Subgroups — C₃³×D₈ #88870

Order 432.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×D₄	C₂	1	2	yes	maximal, complemented
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₈	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³	—	2	2	no	—
5	C₃³×C₄	C₂²	1	1	yes	characteristic
6	C₃²×D₄	C₂×C₃	1	26	yes	complemented
7	C₃²×C₈	C₂×C₃	1	13	yes	complemented
8	C₂×C₃³	—	4	2	no	—
9	C₂×C₃³	D₄	1	1	yes	characteristic
10	C₃×D₈	C₃²	1	13	yes	direct product factor
11	C₂²×C₃²	—	2	26	no	—
12	C₃²×C₄	C₂²×C₃	1	13	yes	—
13	C₃³	D₈	1	1	yes	characteristic, direct product factor, Sylow
14	C₃×D₄	C₂×C₃²	1	26	yes	complemented
15	C₃×C₈	C₂×C₃²	1	13	yes	complemented
16	C₂×C₃²	—	4	26	no	—
17	C₂×C₃²	C₃×D₄	1	13	yes	—
18	D₈	C₃³	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²×C₃	—	2	26	no	—
20	C₃×C₄	C₂²×C₃²	1	13	yes	—
21	C₃²	C₃×D₈	1	13	yes	direct product factor
22	D₄	C₂×C₃³	1	2	yes	complemented
23	C₈	C₂×C₃³	1	1	yes	characteristic, complemented
24	C₂×C₃	—	4	26	no	—
25	C₂×C₃	C₃²×D₄	1	13	yes	—
26	C₂²	—	2	2	no	—
27	C₄	C₂²×C₃³	1	1	yes	characteristic
28	C₃	C₃²×D₈	1	13	yes	direct product factor
29	C₂	—	4	2	no	—
30	C₂	C₃³×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃³	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃³
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ C₃³×C₄ ◁ G

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

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