Finite Group Databasebeta

← D₃×C₁₁×C₄₀₉ #41008809

Subgroups — D₃×C₁₁×C₄₀₉ #41008809

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	C₂×C₁₁×C₄₀₉	—	3	1	no	maximal, Hall
3	C₁₁×C₄₀₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₄₀₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄₀₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₄₀₉	—	3	1	no	Hall
7	C₄₀₉	D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	D₃×C₁₁	C₄₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁	C₂×C₄₀₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁	—	3	1	no	Hall
11	C₁₁	D₃×C₄₀₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₁₁×C₄₀₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₁₁×C₄₀₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₄₀₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₁×C₄₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₄₀₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₁×C₄₀₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₄₀₉	C₂	semidirect
3. C₁₁×C₄₀₉	D₃	direct (N × H)
4. D₃×C₄₀₉	C₁₁	direct (N × H)
5. C₃×C₄₀₉	C₂×C₁₁	semidirect
7. C₄₀₉	D₃×C₁₁	direct (N × H)
8. D₃×C₁₁	C₄₀₉	direct (N × H)
9. C₃×C₁₁	C₂×C₄₀₉	semidirect
11. C₁₁	D₃×C₄₀₉	direct (N × H)
12. D₃	C₁₁×C₄₀₉	direct (N × H)
13. C₃	C₂×C₁₁×C₄₀₉	semidirect

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
C₂×C₁₁×C₄₀₉	3
D₃×C₄₀₉	11
D₃×C₁₁	409