Finite Group Databasebeta

← C₇×C₃₁×D₄₃ #32916248

Subgroups — C₇×C₃₁×D₄₃ #32916248

Order 18662.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₄₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	C₇×D₄₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₃₁	—	43	1	no	maximal, Hall
6	C₇×C₄₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
7	C₇×C₃₁	D₄₃	1	1	yes	characteristic, direct product factor, Hall
8	D₄₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃₁	—	43	1	no	Hall
10	C₄₃	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
11	C₃₁	C₇×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	—	43	1	no	Hall
13	C₇	C₃₁×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₃₁	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₇×C₃₁×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×C₄₃	C₂	semidirect
2. C₃₁×D₄₃	C₇	direct (N × H)
3. C₃₁×C₄₃	C₂×C₇	semidirect
4. C₇×D₄₃	C₃₁	direct (N × H)
6. C₇×C₄₃	C₂×C₃₁	semidirect
7. C₇×C₃₁	D₄₃	direct (N × H)
8. D₄₃	C₇×C₃₁	direct (N × H)
10. C₄₃	C₂×C₇×C₃₁	semidirect
11. C₃₁	C₇×D₄₃	direct (N × H)
13. C₇	C₃₁×D₄₃	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×C₃₁×C₄₃	2
C₃₁×D₄₃	7
C₇×D₄₃	31
C₂×C₇×C₃₁	43