Subgroups — C₃³×Q₁₆ #88872

Order 432.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₈	C₂	1	2	yes	maximal
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃²×Q₁₆	C₃	1	13	yes	maximal, direct product factor
4	C₃³×C₄	—	2	2	no	—
5	C₃³×C₄	C₂²	1	1	yes	characteristic
6	C₃²×Q₈	C₂×C₃	1	26	yes	—
7	C₃²×C₈	C₂×C₃	1	13	yes	—
8	C₂×C₃³	D₄	1	1	yes	characteristic
9	C₃×Q₁₆	C₃²	1	13	yes	direct product factor
10	C₃²×C₄	—	2	26	no	—
11	C₃²×C₄	C₂²×C₃	1	13	yes	—
12	C₃³	Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×Q₈	C₂×C₃²	1	26	yes	—
14	C₃×C₈	C₂×C₃²	1	13	yes	—
15	C₂×C₃²	C₃×D₄	1	13	yes	—
16	Q₁₆	C₃³	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₄	—	2	26	no	—
18	C₃×C₄	C₂²×C₃²	1	13	yes	—
19	C₃²	C₃×Q₁₆	1	13	yes	direct product factor
20	Q₈	C₂×C₃³	1	2	yes	—
21	C₈	C₂×C₃³	1	1	yes	characteristic
22	C₂×C₃	C₃²×D₄	1	13	yes	—
23	C₄	—	2	2	no	—
24	C₄	C₂²×C₃³	1	1	yes	characteristic
25	C₃	C₃²×Q₁₆	1	13	yes	direct product factor
26	C₂	C₃³×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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.