Subgroups — #45657331

Order 32634.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654570	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic
4	C₂×#14556419	—	7	1	no	maximal
5	#17987935	—	7	1	no	maximal
6	C₇×D₇×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556419	—	7	1	no	—
8	#14556419	—	7	1	no	—
9	#14556419	—	14	3	no	—
10	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₃₇	—	7	1	no	—
12	C₃×D₇×C₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	#11725076	—	37	1	no	maximal, Hall
14	C₃×C₇×C₃₇	—	2	3	no	—
15	C₃×C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×#66524	—	49	1	no	Hall
18	C₂×C₇×C₃₇	—	7	1	no	—
19	D₇×C₃₇	C₇⋊C₉	1	1	yes	characteristic, complemented
20	#89204	—	37	1	no	Hall
21	#66524	—	49	1	no	Hall
22	C₃×C₇×D₇	C₃₇⋊C₃	1	1	yes	characteristic
23	C₇×C₃₇	—	2	3	no	—
24	C₇×C₃₇	D₇⋊C₉	1	1	yes	characteristic, complemented
25	C₇×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
26	C₂×C₃×C₃₇	—	7	1	no	—
27	C₃×C₇²	C₂×C₃₇⋊C₃	1	1	yes	characteristic
28	C₂×C₇⋊C₉	—	259	1	no	—
29	D₇⋊C₉	—	259	1	no	—
30	C₃×C₃₇	#64423	1	1	yes	characteristic
31	C₇×D₇	#66524	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₇	—	7	1	no	Hall
33	C₇⋊C₉	—	259	1	no	—
34	C₇⋊C₉	—	259	1	no	—
35	C₇⋊C₉	—	518	3	no	—
36	C₇²	C₂×#66524	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	—	7	1	no	—
38	C₃×D₇	#11715913	1	1	yes	characteristic
39	C₃₇	#11725076	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₇	—	2	3	no	—
41	C₃×C₇	#13095535	1	1	yes	characteristic
42	C₃×C₇	C₂×#11715913	1	1	yes	characteristic
43	C₂×C₉	—	1813	1	no	Hall
44	C₂×C₇	—	7	1	no	—
45	D₇	#14556419	1	1	yes	characteristic, complemented
46	C₉	—	1813	1	no	Sylow
47	C₇	—	2	3	no	—
48	C₇	#17987935	1	1	yes	characteristic, complemented
49	C₇	C₂×#14556419	1	1	yes	characteristic, complemented
50	C₂×C₃	—	7	1	no	—
51	C₃	#24925959	1	1	yes	characteristic
52	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#24925959
commutator, hypocenter	C₇²×C₃₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₃₇	C₂×C₃
prime radical	C₃×C₇×D₇×C₃₇	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. #30654570	C₂	semidirect
6. C₇×D₇×C₃₇	C₉	semidirect
10. C₇²×C₃₇	C₂×C₉	semidirect
19. D₇×C₃₇	C₇⋊C₉	semidirect
24. C₇×C₃₇	D₇⋊C₉	semidirect
25. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
31. C₇×D₇	#66524	semidirect
36. C₇²	C₂×#66524	semidirect
39. C₃₇	#11725076	semidirect
45. D₇	#14556419	semidirect
48. C₇	#17987935	semidirect
49. C₇	C₂×#14556419	semidirect

Maximal subgroups

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

subgroup	index
#30654570	2
C₃×C₇×D₇×C₃₇	3
C₂×#14556419	7
#17987935	7
#11725076	37