Subgroups — C₁₆×3₋¹⁺² #88389

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₆	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₆	C₃	1	3	yes	maximal, complemented
4	C₄×3₋¹⁺²	C₄	1	1	yes	characteristic
5	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
6	C₈×C₉	C₂×C₃	1	3	yes	—
7	C₂×3₋¹⁺²	C₈	1	1	yes	characteristic
8	C₃×C₁₆	—	3	1	no	—
9	C₃×C₁₆	C₃²	1	1	yes	characteristic
10	C₃²×C₄	C₃×C₄	1	1	yes	characteristic
11	C₄×C₉	C₃×C₄	1	3	yes	—
12	3₋¹⁺²	C₁₆	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₈	—	3	1	no	—
14	C₃×C₈	C₂×C₃²	1	1	yes	characteristic
15	C₂×C₃²	C₃×C₈	1	1	yes	characteristic
16	C₂×C₉	C₃×C₈	1	3	yes	—
17	C₁₆	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	3	1	no	—
19	C₃×C₄	C₃²×C₄	1	1	yes	characteristic
20	C₃²	C₃×C₁₆	1	1	yes	characteristic
21	C₉	C₃×C₁₆	1	3	yes	complemented
22	C₈	C₂×3₋¹⁺²	1	1	yes	characteristic
23	C₂×C₃	—	3	1	no	—
24	C₂×C₃	C₃²×C₈	1	1	yes	characteristic
25	C₄	C₄×3₋¹⁺²	1	1	yes	characteristic
26	C₃	—	3	1	no	—
27	C₃	C₃²×C₁₆	1	1	yes	characteristic
28	C₂	C₈×3₋¹⁺²	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.