Finite Group Databasebeta

← C₃²×C₇²×C₆₁ #41002016

Subgroups — C₃²×C₇²×C₆₁ #41002016

Order 26901.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₆₁	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₇×C₆₁	C₇	1	8	yes	maximal, direct product factor
3	C₇²×C₆₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₇×C₆₁	C₃×C₇	1	32	yes	direct product factor
5	C₃²×C₆₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₇²	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₆₁	C₃²×C₇	1	8	yes	direct product factor
8	C₃×C₆₁	C₃×C₇²	1	4	yes	direct product factor
9	C₃×C₇²	C₃×C₆₁	1	4	yes	direct product factor
10	C₃²×C₇	C₇×C₆₁	1	8	yes	direct product factor
11	C₆₁	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Sylow
12	C₇²	C₃²×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₇	C₃×C₇×C₆₁	1	32	yes	direct product factor
14	C₃²	C₇²×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₇	C₃²×C₇×C₆₁	1	8	yes	direct product factor
16	C₃	C₃×C₇²×C₆₁	1	4	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. C₃×C₇²×C₆₁	C₃	direct (N × H)
2. C₃²×C₇×C₆₁	C₇	direct (N × H)
3. C₇²×C₆₁	C₃²	direct (N × H)
4. C₃×C₇×C₆₁	C₃×C₇	direct (N × H)
5. C₃²×C₆₁	C₇²	direct (N × H)
6. C₃²×C₇²	C₆₁	direct (N × H)
7. C₇×C₆₁	C₃²×C₇	direct (N × H)
8. C₃×C₆₁	C₃×C₇²	direct (N × H)
9. C₃×C₇²	C₃×C₆₁	direct (N × H)
10. C₃²×C₇	C₇×C₆₁	direct (N × H)
11. C₆₁	C₃²×C₇²	direct (N × H)
12. C₇²	C₃²×C₆₁	direct (N × H)
13. C₃×C₇	C₃×C₇×C₆₁	direct (N × H)
14. C₃²	C₇²×C₆₁	direct (N × H)
15. C₇	C₃²×C₇×C₆₁	direct (N × H)
16. C₃	C₃×C₇²×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
C₃×C₇²×C₆₁	3
C₃²×C₇×C₆₁	7
C₃²×C₇²	61