Finite Group Databasebeta

← C₃×D₇×C₇₆₁ #44544185

Subgroups — C₃×D₇×C₇₆₁ #44544185

Order 31962.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₇₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₇₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₇₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇₆₁	—	7	1	no	maximal, Hall
5	C₃×C₇₆₁	D₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₇₆₁	—	7	1	no	Hall
7	C₇₆₁	C₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×D₇	C₇₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	C₂×C₇₆₁	1	1	yes	characteristic, complemented, Hall
10	D₇	C₃×C₇₆₁	1	1	yes	characteristic, direct product factor, Hall
11	C₇	C₂×C₃×C₇₆₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	7	1	no	Hall
13	C₃	D₇×C₇₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇₆₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₇₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₇₆₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₇₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₇₆₁	C₂	semidirect
2. D₇×C₇₆₁	C₃	direct (N × H)
3. C₇×C₇₆₁	C₂×C₃	semidirect
5. C₃×C₇₆₁	D₇	direct (N × H)
7. C₇₆₁	C₃×D₇	direct (N × H)
8. C₃×D₇	C₇₆₁	direct (N × H)
9. C₃×C₇	C₂×C₇₆₁	semidirect
10. D₇	C₃×C₇₆₁	direct (N × H)
11. C₇	C₂×C₃×C₇₆₁	semidirect
13. C₃	D₇×C₇₆₁	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×C₇×C₇₆₁	2
D₇×C₇₆₁	3
C₂×C₃×C₇₆₁	7
C₃×D₇	761