Finite Group Databasebeta

← C₇₃×D₁₁₁ #30633760

Subgroups — C₇₃×D₁₁₁ #30633760

Order 16206.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₃×D₃₇	—	3	1	no	maximal, Hall
3	C₃₇×C₇₃	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₇₃	—	37	1	no	maximal, Hall
5	D₁₁₁	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇₃	D₃₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇₃	—	111	1	no	Hall
8	C₃×C₃₇	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
9	D₃₇	—	3	1	no	Hall
10	C₇₃	D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₇	D₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
12	D₃	—	37	1	no	Hall
13	C₃	C₇₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	111	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃	D₁₁₁
commutator, cosocle, hypocenter	C₃×C₃₇	C₂×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₃₇×C₇₃	C₂
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₇×C₇₃	C₂	semidirect
3. C₃₇×C₇₃	D₃	semidirect
5. D₁₁₁	C₇₃	direct (N × H)
6. C₃×C₇₃	D₃₇	semidirect
8. C₃×C₃₇	C₂×C₇₃	semidirect
10. C₇₃	D₁₁₁	direct (N × H)
11. C₃₇	D₃×C₇₃	semidirect
13. C₃	C₇₃×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₇₃	2
C₇₃×D₃₇	3
D₃×C₇₃	37
D₁₁₁	73