Finite Group Databasebeta

← D₇×C₁₇×C₅₃ #27162195

Subgroups — D₇×C₁₇×C₅₃ #27162195

Order 12614.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₇×C₅₃	—	7	1	no	maximal, Hall
3	C₁₇×C₅₃	D₇	1	1	yes	characteristic, direct product factor, Hall
4	D₇×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₅₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	D₇×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₇	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅₃	—	7	1	no	Hall
9	C₅₃	D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₇	—	7	1	no	Hall
11	C₁₇	D₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₇	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇	C₂×C₁₇×C₅₃	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₅₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₇×C₅₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₅₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₇×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₇×C₅₃	C₂	semidirect
3. C₁₇×C₅₃	D₇	direct (N × H)
4. D₇×C₅₃	C₁₇	direct (N × H)
5. C₇×C₅₃	C₂×C₁₇	semidirect
6. D₇×C₁₇	C₅₃	direct (N × H)
7. C₇×C₁₇	C₂×C₅₃	semidirect
9. C₅₃	D₇×C₁₇	direct (N × H)
11. C₁₇	D₇×C₅₃	direct (N × H)
12. D₇	C₁₇×C₅₃	direct (N × H)
13. C₇	C₂×C₁₇×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₅₃	2
C₂×C₁₇×C₅₃	7
D₇×C₅₃	17
D₇×C₁₇	53