Finite Group Databasebeta

← D₃×C₂₃×C₁₀₁ #28358261

Subgroups — D₃×C₂₃×C₁₀₁ #28358261

Order 13938.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₃×C₁₀₁	—	3	1	no	maximal, Hall
3	C₂₃×C₁₀₁	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₀₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₀₁	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₀₁	—	3	1	no	Hall
7	D₃×C₂₃	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₀₁	D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₂₃	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₂₃	—	3	1	no	Hall
11	C₂₃	D₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₂₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₂₃×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃×C₁₀₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₂₃×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₁₀₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂₃×C₁₀₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×C₁₀₁	C₂	semidirect
3. C₂₃×C₁₀₁	D₃	direct (N × H)
4. D₃×C₁₀₁	C₂₃	direct (N × H)
5. C₃×C₁₀₁	C₂×C₂₃	semidirect
7. D₃×C₂₃	C₁₀₁	direct (N × H)
8. C₁₀₁	D₃×C₂₃	direct (N × H)
9. C₃×C₂₃	C₂×C₁₀₁	semidirect
11. C₂₃	D₃×C₁₀₁	direct (N × H)
12. D₃	C₂₃×C₁₀₁	direct (N × H)
13. C₃	C₂×C₂₃×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂₃×C₁₀₁	2
C₂×C₂₃×C₁₀₁	3
D₃×C₁₀₁	23
D₃×C₂₃	101