Subgroups — C₂×C₃×Dic₁₈ #88693

Order 432.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₉	C₂	1	2	yes	maximal
3	C₃×Dic₁₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×Dic₆	—	3	1	no	maximal
5	C₂×Dic₁₈	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	2	yes	—
8	C₃×Dic₉	C₂²	1	4	yes	—
9	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
10	C₂×C₃×Dic₃	—	3	2	no	—
11	C₃×Dic₆	—	3	4	no	—
12	C₂×C₄×C₉	—	2	1	no	—
13	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic
14	C₂×Dic₉	C₂×C₃	1	2	yes	—
15	Dic₁₈	C₂×C₃	1	4	yes	direct product factor
16	C₂×C₃×C₉	Q₈	1	2	yes	complemented
17	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
18	C₂×C₃×Q₈	—	9	1	no	—
19	C₂×Dic₆	—	3	1	no	—
20	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
21	C₃²×C₄	C₂×D₃	1	2	yes	—
22	C₃×Dic₃	—	3	4	no	—
23	C₂²×C₉	—	2	1	no	—
24	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
25	C₄×C₉	—	2	2	no	—
26	C₄×C₉	C₂²×C₃	1	2	yes	—
27	Dic₉	C₂²×C₃	1	4	yes	—
28	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
29	C₃×Q₈	—	9	4	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	9	2	no	—
32	C₂×C₃×C₄	D₉	1	1	yes	characteristic
33	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
34	C₂×Dic₃	—	3	2	no	—
35	Dic₆	—	3	4	no	—
36	C₂×C₃²	Dic₆	1	2	yes	—
37	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
38	C₂×C₉	—	2	2	no	—
39	C₂×C₉	—	2	1	no	—
40	C₂×C₉	C₃×Q₈	1	2	yes	complemented
41	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
42	C₂×Q₈	—	9	1	no	Sylow
43	C₂²×C₃	—	2	1	no	—
44	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
45	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
46	C₃×C₄	—	2	2	no	—
47	C₃×C₄	—	9	4	no	—
48	C₃×C₄	C₂×D₉	1	2	yes	—
49	C₃×C₄	C₂×C₃×D₃	1	2	yes	—
50	Dic₃	—	3	4	no	—
51	C₃²	C₂×Dic₆	1	1	yes	characteristic
52	C₉	—	2	1	no	—
53	C₉	C₂×C₃×Q₈	1	1	yes	characteristic, complemented
54	Q₈	—	9	4	no	—
55	C₂×C₄	—	9	2	no	—
56	C₂×C₄	C₃×D₉	1	1	yes	characteristic
57	C₂×C₃	—	2	2	no	—
58	C₂×C₃	—	2	1	no	—
59	C₂×C₃	Dic₁₈	1	2	yes	direct product factor
60	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
61	C₂×C₃	C₃×Dic₆	1	2	yes	—
62	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
63	C₂²	C₂×C₃×D₉	1	1	yes	characteristic
64	C₄	—	9	4	no	—
65	C₄	C₂×C₃×D₉	1	2	yes	—
66	C₃	—	2	1	no	—
67	C₃	C₂×Dic₁₈	1	1	yes	characteristic, direct product factor
68	C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
69	C₂	C₃×Dic₁₈	1	2	yes	direct product factor
70	C₂	C₂²×C₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₉
commutator, cosocle	C₂×C₉	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle, prime radical	C₂²×C₃²	C₂×D₃
hypercenter	C₂×C₃×C₄	D₉
hypocenter	C₉	C₂×C₃×Q₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×Dic₁₈	C₂	direct (N × H)
5. C₂×Dic₁₈	C₃	direct (N × H)
15. Dic₁₈	C₂×C₃	direct (N × H)
16. C₂×C₃×C₉	Q₈	semidirect
28. C₃×C₉	C₂×Q₈	semidirect
40. C₂×C₉	C₃×Q₈	semidirect
53. C₉	C₂×C₃×Q₈	semidirect
59. C₂×C₃	Dic₁₈	direct (N × H)
67. C₃	C₂×Dic₁₈	direct (N × H)
69. C₂	C₃×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
C₂×C₃×C₄×C₉	2
C₂×C₃×Dic₉	2
C₃×Dic₁₈	2
C₂×C₃×Dic₆	3
C₂×Dic₁₈	3

Subgroups — C2×C3×Dic18 #88693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Dic₁₈ #88693