Subgroups — C₉×D₁₆ #63413

Order 288.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₈	C₂	1	2	yes	maximal, complemented
2	C₉×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₆	C₃	1	1	yes	maximal, characteristic
4	D₄×C₉	—	2	2	no	—
5	C₈×C₉	C₂²	1	1	yes	characteristic
6	C₃×D₈	C₂×C₃	1	2	yes	—
7	C₃×C₁₆	C₂×C₃	1	1	yes	characteristic
8	C₂²×C₉	—	4	2	no	—
9	C₄×C₉	D₄	1	1	yes	characteristic
10	D₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×D₄	—	2	2	no	—
12	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₉	—	8	2	no	—
14	C₂×C₉	D₈	1	1	yes	characteristic
15	D₈	C₂×C₉	1	2	yes	complemented
16	C₁₆	C₂×C₉	1	1	yes	characteristic, complemented
17	C₂²×C₃	—	4	2	no	—
18	C₃×C₄	C₃×D₄	1	1	yes	characteristic
19	C₉	D₁₆	1	1	yes	characteristic, direct product factor, Sylow
20	D₄	—	2	2	no	—
21	C₈	C₂²×C₉	1	1	yes	characteristic
22	C₂×C₃	—	8	2	no	—
23	C₂×C₃	C₃×D₈	1	1	yes	characteristic
24	C₂²	—	4	2	no	—
25	C₄	D₄×C₉	1	1	yes	characteristic
26	C₃	C₃×D₁₆	1	1	yes	characteristic
27	C₂	—	8	2	no	—
28	C₂	C₉×D₈	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.