Finite Group Databasebeta

← C₃×D₄₇×C₁₀₃ #44395173

Subgroups — C₃×D₄₇×C₁₀₃ #44395173

Order 29046.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₇×C₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₀₃	—	47	1	no	maximal, Hall
5	C₃×C₁₀₃	D₄₇	1	1	yes	characteristic, direct product factor, Hall
6	C₃×D₄₇	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₀₃	—	47	1	no	Hall
8	C₃×C₄₇	C₂×C₁₀₃	1	1	yes	characteristic, complemented, Hall
9	C₁₀₃	C₃×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
10	D₄₇	C₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
11	C₄₇	C₂×C₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	47	1	no	Hall
13	C₃	D₄₇×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	47	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₀₃	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₃×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₇×C₁₀₃	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₃×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₇×C₁₀₃	C₂	semidirect
2. D₄₇×C₁₀₃	C₃	direct (N × H)
3. C₄₇×C₁₀₃	C₂×C₃	semidirect
5. C₃×C₁₀₃	D₄₇	direct (N × H)
6. C₃×D₄₇	C₁₀₃	direct (N × H)
8. C₃×C₄₇	C₂×C₁₀₃	semidirect
9. C₁₀₃	C₃×D₄₇	direct (N × H)
10. D₄₇	C₃×C₁₀₃	direct (N × H)
11. C₄₇	C₂×C₃×C₁₀₃	semidirect
13. C₃	D₄₇×C₁₀₃	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×C₄₇×C₁₀₃	2
D₄₇×C₁₀₃	3
C₂×C₃×C₁₀₃	47
C₃×D₄₇	103