Subgroups — C₃×Dic₃₆ #88457

Order 432.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₁₈	C₂	1	2	yes	maximal
2	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₁₂	—	3	1	no	maximal
4	Dic₃₆	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₃×Dic₉	—	2	2	no	—
7	C₃×Dic₆	—	3	2	no	—
8	C₃²×C₈	D₃	1	1	yes	characteristic
9	Dic₁₈	C₂×C₃	1	2	yes	—
10	C₈×C₉	—	2	1	no	—
11	C₈×C₉	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×C₉	D₄	1	1	yes	characteristic
13	C₃×Q₁₆	—	9	1	no	—
14	Dic₁₂	—	3	1	no	—
15	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
16	C₃×Dic₃	—	6	2	no	—
17	C₄×C₉	—	2	1	no	—
18	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
19	Dic₉	—	2	2	no	—
20	C₃×C₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₃×Q₈	—	9	2	no	—
22	Dic₆	—	3	2	no	—
23	C₃×C₈	—	2	1	no	—
24	C₃×C₈	D₉	1	1	yes	characteristic
25	C₃×C₈	C₃×D₃	1	1	yes	characteristic
26	C₂×C₃²	D₁₂	1	1	yes	characteristic
27	C₂×C₉	—	2	1	no	—
28	C₂×C₉	C₃×D₄	1	1	yes	characteristic
29	Q₁₆	—	9	1	no	Sylow
30	C₃×C₄	—	2	1	no	—
31	C₃×C₄	—	18	2	no	—
32	C₃×C₄	C₂×D₉	1	1	yes	characteristic
33	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
34	Dic₃	—	6	2	no	—
35	C₃²	Dic₁₂	1	1	yes	characteristic
36	C₉	—	2	1	no	—
37	C₉	C₃×Q₁₆	1	1	yes	characteristic, complemented
38	Q₈	—	9	2	no	—
39	C₈	C₃×D₉	1	1	yes	characteristic
40	C₂×C₃	—	2	1	no	—
41	C₂×C₃	D₃₆	1	1	yes	characteristic
42	C₂×C₃	C₃×D₁₂	1	1	yes	characteristic
43	C₄	—	18	2	no	—
44	C₄	C₂×C₃×D₉	1	1	yes	characteristic
45	C₃	—	2	1	no	—
46	C₃	Dic₃₆	1	1	yes	characteristic, direct product factor
47	C₃	C₃×Dic₁₂	1	1	yes	characteristic
48	C₂	C₃×D₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₃₆
commutator, cosocle	C₄×C₉	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₃×C₈×C₉	C₂
socle, prime radical	C₂×C₃²	D₁₂
hypercenter	C₃×C₈	D₉
hypocenter	C₉	C₃×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
4. Dic₃₆	C₃	direct (N × H)
20. C₃×C₉	Q₁₆	semidirect
37. C₉	C₃×Q₁₆	semidirect
46. C₃	Dic₃₆	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×Dic₁₈	2
C₃×C₈×C₉	2
C₃×Dic₁₂	3
Dic₃₆	3

Subgroups — C3×Dic36 #88457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃₆ #88457