Subgroups — C₂²×C₉⋊A₄ #88900

Order 432.

137 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊A₄	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×A₄	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₂²×3₋¹⁺²	—	4	1	no	maximal
6	C₉⋊A₄	C₂²	1	1	yes	characteristic, direct product factor
7	C₂×C₃×A₄	C₂×C₃	1	3	yes	—
8	C₂³×C₉	—	3	3	no	—
9	C₂³×C₉	—	3	1	no	—
10	C₂³×C₉	C₂×C₃	1	3	yes	complemented
11	C₂×C₂²⋊C₉	C₂×C₃	1	6	yes	complemented
12	C₂×3₋¹⁺²	—	4	3	no	—
13	C₂⁴×C₃	C₃²	1	1	yes	characteristic
14	C₂²×A₄	—	3	1	no	—
15	C₂²×C₃²	—	4	1	no	—
16	C₃×A₄	C₂²×C₃	1	1	yes	characteristic
17	C₂²×C₉	—	3	3	no	—
18	C₂²×C₉	—	3	2	no	—
19	C₂²×C₉	—	3	3	no	—
20	C₂²×C₉	—	3	3	no	—
21	C₂²×C₉	—	4	2	no	—
22	C₂²×C₉	A₄	1	1	yes	characteristic, complemented
23	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
24	C₂²⋊C₉	C₂²×C₃	1	2	yes	complemented
25	3₋¹⁺²	—	4	1	no	Sylow
26	C₂³×C₃	—	3	3	no	—
27	C₂³×C₃	—	3	1	no	—
28	C₂³×C₃	C₂×C₃²	1	3	yes	—
29	C₂×A₄	—	3	3	no	—
30	C₂×C₃²	—	4	3	no	—
31	C₂×C₉	—	3	3	no	—
32	C₂×C₉	—	3	1	no	—
33	C₂×C₉	—	4	6	no	—
34	C₂×C₉	C₂×A₄	1	3	yes	complemented
35	C₂⁴	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₃	—	3	3	no	—
37	C₂²×C₃	—	3	2	no	—
38	C₂²×C₃	—	3	3	no	—
39	C₂²×C₃	—	3	3	no	—
40	C₂²×C₃	—	12	1	no	—
41	C₂²×C₃	C₃×A₄	1	1	yes	characteristic
42	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
43	A₄	—	3	1	no	—
44	C₃²	—	4	1	no	—
45	C₉	—	4	2	no	—
46	C₉	C₂²×A₄	1	1	yes	characteristic, complemented
47	C₂³	—	3	3	no	—
48	C₂³	—	3	1	no	—
49	C₂³	C₂×3₋¹⁺²	1	3	yes	complemented
50	C₂×C₃	—	3	1	no	—
51	C₂×C₃	—	3	3	no	—
52	C₂×C₃	—	12	3	no	—
53	C₂×C₃	C₂×C₃×A₄	1	3	yes	—
54	C₂²	—	3	3	no	—
55	C₂²	—	3	2	no	—
56	C₂²	—	3	3	no	—
57	C₂²	—	3	3	no	—
58	C₂²	C₉⋊A₄	1	1	yes	characteristic, direct product factor
59	C₂²	C₂²×3₋¹⁺²	1	1	yes	characteristic, complemented
60	C₃	—	12	1	no	—
61	C₃	C₂²×C₃×A₄	1	1	yes	characteristic
62	C₂	—	3	1	no	—
63	C₂	—	3	3	no	—
64	C₂	C₂×C₉⋊A₄	1	3	yes	direct product factor

	subgroup	G/H
center	C₂²×C₃	C₃×A₄
commutator, cosocle	C₂²×C₃	C₂²×C₃²
Frattini	C₃	C₂²×C₃×A₄
Fitting	C₂⁴×C₉	C₃
socle	C₂⁴×C₃	C₃²
prime radical	C₂²×C₃×A₄	C₃
hypercenter	C₂²×C₉	A₄
hypocenter	C₂²	C₂²×3₋¹⁺²
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₉⋊A₄	C₂	direct (N × H)
3. C₂⁴×C₉	C₃	semidirect
4. C₂²×C₂²⋊C₉	C₃	semidirect
6. C₉⋊A₄	C₂²	direct (N × H)
10. C₂³×C₉	C₂×C₃	semidirect
11. C₂×C₂²⋊C₉	C₂×C₃	semidirect
22. C₂²×C₉	A₄	semidirect
23. C₂²×C₉	C₂²×C₃	semidirect
24. C₂²⋊C₉	C₂²×C₃	semidirect
34. C₂×C₉	C₂×A₄	semidirect
35. C₂⁴	3₋¹⁺²	semidirect
46. C₉	C₂²×A₄	semidirect
49. C₂³	C₂×3₋¹⁺²	semidirect
58. C₂²	C₉⋊A₄	direct (N × H)
59. C₂²	C₂²×3₋¹⁺²	semidirect
64. C₂	C₂×C₉⋊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
C₂²×C₃×A₄	3
C₂⁴×C₉	3
C₂²×C₂²⋊C₉	3
C₂²×3₋¹⁺²	4

Subgroups — C22×C9⋊A4 #88900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉⋊A₄ #88900