Subgroups — C₂×C₃³×C₈ #88868

Order 432.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₈	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₈	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³	C₄	1	1	yes	characteristic
5	C₃³×C₄	C₄	1	1	yes	characteristic
6	C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	C₂×C₃	1	13	yes	—
8	C₃²×C₈	C₂×C₃	1	26	yes	direct product factor
9	C₂×C₃³	C₈	1	2	yes	direct product factor
10	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₈	C₃²	1	13	yes	direct product factor
12	C₂²×C₃²	C₃×C₄	1	13	yes	—
13	C₃²×C₄	C₃×C₄	1	13	yes	—
14	C₃²×C₄	C₂²×C₃	1	13	yes	—
15	C₃³	C₂×C₈	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₄	C₂×C₃²	1	13	yes	—
17	C₃×C₈	C₂×C₃²	1	26	yes	direct product factor
18	C₂×C₃²	C₃×C₈	1	26	yes	direct product factor
19	C₂×C₃²	C₂×C₃×C₄	1	13	yes	—
20	C₂×C₈	C₃³	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₃	C₃²×C₄	1	13	yes	—
22	C₃×C₄	C₃²×C₄	1	13	yes	—
23	C₃×C₄	C₂²×C₃²	1	13	yes	—
24	C₃²	C₂×C₃×C₈	1	13	yes	direct product factor
25	C₂×C₄	C₂×C₃³	1	1	yes	characteristic
26	C₈	C₂×C₃³	1	2	yes	direct product factor
27	C₂×C₃	C₃²×C₈	1	26	yes	direct product factor
28	C₂×C₃	C₂×C₃²×C₄	1	13	yes	—
29	C₂²	C₃³×C₄	1	1	yes	characteristic
30	C₄	C₃³×C₄	1	1	yes	characteristic
31	C₄	C₂²×C₃³	1	1	yes	characteristic
32	C₃	C₂×C₃²×C₈	1	13	yes	direct product factor
33	C₂	C₃³×C₈	1	2	yes	direct product factor
34	C₂	C₂×C₃³×C₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃³
socle, prime radical	C₂²×C₃³	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₈	C₂	direct (N × H)
3. C₂×C₃²×C₈	C₃	direct (N × H)
8. C₃²×C₈	C₂×C₃	direct (N × H)
9. C₂×C₃³	C₈	direct (N × H)
11. C₂×C₃×C₈	C₃²	direct (N × H)
15. C₃³	C₂×C₈	direct (N × H)
17. C₃×C₈	C₂×C₃²	direct (N × H)
18. C₂×C₃²	C₃×C₈	direct (N × H)
20. C₂×C₈	C₃³	direct (N × H)
24. C₃²	C₂×C₃×C₈	direct (N × H)
26. C₈	C₂×C₃³	direct (N × H)
27. C₂×C₃	C₃²×C₈	direct (N × H)
32. C₃	C₂×C₃²×C₈	direct (N × H)
33. C₂	C₃³×C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₄	2
C₃³×C₈	2
C₂×C₃²×C₈	3

Subgroups — C2×C33×C8 #88868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₈ #88868