Subgroups — C₃³×Dic₁₈ #14518872

Order 1944.

972 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃³×Dic₉	C₂	1	2	yes	maximal
3	C₃³×Dic₆	—	3	1	no	maximal
4	C₃²×Dic₁₈	C₃	1	13	yes	maximal, direct product factor
5	C₂×C₃³×C₉	C₂²	1	1	yes	characteristic
6	C₃⁴×C₄	D₃	1	1	yes	characteristic
7	C₃³×Dic₃	—	3	2	no	—
8	C₃²×C₄×C₉	—	2	13	no	—
9	C₃²×C₄×C₉	C₂×C₃	1	13	yes	—
10	C₃²×Dic₉	C₂×C₃	1	26	yes	—
11	C₃³×C₉	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃³×Q₈	—	9	1	no	—
13	C₃²×Dic₆	—	3	13	no	—
14	C₃×Dic₁₈	C₃²	1	13	yes	direct product factor
15	C₂×C₃⁴	C₂×D₃	1	1	yes	characteristic
16	C₂×C₃²×C₉	—	2	13	no	—
17	C₂×C₃²×C₉	C₂²×C₃	1	13	yes	—
18	C₃³×C₄	—	2	13	no	—
19	C₃³×C₄	—	9	2	no	—
20	C₃³×C₄	D₉	1	1	yes	characteristic
21	C₃³×C₄	C₃×D₃	1	13	yes	—
22	C₃²×Dic₃	—	3	26	no	—
23	C₃×C₄×C₉	—	2	52	no	—
24	C₃×C₄×C₉	C₂×C₃²	1	13	yes	—
25	C₃×Dic₉	C₂×C₃²	1	26	yes	—
26	C₃⁴	Dic₆	1	1	yes	characteristic
27	C₃²×C₉	—	2	13	no	—
28	C₃²×C₉	C₃×Q₈	1	13	yes	complemented
29	C₃²×Q₈	—	9	13	no	—
30	C₃×Dic₆	—	3	13	no	—
31	Dic₁₈	C₃³	1	1	yes	characteristic, direct product factor
32	C₂×C₃³	—	2	13	no	—
33	C₂×C₃³	C₂×D₉	1	1	yes	characteristic
34	C₂×C₃³	C₂×C₃×D₃	1	13	yes	—
35	C₂×C₃×C₉	—	2	52	no	—
36	C₂×C₃×C₉	C₂²×C₃²	1	13	yes	—
37	C₃²×C₄	—	2	52	no	—
38	C₃²×C₄	—	9	26	no	—
39	C₃²×C₄	C₃×D₉	1	13	yes	—
40	C₃²×C₄	C₃²×D₃	1	13	yes	—
41	C₃×Dic₃	—	3	26	no	—
42	C₄×C₉	—	2	13	no	—
43	C₄×C₉	C₂×C₃³	1	1	yes	characteristic
44	Dic₉	C₂×C₃³	1	2	yes	—
45	C₃³	—	2	13	no	—
46	C₃³	Dic₁₈	1	1	yes	characteristic, direct product factor
47	C₃³	C₃×Dic₆	1	13	yes	—
48	C₃×C₉	—	2	52	no	—
49	C₃×C₉	C₃²×Q₈	1	13	yes	complemented
50	C₃×Q₈	—	9	13	no	—
51	Dic₆	—	3	1	no	—
52	C₂×C₃²	—	2	52	no	—
53	C₂×C₃²	C₂×C₃×D₉	1	13	yes	—
54	C₂×C₃²	C₂×C₃²×D₃	1	13	yes	—
55	C₂×C₉	—	2	13	no	—
56	C₂×C₉	C₂²×C₃³	1	1	yes	characteristic
57	C₃×C₄	—	2	13	no	—
58	C₃×C₄	—	9	26	no	—
59	C₃×C₄	C₃²×D₉	1	13	yes	—
60	C₃×C₄	C₃³×D₃	1	1	yes	characteristic
61	Dic₃	—	3	2	no	—
62	C₃²	—	2	52	no	—
63	C₃²	C₃×Dic₁₈	1	13	yes	direct product factor
64	C₃²	C₃²×Dic₆	1	13	yes	—
65	C₉	—	2	13	no	—
66	C₉	C₃³×Q₈	1	1	yes	characteristic, complemented
67	Q₈	—	9	1	no	Sylow
68	C₂×C₃	—	2	13	no	—
69	C₂×C₃	C₂×C₃²×D₉	1	13	yes	—
70	C₂×C₃	C₂×C₃³×D₃	1	1	yes	characteristic
71	C₄	—	9	2	no	—
72	C₄	C₃³×D₉	1	1	yes	characteristic
73	C₃	—	2	13	no	—
74	C₃	C₃²×Dic₁₈	1	13	yes	direct product factor
75	C₃	C₃³×Dic₆	1	1	yes	characteristic
76	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, prime radical	C₂×C₃⁴	C₂×D₃
hypercenter	C₃³×C₄	D₉
hypocenter	C₉	C₃³×Q₈
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
4. C₃²×Dic₁₈	C₃	direct (N × H)
11. C₃³×C₉	Q₈	semidirect
14. C₃×Dic₁₈	C₃²	direct (N × H)
28. C₃²×C₉	C₃×Q₈	semidirect
31. Dic₁₈	C₃³	direct (N × H)
46. C₃³	Dic₁₈	direct (N × H)
49. C₃×C₉	C₃²×Q₈	semidirect
63. C₃²	C₃×Dic₁₈	direct (N × H)
66. C₉	C₃³×Q₈	semidirect
74. C₃	C₃²×Dic₁₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×C₉	2
C₃³×Dic₉	2
C₃³×Dic₆	3
C₃²×Dic₁₈	3

Subgroups — C33×Dic18 #14518872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×Dic₁₈ #14518872