Subgroups — C₂×C₇×D₇×C₄₇ #22604263

Order 9212.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₇×C₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₇×C₄₇	—	7	1	no	maximal
5	C₂×D₇×C₄₇	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₇×C₄₇	—	2	3	no	—
7	C₂×C₇×C₄₇	—	7	2	no	—
8	C₂×C₇×C₄₇	D₇	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented
10	D₇×C₄₇	C₂×C₇	1	2	yes	direct product factor
11	C₇×C₄₇	—	2	3	no	—
12	C₇×C₄₇	C₂×D₇	1	1	yes	characteristic, direct product factor
13	C₇×C₄₇	C₂²×C₇	1	1	yes	characteristic, complemented
14	C₂×C₇×D₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₄₇	—	7	1	no	Hall
16	C₂×C₇²	C₂×C₄₇	1	1	yes	characteristic, complemented
17	C₇×D₇	C₂×C₄₇	1	2	yes	direct product factor
18	C₂×C₄₇	—	7	2	no	—
19	C₂×C₄₇	C₇×D₇	1	1	yes	characteristic, direct product factor
20	C₇²	C₂²×C₄₇	1	1	yes	characteristic, complemented, Sylow
21	C₄₇	C₂×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₇	—	7	1	no	—
23	C₂×D₇	C₇×C₄₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇	—	2	3	no	—
25	C₂×C₇	—	7	2	no	—
26	C₂×C₇	D₇×C₄₇	1	1	yes	characteristic, direct product factor
27	C₂×C₇	C₂×C₇×C₄₇	1	1	yes	characteristic, complemented
28	D₇	C₂×C₇×C₄₇	1	2	yes	direct product factor
29	C₇	—	2	3	no	—
30	C₇	C₂×D₇×C₄₇	1	1	yes	characteristic, direct product factor
31	C₇	C₂²×C₇×C₄₇	1	1	yes	characteristic, complemented
32	C₂²	—	7	1	no	Sylow
33	C₂	—	7	2	no	—
34	C₂	C₇×D₇×C₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₄₇	D₇
commutator, hypocenter	C₇	C₂²×C₇×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₇×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₇×C₄₇	C₂	direct (N × H)
2. C₂×C₇²×C₄₇	C₂	semidirect
3. C₇²×C₄₇	C₂²	semidirect
5. C₂×D₇×C₄₇	C₇	direct (N × H)
8. C₂×C₇×C₄₇	D₇	direct (N × H)
9. C₂×C₇×C₄₇	C₂×C₇	semidirect
10. D₇×C₄₇	C₂×C₇	direct (N × H)
12. C₇×C₄₇	C₂×D₇	direct (N × H)
13. C₇×C₄₇	C₂²×C₇	semidirect
14. C₂×C₇×D₇	C₄₇	direct (N × H)
16. C₂×C₇²	C₂×C₄₇	semidirect
17. C₇×D₇	C₂×C₄₇	direct (N × H)
19. C₂×C₄₇	C₇×D₇	direct (N × H)
20. C₇²	C₂²×C₄₇	semidirect
21. C₄₇	C₂×C₇×D₇	direct (N × H)
23. C₂×D₇	C₇×C₄₇	direct (N × H)
26. C₂×C₇	D₇×C₄₇	direct (N × H)
27. C₂×C₇	C₂×C₇×C₄₇	semidirect
28. D₇	C₂×C₇×C₄₇	direct (N × H)
30. C₇	C₂×D₇×C₄₇	direct (N × H)
31. C₇	C₂²×C₇×C₄₇	semidirect
34. C₂	C₇×D₇×C₄₇	direct (N × H)

Subgroups — C2×C7×D7×C47 #22604263

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×D₇×C₄₇ #22604263