Subgroups — C₄×C₉×A₄ #88678

Order 432.

81 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
2	C₃×C₄×A₄	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₉×A₄	C₄	1	1	yes	characteristic, direct product factor
6	C₃×C₄×C₉	—	4	1	no	maximal
7	C₂×C₃×A₄	C₂×C₃	1	1	yes	characteristic
8	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
9	C₂×C₂²⋊C₉	C₂×C₃	1	2	yes	—
10	C₂×C₄×C₉	—	3	1	no	—
11	C₂×C₄×C₉	—	3	1	no	—
12	C₂×C₃×C₉	—	4	1	no	—
13	C₂²×C₃×C₄	C₃²	1	1	yes	characteristic
14	C₄×A₄	C₉	1	3	yes	direct product factor
15	C₃×A₄	C₃×C₄	1	1	yes	characteristic
16	C₃²×C₄	—	4	1	no	—
17	C₂²×C₉	—	3	1	no	—
18	C₂²×C₉	—	3	1	no	—
19	C₂²×C₉	C₃×C₄	1	1	yes	characteristic, complemented
20	C₂²⋊C₉	C₃×C₄	1	2	yes	complemented
21	C₄×C₉	—	3	1	no	—
22	C₄×C₉	—	4	2	no	—
23	C₄×C₉	A₄	1	1	yes	characteristic, direct product factor
24	C₃×C₉	—	4	1	no	Sylow
25	C₂³×C₃	C₂×C₃²	1	1	yes	characteristic
26	C₂×A₄	C₂×C₉	1	3	yes	—
27	C₂×C₃×C₄	—	3	1	no	—
28	C₂×C₃×C₄	—	3	1	no	—
29	C₂×C₃²	—	4	1	no	—
30	C₂×C₉	—	3	1	no	—
31	C₂×C₉	—	3	1	no	—
32	C₂×C₉	—	4	2	no	—
33	C₂×C₉	C₂×A₄	1	1	yes	characteristic
34	C₂²×C₄	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	1	no	—
37	C₂²×C₃	C₃²×C₄	1	1	yes	characteristic
38	A₄	C₄×C₉	1	3	yes	direct product factor
39	C₃×C₄	—	3	1	no	—
40	C₃×C₄	—	4	3	no	—
41	C₃×C₄	C₃×A₄	1	1	yes	characteristic
42	C₃²	—	4	1	no	—
43	C₉	—	4	2	no	—
44	C₉	C₄×A₄	1	1	yes	characteristic, direct product factor
45	C₂³	C₂×C₃×C₉	1	1	yes	characteristic
46	C₂×C₄	—	3	1	no	—
47	C₂×C₄	—	3	1	no	—
48	C₂×C₃	—	3	1	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂×C₃	—	4	3	no	—
51	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
52	C₂²	—	3	1	no	—
53	C₂²	—	3	1	no	—
54	C₂²	C₃×C₄×C₉	1	1	yes	characteristic, complemented
55	C₄	—	3	1	no	—
56	C₄	C₉×A₄	1	1	yes	characteristic, direct product factor
57	C₃	—	4	3	no	—
58	C₃	C₃×C₄×A₄	1	1	yes	characteristic
59	C₂	—	3	1	no	—
60	C₂	—	3	1	no	—
61	C₂	C₂×C₉×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	A₄
commutator, hypocenter	C₂²	C₃×C₄×C₉
Frattini	C₂×C₃	C₂×C₃×A₄
Fitting	C₂²×C₄×C₉	C₃
socle, cosocle	C₂³×C₃	C₂×C₃²
prime radical	C₂×C₃×A₄	C₂×C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₉	C₃	semidirect
4. C₄×C₂²⋊C₉	C₃	semidirect
5. C₉×A₄	C₄	direct (N × H)
14. C₄×A₄	C₉	direct (N × H)
19. C₂²×C₉	C₃×C₄	semidirect
20. C₂²⋊C₉	C₃×C₄	semidirect
23. C₄×C₉	A₄	direct (N × H)
34. C₂²×C₄	C₃×C₉	semidirect
38. A₄	C₄×C₉	direct (N × H)
44. C₉	C₄×A₄	direct (N × H)
54. C₂²	C₃×C₄×C₉	semidirect
56. C₄	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
C₃×C₄×A₄	3
C₂²×C₄×C₉	3
C₄×C₂²⋊C₉	3
C₃×C₄×C₉	4

Subgroups — C4×C9×A4 #88678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×A₄ #88678