Subgroups — C₄²×3₋¹⁺² #88555

Order 432.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×3₋¹⁺²	C₂	1	3	yes	maximal
2	C₃²×C₄²	C₃	1	1	yes	maximal, characteristic
3	C₄²×C₉	C₃	1	3	yes	maximal, complemented
4	C₂²×3₋¹⁺²	C₂²	1	1	yes	characteristic
5	C₄×3₋¹⁺²	C₄	1	6	yes	direct product factor
6	C₂×C₃²×C₄	C₂×C₃	1	3	yes	—
7	C₂×C₄×C₉	C₂×C₃	1	9	yes	—
8	C₂×3₋¹⁺²	C₂×C₄	1	3	yes	—
9	C₃×C₄²	—	3	1	no	—
10	C₃×C₄²	C₃²	1	1	yes	characteristic
11	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
12	C₃²×C₄	C₃×C₄	1	6	yes	—
13	C₂²×C₉	C₂²×C₃	1	3	yes	—
14	C₄×C₉	C₃×C₄	1	18	yes	complemented
15	3₋¹⁺²	C₄²	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₄	—	3	3	no	—
17	C₂×C₃×C₄	C₂×C₃²	1	3	yes	—
18	C₂×C₃²	C₂×C₃×C₄	1	3	yes	—
19	C₂×C₉	C₂×C₃×C₄	1	9	yes	—
20	C₄²	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₃	—	3	1	no	—
22	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
23	C₃×C₄	—	3	6	no	—
24	C₃×C₄	C₃²×C₄	1	6	yes	—
25	C₃²	C₃×C₄²	1	1	yes	characteristic
26	C₉	C₃×C₄²	1	3	yes	complemented
27	C₂×C₄	C₂×3₋¹⁺²	1	3	yes	—
28	C₂×C₃	—	3	3	no	—
29	C₂×C₃	C₂×C₃²×C₄	1	3	yes	—
30	C₂²	C₂²×3₋¹⁺²	1	1	yes	characteristic
31	C₄	C₄×3₋¹⁺²	1	6	yes	direct product factor
32	C₃	—	3	1	no	—
33	C₃	C₃²×C₄²	1	1	yes	characteristic
34	C₂	C₂×C₄×3₋¹⁺²	1	3	yes	—

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.