Finite Group Databasebeta

← C₃×C₄₃×D₈₉ #37525816

Subgroups — C₃×C₄₃×D₈₉ #37525816

Order 22962.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₈₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₈₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₈₉	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₄₃	—	89	1	no	maximal, Hall
7	D₈₉	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₄₃	D₈₉	1	1	yes	characteristic, direct product factor, Hall
9	C₈₉	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₄₃	—	89	1	no	Hall
11	C₄₃	C₃×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	89	1	no	Hall
13	C₃	C₄₃×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	89	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₃	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₃×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₃×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₃×C₈₉	C₂	semidirect
2. C₄₃×D₈₉	C₃	direct (N × H)
3. C₄₃×C₈₉	C₂×C₃	semidirect
4. C₃×D₈₉	C₄₃	direct (N × H)
5. C₃×C₈₉	C₂×C₄₃	semidirect
7. D₈₉	C₃×C₄₃	direct (N × H)
8. C₃×C₄₃	D₈₉	direct (N × H)
9. C₈₉	C₂×C₃×C₄₃	semidirect
11. C₄₃	C₃×D₈₉	direct (N × H)
13. C₃	C₄₃×D₈₉	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×C₄₃×C₈₉	2
C₄₃×D₈₉	3
C₃×D₈₉	43
C₂×C₃×C₄₃	89