Finite Group Databasebeta

← C₃²×C₇×C₁₆₃ #23779727

Subgroups — C₃²×C₇×C₁₆₃ #23779727

Order 10269.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₆₃	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₁₆₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₆₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₁₆₃	C₃×C₇	1	4	yes	direct product factor
5	C₁₆₃	C₃²×C₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₃²×C₇	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇	C₃×C₁₆₃	1	4	yes	direct product factor
8	C₃²	C₇×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₇	C₃²×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₇×C₁₆₃	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×C₇×C₁₆₃	C₃	direct (N × H)
2. C₃²×C₁₆₃	C₇	direct (N × H)
3. C₇×C₁₆₃	C₃²	direct (N × H)
4. C₃×C₁₆₃	C₃×C₇	direct (N × H)
5. C₁₆₃	C₃²×C₇	direct (N × H)
6. C₃²×C₇	C₁₆₃	direct (N × H)
7. C₃×C₇	C₃×C₁₆₃	direct (N × H)
8. C₃²	C₇×C₁₆₃	direct (N × H)
9. C₇	C₃²×C₁₆₃	direct (N × H)
10. C₃	C₃×C₇×C₁₆₃	direct (N × H)