Finite Group Databasebeta

← C₃×C₇×C₂₃×C₆₇ #44569005

Subgroups — C₃×C₇×C₂₃×C₆₇ #44569005

Order 32361.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×C₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₃×C₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₆₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₇×C₆₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₂₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₆₇	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₆₇	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₂₃	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₃	C₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₆₇	C₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₃	C₃×C₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₇	C₂₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
13	C₇	C₃×C₂₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₇×C₂₃×C₆₇	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. C₇×C₂₃×C₆₇	C₃	direct (N × H)
2. C₃×C₂₃×C₆₇	C₇	direct (N × H)
3. C₂₃×C₆₇	C₃×C₇	direct (N × H)
4. C₃×C₇×C₆₇	C₂₃	direct (N × H)
5. C₃×C₇×C₂₃	C₆₇	direct (N × H)
6. C₇×C₆₇	C₃×C₂₃	direct (N × H)
7. C₃×C₆₇	C₇×C₂₃	direct (N × H)
8. C₇×C₂₃	C₃×C₆₇	direct (N × H)
9. C₃×C₂₃	C₇×C₆₇	direct (N × H)
10. C₆₇	C₃×C₇×C₂₃	direct (N × H)
11. C₂₃	C₃×C₇×C₆₇	direct (N × H)
12. C₃×C₇	C₂₃×C₆₇	direct (N × H)
13. C₇	C₃×C₂₃×C₆₇	direct (N × H)
14. C₃	C₇×C₂₃×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₃×C₆₇	3
C₃×C₂₃×C₆₇	7
C₃×C₇×C₆₇	23
C₃×C₇×C₂₃	67