Subgroups — #44532095

Order 31347.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782744	C₃	1	3	yes	maximal, complemented
2	C₃²×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₄₃⋊C₈₁	—	3	3	no	—
4	C₃²×C₉×C₄₃	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₄₃	—	3	1	no	—
6	C₃×C₂₇×C₄₃	—	3	2	no	—
7	C₃×C₂₇×C₄₃	C₉	1	2	yes	—
8	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
9	C₃³×C₄₃	C₂₇	1	1	yes	characteristic
10	C₃×C₉×C₄₃	—	3	1	no	—
11	C₃×C₉×C₄₃	—	3	2	no	—
12	C₃×C₉×C₄₃	C₂₇	1	2	yes	—
13	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
14	C₂₇×C₄₃	—	3	2	no	—
15	C₂₇×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₂₇×C₄₃	3₋¹⁺²	1	2	yes	—
17	#10624502	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	3	3	no	—
20	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
21	C₉×C₄₃	—	3	2	no	—
22	C₉×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
23	C₉×C₄₃	C₂₇⋊C₃	1	2	yes	—
24	C₃²×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
25	C₈₁⋊C₃	—	43	3	no	—
26	C₃×C₄₃	—	3	3	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	C₃²⋊C₂₇	1	1	yes	characteristic
29	C₃²×C₉	C₄₃⋊C₉	1	1	yes	characteristic
30	C₃×C₂₇	—	3	1	no	—
31	C₃×C₂₇	—	3	2	no	—
32	C₃×C₂₇	C₄₃⋊C₉	1	2	yes	—
33	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
34	C₈₁	—	129	3	no	—
35	C₄₃	#10624502	1	1	yes	characteristic, complemented, Sylow
36	C₃³	C₄₃⋊C₂₇	1	1	yes	characteristic
37	C₃×C₉	—	3	1	no	—
38	C₃×C₉	—	3	2	no	—
39	C₃×C₉	C₄₃⋊C₂₇	1	2	yes	—
40	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
41	C₂₇	—	3	2	no	—
42	C₂₇	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
43	C₂₇	#11923958	1	2	yes	—
44	C₃²	—	3	3	no	—
45	C₃²	—	3	1	no	—
46	C₃²	C₃×C₄₃⋊C₂₇	1	1	yes	characteristic
47	C₉	—	3	2	no	—
48	C₉	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
49	C₉	#16812505	1	2	yes	—
50	C₃	—	3	3	no	—
51	C₃	—	3	1	no	—
52	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	C₃²×C₂₇×C₄₃	C₃
socle	C₃×C₄₃	C₃²⋊C₂₇
prime radical	C₃³×C₄₃	C₂₇
cosocle	C₃×C₂₇×C₄₃	C₃²
hypercenter	C₃²×C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624502
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂₇ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
1. #23782744	C₃	semidirect
35. C₄₃	#10624502	semidirect

Maximal subgroups

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

subgroup	index
#23782744	3
C₃²×C₂₇×C₄₃	3
#10624502	43