Subgroups — C₃×C₉×Q₁₆ #88574

Order 432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₂	1	2	yes	maximal
2	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃²×Q₁₆	C₃	1	1	yes	maximal, characteristic
4	C₉×Q₁₆	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₄×C₉	—	2	2	no	—
6	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₃²×Q₈	C₂×C₃	1	2	yes	—
8	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
9	Q₈×C₉	C₂×C₃	1	6	yes	—
10	C₈×C₉	C₂×C₃	1	3	yes	—
11	C₂×C₃×C₉	D₄	1	1	yes	characteristic
12	C₃×Q₁₆	C₉	1	3	yes	direct product factor
13	C₃×Q₁₆	C₃²	1	1	yes	characteristic
14	C₃²×C₄	—	2	2	no	—
15	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
16	C₄×C₉	—	2	6	no	—
17	C₄×C₉	C₂²×C₃	1	3	yes	—
18	C₃×C₉	Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×Q₈	C₂×C₉	1	6	yes	—
20	C₃×Q₈	C₂×C₃²	1	2	yes	—
21	C₃×C₈	C₂×C₉	1	3	yes	—
22	C₃×C₈	C₂×C₃²	1	1	yes	characteristic
23	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
24	C₂×C₉	C₃×D₄	1	3	yes	—
25	Q₁₆	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₄	—	2	6	no	—
27	C₃×C₄	—	2	2	no	—
28	C₃×C₄	C₂²×C₉	1	3	yes	—
29	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
30	C₃²	C₃×Q₁₆	1	1	yes	characteristic
31	C₉	C₃×Q₁₆	1	3	yes	direct product factor
32	Q₈	C₂×C₃×C₉	1	2	yes	—
33	C₈	C₂×C₃×C₉	1	1	yes	characteristic
34	C₂×C₃	D₄×C₉	1	3	yes	—
35	C₂×C₃	C₃²×D₄	1	1	yes	characteristic
36	C₄	—	2	2	no	—
37	C₄	C₂²×C₃×C₉	1	1	yes	characteristic
38	C₃	C₉×Q₁₆	1	3	yes	direct product factor
39	C₃	C₃²×Q₁₆	1	1	yes	characteristic
40	C₂	C₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₉	D₄
commutator	C₄	C₂²×C₃×C₉
Frattini, cosocle	C₃×C₄	C₂²×C₃²
socle, prime radical	C₂×C₃²	C₃×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₉ ◁ C₃×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₉×Q₁₆	C₃	direct (N × H)
12. C₃×Q₁₆	C₉	direct (N × H)
18. C₃×C₉	Q₁₆	direct (N × H)
25. Q₁₆	C₃×C₉	direct (N × H)
31. C₉	C₃×Q₁₆	direct (N × H)
38. C₃	C₉×Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₉	2
C₃×C₈×C₉	2
C₃²×Q₁₆	3
C₉×Q₁₆	3

Subgroups — C3×C9×Q16 #88574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×Q₁₆ #88574