	1	no	—
12	C₃×C₄₃⋊C₉	C₂₇	1	1	yes	characteristic
13	C₃×C₄₃⋊C₉	C₂₇	1	1	yes	characteristic
14	C₃×C₄₃⋊C₉	C₂₇	1	1	yes	characteristic
15	C₄₃⋊C₂₇	—	3	1	no	—
16	C₄₃⋊C₂₇	—	3	1	no	—
17	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
18	C₂₇×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	C₂₇×C₄₃	3₋¹⁺²	1	1	yes	characteristic
20	C₂₇×C₄₃	3₋¹⁺²	1	1	yes	characteristic
21	C₉⋊C₈₁	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
23	C₉×C₄₃	C₉⋊C₉	1	1	yes	characteristic
24	C₉×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
25	C₉×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
26	C₄₃⋊C₉	—	3	1	no	—
27	C₄₃⋊C₉	—	3	1	no	—
28	C₄₃⋊C₉	C₈₁	1	3	yes	complemented
29	C₃×C₈₁	—	43	1	no	—
30	C₃×C₈₁	—	43	1	no	—
31	C₃×C₈₁	C₄₃⋊C₃	1	1	yes	characteristic
32	C₉×C₂₇	—	43	1	no	—
33	C₃×C₄₃	C₉⋊C₂₇	1	1	yes	characteristic
34	C₃×C₄₃	C₃×C₈₁	1	1	yes	characteristic
35	C₃×C₄₃	C₈₁⋊C₃	1	1	yes	characteristic
36	C₃×C₄₃	C₈₁⋊C₃	1	1	yes	characteristic
37	C₃×C₂₇	—	43	1	no	—
38	C₃×C₂₇	—	43	1	no	—
39	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
40	C₉²	—	43	1	no	—
41	C₈₁	—	3	1	no	—
42	C₈₁	—	129	1	no	—
43	C₈₁	—	129	1	no	—
44	C₄₃	C₉⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
45	C₃×C₉	—	43	1	no	—
46	C₃×C₉	—	43	1	no	—
47	C₃×C₉	—	43	1	no	—
48	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
49	C₂₇	—	129	1	no	—
50	C₂₇	—	129	1	no	—
51	C₂₇	#11923956	1	1	yes	characteristic
52	C₂₇	#11923957	1	1	yes	characteristic
53	C₂₇	#11923958	1	1	yes	characteristic
54	C₃²	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
55	C₉	—	43	3	no	—
56	C₉	—	129	1	no	—
57	C₉	—	129	1	no	—
58	C₉	(C₄₃⋊C₉)⋊C₉	1	1	yes	characteristic
59	C₉	#16812503	1	1	yes	characteristic
60	C₉	#16812504	1	1	yes	characteristic
61	C₃	(C₄₃⋊C₉)⋊C₂₇	1	1	yes	characteristic
62	C₃	C₈₁×C₄₃⋊C₃	1	1	yes	characteristic
63	C₃	#23782742	1	1	yes	characteristic
64	C₃	#23782743	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃×C₂₇	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₈₁
Fitting	C₃×C₄₃×C₈₁	C₃
socle, prime radical	C₃²×C₄₃	C₃×C₂₇
cosocle	C₃×C₂₇×C₄₃	C₃²
hypercenter	C₃×C₈₁	C₄₃⋊C₃
hypocenter	C₄₃	C₉⋊C₈₁
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃×C₈₁

Complements

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

N	H ≅ G/N	type
28. C₄₃⋊C₉	C₈₁	semidirect
44. C₄₃	C₉⋊C₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₃⋊C₈₁	3
C₂₇×C₄₃⋊C₉	3
C₃×C₄₃×C₈₁	3
C₉⋊C₈₁	43

Subgroups — (C43⋊C9)⋊C81 #44532197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₄₃⋊C₉)⋊C₈₁ #44532197