Finite Group Databasebeta

← D₃×C₇×C₃₀₇ #27166310

Subgroups — D₃×C₇×C₃₀₇ #27166310

Order 12894.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇×C₃₀₇	—	3	1	no	maximal, Hall
3	C₇×C₃₀₇	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₃₀₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₃₀₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃₀₇	—	3	1	no	Hall
7	C₃₀₇	D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
8	D₃×C₇	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	C₂×C₃₀₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇	—	3	1	no	Hall
11	C₇	D₃×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₇×C₃₀₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₇×C₃₀₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₃₀₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₇×C₃₀₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₃₀₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₇×C₃₀₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₃₀₇	C₂	semidirect
3. C₇×C₃₀₇	D₃	direct (N × H)
4. D₃×C₃₀₇	C₇	direct (N × H)
5. C₃×C₃₀₇	C₂×C₇	semidirect
7. C₃₀₇	D₃×C₇	direct (N × H)
8. D₃×C₇	C₃₀₇	direct (N × H)
9. C₃×C₇	C₂×C₃₀₇	semidirect
11. C₇	D₃×C₃₀₇	direct (N × H)
12. D₃	C₇×C₃₀₇	direct (N × H)
13. C₃	C₂×C₇×C₃₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₃₀₇	2
C₂×C₇×C₃₀₇	3
D₃×C₃₀₇	7
D₃×C₇	307