Finite Group Databasebeta

← C₁₇×D₈₇₁ #44444147

Subgroups — C₁₇×D₈₇₁ #44444147

Order 29614.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₆₇	—	13	1	no	maximal, Hall
3	D₈₇₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₆₇	D₁₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₆₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₁₃	—	67	1	no	maximal, Hall
7	C₁₃×C₁₇	D₆₇	1	1	yes	characteristic, complemented, Hall
8	D₆₇	—	13	1	no	Hall
9	C₆₇	C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₇	—	871	1	no	Hall
11	D₁₃	—	67	1	no	Hall
12	C₁₇	D₈₇₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	C₁₇×D₆₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	871	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₈₇₁
commutator, cosocle, hypocenter	C₁₃×C₆₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₆₇	C₂
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₆₇	C₂	semidirect
3. D₈₇₁	C₁₇	direct (N × H)
4. C₁₇×C₆₇	D₁₃	semidirect
5. C₁₃×C₆₇	C₂×C₁₇	semidirect
7. C₁₃×C₁₇	D₆₇	semidirect
9. C₆₇	C₁₇×D₁₃	semidirect
12. C₁₇	D₈₇₁	direct (N × H)
13. C₁₃	C₁₇×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₇×C₆₇	2
C₁₇×D₆₇	13
D₈₇₁	17
C₁₇×D₁₃	67