Finite Group Databasebeta

← C₃³×C₃₁×C₃₇ #72207708

Subgroups — C₃³×C₃₁×C₃₇ #72207708

Order 30969.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×C₃₇	C₃	1	13	yes	maximal, direct product factor
2	C₃×C₃₁×C₃₇	C₃²	1	13	yes	direct product factor
3	C₃₁×C₃₇	C₃³	1	1	yes	characteristic, direct product factor, Hall
4	C₃³×C₃₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃³×C₃₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₃₇	C₃×C₃₁	1	13	yes	direct product factor
7	C₃²×C₃₁	C₃×C₃₇	1	13	yes	direct product factor
8	C₃×C₃₇	C₃²×C₃₁	1	13	yes	direct product factor
9	C₃×C₃₁	C₃²×C₃₇	1	13	yes	direct product factor
10	C₃₇	C₃³×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₃³×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₃³	C₃₁×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²	C₃×C₃₁×C₃₇	1	13	yes	direct product factor
14	C₃	C₃²×C₃₁×C₃₇	1	13	yes	direct product factor

	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. C₃²×C₃₁×C₃₇	C₃	direct (N × H)
2. C₃×C₃₁×C₃₇	C₃²	direct (N × H)
3. C₃₁×C₃₇	C₃³	direct (N × H)
4. C₃³×C₃₇	C₃₁	direct (N × H)
5. C₃³×C₃₁	C₃₇	direct (N × H)
6. C₃²×C₃₇	C₃×C₃₁	direct (N × H)
7. C₃²×C₃₁	C₃×C₃₇	direct (N × H)
8. C₃×C₃₇	C₃²×C₃₁	direct (N × H)
9. C₃×C₃₁	C₃²×C₃₇	direct (N × H)
10. C₃₇	C₃³×C₃₁	direct (N × H)
11. C₃₁	C₃³×C₃₇	direct (N × H)
12. C₃³	C₃₁×C₃₇	direct (N × H)
13. C₃²	C₃×C₃₁×C₃₇	direct (N × H)
14. C₃	C₃²×C₃₁×C₃₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₃₁×C₃₇	3
C₃³×C₃₇	31
C₃³×C₃₁	37