Finite Group Databasebeta

← C₁₁×C₁₇×D₂₉ #24925728

Subgroups — C₁₁×C₁₇×D₂₉ #24925728

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	C₁₇×D₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×D₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₂₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₇	—	29	1	no	maximal, Hall
6	C₁₁×C₂₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₁₇	D₂₉	1	1	yes	characteristic, direct product factor, Hall
8	D₂₉	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₇	—	29	1	no	Hall
10	C₂₉	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₁₁	—	29	1	no	Hall
12	C₁₇	C₁₁×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₁₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₂₉	C₂	semidirect
2. C₁₇×D₂₉	C₁₁	direct (N × H)
3. C₁₁×D₂₉	C₁₇	direct (N × H)
4. C₁₇×C₂₉	C₂×C₁₁	semidirect
6. C₁₁×C₂₉	C₂×C₁₇	semidirect
7. C₁₁×C₁₇	D₂₉	direct (N × H)
8. D₂₉	C₁₁×C₁₇	direct (N × H)
10. C₂₉	C₂×C₁₁×C₁₇	semidirect
12. C₁₇	C₁₁×D₂₉	direct (N × H)
13. C₁₁	C₁₇×D₂₉	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
C₁₇×D₂₉	11
C₁₁×D₂₉	17
C₂×C₁₁×C₁₇	29