Finite Group Databasebeta

← C₃×C₃₇×D₇₁ #30628792

Subgroups — C₃×C₃₇×D₇₁ #30628792

Order 15762.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₇×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₃₇	—	71	1	no	maximal, Hall
6	C₃×C₇₁	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
7	D₇₁	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₃₇	D₇₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃₇	—	71	1	no	Hall
10	C₇₁	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
11	C₃₇	C₃×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	71	1	no	Hall
13	C₃	C₃₇×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₇	D₇₁
commutator, cosocle, hypocenter	C₇₁	C₂×C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₃₇×C₇₁	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₃×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₇×C₇₁	C₂	semidirect
2. C₃₇×D₇₁	C₃	direct (N × H)
3. C₃₇×C₇₁	C₂×C₃	semidirect
4. C₃×D₇₁	C₃₇	direct (N × H)
6. C₃×C₇₁	C₂×C₃₇	semidirect
7. D₇₁	C₃×C₃₇	direct (N × H)
8. C₃×C₃₇	D₇₁	direct (N × H)
10. C₇₁	C₂×C₃×C₃₇	semidirect
11. C₃₇	C₃×D₇₁	direct (N × H)
13. C₃	C₃₇×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₇₁	2
C₃₇×D₇₁	3
C₃×D₇₁	37
C₂×C₃×C₃₇	71