Subgroups — C₃⋊(C₉⋊C₁₆) #88385

Order 432.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊C₁₆)	—	3	1	no	maximal
3	C₉⋊C₁₆	—	3	3	no	maximal
4	C₃×C₄×C₉	C₄	1	1	yes	characteristic
5	C₃²×C₈	D₃	1	1	yes	characteristic
6	C₈×C₉	D₃	1	3	yes	—
7	C₂×C₃×C₉	C₈	1	1	yes	characteristic
8	C₃⋊C₁₆	—	9	3	no	—
9	C₃⋊C₁₆	—	9	1	no	—
10	C₃²×C₄	Dic₃	1	1	yes	characteristic
11	C₄×C₉	Dic₃	1	3	yes	—
12	C₃×C₉	C₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₈	D₉	1	3	yes	—
14	C₃×C₈	C₃⋊D₃	1	1	yes	characteristic
15	C₂×C₃²	C₃⋊C₈	1	1	yes	characteristic
16	C₂×C₉	C₃⋊C₈	1	3	yes	—
17	C₁₆	—	27	1	no	Sylow
18	C₃×C₄	Dic₉	1	3	yes	—
19	C₃×C₄	C₃⋊Dic₃	1	1	yes	characteristic
20	C₃²	C₃⋊C₁₆	1	1	yes	characteristic
21	C₉	C₃⋊C₁₆	1	3	yes	complemented
22	C₈	C₃⋊D₉	1	1	yes	characteristic
23	C₂×C₃	C₉⋊C₈	1	3	yes	—
24	C₂×C₃	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
25	C₄	C₃⋊Dic₉	1	1	yes	characteristic
26	C₃	C₉⋊C₁₆	1	3	yes	complemented
27	C₃	C₃⋊(C₃⋊C₁₆)	1	1	yes	characteristic
28	C₂	C₃⋊(C₉⋊C₈)	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.