Finite Group Databasebeta

← C₂×C₇×C₁₀₃⋊C₁₇ #37589192

Subgroups — C₂×C₇×C₁₀₃⋊C₁₇ #37589192

Order 24514.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₀₃⋊C₁₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₀₃⋊C₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₀₃⋊C₁₇	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₀₃	C₁₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₁₀₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₇	—	103	1	no	maximal, Hall
7	C₂×C₁₀₃	C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₇	—	103	1	no	Hall
9	C₁₀₃	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₇	—	103	1	no	Hall
11	C₁₇	—	103	1	no	Sylow
12	C₂×C₇	C₁₀₃⋊C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₇	C₂×C₁₀₃⋊C₁₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₇×C₁₀₃⋊C₁₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	C₁₀₃⋊C₁₇
commutator, cosocle, hypocenter	C₁₀₃	C₂×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₀₃	C₁₇
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₀₃⋊C₁₇	C₂	direct (N × H)
2. C₂×C₁₀₃⋊C₁₇	C₇	direct (N × H)
3. C₁₀₃⋊C₁₇	C₂×C₇	direct (N × H)
4. C₂×C₇×C₁₀₃	C₁₇	semidirect
5. C₇×C₁₀₃	C₂×C₁₇	semidirect
7. C₂×C₁₀₃	C₇×C₁₇	semidirect
9. C₁₀₃	C₂×C₇×C₁₇	semidirect
12. C₂×C₇	C₁₀₃⋊C₁₇	direct (N × H)
13. C₇	C₂×C₁₀₃⋊C₁₇	direct (N × H)
14. C₂	C₇×C₁₀₃⋊C₁₇	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×C₁₀₃⋊C₁₇	2
C₂×C₁₀₃⋊C₁₇	7
C₂×C₇×C₁₀₃	17
C₂×C₇×C₁₇	103