Subgroups — C₃³×D₃₆ #14518875

Order 1944.

1140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×D₉	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×D₁₂	—	3	1	no	maximal
4	C₃²×D₃₆	C₃	1	13	yes	maximal, direct product factor
5	C₂×C₃³×C₉	C₂²	1	1	yes	characteristic
6	C₃³×D₉	—	2	2	no	—
7	C₂×C₃³×D₃	—	3	2	no	—
8	C₃⁴×C₄	D₃	1	1	yes	characteristic
9	C₂×C₃²×D₉	C₂×C₃	1	26	yes	complemented
10	C₃²×C₄×C₉	—	2	13	no	—
11	C₃²×C₄×C₉	C₂×C₃	1	13	yes	complemented
12	C₃³×C₉	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃³×D₄	—	9	1	no	—
14	C₃²×D₁₂	—	3	13	no	—
15	C₃×D₃₆	C₃²	1	13	yes	direct product factor
16	C₂×C₃⁴	C₂×D₃	1	1	yes	characteristic
17	C₃³×D₃	—	6	2	no	—
18	C₂×C₃²×C₉	—	2	13	no	—
19	C₂×C₃²×C₉	C₂²×C₃	1	13	yes	—
20	C₃²×D₉	—	2	26	no	—
21	C₂²×C₃³	—	9	2	no	—
22	C₂×C₃²×D₃	—	3	26	no	—
23	C₃³×C₄	—	2	13	no	—
24	C₃³×C₄	D₉	1	1	yes	characteristic, complemented
25	C₃³×C₄	C₃×D₃	1	13	yes	—
26	C₂×C₃×D₉	C₂×C₃²	1	26	yes	complemented
27	C₃×C₄×C₉	—	2	52	no	—
28	C₃×C₄×C₉	C₂×C₃²	1	13	yes	complemented
29	C₃⁴	D₁₂	1	1	yes	characteristic
30	C₃²×C₉	—	2	13	no	—
31	C₃²×C₉	C₃×D₄	1	13	yes	complemented
32	C₃²×D₄	—	9	13	no	—
33	C₃×D₁₂	—	3	13	no	—
34	D₃₆	C₃³	1	1	yes	characteristic, direct product factor
35	C₂×C₃³	—	2	13	no	—
36	C₂×C₃³	—	18	2	no	—
37	C₂×C₃³	C₂×D₉	1	1	yes	characteristic
38	C₂×C₃³	C₂×C₃×D₃	1	13	yes	—
39	C₃²×D₃	—	6	26	no	—
40	C₂×C₃×C₉	—	2	52	no	—
41	C₂×C₃×C₉	C₂²×C₃²	1	13	yes	—
42	C₃×D₉	—	2	26	no	—
43	C₂²×C₃²	—	9	26	no	—
44	C₂×C₃×D₃	—	3	26	no	—
45	C₃²×C₄	—	2	52	no	—
46	C₃²×C₄	C₃×D₉	1	13	yes	complemented
47	C₃²×C₄	C₃²×D₃	1	13	yes	—
48	C₂×D₉	C₂×C₃³	1	2	yes	complemented
49	C₄×C₉	—	2	13	no	—
50	C₄×C₉	C₂×C₃³	1	1	yes	characteristic, complemented
51	C₃³	—	2	13	no	—
52	C₃³	D₃₆	1	1	yes	characteristic, direct product factor
53	C₃³	C₃×D₁₂	1	13	yes	—
54	C₃×C₉	—	2	52	no	—
55	C₃×C₉	C₃²×D₄	1	13	yes	complemented
56	C₃×D₄	—	9	13	no	—
57	D₁₂	—	3	1	no	—
58	C₂×C₃²	—	2	52	no	—
59	C₂×C₃²	—	18	26	no	—
60	C₂×C₃²	C₂×C₃×D₉	1	13	yes	—
61	C₂×C₃²	C₂×C₃²×D₃	1	13	yes	—
62	C₃×D₃	—	6	26	no	—
63	C₂×C₉	—	2	13	no	—
64	C₂×C₉	C₂²×C₃³	1	1	yes	characteristic
65	D₉	—	2	2	no	—
66	C₂²×C₃	—	9	26	no	—
67	C₂×D₃	—	3	2	no	—
68	C₃×C₄	—	2	13	no	—
69	C₃×C₄	C₃²×D₉	1	13	yes	complemented
70	C₃×C₄	C₃³×D₃	1	1	yes	characteristic
71	C₃²	—	2	52	no	—
72	C₃²	C₃×D₃₆	1	13	yes	direct product factor
73	C₃²	C₃²×D₁₂	1	13	yes	—
74	C₉	—	2	13	no	—
75	C₉	C₃³×D₄	1	1	yes	characteristic, complemented
76	D₄	—	9	1	no	Sylow
77	C₂×C₃	—	2	13	no	—
78	C₂×C₃	—	18	26	no	—
79	C₂×C₃	C₂×C₃²×D₉	1	13	yes	—
80	C₂×C₃	C₂×C₃³×D₃	1	1	yes	characteristic
81	D₃	—	6	2	no	—
82	C₂²	—	9	2	no	—
83	C₄	C₃³×D₉	1	1	yes	characteristic, complemented
84	C₃	—	2	13	no	—
85	C₃	C₃²×D₃₆	1	13	yes	direct product factor
86	C₃	C₃³×D₁₂	1	1	yes	characteristic
87	C₂	—	18	2	no	—
88	C₂	C₂×C₃³×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃³	C₂×D₉
commutator, cosocle	C₂×C₉	C₂²×C₃³
Frattini	C₂×C₃	C₂×C₃³×D₃
Fitting	C₃³×C₄×C₉	C₂
socle	C₂×C₃⁴	C₂×D₃
hypercenter	C₃³×C₄	D₉
hypocenter	C₉	C₃³×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃³ ◁ C₃³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×D₉	C₂	semidirect
2. C₃³×C₄×C₉	C₂	semidirect
4. C₃²×D₃₆	C₃	direct (N × H)
9. C₂×C₃²×D₉	C₂×C₃	semidirect
11. C₃²×C₄×C₉	C₂×C₃	semidirect
12. C₃³×C₉	D₄	semidirect
15. C₃×D₃₆	C₃²	direct (N × H)
24. C₃³×C₄	D₉	semidirect
26. C₂×C₃×D₉	C₂×C₃²	semidirect
28. C₃×C₄×C₉	C₂×C₃²	semidirect
31. C₃²×C₉	C₃×D₄	semidirect
34. D₃₆	C₃³	direct (N × H)
46. C₃²×C₄	C₃×D₉	semidirect
48. C₂×D₉	C₂×C₃³	semidirect
50. C₄×C₉	C₂×C₃³	semidirect
52. C₃³	D₃₆	direct (N × H)
55. C₃×C₉	C₃²×D₄	semidirect
69. C₃×C₄	C₃²×D₉	semidirect
72. C₃²	C₃×D₃₆	direct (N × H)
75. C₉	C₃³×D₄	semidirect
83. C₄	C₃³×D₉	semidirect
85. C₃	C₃²×D₃₆	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×C₃³×D₉	2
C₃³×C₄×C₉	2
C₃³×D₁₂	3
C₃²×D₃₆	3

Subgroups — C33×D36 #14518875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×D₃₆ #14518875