Subgroups — C₄₃⋊#10624562 #44532328

Order 31347.

2138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃²⋊(C₄₃⋊C₃)	C₃	1	12	yes	maximal, complemented
2	C₃²×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₄₃⋊C₃	C₃²	1	9	yes	—
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	108	no	—
5	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	36	no	—
6	C₃⁴×C₄₃	C₃²	1	4	yes	—
7	C₃×H(3,𝔽₃)×C₄₃	—	3	12	no	—
8	C₃²×C₄₃⋊C₃	—	3	72	no	—
9	C₃²×C₄₃⋊C₃	—	3	36	no	—
10	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	27	yes	complemented
11	C₃²⋊(C₄₃⋊C₃)	—	3	324	no	—
12	C₃³×C₄₃	—	3	12	no	—
13	C₃³×C₄₃	—	3	36	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	12	yes	complemented
15	C₃³×C₄₃	C₃³	1	1	yes	characteristic
16	H(3,𝔽₃)×C₄₃	—	3	27	no	—
17	#10624562	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	—	3	12	no	—
19	C₃²×C₄₃	—	3	36	no	—
20	C₃²×C₄₃	—	9	36	no	—
21	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	9	yes	—
22	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	4	yes	—
23	C₃×C₄₃⋊C₃	—	3	108	no	—
24	C₃×C₄₃⋊C₃	—	9	72	no	—
25	C₃×C₄₃⋊C₃	—	9	9	no	—
26	C₃²×H(3,𝔽₃)	—	43	12	no	—
27	C₃²×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
28	C₃×C₄₃	—	9	12	no	—
29	C₃×C₄₃	C₃²⋊H(3,𝔽₃)	1	12	yes	—
30	C₃×C₄₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
31	C₄₃⋊C₃	—	9	27	no	—
32	C₃⁴	—	43	9	no	—
33	C₃⁴	C₃×C₄₃⋊C₃	1	4	yes	—
34	C₃×H(3,𝔽₃)	—	3	12	no	—
35	C₃×H(3,𝔽₃)	—	129	108	no	—
36	C₃×H(3,𝔽₃)	—	129	36	no	—
37	C₄₃	#10624562	1	1	yes	characteristic, complemented, Sylow
38	C₃³	—	3	36	no	—
39	C₃³	—	3	12	no	—
40	C₃³	—	43	27	no	—
41	C₃³	—	129	72	no	—
42	C₃³	—	129	36	no	—
43	C₃³	C₃²⋊(C₄₃⋊C₃)	1	12	yes	complemented
44	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
45	H(3,𝔽₃)	—	3	27	no	—
46	H(3,𝔽₃)	—	129	324	no	—
47	C₃²	—	3	36	no	—
48	C₃²	—	3	12	no	—
49	C₃²	—	9	36	no	—
50	C₃²	—	129	108	no	—
51	C₃²	—	387	72	no	—
52	C₃²	—	387	9	no	—
53	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	9	yes	—
54	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	4	yes	—
55	C₃	—	9	12	no	—
56	C₃	—	387	27	no	—
57	C₃	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	1	12	yes	—
58	C₃	#23782794	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃³×C₄₃	C₃³
Fitting	C₃²×H(3,𝔽₃)×C₄₃	C₃
hypercenter	C₃²×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	#10624562
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
2. C₃²×H(3,𝔽₃)×C₄₃	C₃	semidirect
10. C₃²×C₄₃⋊C₃	H(3,𝔽₃)	semidirect
14. C₃³×C₄₃	H(3,𝔽₃)	semidirect
27. C₃²×H(3,𝔽₃)	C₄₃⋊C₃	semidirect
37. C₄₃	#10624562	semidirect
43. C₃³	C₃²⋊(C₄₃⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₃²⋊(C₄₃⋊C₃)	3
C₃²×H(3,𝔽₃)×C₄₃	3
#10624562	43

Subgroups — C43⋊#10624562 #44532328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊#10624562 #44532328