Finite Group Databasebeta

← C₂⁴×C₃³ #89128

Subgroups — C₂⁴×C₃³ #89128

Order 432.

1876 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₃²	C₃	1	13	yes	maximal, direct product factor
3	C₂²×C₃³	C₂²	1	35	yes	direct product factor
4	C₂³×C₃²	C₂×C₃	1	195	yes	direct product factor
5	C₂×C₃³	C₂³	1	15	yes	direct product factor
6	C₂⁴×C₃	C₃²	1	13	yes	direct product factor
7	C₂²×C₃²	C₂²×C₃	1	455	yes	direct product factor
8	C₃³	C₂⁴	1	1	yes	characteristic, direct product factor, Sylow
9	C₂³×C₃	C₂×C₃²	1	195	yes	direct product factor
10	C₂×C₃²	C₂³×C₃	1	195	yes	direct product factor
11	C₂⁴	C₃³	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₃	C₂²×C₃²	1	455	yes	direct product factor
13	C₃²	C₂⁴×C₃	1	13	yes	direct product factor
14	C₂³	C₂×C₃³	1	15	yes	direct product factor
15	C₂×C₃	C₂³×C₃²	1	195	yes	direct product factor
16	C₂²	C₂²×C₃³	1	35	yes	direct product factor
17	C₃	C₂⁴×C₃²	1	13	yes	direct product factor
18	C₂	C₂³×C₃³	1	15	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. C₂³×C₃³	C₂	direct (N × H)
2. C₂⁴×C₃²	C₃	direct (N × H)
3. C₂²×C₃³	C₂²	direct (N × H)
4. C₂³×C₃²	C₂×C₃	direct (N × H)
5. C₂×C₃³	C₂³	direct (N × H)
6. C₂⁴×C₃	C₃²	direct (N × H)
7. C₂²×C₃²	C₂²×C₃	direct (N × H)
8. C₃³	C₂⁴	direct (N × H)
9. C₂³×C₃	C₂×C₃²	direct (N × H)
10. C₂×C₃²	C₂³×C₃	direct (N × H)
11. C₂⁴	C₃³	direct (N × H)
12. C₂²×C₃	C₂²×C₃²	direct (N × H)
13. C₃²	C₂⁴×C₃	direct (N × H)
14. C₂³	C₂×C₃³	direct (N × H)
15. C₂×C₃	C₂³×C₃²	direct (N × H)
16. C₂²	C₂²×C₃³	direct (N × H)
17. C₃	C₂⁴×C₃²	direct (N × H)
18. C₂	C₂³×C₃³	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×C₃³	2
C₂⁴×C₃²	3