Subgroups — C₃²×C₉⋊A₄ #11758096

Order 972.

626 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×A₄	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₃²×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃×C₉⋊A₄	C₃	1	36	yes	maximal, direct product factor
5	C₃²×3₋¹⁺²	—	4	1	no	maximal, Sylow
6	C₂×C₃²×C₉	—	3	1	no	—
7	C₂²×C₃³	C₃²	1	1	yes	characteristic
8	C₃²×A₄	—	3	9	no	—
9	C₃²×A₄	C₃²	1	12	yes	—
10	C₂²×C₃×C₉	C₃²	1	12	yes	complemented
11	C₃×C₂²⋊C₉	C₃²	1	24	yes	complemented
12	C₉⋊A₄	C₃²	1	81	yes	direct product factor
13	C₃⁴	—	4	1	no	—
14	C₃×3₋¹⁺²	—	4	36	no	—
15	C₃²×C₉	—	4	2	no	—
16	C₃²×C₉	A₄	1	1	yes	characteristic, complemented
17	C₂×C₃³	—	3	1	no	—
18	C₂×C₃×C₉	—	3	12	no	—
19	C₂²×C₃²	3₋¹⁺²	1	9	yes	complemented
20	C₂²×C₃²	C₃³	1	4	yes	—
21	C₃×A₄	—	3	36	no	—
22	C₃×A₄	C₃³	1	9	yes	—
23	C₂²×C₉	C₃³	1	9	yes	complemented
24	C₂²⋊C₉	C₃³	1	18	yes	complemented
25	C₃³	—	4	12	no	—
26	C₃³	—	12	9	no	—
27	C₃³	C₃×A₄	1	1	yes	characteristic
28	3₋¹⁺²	—	4	81	no	—
29	C₃×C₉	—	4	24	no	—
30	C₃×C₉	C₃×A₄	1	12	yes	complemented
31	C₂×C₃²	—	3	9	no	—
32	C₂×C₃²	—	3	4	no	—
33	C₂×C₉	—	3	9	no	—
34	C₂²×C₃	C₃×3₋¹⁺²	1	12	yes	complemented
35	C₂²×C₃	C₃⁴	1	1	yes	characteristic
36	A₄	—	3	9	no	—
37	C₃²	—	4	9	no	—
38	C₃²	—	12	36	no	—
39	C₃²	C₉⋊A₄	1	9	yes	direct product factor
40	C₃²	C₃²×A₄	1	4	yes	—
41	C₉	—	4	18	no	—
42	C₉	C₃²×A₄	1	9	yes	complemented
43	C₂×C₃	—	3	12	no	—
44	C₂×C₃	—	3	1	no	—
45	C₂²	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
46	C₃	—	12	9	no	—
47	C₃	C₃×C₉⋊A₄	1	12	yes	direct product factor
48	C₃	C₃³×A₄	1	1	yes	characteristic
49	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃³	C₃×A₄
commutator, cosocle	C₂²×C₃	C₃⁴
Frattini	C₃	C₃³×A₄
Fitting	C₂²×C₃²×C₉	C₃
socle	C₂²×C₃³	C₃²
prime radical	C₃³×A₄	C₃
hypercenter	C₃²×C₉	A₄
hypocenter	C₂²	C₃²×3₋¹⁺²
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×C₉	C₃	semidirect
3. C₃²×C₂²⋊C₉	C₃	semidirect
4. C₃×C₉⋊A₄	C₃	direct (N × H)
10. C₂²×C₃×C₉	C₃²	semidirect
11. C₃×C₂²⋊C₉	C₃²	semidirect
12. C₉⋊A₄	C₃²	direct (N × H)
16. C₃²×C₉	A₄	semidirect
19. C₂²×C₃²	3₋¹⁺²	semidirect
23. C₂²×C₉	C₃³	semidirect
24. C₂²⋊C₉	C₃³	semidirect
30. C₃×C₉	C₃×A₄	semidirect
34. C₂²×C₃	C₃×3₋¹⁺²	semidirect
39. C₃²	C₉⋊A₄	direct (N × H)
42. C₉	C₃²×A₄	semidirect
45. C₂²	C₃²×3₋¹⁺²	semidirect
47. C₃	C₃×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
C₃³×A₄	3
C₂²×C₃²×C₉	3
C₃²×C₂²⋊C₉	3
C₃×C₉⋊A₄	3
C₃²×3₋¹⁺²	4

Subgroups — C32×C9⋊A4 #11758096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₉⋊A₄ #11758096