Finite Group Databasebeta

← C₃×C₇²×C₁₆₃ #37561749

Subgroups — C₃×C₇²×C₁₆₃ #37561749

Order 23961.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₆₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇×C₁₆₃	C₇	1	8	yes	maximal, direct product factor
3	C₇×C₁₆₃	C₃×C₇	1	8	yes	direct product factor
4	C₃×C₁₆₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
5	C₁₆₃	C₃×C₇²	1	1	yes	characteristic, direct product factor, Sylow
6	C₃×C₇²	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇²	C₃×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×C₇	C₇×C₁₆₃	1	8	yes	direct product factor
9	C₇	C₃×C₇×C₁₆₃	1	8	yes	direct product factor
10	C₃	C₇²×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. C₇²×C₁₆₃	C₃	direct (N × H)
2. C₃×C₇×C₁₆₃	C₇	direct (N × H)
3. C₇×C₁₆₃	C₃×C₇	direct (N × H)
4. C₃×C₁₆₃	C₇²	direct (N × H)
5. C₁₆₃	C₃×C₇²	direct (N × H)
6. C₃×C₇²	C₁₆₃	direct (N × H)
7. C₇²	C₃×C₁₆₃	direct (N × H)
8. C₃×C₇	C₇×C₁₆₃	direct (N × H)
9. C₇	C₃×C₇×C₁₆₃	direct (N × H)
10. C₃	C₇²×C₁₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₆₃	3
C₃×C₇×C₁₆₃	7
C₃×C₇²	163