Subgroups — #44532200

Order 31347.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782744	C₃	1	1	yes	maximal, characteristic
2	#23782744	C₃	1	1	yes	maximal, characteristic
3	#23782706	C₃	1	1	yes	maximal, characteristic
4	C₄₃×C₈₁⋊C₃	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	—	3	1	no	—
13	C₄₃⋊C₂₇	—	3	1	no	—
14	C₄₃⋊C₂₇	C₂₇	1	3	yes	—
15	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
16	C₂₇×C₄₃	3₋¹⁺²	1	1	yes	characteristic
17	C₂₇×C₄₃	3₋¹⁺²	1	1	yes	characteristic
18	C₂₇×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	#10624532	—	43	1	no	maximal, Sylow
20	C₃²×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
21	C₉×C₄₃	C₉⋊C₉	1	1	yes	characteristic
22	C₉×C₄₃	C₃×C₂₇	1	1	yes	characteristic
23	C₉×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
24	C₄₃⋊C₉	—	9	1	no	—
25	C₈₁⋊C₃	—	43	1	no	—
26	C₈₁⋊C₃	—	43	1	no	—
27	C₈₁⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic
28	#6864	—	43	1	no	—
29	C₃×C₄₃	—	3	1	no	—
30	C₃×C₄₃	C₉⋊C₂₇	1	1	yes	characteristic
31	C₃×C₂₇	—	43	1	no	—
32	C₃×C₂₇	—	43	1	no	—
33	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
34	C₉²	—	43	1	no	—
35	C₈₁	—	3	1	no	—
36	C₈₁	—	129	1	no	—
37	C₈₁	—	129	1	no	—
38	C₄₃	#10624532	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₉	—	129	1	no	—
40	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
41	C₂₇	—	43	3	no	—
42	C₂₇	—	129	1	no	—
43	C₂₇	#11923956	1	1	yes	characteristic
44	C₂₇	#11923957	1	1	yes	characteristic
45	C₂₇	#11923958	1	1	yes	characteristic
46	C₃²	#16812503	1	1	yes	characteristic
47	C₉	—	387	1	no	—
48	C₉	(C₄₃⋊C₉)⋊C₉	1	1	yes	characteristic
49	C₉	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
50	C₉	#16812504	1	1	yes	characteristic
51	C₃	—	3	1	no	—
52	C₃	(C₄₃⋊C₉)⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₉	(C₄₃⋊C₉)⋊C₉
commutator	C₉×C₄₃	C₃×C₂₇
Frattini	C₃×C₂₇	C₃×C₄₃⋊C₃
Fitting	C₄₃×C₈₁⋊C₃	C₃
socle	C₃×C₄₃	C₉⋊C₂₇
prime radical	C₃²×C₄₃	C₂₇⋊C₃
cosocle	C₃×C₂₇×C₄₃	C₃²
hypercenter	C₈₁⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#10624532
LCS	G ▷ C₉×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃×C₂₇ ◁ C₈₁⋊C₃

Complements

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

N	H ≅ G/N	type
38. C₄₃	#10624532	semidirect

Maximal subgroups

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

subgroup	index
#23782744	3
#23782706	3
C₄₃×C₈₁⋊C₃	3
#10624532	43