Subgroups — C₃²×Dic₃₆ #13047789

Order 1296.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Dic₁₈	C₂	1	2	yes	maximal
2	C₃²×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃²×Dic₁₂	—	3	1	no	maximal
4	C₃×Dic₃₆	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₃²×Dic₉	—	2	2	no	—
7	C₃²×Dic₆	—	3	2	no	—
8	C₃³×C₈	D₃	1	1	yes	characteristic
9	C₃×Dic₁₈	C₂×C₃	1	8	yes	—
10	C₃×C₈×C₉	—	2	4	no	—
11	C₃×C₈×C₉	C₂×C₃	1	4	yes	—
12	C₂×C₃²×C₉	D₄	1	1	yes	characteristic
13	C₃²×Q₁₆	—	9	1	no	—
14	C₃×Dic₁₂	—	3	4	no	—
15	Dic₃₆	C₃²	1	1	yes	characteristic, direct product factor
16	C₃³×C₄	C₂×D₃	1	1	yes	characteristic
17	C₃²×Dic₃	—	6	2	no	—
18	C₃×C₄×C₉	—	2	4	no	—
19	C₃×C₄×C₉	C₂²×C₃	1	4	yes	—
20	C₃×Dic₉	—	2	8	no	—
21	C₃²×C₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₃²×Q₈	—	9	2	no	—
23	C₃×Dic₆	—	3	8	no	—
24	C₃²×C₈	—	2	4	no	—
25	C₃²×C₈	D₉	1	1	yes	characteristic
26	C₃²×C₈	C₃×D₃	1	4	yes	—
27	Dic₁₈	C₂×C₃²	1	2	yes	—
28	C₈×C₉	—	2	4	no	—
29	C₈×C₉	C₂×C₃²	1	1	yes	characteristic
30	C₂×C₃³	D₁₂	1	1	yes	characteristic
31	C₂×C₃×C₉	—	2	4	no	—
32	C₂×C₃×C₉	C₃×D₄	1	4	yes	—
33	C₃×Q₁₆	—	9	4	no	—
34	Dic₁₂	—	3	1	no	—
35	C₃²×C₄	—	2	4	no	—
36	C₃²×C₄	—	18	2	no	—
37	C₃²×C₄	C₂×D₉	1	1	yes	characteristic
38	C₃²×C₄	C₂×C₃×D₃	1	4	yes	—
39	C₃×Dic₃	—	6	8	no	—
40	C₄×C₉	—	2	4	no	—
41	C₄×C₉	C₂²×C₃²	1	1	yes	characteristic
42	Dic₉	—	2	2	no	—
43	C₃³	Dic₁₂	1	1	yes	characteristic
44	C₃×C₉	—	2	4	no	—
45	C₃×C₉	C₃×Q₁₆	1	4	yes	complemented
46	C₃×Q₈	—	9	8	no	—
47	Dic₆	—	3	2	no	—
48	C₃×C₈	—	2	4	no	—
49	C₃×C₈	C₃×D₉	1	4	yes	—
50	C₃×C₈	C₃²×D₃	1	1	yes	characteristic
51	C₂×C₃²	—	2	4	no	—
52	C₂×C₃²	D₃₆	1	1	yes	characteristic
53	C₂×C₃²	C₃×D₁₂	1	4	yes	—
54	C₂×C₉	—	2	4	no	—
55	C₂×C₉	C₃²×D₄	1	1	yes	characteristic
56	Q₁₆	—	9	1	no	Sylow
57	C₃×C₄	—	2	4	no	—
58	C₃×C₄	—	18	8	no	—
59	C₃×C₄	C₂×C₃×D₉	1	4	yes	—
60	C₃×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
61	Dic₃	—	6	2	no	—
62	C₃²	—	2	4	no	—
63	C₃²	Dic₃₆	1	1	yes	characteristic, direct product factor
64	C₃²	C₃×Dic₁₂	1	4	yes	—
65	C₉	—	2	4	no	—
66	C₉	C₃²×Q₁₆	1	1	yes	characteristic, complemented
67	Q₈	—	9	2	no	—
68	C₈	C₃²×D₉	1	1	yes	characteristic
69	C₂×C₃	—	2	4	no	—
70	C₂×C₃	C₃×D₃₆	1	4	yes	—
71	C₂×C₃	C₃²×D₁₂	1	1	yes	characteristic
72	C₄	—	18	2	no	—
73	C₄	C₂×C₃²×D₉	1	1	yes	characteristic
74	C₃	—	2	4	no	—
75	C₃	C₃×Dic₃₆	1	4	yes	direct product factor
76	C₃	C₃²×Dic₁₂	1	1	yes	characteristic
77	C₂	C₃²×D₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	D₃₆
commutator, cosocle	C₄×C₉	C₂²×C₃²
Frattini	C₃×C₄	C₂×C₃²×D₃
Fitting	C₃²×C₈×C₉	C₂
socle, prime radical	C₂×C₃³	D₁₂
hypercenter	C₃²×C₈	D₉
hypocenter	C₉	C₃²×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
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×Dic₃₆	C₃	direct (N × H)
15. Dic₃₆	C₃²	direct (N × H)
21. C₃²×C₉	Q₁₆	semidirect
45. C₃×C₉	C₃×Q₁₆	semidirect
63. C₃²	Dic₃₆	direct (N × H)
66. C₉	C₃²×Q₁₆	semidirect
75. C₃	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
C₃²×Dic₁₈	2
C₃²×C₈×C₉	2
C₃²×Dic₁₂	3
C₃×Dic₃₆	3

Subgroups — C32×Dic36 #13047789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₃₆ #13047789