Finite Group Databasebeta

← C₂×C₇×C₃₀₇⋊C₃ #27166303

Subgroups — C₂×C₇×C₃₀₇⋊C₃ #27166303

Order 12894.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₀₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₃₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₃₀₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₀₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₀₇⋊C₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₀₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
7	C₃₀₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₇	—	307	1	no	maximal, Hall
9	C₃×C₇	—	307	1	no	Hall
10	C₂×C₇	C₃₀₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₇	C₂×C₃₀₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	307	1	no	Hall
13	C₃	—	307	1	no	Sylow
14	C₂	C₇×C₃₀₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₀₇⋊C₃	C₂	direct (N × H)
2. C₂×C₇×C₃₀₇	C₃	semidirect
3. C₇×C₃₀₇	C₂×C₃	semidirect
4. C₂×C₃₀₇⋊C₃	C₇	direct (N × H)
5. C₃₀₇⋊C₃	C₂×C₇	direct (N × H)
6. C₂×C₃₀₇	C₃×C₇	semidirect
7. C₃₀₇	C₂×C₃×C₇	semidirect
10. C₂×C₇	C₃₀₇⋊C₃	direct (N × H)
11. C₇	C₂×C₃₀₇⋊C₃	direct (N × H)
14. C₂	C₇×C₃₀₇⋊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
C₇×C₃₀₇⋊C₃	2
C₂×C₇×C₃₀₇	3
C₂×C₃₀₇⋊C₃	7
C₂×C₃×C₇	307