Finite Group Databasebeta

← C₇×C₄₃×C₃₁⋊C₃ #43241978

Subgroups — C₇×C₄₃×C₃₁⋊C₃ #43241978

Order 27993.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×C₃₁⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₄₃	—	31	1	no	maximal, Hall
5	C₇×C₃₁⋊C₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₄₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₃₁	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₃	—	31	1	no	Hall
9	C₃₁⋊C₃	C₇×C₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₄₃	C₇×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₃×C₇×C₄₃	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₇	—	31	1	no	Hall
13	C₇	C₄₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₄₃	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃×C₇×C₄₃
Frattini	C₁	G
Fitting, socle	C₇×C₃₁×C₄₃	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₇×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×C₄₃	C₃	semidirect
2. C₄₃×C₃₁⋊C₃	C₇	direct (N × H)
3. C₃₁×C₄₃	C₃×C₇	semidirect
5. C₇×C₃₁⋊C₃	C₄₃	direct (N × H)
6. C₇×C₄₃	C₃₁⋊C₃	direct (N × H)
7. C₇×C₃₁	C₃×C₄₃	semidirect
9. C₃₁⋊C₃	C₇×C₄₃	direct (N × H)
10. C₄₃	C₇×C₃₁⋊C₃	direct (N × H)
11. C₃₁	C₃×C₇×C₄₃	semidirect
13. C₇	C₄₃×C₃₁⋊C₃	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	3
C₄₃×C₃₁⋊C₃	7
C₃×C₇×C₄₃	31
C₇×C₃₁⋊C₃	43