Finite Group Databasebeta

← C₃×C₂₃×C₃₄₃ #72201014

Subgroups — C₃×C₂₃×C₃₄₃ #72201014

Order 23667.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₃×C₄₉	C₇	1	1	yes	maximal, characteristic
3	C₂₃×C₄₉	C₃×C₇	1	1	yes	characteristic
4	C₃×C₃₄₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₂₃	C₄₉	1	1	yes	characteristic
6	C₃₄₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₇×C₂₃	C₃×C₄₉	1	1	yes	characteristic
8	C₃×C₄₉	C₇×C₂₃	1	1	yes	characteristic
9	C₃×C₂₃	C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₄₉	C₃×C₇×C₂₃	1	1	yes	characteristic
11	C₂₃	C₃×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₇	C₂₃×C₄₉	1	1	yes	characteristic
13	C₇	C₃×C₂₃×C₄₉	1	1	yes	characteristic
14	C₃	C₂₃×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄₉	C₃×C₇×C₂₃
socle, prime radical	C₃×C₇×C₂₃	C₄₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×C₃₄₃	C₃	direct (N × H)
4. C₃×C₃₄₃	C₂₃	direct (N × H)
6. C₃₄₃	C₃×C₂₃	direct (N × H)
9. C₃×C₂₃	C₃₄₃	direct (N × H)
11. C₂₃	C₃×C₃₄₃	direct (N × H)
14. C₃	C₂₃×C₃₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×C₃₄₃	3
C₃×C₂₃×C₄₉	7
C₃×C₃₄₃	23