Subgroups — #44534465

Order 31347.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782744	C₃	1	8	yes	maximal, complemented
2	C₃×C₄₃⋊C₈₁	C₃	1	4	yes	maximal, complemented
3	C₄₃×#6903	C₃	1	1	yes	maximal, characteristic
4	C₄₃⋊C₈₁	C₃²	1	1	yes	characteristic
5	C₄₃⋊C₈₁	C₃²	1	8	yes	—
6	C₄₃×#737	C₉	1	1	yes	characteristic
7	C₄₃×C₂₇⋊C₃	C₉	1	8	yes	—
8	C₃×C₂₇×C₄₃	C₃²	1	4	yes	—
9	3₋¹⁺²×C₄₃	C₂₇	1	8	yes	—
10	H(3,𝔽₃)×C₄₃	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₄₃	C₃×C₉	1	4	yes	—
12	C₂₇×C₄₃	C₃×C₉	1	8	yes	—
13	C₂₇×C₄₃	C₃³	1	1	yes	characteristic
14	#10624833	—	43	1	no	maximal, Sylow
15	C₃²×C₄₃	C₃×C₂₇	1	4	yes	—
16	C₉×C₄₃	C₃×C₂₇	1	8	yes	—
17	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
18	#6903	C₄₃⋊C₃	1	1	yes	characteristic
19	C₈₁⋊C₃	—	43	8	no	—
20	C₃×C₈₁	—	43	4	no	—
21	C₃×C₄₃	—	3	4	no	—
22	C₃×C₄₃	C₃²×C₂₇	1	1	yes	characteristic
23	#737	C₄₃⋊C₉	1	1	yes	characteristic
24	C₂₇⋊C₃	C₄₃⋊C₉	1	8	yes	—
25	C₃×C₂₇	C₃×C₄₃⋊C₃	1	4	yes	—
26	C₈₁	—	43	1	no	—
27	C₈₁	—	43	8	no	—
28	C₄₃	#10624833	1	1	yes	characteristic, complemented, Sylow
29	3₋¹⁺²	C₄₃⋊C₂₇	1	8	yes	—
30	H(3,𝔽₃)	C₄₃⋊C₂₇	1	1	yes	characteristic
31	C₃×C₉	C₃×C₄₃⋊C₉	1	4	yes	—
32	C₂₇	C₃×C₄₃⋊C₉	1	8	yes	—
33	C₂₇	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
34	C₃²	C₃×C₄₃⋊C₂₇	1	4	yes	—
35	C₉	C₃×C₄₃⋊C₂₇	1	8	yes	—
36	C₉	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
37	C₃	—	3	4	no	—
38	C₃	C₃²×C₄₃⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂₇	C₃²×C₄₃⋊C₃
commutator, socle	C₃×C₄₃	C₃²×C₂₇
Fitting	C₄₃×#6903	C₃
prime radical	H(3,𝔽₃)×C₄₃	C₂₇
cosocle	C₂₇×C₄₃	C₃³
hypercenter	#6903	C₄₃⋊C₃
hypocenter	C₄₃	#10624833
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ 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
28. C₄₃	#10624833	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
#10624833	43