Subgroups — C₁₆×D₉ #63356

Order 288.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₆	—	3	1	no	maximal
5	C₄×D₉	C₄	1	1	yes	characteristic
6	C₈×C₉	C₂²	1	1	yes	characteristic
7	C₉⋊C₈	C₄	1	1	yes	characteristic
8	D₃×C₈	—	3	1	no	—
9	C₃×C₁₆	D₃	1	1	yes	characteristic
10	C₃⋊C₁₆	—	3	1	no	—
11	C₂×D₉	C₈	1	1	yes	characteristic
12	C₄×C₉	C₂×C₄	1	1	yes	characteristic
13	Dic₉	C₈	1	1	yes	characteristic
14	C₂×C₁₆	—	9	1	no	Sylow
15	C₄×D₃	—	3	1	no	—
16	C₃×C₈	C₂×D₃	1	1	yes	characteristic
17	C₃⋊C₈	—	3	1	no	—
18	C₂×C₉	C₂×C₈	1	1	yes	characteristic
19	D₉	C₁₆	1	2	yes	direct product factor
20	C₂×C₈	—	9	1	no	—
21	C₁₆	—	9	1	no	—
22	C₁₆	D₉	1	1	yes	characteristic, direct product factor
23	C₂×D₃	—	3	1	no	—
24	C₃×C₄	C₄×D₃	1	1	yes	characteristic
25	Dic₃	—	3	1	no	—
26	C₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄	—	9	1	no	—
28	C₈	—	9	1	no	—
29	C₈	C₂×D₉	1	1	yes	characteristic
30	C₂×C₃	D₃×C₈	1	1	yes	characteristic
31	D₃	—	3	2	no	—
32	C₂²	—	9	1	no	—
33	C₄	—	9	1	no	—
34	C₄	C₄×D₉	1	1	yes	characteristic
35	C₃	D₃×C₁₆	1	1	yes	characteristic
36	C₂	—	9	2	no	—
37	C₂	C₈×D₉	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.