Subgroups — C₇×D₇×#66526 #45657449

Order 32634.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×#66526	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	C₂×C₇×#66526	—	7	1	no	maximal
5	D₇×#66526	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×D₇×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₇×#66526	—	2	3	no	—
8	C₇×#66526	D₇	1	1	yes	characteristic, direct product factor
9	C₇×#66526	C₂×C₇	1	1	yes	characteristic, complemented
10	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₃₇⋊C₃	—	7	1	no	—
12	D₇×C₃₇⋊C₃	C₃×C₇	1	1	yes	characteristic
13	C₇×C₉×D₇	—	37	1	no	maximal, Hall
14	C₇×C₃₇⋊C₃	—	2	3	no	—
15	C₇×C₃₇⋊C₃	C₃×D₇	1	1	yes	characteristic
16	C₇×C₃₇⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic
17	C₂×#66526	—	7	1	no	Hall
18	C₂×C₇×C₃₇	—	7	1	no	—
19	D₇×C₃₇	C₇×C₉	1	1	yes	characteristic, complemented
20	C₇²×C₉	—	37	1	no	Hall
21	#66526	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₇×D₇	—	37	1	no	—
23	C₇×C₃₇	—	2	3	no	—
24	C₇×C₃₇	C₉×D₇	1	1	yes	characteristic, complemented
25	C₇×C₃₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented
26	C₂×C₃₇⋊C₃	—	7	1	no	—
27	C₃×C₇²	—	37	1	no	—
28	C₂×C₇×C₉	—	259	1	no	—
29	C₉×D₇	—	37	1	no	—
30	C₃₇⋊C₃	C₃×C₇×D₇	1	1	yes	characteristic
31	C₇×D₇	#66526	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₃₇	—	7	1	no	Hall
33	C₇×C₉	—	37	1	no	—
34	C₇×C₉	—	37	1	no	—
35	C₇×C₉	—	74	3	no	—
36	C₇²	C₂×#66526	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	—	259	1	no	—
38	C₃×D₇	—	37	1	no	—
39	C₃₇	C₇×C₉×D₇	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₇	—	37	1	no	—
41	C₃×C₇	—	37	1	no	—
42	C₃×C₇	—	74	3	no	—
43	C₂×C₉	—	259	1	no	Hall
44	C₂×C₇	—	7	1	no	—
45	D₇	C₇×#66526	1	1	yes	characteristic, direct product factor
46	C₉	—	37	1	no	Sylow
47	C₇	—	2	3	no	—
48	C₇	D₇×#66526	1	1	yes	characteristic, direct product factor
49	C₇	C₂×C₇×#66526	1	1	yes	characteristic, complemented
50	C₂×C₃	—	259	1	no	—
51	C₃	—	37	1	no	—
52	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₇×#66526
commutator, hypocenter	C₇×C₃₇	C₂×C₇×C₉
Frattini	C₁	G
Fitting, socle	C₇²×C₃₇	C₂×C₉
prime radical	C₇×D₇×C₃₇⋊C₃	C₃
cosocle	C₇×C₃₇⋊C₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇²×#66526	C₂	semidirect
5. D₇×#66526	C₇	direct (N × H)
6. C₇×D₇×C₃₇	C₉	semidirect
8. C₇×#66526	D₇	direct (N × H)
9. C₇×#66526	C₂×C₇	semidirect
10. C₇²×C₃₇	C₂×C₉	semidirect
19. D₇×C₃₇	C₇×C₉	semidirect
21. #66526	C₇×D₇	direct (N × H)
24. C₇×C₃₇	C₉×D₇	semidirect
25. C₇×C₃₇	C₂×C₇×C₉	semidirect
31. C₇×D₇	#66526	direct (N × H)
36. C₇²	C₂×#66526	semidirect
39. C₃₇	C₇×C₉×D₇	semidirect
45. D₇	C₇×#66526	direct (N × H)
48. C₇	D₇×#66526	direct (N × H)
49. C₇	C₂×C₇×#66526	semidirect

Maximal subgroups

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

subgroup	index
C₇²×#66526	2
C₇×D₇×C₃₇⋊C₃	3
C₂×C₇×#66526	7
D₇×#66526	7
C₇×C₉×D₇	37

Subgroups — C7×D7×#66526 #45657449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×#66526 #45657449