Finite Group Databasebeta

← C₃×D₄₃×C₁₂₇ #45658773

Subgroups — C₃×D₄₃×C₁₂₇ #45658773

Order 32766.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₃×C₁₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₂₇	—	43	1	no	maximal, Hall
5	C₃×C₁₂₇	D₄₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×D₄₃	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₂₇	—	43	1	no	Hall
8	C₃×C₄₃	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Hall
9	C₁₂₇	C₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
10	D₄₃	C₃×C₁₂₇	1	1	yes	characteristic, direct product factor, Hall
11	C₄₃	C₂×C₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	43	1	no	Hall
13	C₃	D₄₃×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₂₇	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₃×C₄₃×C₁₂₇	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₁₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₃×C₁₂₇	C₂	semidirect
2. D₄₃×C₁₂₇	C₃	direct (N × H)
3. C₄₃×C₁₂₇	C₂×C₃	semidirect
5. C₃×C₁₂₇	D₄₃	direct (N × H)
6. C₃×D₄₃	C₁₂₇	direct (N × H)
8. C₃×C₄₃	C₂×C₁₂₇	semidirect
9. C₁₂₇	C₃×D₄₃	direct (N × H)
10. D₄₃	C₃×C₁₂₇	direct (N × H)
11. C₄₃	C₂×C₃×C₁₂₇	semidirect
13. C₃	D₄₃×C₁₂₇	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×C₄₃×C₁₂₇	2
D₄₃×C₁₂₇	3
C₂×C₃×C₁₂₇	43
C₃×D₄₃	127