Subgroups — C₂×C₃×D₄×C₉ #88756

Order 432.

270 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₃×C₉	C₂²
commutator	C₂	C₂³×C₃×C₉
Frattini, cosocle	C₂×C₃	C₂³×C₃²
socle	C₂²×C₃²	C₂²×C₃
prime radical	C₂×C₃²×D₄	C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₉	C₂	semidirect
2. C₃×D₄×C₉	C₂	direct (N × H)
3. C₂×C₃×C₄×C₉	C₂	semidirect
5. C₂×D₄×C₉	C₃	direct (N × H)
8. C₂²×C₃×C₉	C₂²	semidirect
9. C₃×C₄×C₉	C₂²	semidirect
13. C₂³×C₉	C₂×C₃	semidirect
14. D₄×C₉	C₂×C₃	direct (N × H)
15. C₂×C₄×C₉	C₂×C₃	semidirect
17. C₂×C₃×C₉	D₄	direct (N × H)
19. C₂×C₃×D₄	C₉	direct (N × H)
27. C₂²×C₉	C₂²×C₃	semidirect
28. C₄×C₉	C₂²×C₃	semidirect
29. C₃×C₉	C₂×D₄	direct (N × H)
30. C₂³×C₃	C₂×C₉	semidirect
32. C₃×D₄	C₂×C₉	direct (N × H)
34. C₂×C₃×C₄	C₂×C₉	semidirect
40. C₂×C₉	C₃×D₄	direct (N × H)
42. C₂×D₄	C₃×C₉	direct (N × H)
46. C₂²×C₃	C₂²×C₉	semidirect
49. C₃×C₄	C₂²×C₉	semidirect
52. C₉	C₂×C₃×D₄	direct (N × H)
53. C₂³	C₂×C₃×C₉	semidirect
54. D₄	C₂×C₃×C₉	direct (N × H)
55. C₂×C₄	C₂×C₃×C₉	semidirect
58. C₂×C₃	D₄×C₉	direct (N × H)
64. C₂²	C₂²×C₃×C₉	semidirect
65. C₄	C₂²×C₃×C₉	semidirect
66. C₃	C₂×D₄×C₉	direct (N × H)
69. C₂	C₃×D₄×C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₉	2
C₃×D₄×C₉	2
C₂×C₃×C₄×C₉	2
C₂×C₃²×D₄	3
C₂×D₄×C₉	3

Subgroups — C2×C3×D4×C9 #88756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄×C₉ #88756