Finite Group Databasebeta

← C₇×D₇₆₃ #24922698

Subgroups — C₇×D₇₆₃ #24922698

Order 10682.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₆₃	C₇	1	1	yes	maximal, characteristic, direct product factor
3	C₇×D₁₀₉	—	7	1	no	maximal
4	C₇×C₁₀₉	—	2	3	no	—
5	C₇×C₁₀₉	D₇	1	1	yes	characteristic, complemented
6	C₇×C₁₀₉	C₂×C₇	1	1	yes	characteristic, complemented
7	D₁₀₉	—	7	1	no	Hall
8	C₁₀₉	C₇×D₇	1	1	yes	characteristic, complemented, Sylow
9	C₇×D₇	—	109	1	no	maximal, Hall
10	C₇²	D₁₀₉	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₇	—	763	1	no	—
12	D₇	—	109	1	no	—
13	C₇	—	2	3	no	—
14	C₇	C₇×D₁₀₉	1	1	yes	characteristic, complemented
15	C₇	D₇₆₃	1	1	yes	characteristic, direct product factor
16	C₂	—	763	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₇₆₃
commutator, cosocle, hypocenter	C₇×C₁₀₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₀₉	C₂
LCS	G ▷ C₇×C₁₀₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇²×C₁₀₉	C₂	semidirect
2. D₇₆₃	C₇	direct (N × H)
5. C₇×C₁₀₉	D₇	semidirect
6. C₇×C₁₀₉	C₂×C₇	semidirect
8. C₁₀₉	C₇×D₇	semidirect
10. C₇²	D₁₀₉	semidirect
14. C₇	C₇×D₁₀₉	semidirect
15. C₇	D₇₆₃	direct (N × H)