Subgroups — C₃×C₉×M₁₆ #88565

Order 432.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₉	C₂	1	2	yes	maximal, complemented
3	C₃²×M₁₆	C₃	1	1	yes	maximal, characteristic
4	C₉×M₁₆	C₃	1	3	yes	maximal, direct product factor
5	C₂²×C₃×C₉	C₄	1	1	yes	characteristic
6	C₃×C₄×C₉	C₄	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
9	C₃²×C₈	C₂×C₃	1	2	yes	—
10	C₂×C₄×C₉	C₂×C₃	1	3	yes	—
11	C₈×C₉	C₂×C₃	1	6	yes	complemented
12	C₂×C₃×C₉	—	2	1	no	—
13	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
14	C₃×M₁₆	C₉	1	3	yes	direct product factor
15	C₃×M₁₆	C₃²	1	1	yes	characteristic
16	C₂²×C₃²	C₃×C₄	1	1	yes	characteristic
17	C₃²×C₄	C₃×C₄	1	1	yes	characteristic
18	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
19	C₂²×C₉	C₃×C₄	1	3	yes	—
20	C₄×C₉	C₃×C₄	1	3	yes	—
21	C₄×C₉	C₂²×C₃	1	3	yes	—
22	C₃×C₉	M₁₆	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₃×C₄	C₂×C₉	1	3	yes	—
24	C₂×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
25	C₃×C₈	C₂×C₉	1	6	yes	complemented
26	C₃×C₈	C₂×C₃²	1	2	yes	—
27	C₂×C₃²	—	2	1	no	—
28	C₂×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
29	C₂×C₉	—	2	3	no	—
30	C₂×C₉	C₂×C₃×C₄	1	3	yes	—
31	M₁₆	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²×C₃	C₄×C₉	1	3	yes	—
33	C₂²×C₃	C₃²×C₄	1	1	yes	characteristic
34	C₃×C₄	C₄×C₉	1	3	yes	—
35	C₃×C₄	C₂²×C₉	1	3	yes	—
36	C₃×C₄	C₃²×C₄	1	1	yes	characteristic
37	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
38	C₃²	C₃×M₁₆	1	1	yes	characteristic
39	C₉	C₃×M₁₆	1	3	yes	direct product factor
40	C₂×C₄	C₂×C₃×C₉	1	1	yes	characteristic
41	C₈	C₂×C₃×C₉	1	2	yes	complemented
42	C₂×C₃	—	2	3	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	C₂×C₄×C₉	1	3	yes	—
45	C₂×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
46	C₂²	C₃×C₄×C₉	1	1	yes	characteristic
47	C₄	C₃×C₄×C₉	1	1	yes	characteristic
48	C₄	C₂²×C₃×C₉	1	1	yes	characteristic
49	C₃	C₉×M₁₆	1	3	yes	direct product factor
50	C₃	C₃²×M₁₆	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	C₂×C₃×C₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₉	C₂²
commutator	C₂	C₂×C₃×C₄×C₉
Frattini, cosocle	C₃×C₄	C₂²×C₃²
socle	C₂×C₃²	C₂×C₃×C₄
prime radical	C₂²×C₃²	C₃×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×C₈×C₉	C₂	semidirect
4. C₉×M₁₆	C₃	direct (N × H)
11. C₈×C₉	C₂×C₃	semidirect
14. C₃×M₁₆	C₉	direct (N × H)
22. C₃×C₉	M₁₆	direct (N × H)
25. C₃×C₈	C₂×C₉	semidirect
31. M₁₆	C₃×C₉	direct (N × H)
39. C₉	C₃×M₁₆	direct (N × H)
41. C₈	C₂×C₃×C₉	semidirect
49. C₃	C₉×M₁₆	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₄×C₉	2
C₃×C₈×C₉	2
C₃²×M₁₆	3
C₉×M₁₆	3

Subgroups — C3×C9×M16 #88565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×M₁₆ #88565