Subgroups — #45657471

Order 32634.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654582	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#17987959	—	7	1	no	maximal
5	#17987958	—	7	1	no	maximal
6	C₇²×D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556423	—	7	1	no	—
8	#14556422	—	7	1	no	—
9	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₇×D₃₇⋊C₃	—	3	2	no	—
11	C₇×D₃₇⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₇×D₃₇⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₂×#89205	—	37	1	no	maximal, Hall
14	C₇×C₃₇⋊C₃	—	3	2	no	—
15	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	#66526⋊C₂	—	49	1	no	Hall
18	C₇×D₃₇	—	3	2	no	—
19	C₇×D₃₇	C₇⋊C₉	1	1	yes	characteristic, complemented
20	C₇×D₃₇	C₇⋊C₉	1	1	yes	characteristic, complemented
21	#89205	—	37	1	no	Hall
22	#66526	—	49	1	no	Hall
23	C₂×C₃×C₇²	—	37	1	no	—
24	C₇×C₃₇	—	3	2	no	—
25	C₇×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
26	C₇×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
27	D₃₇⋊C₃	#3862	1	1	yes	characteristic
28	C₃×C₇²	—	37	1	no	—
29	C₂×C₇⋊C₉	—	259	1	no	—
30	C₂×C₇⋊C₉	—	259	1	no	—
31	C₃₇⋊C₃	C₂×#3862	1	1	yes	characteristic
32	C₂×C₇²	—	37	1	no	Hall
33	D₃₇	#89205	1	1	yes	characteristic, complemented, Hall
34	C₇⋊C₉	—	259	1	no	—
35	C₇⋊C₉	—	259	1	no	—
36	C₇²	#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	—	37	1	no	—
38	C₂×C₃×C₇	—	37	1	no	—
39	C₂×C₃×C₇	—	111	2	no	—
40	C₃₇	C₂×#89205	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₇	—	37	1	no	—
42	C₃×C₇	—	37	1	no	—
43	C₃×C₇	—	111	2	no	—
44	C₂×C₉	—	1813	1	no	Hall
45	C₂×C₇	—	37	1	no	—
46	C₂×C₇	—	37	1	no	—
47	C₂×C₇	—	111	2	no	—
48	C₉	—	1813	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	#17987958	1	1	yes	characteristic, complemented
51	C₇	#17987959	1	1	yes	characteristic, complemented
52	C₂×C₃	—	37	1	no	—
53	C₃	—	37	1	no	—
54	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₃₇	C₂×C₉
prime radical	C₇²×D₃₇⋊C₃	C₃
cosocle	C₇²×C₃₇⋊C₃	C₂×C₃
LCS	G ▷ C₇²×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #30654582	C₂	semidirect
6. C₇²×D₃₇	C₉	semidirect
9. C₇²×C₃₇	C₂×C₉	semidirect
19. C₇×D₃₇	C₇⋊C₉	semidirect
20. C₇×D₃₇	C₇⋊C₉	semidirect
25. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
26. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
33. D₃₇	#89205	semidirect
36. C₇²	#66526⋊C₂	semidirect
40. C₃₇	C₂×#89205	semidirect
50. C₇	#17987958	semidirect
51. C₇	#17987959	semidirect

Maximal subgroups

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

subgroup	index
#30654582	2
C₇²×D₃₇⋊C₃	3
#17987959	7
#17987958	7
C₂×#89205	37