Subgroups — #45657443

Order 32634.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14556423	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×(C₃₇⋊C₃)⋊D₇	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#66526⋊D₇	—	7	1	no	maximal
5	#17987959	—	7	1	no	maximal
6	C₇×D₂₅₉	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556423	D₇	1	1	yes	characteristic, complemented
8	C₇×#66526	—	7	1	no	—
9	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	(C₃₇⋊C₃)⋊D₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₇×D₃₇⋊C₃	—	7	1	no	—
12	D₇×C₇⋊C₉	—	37	1	no	maximal, Hall
13	C₇×C₃₇⋊C₃	—	6	1	no	—
14	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₇×C₃₇⋊C₃	C₃×D₇	1	1	yes	characteristic
16	#66526⋊C₂	—	49	1	no	Hall
17	D₂₅₉	C₇⋊C₉	1	1	yes	characteristic, complemented
18	C₇×D₃₇	—	7	1	no	—
19	C₇×C₇⋊C₉	—	37	1	no	Hall
20	#66526	—	7	1	no	Hall
21	C₃×C₇×D₇	—	37	1	no	—
22	C₇×C₃₇	—	6	1	no	—
23	C₇×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
24	C₇×C₃₇	C₉×D₇	1	1	yes	characteristic, complemented
25	D₃₇⋊C₃	—	7	1	no	—
26	C₃×C₇²	—	37	1	no	—
27	C₉×D₇	—	259	1	no	—
28	C₂×C₇⋊C₉	—	259	1	no	—
29	C₃₇⋊C₃	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₇×D₇	—	37	1	no	Hall
31	D₃₇	—	7	1	no	Hall
32	C₇×C₉	—	259	1	no	—
33	C₇⋊C₉	—	37	1	no	—
34	C₇²	#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	259	1	no	—
36	C₃×D₇	—	37	1	no	—
37	C₃₇	D₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₇	—	37	1	no	—
39	C₃×C₇	—	37	1	no	—
40	C₃×C₇	—	222	1	no	—
41	C₂×C₉	—	1813	1	no	Hall
42	C₂×C₇	—	259	1	no	—
43	D₇	—	37	1	no	—
44	C₉	—	259	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	#17987959	1	1	yes	characteristic, complemented
47	C₇	#66526⋊D₇	1	1	yes	characteristic, complemented
48	C₂×C₃	—	259	1	no	—
49	C₃	—	37	1	no	—
50	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₃₇	C₂×C₉
prime radical	C₇×(C₃₇⋊C₃)⋊D₇	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×#14556423	C₂	semidirect
6. C₇×D₂₅₉	C₉	semidirect
7. #14556423	D₇	semidirect
9. C₇²×C₃₇	C₂×C₉	semidirect
17. D₂₅₉	C₇⋊C₉	semidirect
23. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
24. C₇×C₃₇	C₉×D₇	semidirect
34. C₇²	#66526⋊C₂	semidirect
37. C₃₇	D₇×C₇⋊C₉	semidirect
46. C₇	#17987959	semidirect
47. C₇	#66526⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×#14556423	2
C₇×(C₃₇⋊C₃)⋊D₇	3
#66526⋊D₇	7
#17987959	7
D₇×C₇⋊C₉	37