Finite Group Databasebeta

← D₃×C₇₃×C₈₃ #49138255

Subgroups — D₃×C₇₃×C₈₃ #49138255

Order 36354.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₃×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇₃×C₈₃	—	3	1	no	maximal, Hall
3	C₇₃×C₈₃	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₈₃	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₇₃	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₈₃	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇₃	C₂×C₈₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₈₃	—	3	1	no	Hall
9	C₂×C₇₃	—	3	1	no	Hall
10	C₈₃	D₃×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₇₃	D₃×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₇₃×C₈₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₇₃×C₈₃	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃×C₈₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₇₃×C₈₃
Frattini	C₁	G
Fitting, socle	C₃×C₇₃×C₈₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₇₃×C₈₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₃×C₈₃	C₂	semidirect
3. C₇₃×C₈₃	D₃	direct (N × H)
4. D₃×C₈₃	C₇₃	direct (N × H)
5. D₃×C₇₃	C₈₃	direct (N × H)
6. C₃×C₈₃	C₂×C₇₃	semidirect
7. C₃×C₇₃	C₂×C₈₃	semidirect
10. C₈₃	D₃×C₇₃	direct (N × H)
11. C₇₃	D₃×C₈₃	direct (N × H)
12. D₃	C₇₃×C₈₃	direct (N × H)
13. C₃	C₂×C₇₃×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇₃×C₈₃	2
C₂×C₇₃×C₈₃	3
D₃×C₈₃	73
D₃×C₇₃	83