Subgroups — C₂×C₉×D₁₂ #88699

Order 432.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×C₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×D₁₂	C₃	1	1	yes	maximal, characteristic
5	C₂×D₄×C₉	—	3	1	no	maximal
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₂×D₃×C₉	—	2	4	no	—
8	C₂×D₃×C₉	C₂²	1	4	yes	complemented
9	C₃×C₄×C₉	C₂²	1	2	yes	complemented
10	C₂²×C₃×D₃	C₂×C₃	1	2	yes	—
11	C₂×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
12	C₃×D₁₂	C₂×C₃	1	4	yes	—
13	C₂³×C₉	—	3	2	no	—
14	D₄×C₉	—	3	4	no	—
15	C₂×C₄×C₉	—	2	1	no	—
16	C₂×C₄×C₉	D₃	1	1	yes	characteristic, complemented
17	C₂×C₃×C₉	D₄	1	2	yes	complemented
18	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
19	D₃×C₉	—	2	4	no	—
20	C₂×C₃×D₄	—	3	1	no	—
21	C₂×D₁₂	C₉	1	1	yes	characteristic, direct product factor
22	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₃×D₃	—	2	4	no	—
24	C₂×C₃×D₃	C₂²×C₃	1	4	yes	—
25	C₃²×C₄	C₂²×C₃	1	2	yes	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	—	3	4	no	—
28	C₂²×C₉	—	6	4	no	—
29	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
30	C₄×C₉	—	2	2	no	—
31	C₄×C₉	C₂×D₃	1	2	yes	complemented
32	C₃×C₉	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
33	C₂³×C₃	—	3	2	no	—
34	C₂²×D₃	C₂×C₉	1	2	yes	complemented
35	C₃×D₄	—	3	4	no	—
36	C₂×C₃×C₄	—	2	1	no	—
37	C₂×C₃×C₄	C₂×C₉	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
39	D₁₂	C₂×C₉	1	4	yes	direct product factor
40	C₂×C₃²	C₃×D₄	1	2	yes	—
41	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
42	C₃×D₃	—	2	4	no	—
43	C₂×C₉	—	2	2	no	—
44	C₂×C₉	—	2	1	no	—
45	C₂×C₉	—	6	4	no	—
46	C₂×C₉	D₁₂	1	2	yes	direct product factor
47	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
48	C₂×D₄	—	3	1	no	Sylow
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	3	4	no	—
51	C₂²×C₃	—	6	4	no	—
52	C₂²×C₃	C₂²×C₉	1	1	yes	characteristic
53	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
54	C₂×D₃	—	2	4	no	—
55	C₂×D₃	C₂²×C₉	1	4	yes	complemented
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	C₂²×C₉	1	2	yes	complemented
58	C₃×C₄	C₂×C₃×D₃	1	2	yes	—
59	C₃²	C₂×C₃×D₄	1	1	yes	characteristic
60	C₉	—	2	1	no	—
61	C₉	C₂×D₁₂	1	1	yes	characteristic, direct product factor
62	C₂³	—	3	2	no	—
63	D₄	—	3	4	no	—
64	C₂×C₄	D₃×C₉	1	1	yes	characteristic, complemented
65	C₂×C₃	—	2	2	no	—
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	6	4	no	—
68	C₂×C₃	D₄×C₉	1	2	yes	complemented
69	C₂×C₃	C₂³×C₉	1	1	yes	characteristic
70	C₂×C₃	C₃×D₁₂	1	2	yes	—
71	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
72	D₃	—	2	4	no	—
73	C₂²	—	3	4	no	—
74	C₂²	—	6	4	no	—
75	C₂²	C₂×D₃×C₉	1	1	yes	characteristic
76	C₄	C₂×D₃×C₉	1	2	yes	complemented
77	C₃	—	2	1	no	—
78	C₃	C₂×D₄×C₉	1	1	yes	characteristic, complemented
79	C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
80	C₂	—	6	4	no	—
81	C₂	C₉×D₁₂	1	2	yes	direct product factor
82	C₂	C₂²×D₃×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂×D₃
commutator	C₂×C₃	C₂³×C₉
Frattini	C₂×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle	C₂²×C₃²	C₂²×C₃
prime radical	C₂×C₃×D₁₂	C₃
cosocle	C₂×C₃²	C₂³×C₃
hypercenter	C₂×C₄×C₉	D₃
hypocenter	C₃	C₂×D₄×C₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×C₉	C₂	semidirect
2. C₂×C₃×C₄×C₉	C₂	semidirect
3. C₉×D₁₂	C₂	direct (N × H)
8. C₂×D₃×C₉	C₂²	semidirect
9. C₃×C₄×C₉	C₂²	semidirect
16. C₂×C₄×C₉	D₃	semidirect
17. C₂×C₃×C₉	D₄	semidirect
21. C₂×D₁₂	C₉	direct (N × H)
31. C₄×C₉	C₂×D₃	semidirect
32. C₃×C₉	C₂×D₄	semidirect
34. C₂²×D₃	C₂×C₉	semidirect
37. C₂×C₃×C₄	C₂×C₉	semidirect
39. D₁₂	C₂×C₉	direct (N × H)
46. C₂×C₉	D₁₂	direct (N × H)
55. C₂×D₃	C₂²×C₉	semidirect
57. C₃×C₄	C₂²×C₉	semidirect
61. C₉	C₂×D₁₂	direct (N × H)
64. C₂×C₄	D₃×C₉	semidirect
68. C₂×C₃	D₄×C₉	semidirect
76. C₄	C₂×D₃×C₉	semidirect
78. C₃	C₂×D₄×C₉	semidirect
81. C₂	C₉×D₁₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₃×C₉	2
C₂×C₃×C₄×C₉	2
C₉×D₁₂	2
C₂×C₃×D₁₂	3
C₂×D₄×C₉	3

Subgroups — C2×C9×D12 #88699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₁₂ #88699