Finite Group Databasebeta

← C₁₇×D₁₁×C₂₉ #24925731

Subgroups — C₁₇×D₁₁×C₂₉ #24925731

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	C₂×C₁₇×C₂₉	—	11	1	no	maximal, Hall
3	D₁₁×C₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₂₉	D₁₁	1	1	yes	characteristic, direct product factor, Hall
5	C₁₇×D₁₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₂₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₁₇	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₂₉	—	11	1	no	Hall
9	C₂×C₁₇	—	11	1	no	Hall
10	C₂₉	C₁₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
11	D₁₁	C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
12	C₁₇	D₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₂×C₁₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₂₉	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₁₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇×C₂₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₇×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₂₉	C₂	semidirect
3. D₁₁×C₂₉	C₁₇	direct (N × H)
4. C₁₇×C₂₉	D₁₁	direct (N × H)
5. C₁₇×D₁₁	C₂₉	direct (N × H)
6. C₁₁×C₂₉	C₂×C₁₇	semidirect
7. C₁₁×C₁₇	C₂×C₂₉	semidirect
10. C₂₉	C₁₇×D₁₁	direct (N × H)
11. D₁₁	C₁₇×C₂₉	direct (N × H)
12. C₁₇	D₁₁×C₂₉	direct (N × H)
13. C₁₁	C₂×C₁₇×C₂₉	semidirect

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
C₂×C₁₇×C₂₉	11
D₁₁×C₂₉	17
C₁₇×D₁₁	29