Subgroups — C₃³×SD₁₆ #88871

Order 432.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃³×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×SD₁₆	C₃	1	13	yes	maximal, direct product factor
5	C₂²×C₃³	—	2	1	no	—
6	C₃³×C₄	—	2	1	no	—
7	C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₃²×Q₈	C₂×C₃	1	13	yes	complemented
9	C₃²×D₄	C₂×C₃	1	13	yes	—
10	C₃²×C₈	C₂×C₃	1	13	yes	complemented
11	C₂×C₃³	—	4	1	no	—
12	C₂×C₃³	D₄	1	1	yes	characteristic
13	C₃×SD₁₆	C₃²	1	13	yes	direct product factor
14	C₂²×C₃²	—	2	13	no	—
15	C₃²×C₄	—	2	13	no	—
16	C₃²×C₄	C₂²×C₃	1	13	yes	—
17	C₃³	SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×Q₈	C₂×C₃²	1	13	yes	complemented
19	C₃×D₄	C₂×C₃²	1	13	yes	—
20	C₃×C₈	C₂×C₃²	1	13	yes	complemented
21	C₂×C₃²	—	4	13	no	—
22	C₂×C₃²	C₃×D₄	1	13	yes	—
23	SD₁₆	C₃³	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	—	2	13	no	—
25	C₃×C₄	—	2	13	no	—
26	C₃×C₄	C₂²×C₃²	1	13	yes	—
27	C₃²	C₃×SD₁₆	1	13	yes	direct product factor
28	Q₈	C₂×C₃³	1	1	yes	characteristic, complemented
29	D₄	C₂×C₃³	1	1	yes	characteristic
30	C₈	C₂×C₃³	1	1	yes	characteristic, complemented
31	C₂×C₃	—	4	13	no	—
32	C₂×C₃	C₃²×D₄	1	13	yes	—
33	C₂²	—	2	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂²×C₃³	1	1	yes	characteristic
36	C₃	C₃²×SD₁₆	1	13	yes	direct product factor
37	C₂	—	4	1	no	—
38	C₂	C₃³×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃³	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃³
prime radical	C₃³×D₄	C₂
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.