Subgroups — C₂×D₉⋊A₄ #88892

Order 432.

121 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	D₉⋊A₄	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×AGL(1,ℤ/9)	—	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	C₂×3₋¹⁺²	—	4	1	no	—
16	AGL(1,ℤ/9)	—	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, complemented
30	C₂²⋊C₉	—	2	1	no	—
31	3₋¹⁺²	—	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	—	3	1	no	—
38	C₂×A₄	—	9	2	no	—
39	C₂×C₃²	—	4	1	no	—
40	C₃×D₃	—	12	2	no	—
41	C₂×C₉	—	3	1	no	—
42	C₂×C₉	—	3	1	no	—
43	C₂×C₉	—	8	1	no	—
44	C₂×C₉	C₂×A₄	1	1	yes	characteristic, complemented
45	D₉	—	3	2	no	—
46	D₉	C₂×A₄	1	2	yes	complemented
47	C₂⁴	—	9	1	no	Sylow
48	C₂²×C₃	—	3	1	no	—
49	C₂²×C₃	—	3	1	no	—
50	C₂²×C₃	—	36	1	no	—
51	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
52	C₂×D₃	—	3	1	no	—
53	C₂×D₃	—	9	2	no	—
54	C₂×D₃	—	9	2	no	—
55	C₂×D₃	—	9	2	no	—
56	C₂×D₃	—	9	1	no	—
57	C₂×D₃	—	9	2	no	—
58	A₄	—	3	1	no	—
59	C₃²	—	4	1	no	—
60	C₉	—	8	1	no	—
61	C₉	C₂²×A₄	1	1	yes	characteristic, complemented
62	C₂³	—	9	2	no	—
63	C₂³	—	27	1	no	—
64	C₂³	—	27	2	no	—
65	C₂³	—	27	1	no	—
66	C₂³	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
67	C₂×C₃	—	3	1	no	—
68	C₂×C₃	—	3	1	no	—
69	C₂×C₃	—	12	1	no	—
70	C₂×C₃	—	36	2	no	—
71	C₂×C₃	D₃×A₄	1	1	yes	characteristic
72	D₃	—	3	2	no	—
73	D₃	—	9	2	no	—
74	C₂²	—	3	1	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	9	1	no	—
77	C₂²	—	27	2	no	—
78	C₂²	—	27	2	no	—
79	C₂²	—	27	2	no	—
80	C₂²	—	27	2	no	—
81	C₂²	—	27	1	no	—
82	C₂²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
83	C₃	—	12	1	no	—
84	C₃	C₂×D₃×A₄	1	1	yes	characteristic
85	C₂	—	3	1	no	—
86	C₂	—	3	1	no	—
87	C₂	—	9	2	no	—
88	C₂	—	27	2	no	—
89	C₂	D₉⋊A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉⋊A₄
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. D₉⋊A₄	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	semidirect
44. C₂×C₉	C₂×A₄	semidirect
46. D₉	C₂×A₄	semidirect
61. C₉	C₂²×A₄	semidirect
66. C₂³	AGL(1,ℤ/9)	semidirect
82. C₂²	C₂×AGL(1,ℤ/9)	semidirect
89. C₂	D₉⋊A₄	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
D₉⋊A₄	2
C₂×D₃×A₄	3
C₂³×D₉	3
C₂×AGL(1,ℤ/9)	4

Subgroups — C2×D9⋊A4 #88892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉⋊A₄ #88892