Subgroups — #45657388

Order 32634.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654588	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×#64418	C₃	1	1	yes	maximal, characteristic, complemented
3	#24925960	—	3	1	no	maximal
4	C₃₇×#3862	C₂×C₃	1	1	yes	characteristic, complemented
5	#19129589	D₃	1	1	yes	characteristic, complemented
6	C₇×#11715913	—	2	1	no	—
7	C₇×D₇×C₃₇	—	3	1	no	Hall
8	ΓL(1,𝔽₈)×C₃₇⋊C₃	—	14	1	no	—
9	C₇²×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×#11715912	—	21	1	no	—
11	#13095536	—	21	1	no	—
12	#64418⋊C₃	—	37	1	no	maximal, Hall
13	#11715913	—	2	1	no	—
14	#11715912	—	14	1	no	—
15	#11715912	—	21	1	no	—
16	#11715912	—	21	1	no	—
17	C₇×C₃₇⋊C₃	—	14	1	no	—
18	ΓL(1,𝔽₈)×C₃₇	—	14	1	no	—
19	D₃×C₃₇⋊C₃	—	49	1	no	maximal, Hall
20	C₂×C₇×C₃₇	—	21	1	no	—
21	D₇×C₃₇	—	3	1	no	—
22	ΓL(1,𝔽₈)²	—	37	1	no	Hall
23	C₃×C₃₇⋊C₃	—	49	1	no	Hall
24	#64423	—	111	1	no	—
25	#64418	C₃₇⋊C₃	1	1	yes	characteristic, complemented
26	C₇×C₃₇	—	2	1	no	—
27	C₇×C₃₇	—	3	1	no	—
28	C₇×C₃₇	—	3	1	no	—
29	D₃×C₃₇	—	49	1	no	—
30	C₂×C₃₇⋊C₃	—	147	1	no	—
31	#3862	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
32	#3861	—	37	1	no	—
33	C₇×ΓL(1,𝔽₈)	—	74	1	no	—
34	C₃×C₃₇	—	49	1	no	—
35	C₃₇⋊C₃	—	14	1	no	—
36	C₃₇⋊C₃	—	49	1	no	—
37	C₇×D₇	—	3	1	no	Hall
38	C₂×C₃₇	—	21	1	no	Hall
39	C₃×ΓL(1,𝔽₈)	—	518	1	no	—
40	C₇²	D₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×ΓL(1,𝔽₈)	—	777	1	no	—
42	AGL(1,𝔽₇)	—	777	1	no	—
43	C₃₇	#64418⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₇	—	518	1	no	—
45	ΓL(1,𝔽₈)	—	518	1	no	—
46	ΓL(1,𝔽₈)	—	777	1	no	—
47	ΓL(1,𝔽₈)	—	777	1	no	—
48	ΓL(1,𝔽₈)	—	14	1	no	—
49	ΓL(1,𝔽₈)	—	74	1	no	—
50	C₃×D₃	—	1813	1	no	Hall
51	C₂×C₇	—	21	1	no	—
52	D₇	—	3	1	no	—
53	C₃²	—	1813	1	no	Sylow
54	C₇	—	2	1	no	—
55	C₇	—	3	1	no	—
56	C₇	—	3	1	no	—
57	C₂×C₃	—	5439	1	no	—
58	D₃	—	49	1	no	—
59	C₃	—	518	1	no	—
60	C₃	—	1813	1	no	—
61	C₃	—	49	1	no	—
62	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃₇×#3862	C₂×C₃
Fitting, socle	C₇²×C₃₇	C₃×D₃
LCS	G ▷ C₃₇×#3862
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #30654588	C₂	semidirect
2. C₃₇×#64418	C₃	semidirect
4. C₃₇×#3862	C₂×C₃	semidirect
5. #19129589	D₃	semidirect
9. C₇²×C₃₇	C₃×D₃	semidirect
25. #64418	C₃₇⋊C₃	semidirect
31. #3862	C₂×C₃₇⋊C₃	semidirect
40. C₇²	D₃×C₃₇⋊C₃	semidirect
43. C₃₇	#64418⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#30654588	2
C₃₇×#64418	3
#24925960	3
#64418⋊C₃	37
D₃×C₃₇⋊C₃	49