Finite Group Databasebeta

← C₁₁×C₂₉×D₅₃ #46799015

Subgroups — C₁₁×C₂₉×D₅₃ #46799015

Order 33814.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₅₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₅₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₅₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₂₉	—	53	1	no	maximal, Hall
6	C₁₁×C₅₃	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₂₉	D₅₃	1	1	yes	characteristic, direct product factor, Hall
8	D₅₃	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₂₉	—	53	1	no	Hall
10	C₅₃	C₂×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
11	C₂₉	C₁₁×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₁₁	—	53	1	no	Hall
13	C₁₁	C₂₉×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	53	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₂₉	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂×C₁₁×C₂₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₂₉×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₁₁×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₉×C₅₃	C₂	semidirect
2. C₂₉×D₅₃	C₁₁	direct (N × H)
3. C₂₉×C₅₃	C₂×C₁₁	semidirect
4. C₁₁×D₅₃	C₂₉	direct (N × H)
6. C₁₁×C₅₃	C₂×C₂₉	semidirect
7. C₁₁×C₂₉	D₅₃	direct (N × H)
8. D₅₃	C₁₁×C₂₉	direct (N × H)
10. C₅₃	C₂×C₁₁×C₂₉	semidirect
11. C₂₉	C₁₁×D₅₃	direct (N × H)
13. C₁₁	C₂₉×D₅₃	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×C₂₉×C₅₃	2
C₂₉×D₅₃	11
C₁₁×D₅₃	29
C₂×C₁₁×C₂₉	53