Finite Group Databasebeta

← C₁₉×D₁₁×C₄₁ #30686201

Subgroups — C₁₉×D₁₁×C₄₁ #30686201

Order 17138.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₉×C₄₁	—	11	1	no	maximal, Hall
3	D₁₁×C₄₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₄₁	D₁₁	1	1	yes	characteristic, direct product factor, Hall
5	C₁₁×C₄₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₁₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₁₉	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₁	—	11	1	no	Hall
9	C₄₁	C₁₉×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₉	—	11	1	no	Hall
11	D₁₁	C₁₉×C₄₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₉	D₁₁×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₂×C₁₉×C₄₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₄₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₁₉×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₄₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₉×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₄₁	C₂	semidirect
3. D₁₁×C₄₁	C₁₉	direct (N × H)
4. C₁₉×C₄₁	D₁₁	direct (N × H)
5. C₁₁×C₄₁	C₂×C₁₉	semidirect
6. C₁₉×D₁₁	C₄₁	direct (N × H)
7. C₁₁×C₁₉	C₂×C₄₁	semidirect
9. C₄₁	C₁₉×D₁₁	direct (N × H)
11. D₁₁	C₁₉×C₄₁	direct (N × H)
12. C₁₉	D₁₁×C₄₁	direct (N × H)
13. C₁₁	C₂×C₁₉×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₄₁	2
C₂×C₁₉×C₄₁	11
D₁₁×C₄₁	19
C₁₉×D₁₁	41