Finite Group Databasebeta

← C₂×C₃×C₇₀₁⋊C₇ #44441237

Subgroups — C₂×C₃×C₇₀₁⋊C₇ #44441237

Order 29442.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₀₁⋊C₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇₀₁⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇₀₁⋊C₇	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇₀₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₇₀₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇₀₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇₀₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₇	—	701	1	no	maximal, Hall
9	C₃×C₇	—	701	1	no	Hall
10	C₂×C₇	—	701	1	no	Hall
11	C₇	—	701	1	no	Sylow
12	C₂×C₃	C₇₀₁⋊C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₇₀₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₇₀₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	C₇₀₁⋊C₇
commutator, cosocle, hypocenter	C₇₀₁	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇₀₁	C₇
LCS	G ▷ C₇₀₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₀₁⋊C₇	C₂	direct (N × H)
2. C₂×C₇₀₁⋊C₇	C₃	direct (N × H)
3. C₇₀₁⋊C₇	C₂×C₃	direct (N × H)
4. C₂×C₃×C₇₀₁	C₇	semidirect
5. C₃×C₇₀₁	C₂×C₇	semidirect
6. C₂×C₇₀₁	C₃×C₇	semidirect
7. C₇₀₁	C₂×C₃×C₇	semidirect
12. C₂×C₃	C₇₀₁⋊C₇	direct (N × H)
13. C₃	C₂×C₇₀₁⋊C₇	direct (N × H)
14. C₂	C₃×C₇₀₁⋊C₇	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×C₇₀₁⋊C₇	2
C₂×C₇₀₁⋊C₇	3
C₂×C₃×C₇₀₁	7
C₂×C₃×C₇	701