Subgroups — #44532097

Order 31347.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782744	C₃	1	2	yes	maximal, complemented
2	C₃×C₄₃⋊C₈₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#6903	C₃	1	1	yes	maximal, characteristic
4	C₄₃⋊C₈₁	—	3	1	no	—
5	C₄₃⋊C₈₁	—	3	2	no	—
6	C₄₃×#737	C₉	1	1	yes	characteristic
7	C₄₃×C₂₇⋊C₃	—	3	2	no	—
8	C₄₃×C₂₇⋊C₃	C₉	1	2	yes	—
9	C₃×C₂₇×C₄₃	—	3	1	no	—
10	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
11	3₋¹⁺²×C₄₃	—	3	2	no	—
12	3₋¹⁺²×C₄₃	C₂₇	1	2	yes	—
13	H(3,𝔽₃)×C₄₃	C₂₇	1	1	yes	characteristic
14	C₃×C₉×C₄₃	—	3	1	no	—
15	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
16	C₂₇×C₄₃	—	3	2	no	—
17	C₂₇×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₂₇×C₄₃	3₋¹⁺²	1	2	yes	—
19	#10624503	—	43	1	no	maximal, Sylow
20	C₃²×C₄₃	—	3	1	no	—
21	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
22	C₉×C₄₃	—	3	2	no	—
23	C₉×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
24	C₉×C₄₃	C₂₇⋊C₃	1	2	yes	—
25	#6903	C₄₃⋊C₃	1	1	yes	characteristic
26	C₈₁⋊C₃	—	43	2	no	—
27	C₃×C₈₁	—	43	1	no	—
28	C₃×C₄₃	—	3	1	no	—
29	C₃×C₄₃	—	9	1	no	—
30	C₃×C₄₃	C₃²⋊C₂₇	1	1	yes	characteristic
31	#737	C₄₃⋊C₉	1	1	yes	characteristic
32	C₂₇⋊C₃	—	3	2	no	—
33	C₂₇⋊C₃	C₄₃⋊C₉	1	2	yes	—
34	C₃×C₂₇	—	3	1	no	—
35	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
36	C₈₁	—	129	1	no	—
37	C₈₁	—	129	2	no	—
38	C₄₃	#10624503	1	1	yes	characteristic, complemented, Sylow
39	3₋¹⁺²	—	3	2	no	—
40	3₋¹⁺²	C₄₃⋊C₂₇	1	2	yes	—
41	H(3,𝔽₃)	C₄₃⋊C₂₇	1	1	yes	characteristic
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
44	C₂₇	—	3	2	no	—
45	C₂₇	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
46	C₂₇	#11923958	1	2	yes	—
47	C₃²	—	3	1	no	—
48	C₃²	C₃×C₄₃⋊C₂₇	1	1	yes	characteristic
49	C₉	—	3	2	no	—
50	C₉	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
51	C₉	#16812505	1	2	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	C₃	C₃²⋊(C₄₃⋊C₂₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂₇	C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₃×C₂₇
Frattini	C₃×C₂₇	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6903	C₃
socle	C₃×C₄₃	C₃²⋊C₂₇
prime radical	H(3,𝔽₃)×C₄₃	C₂₇
cosocle	C₃×C₂₇×C₄₃	C₃²
hypercenter	#6903	C₄₃⋊C₃
hypocenter	C₄₃	#10624503
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂₇ ◁ C₃×C₂₇ ◁ #6903

Complements

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

N	H ≅ G/N	type
1. #23782744	C₃	semidirect
2. C₃×C₄₃⋊C₈₁	C₃	semidirect
38. C₄₃	#10624503	semidirect

Maximal subgroups

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

subgroup	index
#23782744	3
C₃×C₄₃⋊C₈₁	3
C₄₃×#6903	3
#10624503	43