Finite Group Databasebeta

← C₂×C₃₇×C₇₃⋊C₃ #30633751

Subgroups — C₂×C₃₇×C₇₃⋊C₃ #30633751

Order 16206.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃₇×C₇₃⋊C₃	C₂	direct (N × H)
2. C₂×C₃₇×C₇₃	C₃	semidirect
3. C₃₇×C₇₃	C₂×C₃	semidirect
4. C₂×C₇₃⋊C₃	C₃₇	direct (N × H)
6. C₇₃⋊C₃	C₂×C₃₇	direct (N × H)
7. C₂×C₇₃	C₃×C₃₇	semidirect
9. C₂×C₃₇	C₇₃⋊C₃	direct (N × H)
10. C₇₃	C₂×C₃×C₃₇	semidirect
11. C₃₇	C₂×C₇₃⋊C₃	direct (N × H)
14. C₂	C₃₇×C₇₃⋊C₃	direct (N × H)

Maximal subgroups

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

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