Subgroups — C₃²×Dic₁₂ #88821

Order 432.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Dic₆	C₂	1	2	yes	maximal
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃²×Q₁₆	—	3	1	no	maximal
4	C₃×Dic₁₂	C₃	1	4	yes	maximal, direct product factor
5	C₃³×C₄	C₂²	1	1	yes	characteristic
6	C₃²×Dic₃	—	2	2	no	—
7	C₃²×Q₈	—	3	2	no	—
8	C₃×Dic₆	C₂×C₃	1	8	yes	—
9	C₃²×C₈	—	2	4	no	—
10	C₃²×C₈	D₃	1	1	yes	characteristic
11	C₃²×C₈	C₂×C₃	1	4	yes	—
12	C₂×C₃³	D₄	1	1	yes	characteristic
13	C₃×Q₁₆	—	3	4	no	—
14	Dic₁₂	C₃²	1	1	yes	characteristic, direct product factor
15	C₃²×C₄	—	2	4	no	—
16	C₃²×C₄	—	6	2	no	—
17	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
18	C₃²×C₄	C₂²×C₃	1	4	yes	—
19	C₃×Dic₃	—	2	8	no	—
20	C₃³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₃×Q₈	—	3	8	no	—
22	Dic₆	C₂×C₃²	1	2	yes	—
23	C₃×C₈	—	2	4	no	—
24	C₃×C₈	C₃×D₃	1	4	yes	—
25	C₃×C₈	C₂×C₃²	1	1	yes	characteristic
26	C₂×C₃²	—	2	4	no	—
27	C₂×C₃²	D₁₂	1	1	yes	characteristic
28	C₂×C₃²	C₃×D₄	1	4	yes	—
29	Q₁₆	—	3	1	no	Sylow
30	C₃×C₄	—	2	4	no	—
31	C₃×C₄	—	6	8	no	—
32	C₃×C₄	C₂×C₃×D₃	1	4	yes	—
33	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
34	Dic₃	—	2	2	no	—
35	C₃²	—	2	4	no	—
36	C₃²	Dic₁₂	1	1	yes	characteristic, direct product factor
37	C₃²	C₃×Q₁₆	1	4	yes	complemented
38	Q₈	—	3	2	no	—
39	C₈	C₃²×D₃	1	1	yes	characteristic
40	C₂×C₃	—	2	4	no	—
41	C₂×C₃	C₃×D₁₂	1	4	yes	—
42	C₂×C₃	C₃²×D₄	1	1	yes	characteristic
43	C₄	—	6	2	no	—
44	C₄	C₂×C₃²×D₃	1	1	yes	characteristic
45	C₃	—	2	4	no	—
46	C₃	C₃×Dic₁₂	1	4	yes	direct product factor
47	C₃	C₃²×Q₁₆	1	1	yes	characteristic, complemented
48	C₂	C₃²×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	D₁₂
commutator, cosocle	C₃×C₄	C₂²×C₃²
Frattini	C₄	C₂×C₃²×D₃
Fitting	C₃³×C₈	C₂
socle, prime radical	C₂×C₃³	D₄
hypercenter	C₃²×C₈	D₃
hypocenter	C₃	C₃²×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄ ◁ C₃²×C₈

Complements

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

N	H ≅ G/N	type
4. C₃×Dic₁₂	C₃	direct (N × H)
14. Dic₁₂	C₃²	direct (N × H)
20. C₃³	Q₁₆	semidirect
36. C₃²	Dic₁₂	direct (N × H)
37. C₃²	C₃×Q₁₆	semidirect
46. C₃	C₃×Dic₁₂	direct (N × H)
47. C₃	C₃²×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃²×Dic₆	2
C₃³×C₈	2
C₃²×Q₁₆	3
C₃×Dic₁₂	3

Subgroups — C32×Dic12 #88821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₁₂ #88821