Subgroups — C₂×C₄×D₃×C₉ #88698

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	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₃×C₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×C₄×D₃	C₃	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₉	—	3	1	no	maximal
7	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
8	C₂×D₃×C₉	C₄	1	4	yes	direct product factor
9	C₂×D₃×C₉	C₂²	1	2	yes	—
10	C₃×C₄×C₉	C₂²	1	2	yes	complemented
11	C₉×Dic₃	C₂²	1	2	yes	complemented
12	C₂²×C₃×D₃	C₂×C₃	1	1	yes	characteristic
13	C₂×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
15	C₃×C₄×D₃	C₂×C₃	1	4	yes	—
16	C₂³×C₉	—	3	1	no	—
17	C₂×C₄×C₉	—	2	1	no	—
18	C₂×C₄×C₉	—	3	1	no	—
19	C₂×C₄×C₉	—	3	4	no	—
20	C₂×C₄×C₉	D₃	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₉	C₂×C₄	1	2	yes	complemented
22	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
23	D₃×C₉	C₂×C₄	1	4	yes	direct product factor
24	C₂²×C₃×C₄	—	3	1	no	—
25	C₂×C₄×D₃	C₉	1	1	yes	characteristic, direct product factor
26	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
27	C₂×C₃×D₃	C₃×C₄	1	4	yes	—
28	C₂×C₃×D₃	C₂²×C₃	1	2	yes	—
29	C₃²×C₄	C₂²×C₃	1	2	yes	—
30	C₃×Dic₃	C₂²×C₃	1	2	yes	—
31	C₂²×C₉	—	2	1	no	—
32	C₂²×C₉	—	3	4	no	—
33	C₂²×C₉	—	3	2	no	—
34	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
35	C₄×C₉	—	2	2	no	—
36	C₄×C₉	—	3	2	no	—
37	C₄×C₉	C₂×D₃	1	2	yes	direct product factor
38	C₃×C₉	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂³×C₃	—	3	1	no	—
40	C₂²×D₃	C₂×C₉	1	1	yes	characteristic
41	C₂×C₃×C₄	—	2	1	no	—
42	C₂×C₃×C₄	—	3	1	no	—
43	C₂×C₃×C₄	—	3	4	no	—
44	C₂×C₃×C₄	C₂×C₉	1	1	yes	characteristic, complemented
45	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
46	C₂×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
47	C₄×D₃	C₂×C₉	1	4	yes	direct product factor
48	C₂×C₃²	C₂×C₃×C₄	1	2	yes	—
49	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
50	C₃×D₃	C₂×C₃×C₄	1	4	yes	—
51	C₂×C₉	—	2	2	no	—
52	C₂×C₉	—	2	1	no	—
53	C₂×C₉	—	3	4	no	—
54	C₂×C₉	C₄×D₃	1	2	yes	direct product factor
55	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
56	C₂²×C₄	—	3	1	no	Sylow
57	C₂²×C₃	—	2	1	no	—
58	C₂²×C₃	—	3	4	no	—
59	C₂²×C₃	—	3	2	no	—
60	C₂²×C₃	C₂²×C₉	1	1	yes	characteristic
61	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
62	C₂×D₃	C₄×C₉	1	4	yes	direct product factor
63	C₂×D₃	C₂²×C₉	1	2	yes	—
64	C₃×C₄	—	2	2	no	—
65	C₃×C₄	—	3	2	no	—
66	C₃×C₄	C₂²×C₉	1	2	yes	complemented
67	C₃×C₄	C₂×C₃×D₃	1	2	yes	—
68	Dic₃	C₂²×C₉	1	2	yes	complemented
69	C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
70	C₉	—	2	1	no	—
71	C₉	C₂×C₄×D₃	1	1	yes	characteristic, direct product factor
72	C₂³	—	3	1	no	—
73	C₂×C₄	—	3	1	no	—
74	C₂×C₄	—	3	4	no	—
75	C₂×C₄	D₃×C₉	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	3	4	no	—
79	C₂×C₃	C₂×C₄×C₉	1	2	yes	complemented
80	C₂×C₃	C₂³×C₉	1	1	yes	characteristic
81	C₂×C₃	C₃×C₄×D₃	1	2	yes	—
82	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
83	D₃	C₂×C₄×C₉	1	4	yes	direct product factor
84	C₂²	—	3	4	no	—
85	C₂²	—	3	2	no	—
86	C₂²	C₂×D₃×C₉	1	1	yes	characteristic
87	C₄	—	3	2	no	—
88	C₄	C₂×D₃×C₉	1	2	yes	direct product factor
89	C₃	—	2	1	no	—
90	C₃	C₂²×C₄×C₉	1	1	yes	characteristic, complemented
91	C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
92	C₂	—	3	4	no	—
93	C₂	C₄×D₃×C₉	1	2	yes	direct product factor
94	C₂	C₂²×D₃×C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₉	C₂	semidirect
3. C₂×C₉×Dic₃	C₂	semidirect
4. C₄×D₃×C₉	C₂	direct (N × H)
8. C₂×D₃×C₉	C₄	direct (N × H)
10. C₃×C₄×C₉	C₂²	semidirect
11. C₉×Dic₃	C₂²	semidirect
20. C₂×C₄×C₉	D₃	direct (N × H)
21. C₂×C₃×C₉	C₂×C₄	semidirect
23. D₃×C₉	C₂×C₄	direct (N × H)
25. C₂×C₄×D₃	C₉	direct (N × H)
37. C₄×C₉	C₂×D₃	direct (N × H)
38. C₃×C₉	C₂²×C₄	semidirect
44. C₂×C₃×C₄	C₂×C₉	semidirect
46. C₂×Dic₃	C₂×C₉	semidirect
47. C₄×D₃	C₂×C₉	direct (N × H)
54. C₂×C₉	C₄×D₃	direct (N × H)
62. C₂×D₃	C₄×C₉	direct (N × H)
66. C₃×C₄	C₂²×C₉	semidirect
68. Dic₃	C₂²×C₉	semidirect
71. C₉	C₂×C₄×D₃	direct (N × H)
75. C₂×C₄	D₃×C₉	direct (N × H)
79. C₂×C₃	C₂×C₄×C₉	semidirect
83. D₃	C₂×C₄×C₉	direct (N × H)
88. C₄	C₂×D₃×C₉	direct (N × H)
90. C₃	C₂²×C₄×C₉	semidirect
93. C₂	C₄×D₃×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
C₂²×D₃×C₉	2
C₂×C₃×C₄×C₉	2
C₂×C₉×Dic₃	2
C₄×D₃×C₉	2
C₂×C₃×C₄×D₃	3
C₂²×C₄×C₉	3

Subgroups — C2×C4×D3×C9 #88698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₃×C₉ #88698