Finite Group Databasebeta

← C₂×C₇×C₃₇×C₆₁ #44539137

Subgroups — C₂×C₇×C₃₇×C₆₁ #44539137

Order 31598.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₇×C₆₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃₇×C₆₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₇×C₆₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₆₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₃₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₆₁	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₃₇	C₂×C₆₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₆₁	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃₇	C₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
10	C₆₁	C₂×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₇	C₂×C₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	C₃₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
13	C₇	C₂×C₃₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₇×C₃₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₇×C₆₁	C₂	direct (N × H)
2. C₂×C₃₇×C₆₁	C₇	direct (N × H)
3. C₃₇×C₆₁	C₂×C₇	direct (N × H)
4. C₂×C₇×C₆₁	C₃₇	direct (N × H)
5. C₂×C₇×C₃₇	C₆₁	direct (N × H)
6. C₇×C₆₁	C₂×C₃₇	direct (N × H)
7. C₇×C₃₇	C₂×C₆₁	direct (N × H)
8. C₂×C₆₁	C₇×C₃₇	direct (N × H)
9. C₂×C₃₇	C₇×C₆₁	direct (N × H)
10. C₆₁	C₂×C₇×C₃₇	direct (N × H)
11. C₃₇	C₂×C₇×C₆₁	direct (N × H)
12. C₂×C₇	C₃₇×C₆₁	direct (N × H)
13. C₇	C₂×C₃₇×C₆₁	direct (N × H)
14. C₂	C₇×C₃₇×C₆₁	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×C₆₁	2
C₂×C₃₇×C₆₁	7
C₂×C₇×C₆₁	37
C₂×C₇×C₃₇	61