Finite Group Databasebeta

← C₇×C₄₁×C₄₃⋊C₃ #49150034

Subgroups — C₇×C₄₁×C₄₃⋊C₃ #49150034

Order 37023.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄₁×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×C₄₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₁×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
4	C₇×C₄₃⋊C₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₄₁	—	43	1	no	maximal, Hall
6	C₇×C₄₃	C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
7	C₇×C₄₁	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₄₃⋊C₃	C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄₁	—	43	1	no	Hall
10	C₄₃	C₃×C₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
11	C₄₁	C₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₇	—	43	1	no	Hall
13	C₇	C₄₁×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₄₁	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₃×C₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₇×C₄₁×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₇×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₄₁×C₄₃	C₃	semidirect
2. C₄₁×C₄₃⋊C₃	C₇	direct (N × H)
3. C₄₁×C₄₃	C₃×C₇	semidirect
4. C₇×C₄₃⋊C₃	C₄₁	direct (N × H)
6. C₇×C₄₃	C₃×C₄₁	semidirect
7. C₇×C₄₁	C₄₃⋊C₃	direct (N × H)
8. C₄₃⋊C₃	C₇×C₄₁	direct (N × H)
10. C₄₃	C₃×C₇×C₄₁	semidirect
11. C₄₁	C₇×C₄₃⋊C₃	direct (N × H)
13. C₇	C₄₁×C₄₃⋊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×C₄₁×C₄₃	3
C₄₁×C₄₃⋊C₃	7
C₇×C₄₃⋊C₃	41
C₃×C₇×C₄₁	43