Finite Group Databasebeta

← C₃×D₁₁×C₄₀₉ #41008807

Subgroups — C₃×D₁₁×C₄₀₉ #41008807

Order 26994.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₄₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×C₄₀₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₄₀₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₄₀₉	—	11	1	no	maximal, Hall
5	C₃×C₄₀₉	D₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄₀₉	—	11	1	no	Hall
7	C₄₀₉	C₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×D₁₁	C₄₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁	C₂×C₄₀₉	1	1	yes	characteristic, complemented, Hall
10	D₁₁	C₃×C₄₀₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁	C₂×C₃×C₄₀₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	11	1	no	Hall
13	C₃	D₁₁×C₄₀₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₀₉	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₄₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₄₀₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₄₀₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₄₀₉	C₂	semidirect
2. D₁₁×C₄₀₉	C₃	direct (N × H)
3. C₁₁×C₄₀₉	C₂×C₃	semidirect
5. C₃×C₄₀₉	D₁₁	direct (N × H)
7. C₄₀₉	C₃×D₁₁	direct (N × H)
8. C₃×D₁₁	C₄₀₉	direct (N × H)
9. C₃×C₁₁	C₂×C₄₀₉	semidirect
10. D₁₁	C₃×C₄₀₉	direct (N × H)
11. C₁₁	C₂×C₃×C₄₀₉	semidirect
13. C₃	D₁₁×C₄₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁×C₄₀₉	2
D₁₁×C₄₀₉	3
C₂×C₃×C₄₀₉	11
C₃×D₁₁	409