Subgroups — #45657402

Order 32634.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14556422	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	D₇×#66526	—	7	1	no	maximal
5	#17987954	—	7	1	no	maximal
6	C₃₇×C₇⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556422	D₇	1	1	yes	characteristic, complemented
8	C₇×#66526	—	7	1	no	—
9	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	D₇×C₃₇⋊C₃	—	7	1	no	—
11	D₇×C₃₇⋊C₃	—	7	1	no	—
12	D₇×C₃₇⋊C₃	—	21	2	no	—
13	(C₇⋊C₉)⋊D₇	—	37	1	no	maximal, Hall
14	C₇×C₃₇⋊C₃	—	3	2	no	—
15	C₇×C₃₇⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₇×C₃₇⋊C₃	C₃×D₇	1	1	yes	characteristic
17	C₂×#66526	—	49	1	no	Hall
18	D₇×C₃₇	—	7	1	no	—
19	D₇×C₃₇	—	7	1	no	—
20	D₇×C₃₇	—	21	2	no	—
21	C₇×C₇⋊C₉	—	37	1	no	Hall
22	#66526	—	7	1	no	Hall
23	C₃×C₇⋊D₇	—	37	1	no	—
24	C₇×C₃₇	—	3	2	no	—
25	C₇×C₃₇	D₇⋊C₉	1	1	yes	characteristic, complemented
26	C₇×C₃₇	C₉×D₇	1	1	yes	characteristic, complemented
27	C₂×C₃₇⋊C₃	—	49	1	no	—
28	C₃×C₇²	—	37	1	no	—
29	C₉×D₇	—	259	1	no	—
30	D₇⋊C₉	—	259	1	no	—
31	C₃₇⋊C₃	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic
32	C₇⋊D₇	#66526	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃₇	—	49	1	no	Hall
34	C₇×C₉	—	259	1	no	—
35	C₇⋊C₉	—	37	1	no	—
36	C₇²	C₂×#66526	1	1	yes	characteristic, complemented, Sylow
37	C₃×D₇	—	259	1	no	—
38	C₃×D₇	—	259	1	no	—
39	C₃×D₇	—	777	2	no	—
40	C₃₇	(C₇⋊C₉)⋊D₇	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	D₇	—	7	1	no	—
46	D₇	—	7	1	no	—
47	D₇	—	21	2	no	—
48	C₉	—	259	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	#17987954	1	1	yes	characteristic, complemented
51	C₇	D₇×#66526	1	1	yes	characteristic, complemented
52	C₂×C₃	—	1813	1	no	—
53	C₃	—	37	1	no	—
54	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₃₇	C₂×C₉
prime radical	C₇⋊D₇×C₃₇⋊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. C₇×#14556422	C₂	semidirect
6. C₃₇×C₇⋊D₇	C₉	semidirect
7. #14556422	D₇	semidirect
9. C₇²×C₃₇	C₂×C₉	semidirect
25. C₇×C₃₇	D₇⋊C₉	semidirect
26. C₇×C₃₇	C₉×D₇	semidirect
32. C₇⋊D₇	#66526	semidirect
36. C₇²	C₂×#66526	semidirect
40. C₃₇	(C₇⋊C₉)⋊D₇	semidirect
50. C₇	#17987954	semidirect
51. C₇	D₇×#66526	semidirect

Maximal subgroups

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

subgroup	index
C₇×#14556422	2
C₇⋊D₇×C₃₇⋊C₃	3
D₇×#66526	7
#17987954	7
(C₇⋊C₉)⋊D₇	37