Finite Group Databasebeta

← D₂₁×C₈₅₉ #49115271

Subgroups — D₂₁×C₈₅₉ #49115271

Order 36078.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₈₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₈₅₉	—	3	1	no	maximal, Hall
3	C₇×C₈₅₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₈₅₉	—	7	1	no	maximal, Hall
5	C₃×C₈₅₉	D₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₈₅₉	—	21	1	no	Hall
7	C₈₅₉	D₂₁	1	1	yes	characteristic, direct product factor, Sylow
8	D₂₁	C₈₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	C₂×C₈₅₉	1	1	yes	characteristic, complemented, Hall
10	D₇	—	3	1	no	Hall
11	C₇	D₃×C₈₅₉	1	1	yes	characteristic, complemented, Sylow
12	D₃	—	7	1	no	Hall
13	C₃	D₇×C₈₅₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₅₉	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₈₅₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₈₅₉	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₈₅₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₈₅₉	C₂	semidirect
3. C₇×C₈₅₉	D₃	semidirect
5. C₃×C₈₅₉	D₇	semidirect
7. C₈₅₉	D₂₁	direct (N × H)
8. D₂₁	C₈₅₉	direct (N × H)
9. C₃×C₇	C₂×C₈₅₉	semidirect
11. C₇	D₃×C₈₅₉	semidirect
13. C₃	D₇×C₈₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₈₅₉	2
D₇×C₈₅₉	3
D₃×C₈₅₉	7
D₂₁	859