Subgroups — C₂×A₄×D₉ #88893

Order 432.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	A₄×D₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×A₄	—	3	1	no	maximal
4	C₂³×D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×D₉	—	4	1	no	maximal
6	C₉×A₄	C₂²	1	1	yes	characteristic, complemented
7	C₂×C₃×A₄	D₃	1	1	yes	characteristic
8	D₃×A₄	—	3	2	no	—
9	C₂³×C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂²×D₉	—	3	1	no	—
11	C₂²×D₉	—	3	1	no	—
12	C₂²×D₉	—	3	2	no	—
13	C₂²×D₉	C₂×C₃	1	2	yes	complemented
14	C₂×C₂²⋊C₉	—	2	1	no	—
15	C₂×C₃×C₉	—	4	1	no	—
16	C₃×D₉	—	4	2	no	—
17	C₂³×D₃	—	3	1	no	—
18	C₂²×A₄	—	9	1	no	—
19	C₂×C₃×D₃	—	12	1	no	—
20	C₃×A₄	C₂×D₃	1	1	yes	characteristic
21	C₂²×C₉	—	3	1	no	—
22	C₂²×C₉	—	3	1	no	—
23	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
24	C₂×D₉	—	3	2	no	—
25	C₂×D₉	—	3	1	no	—
26	C₂×D₉	—	3	2	no	—
27	C₂×D₉	—	3	2	no	—
28	C₂×D₉	—	3	2	no	—
29	C₂×D₉	A₄	1	1	yes	characteristic, direct product factor
30	C₂²⋊C₉	—	2	1	no	—
31	C₃×C₉	—	4	1	no	Sylow
32	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
33	C₂²×D₃	—	3	2	no	—
34	C₂²×D₃	—	9	1	no	—
35	C₂²×D₃	—	9	2	no	—
36	C₂²×D₃	—	9	1	no	—
37	C₂×A₄	—	2	1	no	—
38	C₂×A₄	—	9	2	no	—
39	C₂×A₄	D₉	1	1	yes	characteristic, direct product factor
40	C₂×C₃²	—	4	1	no	—
41	C₃×D₃	—	12	2	no	—
42	C₂×C₉	—	3	1	no	—
43	C₂×C₉	—	3	1	no	—
44	C₂×C₉	—	8	1	no	—
45	C₂×C₉	C₂×A₄	1	1	yes	characteristic, complemented
46	D₉	—	3	2	no	—
47	D₉	C₂×A₄	1	2	yes	direct product factor
48	C₂⁴	—	9	1	no	Sylow
49	C₂²×C₃	—	3	1	no	—
50	C₂²×C₃	—	3	1	no	—
51	C₂²×C₃	—	36	1	no	—
52	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
53	C₂×D₃	—	3	1	no	—
54	C₂×D₃	—	9	2	no	—
55	C₂×D₃	—	9	2	no	—
56	C₂×D₃	—	9	2	no	—
57	C₂×D₃	—	9	1	no	—
58	C₂×D₃	—	9	2	no	—
59	A₄	—	2	1	no	—
60	A₄	C₂×D₉	1	1	yes	characteristic, direct product factor
61	C₃²	—	4	1	no	—
62	C₉	—	8	1	no	—
63	C₉	C₂²×A₄	1	1	yes	characteristic, complemented
64	C₂³	—	9	2	no	—
65	C₂³	—	27	1	no	—
66	C₂³	—	27	2	no	—
67	C₂³	—	27	1	no	—
68	C₂³	C₃×D₉	1	1	yes	characteristic, complemented
69	C₂×C₃	—	3	1	no	—
70	C₂×C₃	—	3	1	no	—
71	C₂×C₃	—	4	1	no	—
72	C₂×C₃	—	8	1	no	—
73	C₂×C₃	—	36	2	no	—
74	C₂×C₃	D₃×A₄	1	1	yes	characteristic
75	D₃	—	3	2	no	—
76	D₃	—	9	2	no	—
77	C₂²	—	3	1	no	—
78	C₂²	—	3	1	no	—
79	C₂²	—	9	1	no	—
80	C₂²	—	27	2	no	—
81	C₂²	—	27	2	no	—
82	C₂²	—	27	2	no	—
83	C₂²	—	27	2	no	—
84	C₂²	—	27	1	no	—
85	C₂²	C₂×C₃×D₉	1	1	yes	characteristic, complemented
86	C₃	—	4	1	no	—
87	C₃	—	8	1	no	—
88	C₃	C₂×D₃×A₄	1	1	yes	characteristic
89	C₂	—	3	1	no	—
90	C₂	—	3	1	no	—
91	C₂	—	9	2	no	—
92	C₂	—	27	2	no	—
93	C₂	A₄×D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	A₄×D₉
commutator, cosocle, hypocenter	C₂²×C₉	C₂²×C₃
Frattini	C₃	C₂×D₃×A₄
Fitting	C₂³×C₉	C₂×C₃
socle	C₂³×C₃	C₃×D₃
LCS	G ▷ C₂²×C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×A₄	C₂	semidirect
2. A₄×D₉	C₂	direct (N × H)
4. C₂³×D₉	C₃	semidirect
6. C₉×A₄	C₂²	semidirect
9. C₂³×C₉	C₂×C₃	semidirect
13. C₂²×D₉	C₂×C₃	semidirect
23. C₂²×C₉	C₂²×C₃	semidirect
29. C₂×D₉	A₄	direct (N × H)
39. C₂×A₄	D₉	direct (N × H)
45. C₂×C₉	C₂×A₄	semidirect
47. D₉	C₂×A₄	direct (N × H)
60. A₄	C₂×D₉	direct (N × H)
63. C₉	C₂²×A₄	semidirect
68. C₂³	C₃×D₉	semidirect
85. C₂²	C₂×C₃×D₉	semidirect
93. C₂	A₄×D₉	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×C₉×A₄	2
A₄×D₉	2
C₂×D₃×A₄	3
C₂³×D₉	3
C₂×C₃×D₉	4

Subgroups — C2×A4×D9 #88893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×A₄×D₉ #88893