Finite Group Databasebeta

← C₂³×C₃×C₂₅₇ #72185366

Subgroups — C₂³×C₃×C₂₅₇ #72185366

Order 6168.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂₅₇	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₂₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₂₅₇	C₂²	1	7	yes	direct product factor
4	C₂²×C₂₅₇	C₂×C₃	1	7	yes	direct product factor
5	C₃×C₂₅₇	C₂³	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₂₅₇	C₂²×C₃	1	7	yes	direct product factor
7	C₂₅₇	C₂³×C₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂³×C₃	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃	C₂×C₂₅₇	1	7	yes	direct product factor
10	C₂³	C₃×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₃	C₂²×C₂₅₇	1	7	yes	direct product factor
12	C₂²	C₂×C₃×C₂₅₇	1	7	yes	direct product factor
13	C₃	C₂³×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₂²×C₃×C₂₅₇	1	7	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. C₂²×C₃×C₂₅₇	C₂	direct (N × H)
2. C₂³×C₂₅₇	C₃	direct (N × H)
3. C₂×C₃×C₂₅₇	C₂²	direct (N × H)
4. C₂²×C₂₅₇	C₂×C₃	direct (N × H)
5. C₃×C₂₅₇	C₂³	direct (N × H)
6. C₂×C₂₅₇	C₂²×C₃	direct (N × H)
7. C₂₅₇	C₂³×C₃	direct (N × H)
8. C₂³×C₃	C₂₅₇	direct (N × H)
9. C₂²×C₃	C₂×C₂₅₇	direct (N × H)
10. C₂³	C₃×C₂₅₇	direct (N × H)
11. C₂×C₃	C₂²×C₂₅₇	direct (N × H)
12. C₂²	C₂×C₃×C₂₅₇	direct (N × H)
13. C₃	C₂³×C₂₅₇	direct (N × H)
14. C₂	C₂²×C₃×C₂₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₂₅₇	2
C₂³×C₂₅₇	3
C₂³×C₃	257