Subgroups — C₂×C₃²×C₄×D₃ #89054

Order 432.

388 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄×D₃	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₃²×C₄	—	3	1	no	maximal
6	C₂×C₃×C₄×D₃	C₃	1	4	yes	maximal, direct product factor
7	C₂²×C₃³	C₂²	1	1	yes	characteristic
8	C₂×C₃²×D₃	C₄	1	4	yes	direct product factor
9	C₂×C₃²×D₃	C₂²	1	2	yes	—
10	C₃³×C₄	C₂²	1	2	yes	complemented
11	C₃²×Dic₃	C₂²	1	2	yes	complemented
12	C₂³×C₃²	—	3	1	no	—
13	C₂²×C₃×D₃	C₂×C₃	1	4	yes	—
14	C₂×C₃²×C₄	—	2	4	no	—
15	C₂×C₃²×C₄	—	3	1	no	—
16	C₂×C₃²×C₄	—	3	4	no	—
17	C₂×C₃²×C₄	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₄	C₂×C₃	1	4	yes	complemented
19	C₂×C₃×Dic₃	C₂×C₃	1	4	yes	complemented
20	C₃×C₄×D₃	C₂×C₃	1	16	yes	direct product factor
21	C₂×C₃³	C₂×C₄	1	2	yes	complemented
22	C₂×C₃³	C₂³	1	1	yes	characteristic
23	C₃²×D₃	C₂×C₄	1	4	yes	direct product factor
24	C₂²×C₃×C₄	—	3	4	no	—
25	C₂×C₄×D₃	C₃²	1	1	yes	characteristic, direct product factor
26	C₂²×C₃²	—	2	4	no	—
27	C₂²×C₃²	—	3	4	no	—
28	C₂²×C₃²	—	3	2	no	—
29	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
30	C₂²×C₃²	C₂²×C₃	1	4	yes	—
31	C₂×C₃×D₃	C₃×C₄	1	16	yes	direct product factor
32	C₂×C₃×D₃	C₂²×C₃	1	8	yes	—
33	C₃²×C₄	—	2	8	no	—
34	C₃²×C₄	—	3	2	no	—
35	C₃²×C₄	C₂×D₃	1	2	yes	direct product factor
36	C₃²×C₄	C₂²×C₃	1	8	yes	complemented
37	C₃×Dic₃	C₂²×C₃	1	8	yes	complemented
38	C₃³	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂³×C₃	—	3	4	no	—
40	C₂²×D₃	C₂×C₃²	1	1	yes	characteristic
41	C₂×C₃×C₄	—	2	4	no	—
42	C₂×C₃×C₄	—	3	4	no	—
43	C₂×C₃×C₄	—	3	16	no	—
44	C₂×C₃×C₄	C₃×D₃	1	4	yes	direct product factor
45	C₂×C₃×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
46	C₂×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
47	C₄×D₃	C₂×C₃²	1	4	yes	direct product factor
48	C₂×C₃²	—	2	8	no	—
49	C₂×C₃²	—	2	4	no	—
50	C₂×C₃²	—	3	4	no	—
51	C₂×C₃²	C₄×D₃	1	2	yes	direct product factor
52	C₂×C₃²	C₂×C₃×C₄	1	8	yes	complemented
53	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
54	C₂×C₃²	C₂³×C₃	1	4	yes	—
55	C₃×D₃	C₂×C₃×C₄	1	16	yes	direct product factor
56	C₂²×C₄	—	3	1	no	Sylow
57	C₂²×C₃	—	2	4	no	—
58	C₂²×C₃	—	3	16	no	—
59	C₂²×C₃	—	3	8	no	—
60	C₂²×C₃	C₂×C₃×D₃	1	4	yes	—
61	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
62	C₂×D₃	C₃²×C₄	1	4	yes	direct product factor
63	C₂×D₃	C₂²×C₃²	1	2	yes	—
64	C₃×C₄	—	2	8	no	—
65	C₃×C₄	—	3	8	no	—
66	C₃×C₄	C₂×C₃×D₃	1	8	yes	direct product factor
67	C₃×C₄	C₂²×C₃²	1	2	yes	complemented
68	Dic₃	C₂²×C₃²	1	2	yes	complemented
69	C₃²	—	2	4	no	—
70	C₃²	C₂×C₄×D₃	1	1	yes	characteristic, direct product factor
71	C₃²	C₂²×C₃×C₄	1	4	yes	complemented
72	C₂³	—	3	1	no	—
73	C₂×C₄	—	3	1	no	—
74	C₂×C₄	—	3	4	no	—
75	C₂×C₄	C₃²×D₃	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	2	8	no	—
77	C₂×C₃	—	2	4	no	—
78	C₂×C₃	—	3	16	no	—
79	C₂×C₃	C₃×C₄×D₃	1	8	yes	direct product factor
80	C₂×C₃	C₂×C₃²×C₄	1	2	yes	complemented
81	C₂×C₃	C₂²×C₃×D₃	1	4	yes	—
82	C₂×C₃	C₂³×C₃²	1	1	yes	characteristic
83	D₃	C₂×C₃²×C₄	1	4	yes	direct product factor
84	C₂²	—	3	4	no	—
85	C₂²	—	3	2	no	—
86	C₂²	C₂×C₃²×D₃	1	1	yes	characteristic
87	C₄	—	3	2	no	—
88	C₄	C₂×C₃²×D₃	1	2	yes	direct product factor
89	C₃	—	2	4	no	—
90	C₃	C₂×C₃×C₄×D₃	1	4	yes	direct product factor
91	C₃	C₂²×C₃²×C₄	1	1	yes	characteristic, complemented
92	C₂	—	3	4	no	—
93	C₂	C₃²×C₄×D₃	1	2	yes	direct product factor
94	C₂	C₂²×C₃²×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₄	D₃
commutator, hypocenter	C₃	C₂²×C₃²×C₄
Frattini	C₂	C₂²×C₃²×D₃
Fitting	C₂×C₃³×C₄	C₂
socle	C₂²×C₃³	C₂²
prime radical	C₂²×C₃²×D₃	C₂
cosocle	C₂×C₃	C₂³×C₃²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×C₄	C₂	semidirect
3. C₂×C₃²×Dic₃	C₂	semidirect
4. C₃²×C₄×D₃	C₂	direct (N × H)
6. C₂×C₃×C₄×D₃	C₃	direct (N × H)
8. C₂×C₃²×D₃	C₄	direct (N × H)
10. C₃³×C₄	C₂²	semidirect
11. C₃²×Dic₃	C₂²	semidirect
17. C₂×C₃²×C₄	D₃	direct (N × H)
18. C₂×C₃²×C₄	C₂×C₃	semidirect
19. C₂×C₃×Dic₃	C₂×C₃	semidirect
20. C₃×C₄×D₃	C₂×C₃	direct (N × H)
21. C₂×C₃³	C₂×C₄	semidirect
23. C₃²×D₃	C₂×C₄	direct (N × H)
25. C₂×C₄×D₃	C₃²	direct (N × H)
31. C₂×C₃×D₃	C₃×C₄	direct (N × H)
35. C₃²×C₄	C₂×D₃	direct (N × H)
36. C₃²×C₄	C₂²×C₃	semidirect
37. C₃×Dic₃	C₂²×C₃	semidirect
38. C₃³	C₂²×C₄	semidirect
44. C₂×C₃×C₄	C₃×D₃	direct (N × H)
45. C₂×C₃×C₄	C₂×C₃²	semidirect
46. C₂×Dic₃	C₂×C₃²	semidirect
47. C₄×D₃	C₂×C₃²	direct (N × H)
51. C₂×C₃²	C₄×D₃	direct (N × H)
52. C₂×C₃²	C₂×C₃×C₄	semidirect
55. C₃×D₃	C₂×C₃×C₄	direct (N × H)
62. C₂×D₃	C₃²×C₄	direct (N × H)
66. C₃×C₄	C₂×C₃×D₃	direct (N × H)
67. C₃×C₄	C₂²×C₃²	semidirect
68. Dic₃	C₂²×C₃²	semidirect
70. C₃²	C₂×C₄×D₃	direct (N × H)
71. C₃²	C₂²×C₃×C₄	semidirect
75. C₂×C₄	C₃²×D₃	direct (N × H)
79. C₂×C₃	C₃×C₄×D₃	direct (N × H)
80. C₂×C₃	C₂×C₃²×C₄	semidirect
83. D₃	C₂×C₃²×C₄	direct (N × H)
88. C₄	C₂×C₃²×D₃	direct (N × H)
90. C₃	C₂×C₃×C₄×D₃	direct (N × H)
91. C₃	C₂²×C₃²×C₄	semidirect
93. C₂	C₃²×C₄×D₃	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×C₃²×D₃	2
C₂×C₃³×C₄	2
C₂×C₃²×Dic₃	2
C₃²×C₄×D₃	2
C₂²×C₃²×C₄	3
C₂×C₃×C₄×D₃	3

Subgroups — C2×C32×C4×D3 #89054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₄×D₃ #89054