Subgroups — C₃²×M₁₆ #3762

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₈	C₂	1	2	yes	maximal, complemented
3	C₃×M₁₆	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²	C₄	1	1	yes	characteristic
5	C₃²×C₄	C₄	1	1	yes	characteristic
6	C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄	C₂×C₃	1	4	yes	—
8	C₃×C₈	C₂×C₃	1	8	yes	complemented
9	C₂×C₃²	—	2	1	no	—
10	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
11	M₁₆	C₃²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₃	C₃×C₄	1	4	yes	—
13	C₃×C₄	C₃×C₄	1	4	yes	—
14	C₃×C₄	C₂²×C₃	1	4	yes	—
15	C₃²	M₁₆	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₄	C₂×C₃²	1	1	yes	characteristic
17	C₈	C₂×C₃²	1	2	yes	complemented
18	C₂×C₃	—	2	4	no	—
19	C₂×C₃	C₂×C₃×C₄	1	4	yes	—
20	C₂²	C₃²×C₄	1	1	yes	characteristic
21	C₄	C₃²×C₄	1	1	yes	characteristic
22	C₄	C₂²×C₃²	1	1	yes	characteristic
23	C₃	C₃×M₁₆	1	4	yes	direct product factor
24	C₂	—	2	1	no	—
25	C₂	C₂×C₃²×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.