Subgroups — #44532086

Order 31347.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃⋊C₈₁	C₃	1	2	yes	maximal
2	C₂₇×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃×C₈₁	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃⋊C₂₇	C₉	1	2	yes	—
5	C₉×C₄₃⋊C₉	C₉	1	1	yes	characteristic
6	C₄₃⋊C₈₁	C₉	1	6	yes	complemented
7	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₈₁	C₉	1	3	yes	complemented
9	C₃×C₄₃⋊C₉	C₂₇	1	3	yes	—
10	C₄₃⋊C₂₇	C₂₇	1	6	yes	—
11	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
12	C₂₇×C₄₃	C₃×C₉	1	2	yes	—
13	C₂₇×C₄₃	C₃×C₉	1	1	yes	characteristic
14	#10624499	—	43	1	no	maximal, Sylow
15	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₄₃	C₉²	1	1	yes	characteristic
17	C₉×C₄₃	C₃×C₂₇	1	2	yes	—
18	C₄₃⋊C₉	—	3	3	no	—
19	C₃×C₈₁	—	43	2	no	—
20	C₃×C₈₁	C₄₃⋊C₃	1	1	yes	characteristic
21	C₉×C₂₇	—	43	1	no	—
22	C₃×C₄₃	C₉×C₂₇	1	1	yes	characteristic
23	C₃×C₄₃	C₈₁⋊C₃	1	3	yes	—
24	C₃×C₂₇	—	43	2	no	—
25	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
26	C₉²	—	43	1	no	—
27	C₈₁	—	43	6	no	—
28	C₈₁	C₄₃⋊C₉	1	3	yes	complemented
29	C₄₃	#10624499	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₉	—	43	3	no	—
31	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
32	C₂₇	—	43	6	no	—
33	C₂₇	C₉×C₄₃⋊C₃	1	2	yes	—
34	C₂₇	C₃×C₄₃⋊C₉	1	1	yes	characteristic
35	C₃²	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
36	C₉	—	129	3	no	—
37	C₉	C₉×C₄₃⋊C₉	1	1	yes	characteristic
38	C₉	C₂₇×C₄₃⋊C₃	1	2	yes	—
39	C₃	C₂₇×C₄₃⋊C₉	1	1	yes	characteristic
40	C₃	#23782742	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₂₇	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₉×C₂₇
Fitting	C₃×C₄₃×C₈₁	C₃
socle, prime radical	C₃²×C₄₃	C₃×C₂₇
cosocle	C₃×C₂₇×C₄₃	C₃²
hypercenter	C₃×C₈₁	C₄₃⋊C₃
hypocenter	C₄₃	#10624499
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
6. C₄₃⋊C₈₁	C₉	semidirect
8. C₄₃×C₈₁	C₉	semidirect
28. C₈₁	C₄₃⋊C₉	semidirect
29. C₄₃	#10624499	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
#10624499	43