Subgroups — C₂×C₇×D₇×C₁₀₇ #35230489

Order 20972.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₇×C₁₀₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₁₀₇	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₇×C₁₀₇	—	7	1	no	maximal
6	C₂×C₇×C₁₀₇	—	2	3	no	—
7	C₂×C₇×C₁₀₇	—	7	2	no	—
8	C₂×C₇×C₁₀₇	D₇	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₁₀₇	C₂×C₇	1	1	yes	characteristic, complemented
10	D₇×C₁₀₇	C₂×C₇	1	2	yes	direct product factor
11	C₇×C₁₀₇	—	2	3	no	—
12	C₇×C₁₀₇	C₂×D₇	1	1	yes	characteristic, direct product factor
13	C₇×C₁₀₇	C₂²×C₇	1	1	yes	characteristic, complemented
14	C₂²×C₁₀₇	—	7	1	no	Hall
15	C₂×C₁₀₇	—	7	2	no	—
16	C₂×C₁₀₇	C₇×D₇	1	1	yes	characteristic, direct product factor
17	C₂×C₇×D₇	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₀₇	C₂×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇²	C₂×C₁₀₇	1	1	yes	characteristic, complemented
20	C₇×D₇	C₂×C₁₀₇	1	2	yes	direct product factor
21	C₇²	C₂²×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₇	—	7	1	no	—
23	C₂×D₇	C₇×C₁₀₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇	—	2	3	no	—
25	C₂×C₇	—	7	2	no	—
26	C₂×C₇	D₇×C₁₀₇	1	1	yes	characteristic, direct product factor
27	C₂×C₇	C₂×C₇×C₁₀₇	1	1	yes	characteristic, complemented
28	D₇	C₂×C₇×C₁₀₇	1	2	yes	direct product factor
29	C₇	—	2	3	no	—
30	C₇	C₂²×C₇×C₁₀₇	1	1	yes	characteristic, complemented
31	C₇	C₂×D₇×C₁₀₇	1	1	yes	characteristic, direct product factor
32	C₂²	—	7	1	no	Sylow
33	C₂	—	7	2	no	—
34	C₂	C₇×D₇×C₁₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₀₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₇×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₀₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₇×C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₇×C₁₀₇	C₂	direct (N × H)
2. C₂×C₇²×C₁₀₇	C₂	semidirect
3. C₇²×C₁₀₇	C₂²	semidirect
4. C₂×D₇×C₁₀₇	C₇	direct (N × H)
8. C₂×C₇×C₁₀₇	D₇	direct (N × H)
9. C₂×C₇×C₁₀₇	C₂×C₇	semidirect
10. D₇×C₁₀₇	C₂×C₇	direct (N × H)
12. C₇×C₁₀₇	C₂×D₇	direct (N × H)
13. C₇×C₁₀₇	C₂²×C₇	semidirect
16. C₂×C₁₀₇	C₇×D₇	direct (N × H)
17. C₂×C₇×D₇	C₁₀₇	direct (N × H)
18. C₁₀₇	C₂×C₇×D₇	direct (N × H)
19. C₂×C₇²	C₂×C₁₀₇	semidirect
20. C₇×D₇	C₂×C₁₀₇	direct (N × H)
21. C₇²	C₂²×C₁₀₇	semidirect
23. C₂×D₇	C₇×C₁₀₇	direct (N × H)
26. C₂×C₇	D₇×C₁₀₇	direct (N × H)
27. C₂×C₇	C₂×C₇×C₁₀₇	semidirect
28. D₇	C₂×C₇×C₁₀₇	direct (N × H)
30. C₇	C₂²×C₇×C₁₀₇	semidirect
31. C₇	C₂×D₇×C₁₀₇	direct (N × H)
34. C₂	C₇×D₇×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₇×C₁₀₇	2
C₂×C₇²×C₁₀₇	2
C₂×D₇×C₁₀₇	7
C₂²×C₇×C₁₀₇	7
C₂×C₇×D₇	107

Subgroups — C2×C7×D7×C107 #35230489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₇×C₁₀₇ #35230489