Subgroups — #45657335

Order 32634.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654573	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₅₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic
4	#17987937	—	7	1	no	maximal
5	#17987932	—	7	1	no	maximal
6	C₇×D₂₅₉	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556419	—	7	1	no	—
8	#14556418	—	7	1	no	—
9	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₅₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₃×C₇×D₃₇	—	7	1	no	—
12	#11725075	—	37	1	no	maximal, Hall
13	C₃×C₇×C₃₇	—	6	1	no	—
14	C₃×C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	#66524⋊C₂	—	49	1	no	Hall
17	D₂₅₉	C₇⋊C₉	1	1	yes	characteristic, complemented
18	C₇×D₃₇	—	7	1	no	—
19	#89205	—	37	1	no	Hall
20	#66524	—	49	1	no	Hall
21	C₃×C₇×D₇	—	37	1	no	—
22	C₇×C₃₇	—	6	1	no	—
23	C₇×C₃₇	D₇⋊C₉	1	1	yes	characteristic, complemented
24	C₇×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
25	C₃×D₃₇	—	7	1	no	—
26	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic
27	C₂×C₇⋊C₉	—	259	1	no	—
28	D₇⋊C₉	—	259	1	no	—
29	C₃×C₃₇	#64422	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	—	259	1	no	—
34	C₇²	#66524⋊C₂	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	259	1	no	—
36	C₃×D₇	—	37	1	no	—
37	C₃₇	#11725075	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₇	—	6	1	no	—
39	C₃×C₇	#13095532	1	1	yes	characteristic
40	C₃×C₇	#13095537	1	1	yes	characteristic
41	C₂×C₉	—	1813	1	no	Hall
42	C₂×C₇	—	259	1	no	—
43	D₇	—	37	1	no	—
44	C₉	—	1813	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	#17987932	1	1	yes	characteristic, complemented
47	C₇	#17987937	1	1	yes	characteristic, complemented
48	C₂×C₃	—	259	1	no	—
49	C₃	#24925963	1	1	yes	characteristic
50	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#24925963
commutator, hypocenter	C₇²×C₃₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₃₇	C₂×C₃
prime radical	C₃×C₇×D₂₅₉	C₃
LCS	G ▷ C₇²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #30654573	C₂	semidirect
6. C₇×D₂₅₉	C₉	semidirect
9. C₇²×C₃₇	C₂×C₉	semidirect
17. D₂₅₉	C₇⋊C₉	semidirect
23. C₇×C₃₇	D₇⋊C₉	semidirect
24. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
34. C₇²	#66524⋊C₂	semidirect
37. C₃₇	#11725075	semidirect
46. C₇	#17987932	semidirect
47. C₇	#17987937	semidirect

Maximal subgroups

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

subgroup	index
#30654573	2
C₃×C₇×D₂₅₉	3
#17987937	7
#17987932	7
#11725075	37