Finite Group Databasebeta

← C₇×C₄₁×D₃₇ #35234797

Subgroups — C₇×C₄₁×D₃₇ #35234797

Order 21238.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₇×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₇×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₄₁	—	37	1	no	maximal, Hall
5	C₇×D₃₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₄₁	D₃₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₃₇	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₁	—	37	1	no	Hall
9	D₃₇	C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄₁	C₇×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₇	C₂×C₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇	—	37	1	no	Hall
13	C₇	C₄₁×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₄₁	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₇×C₃₇×C₄₁	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₇×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₇×C₄₁	C₂	semidirect
2. C₄₁×D₃₇	C₇	direct (N × H)
3. C₃₇×C₄₁	C₂×C₇	semidirect
5. C₇×D₃₇	C₄₁	direct (N × H)
6. C₇×C₄₁	D₃₇	direct (N × H)
7. C₇×C₃₇	C₂×C₄₁	semidirect
9. D₃₇	C₇×C₄₁	direct (N × H)
10. C₄₁	C₇×D₃₇	direct (N × H)
11. C₃₇	C₂×C₇×C₄₁	semidirect
13. C₇	C₄₁×D₃₇	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×C₃₇×C₄₁	2
C₄₁×D₃₇	7
C₂×C₇×C₄₁	37
C₇×D₃₇	41