Finite Group Databasebeta

← C₇×D₁₄₅₇ #35205205

Subgroups — C₇×D₁₄₅₇ #35205205

Order 20398.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₄₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	C₇×D₄₇	—	31	1	no	maximal, Hall
5	C₇×D₃₁	—	47	1	no	maximal, Hall
6	C₇×C₄₇	D₃₁	1	1	yes	characteristic, complemented, Hall
7	C₇×C₃₁	D₄₇	1	1	yes	characteristic, complemented, Hall
8	D₄₇	—	31	1	no	Hall
9	D₃₁	—	47	1	no	Hall
10	C₄₇	C₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
11	C₃₁	C₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇	—	1457	1	no	Hall
13	C₇	D₁₄₅₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	1457	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₄₅₇
commutator, cosocle, hypocenter	C₃₁×C₄₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₃₁×C₄₇	C₂
LCS	G ▷ C₃₁×C₄₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×C₄₇	C₂	semidirect
2. D₁₄₅₇	C₇	direct (N × H)
3. C₃₁×C₄₇	C₂×C₇	semidirect
6. C₇×C₄₇	D₃₁	semidirect
7. C₇×C₃₁	D₄₇	semidirect
10. C₄₇	C₇×D₃₁	semidirect
11. C₃₁	C₇×D₄₇	semidirect
13. C₇	D₁₄₅₇	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×C₃₁×C₄₇	2
D₁₄₅₇	7
C₇×D₄₇	31
C₇×D₃₁	47