Finite Group Databasebeta

← C₂×C₃₁×C₄₃⋊C₇ #32916247

Subgroups — C₂×C₃₁×C₄₃⋊C₇ #32916247

Order 18662.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

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