Finite Group Databasebeta

← C₂×C₇₁×D₃₇ #24901913

Subgroups — C₂×C₇₁×D₃₇ #24901913

Order 10508.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×D₃₇	C₂	1	2	yes	maximal, direct product factor
3	C₃₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₇₁	—	37	1	no	maximal, Hall
5	C₂×D₃₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇₁	—	37	2	no	—
7	C₂×C₇₁	D₃₇	1	1	yes	characteristic, direct product factor
8	C₂×C₃₇	C₂×C₇₁	1	1	yes	characteristic, complemented
9	D₃₇	C₂×C₇₁	1	2	yes	direct product factor
10	C₇₁	C₂×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₇	C₂²×C₇₁	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	37	1	no	Sylow
13	C₂	—	37	2	no	—
14	C₂	C₇₁×D₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₁	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂²×C₇₁
Frattini	C₁	G
Fitting, socle	C₂×C₃₇×C₇₁	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×C₇₁	C₂	semidirect
2. C₇₁×D₃₇	C₂	direct (N × H)
3. C₃₇×C₇₁	C₂²	semidirect
5. C₂×D₃₇	C₇₁	direct (N × H)
7. C₂×C₇₁	D₃₇	direct (N × H)
8. C₂×C₃₇	C₂×C₇₁	semidirect
9. D₃₇	C₂×C₇₁	direct (N × H)
10. C₇₁	C₂×D₃₇	direct (N × H)
11. C₃₇	C₂²×C₇₁	semidirect
14. C₂	C₇₁×D₃₇	direct (N × H)