Finite Group Databasebeta

← D₁₁×C₂₉×C₄₁ #39908552

Subgroups — D₁₁×C₂₉×C₄₁ #39908552

Order 26158.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₉×C₄₁	—	11	1	no	maximal, Hall
3	C₂₉×C₄₁	D₁₁	1	1	yes	characteristic, direct product factor, Hall
4	D₁₁×C₄₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₁₁×C₂₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₄₁	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₂₉	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₁	—	11	1	no	Hall
9	C₂×C₂₉	—	11	1	no	Hall
10	C₄₁	D₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₉	D₁₁×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₁₁	C₂₉×C₄₁	1	1	yes	characteristic, direct product factor, Hall
13	C₁₁	C₂×C₂₉×C₄₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉×C₄₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₂₉×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₂₉×C₄₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂₉×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₉×C₄₁	C₂	semidirect
3. C₂₉×C₄₁	D₁₁	direct (N × H)
4. D₁₁×C₄₁	C₂₉	direct (N × H)
5. D₁₁×C₂₉	C₄₁	direct (N × H)
6. C₁₁×C₄₁	C₂×C₂₉	semidirect
7. C₁₁×C₂₉	C₂×C₄₁	semidirect
10. C₄₁	D₁₁×C₂₉	direct (N × H)
11. C₂₉	D₁₁×C₄₁	direct (N × H)
12. D₁₁	C₂₉×C₄₁	direct (N × H)
13. C₁₁	C₂×C₂₉×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₂₉×C₄₁	2
C₂×C₂₉×C₄₁	11
D₁₁×C₄₁	29
D₁₁×C₂₉	41