Finite Group Databasebeta

← C₃×D₃×C₈₂₃ #28414510

Subgroups — C₃×D₃×C₈₂₃ #28414510

Order 14814.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃×C₈₂₃	—	3	1	no	maximal
3	D₃×C₈₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₈₂₃	—	2	1	no	—
5	C₃×C₈₂₃	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₈₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₈₂₃	—	3	1	no	Hall
8	C₈₂₃	C₃×D₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×D₃	C₈₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²	C₂×C₈₂₃	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃	—	3	1	no	—
12	D₃	C₃×C₈₂₃	1	1	yes	characteristic, direct product factor
13	C₃	—	2	1	no	—
14	C₃	D₃×C₈₂₃	1	1	yes	characteristic, direct product factor
15	C₃	C₂×C₃×C₈₂₃	1	1	yes	characteristic, complemented
16	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₈₂₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₈₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₈₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₈₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₈₂₃	C₂	semidirect
3. D₃×C₈₂₃	C₃	direct (N × H)
5. C₃×C₈₂₃	D₃	direct (N × H)
6. C₃×C₈₂₃	C₂×C₃	semidirect
8. C₈₂₃	C₃×D₃	direct (N × H)
9. C₃×D₃	C₈₂₃	direct (N × H)
10. C₃²	C₂×C₈₂₃	semidirect
12. D₃	C₃×C₈₂₃	direct (N × H)
14. C₃	D₃×C₈₂₃	direct (N × H)
15. C₃	C₂×C₃×C₈₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₈₂₃	2
C₂×C₃×C₈₂₃	3
D₃×C₈₂₃	3
C₃×D₃	823