Finite Group Databasebeta

← C₂×C₃×C₁₁×C₁₆₃ #24924446

Subgroups — C₂×C₃×C₁₁×C₁₆₃ #24924446

Order 10758.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₆₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₁₆₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₆₃	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₆₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₆₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₆₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₁₆₃	C₂×C₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₃×C₁₁	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁	C₂×C₁₆₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁	C₃×C₁₆₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁	C₂×C₃×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	C₁₁×C₁₆₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₁₁×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₁₁×C₁₆₃	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. C₃×C₁₁×C₁₆₃	C₂	direct (N × H)
2. C₂×C₁₁×C₁₆₃	C₃	direct (N × H)
3. C₁₁×C₁₆₃	C₂×C₃	direct (N × H)
4. C₂×C₃×C₁₆₃	C₁₁	direct (N × H)
5. C₃×C₁₆₃	C₂×C₁₁	direct (N × H)
6. C₂×C₁₆₃	C₃×C₁₁	direct (N × H)
7. C₁₆₃	C₂×C₃×C₁₁	direct (N × H)
8. C₂×C₃×C₁₁	C₁₆₃	direct (N × H)
9. C₃×C₁₁	C₂×C₁₆₃	direct (N × H)
10. C₂×C₁₁	C₃×C₁₆₃	direct (N × H)
11. C₁₁	C₂×C₃×C₁₆₃	direct (N × H)
12. C₂×C₃	C₁₁×C₁₆₃	direct (N × H)
13. C₃	C₂×C₁₁×C₁₆₃	direct (N × H)
14. C₂	C₃×C₁₁×C₁₆₃	direct (N × H)