Finite Group Databasebeta

← C₃₇⋊C₃×D₇₃ #30633763

Subgroups — C₃₇⋊C₃×D₇₃ #30633763

Order 16206.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₃	—	37	1	no	maximal, Hall
5	C₂×C₃₇⋊C₃	—	73	1	no	maximal, Hall
6	C₃×C₇₃	—	37	1	no	Hall
7	D₇₃	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃₇⋊C₃	D₇₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃₇	—	73	1	no	Hall
10	C₇₃	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
11	C₃₇	C₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	2701	1	no	Hall
13	C₃	—	37	1	no	Sylow
14	C₂	—	73	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₇×C₇₃	C₂×C₃
LCS	G ▷ C₃₇×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇₃×C₃₇⋊C₃	C₂	semidirect
2. C₃₇×D₇₃	C₃	semidirect
3. C₃₇×C₇₃	C₂×C₃	semidirect
7. D₇₃	C₃₇⋊C₃	direct (N × H)
8. C₃₇⋊C₃	D₇₃	direct (N × H)
10. C₇₃	C₂×C₃₇⋊C₃	semidirect
11. C₃₇	C₃×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×C₃₇⋊C₃	2
C₃₇×D₇₃	3
C₃×D₇₃	37
C₂×C₃₇⋊C₃	73