Finite Group Databasebeta

← C₈₉×D₆₁⋊C₃ #45654686

Subgroups — C₈₉×D₆₁⋊C₃ #45654686

Order 32574.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₈₉×D₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₁×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₈₉	—	61	1	no	maximal, Hall
5	D₆₁⋊C₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₈₉	—	61	1	no	Hall
7	C₆₁⋊C₃	C₂×C₈₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₈₉	—	61	1	no	Hall
9	D₆₁	C₃×C₈₉	1	1	yes	characteristic, complemented, Hall
10	C₈₉	D₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₆₁	C₂×C₃×C₈₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	61	1	no	Hall
13	C₃	—	61	1	no	Sylow
14	C₂	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₉	D₆₁⋊C₃
commutator, cosocle, hypocenter	C₆₁	C₂×C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₆₁×C₈₉	C₂×C₃
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₈₉

Complements

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

N	H ≅ G/N	type
1. C₈₉×C₆₁⋊C₃	C₂	semidirect
2. C₈₉×D₆₁	C₃	semidirect
3. C₆₁×C₈₉	C₂×C₃	semidirect
5. D₆₁⋊C₃	C₈₉	direct (N × H)
7. C₆₁⋊C₃	C₂×C₈₉	semidirect
9. D₆₁	C₃×C₈₉	semidirect
10. C₈₉	D₆₁⋊C₃	direct (N × H)
11. C₆₁	C₂×C₃×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×C₆₁⋊C₃	2
C₈₉×D₆₁	3
C₂×C₃×C₈₉	61
D₆₁⋊C₃	89