Subgroups — C₃³×M₁₆ #88869

Order 432.

280 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, complemented
3	C₃²×M₁₆	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	complemented
9	C₂×C₃³	—	2	1	no	—
10	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
11	C₃×M₁₆	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	M₁₆	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	complemented
18	C₂×C₃²	—	2	13	no	—
19	C₂×C₃²	C₂×C₃×C₄	1	13	yes	—
20	M₁₆	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	C₃×M₁₆	1	13	yes	direct product factor
25	C₂×C₄	C₂×C₃³	1	1	yes	characteristic
26	C₈	C₂×C₃³	1	2	yes	complemented
27	C₂×C₃	—	2	13	no	—
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	C₃²×M₁₆	1	13	yes	direct product factor
33	C₂	—	2	1	no	—
34	C₂	C₂×C₃³×C₄	1	1	yes	characteristic

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.