Finite Group Databasebeta

← C₁₁×C₂₉×D₁₇ #24925729

Subgroups — C₁₁×C₂₉×D₁₇ #24925729

Order 10846.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₁×C₂₉	—	17	1	no	maximal, Hall
4	C₁₇×C₂₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₁₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₂₉	D₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₁₁×C₁₇	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₂₉	—	17	1	no	Hall
9	D₁₇	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂₉	C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₁	—	17	1	no	Hall
12	C₁₇	C₂×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
13	C₁₁	C₂₉×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₂₉	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₁₁×C₂₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇×C₂₉	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₁×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₂₉	C₂	semidirect
2. C₂₉×D₁₇	C₁₁	direct (N × H)
4. C₁₇×C₂₉	C₂×C₁₁	semidirect
5. C₁₁×D₁₇	C₂₉	direct (N × H)
6. C₁₁×C₂₉	D₁₇	direct (N × H)
7. C₁₁×C₁₇	C₂×C₂₉	semidirect
9. D₁₇	C₁₁×C₂₉	direct (N × H)
10. C₂₉	C₁₁×D₁₇	direct (N × H)
12. C₁₇	C₂×C₁₁×C₂₉	semidirect
13. C₁₁	C₂₉×D₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×C₂₉	2
C₂₉×D₁₇	11
C₂×C₁₁×C₂₉	17
C₁₁×D₁₇	29