Subgroups — C₃×C₉⋊(C₄²⋊C₃) #13047780

Order 1296.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₉⋊(C₄²⋊C₃)	C₃	1	9	yes	maximal, direct product factor
5	C₃×C₉⋊A₄	—	4	1	no	maximal
6	C₂×C₃×C₄×C₉	—	3	1	no	—
7	C₃²×C₄²	C₃²	1	1	yes	characteristic
8	C₃×C₄²⋊C₃	—	3	3	no	—
9	C₃×C₄²⋊C₃	C₃²	1	3	yes	—
10	C₄²×C₉	C₃²	1	3	yes	complemented
11	C₄²⋊C₉	C₃²	1	6	yes	complemented
12	C₃²×A₄	—	4	1	no	—
13	C₂²×C₃×C₉	A₄	1	1	yes	characteristic
14	C₃×C₂²⋊C₉	—	4	2	no	—
15	C₉⋊A₄	—	4	9	no	—
16	C₃×C₄×C₉	—	3	2	no	—
17	C₃×3₋¹⁺²	—	16	1	no	Sylow
18	C₂×C₃²×C₄	—	3	1	no	—
19	C₂×C₄×C₉	—	3	3	no	—
20	C₂×C₃×C₉	—	3	1	no	—
21	C₃×C₄²	3₋¹⁺²	1	3	yes	complemented
22	C₃×C₄²	C₃³	1	1	yes	characteristic
23	C₄²⋊C₃	—	3	3	no	—
24	C₂²×C₃²	C₃×A₄	1	1	yes	characteristic
25	C₃×A₄	—	4	3	no	—
26	C₃×A₄	—	12	3	no	—
27	C₃²×C₄	—	3	2	no	—
28	C₂²×C₉	C₃×A₄	1	3	yes	—
29	C₂²⋊C₉	—	4	6	no	—
30	C₄×C₉	—	3	6	no	—
31	C₃³	—	16	1	no	—
32	3₋¹⁺²	—	16	9	no	—
33	C₃×C₉	—	16	2	no	—
34	C₃×C₉	C₄²⋊C₃	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄	—	3	3	no	—
36	C₂×C₃×C₄	—	3	1	no	—
37	C₂×C₃²	—	3	1	no	—
38	C₂×C₉	—	3	3	no	—
39	C₄²	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₃	C₉⋊A₄	1	3	yes	—
41	C₂²×C₃	C₃²×A₄	1	1	yes	characteristic
42	A₄	—	12	3	no	—
43	C₃×C₄	—	3	2	no	—
44	C₃×C₄	—	3	6	no	—
45	C₃²	—	16	3	no	—
46	C₃²	—	48	3	no	—
47	C₃²	C₃×C₄²⋊C₃	1	1	yes	characteristic
48	C₉	—	16	6	no	—
49	C₉	C₃×C₄²⋊C₃	1	3	yes	complemented
50	C₂×C₄	—	3	1	no	—
51	C₂×C₃	—	3	3	no	—
52	C₂×C₃	—	3	1	no	—
53	C₂²	C₃×C₉⋊A₄	1	1	yes	characteristic
54	C₄	—	3	2	no	—
55	C₃	—	48	3	no	—
56	C₃	C₉⋊(C₄²⋊C₃)	1	3	yes	direct product factor
57	C₃	C₃²×C₄²⋊C₃	1	1	yes	characteristic
58	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃²	C₃×C₄²⋊C₃
commutator, cosocle	C₃×C₄²	C₃³
Frattini	C₂²×C₃	C₃²×A₄
Fitting	C₃×C₄²×C₉	C₃
socle	C₂²×C₃²	C₃×A₄
prime radical	C₃²×C₄²⋊C₃	C₃
hypercenter	C₃×C₉	C₄²⋊C₃
hypocenter	C₄²	C₃×3₋¹⁺²
LCS	G ▷ C₃×C₄² ▷ C₄²
UCS	C₁ ◁ C₃² ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₉	C₃	semidirect
3. C₃×C₄²⋊C₉	C₃	semidirect
4. C₉⋊(C₄²⋊C₃)	C₃	direct (N × H)
10. C₄²×C₉	C₃²	semidirect
11. C₄²⋊C₉	C₃²	semidirect
21. C₃×C₄²	3₋¹⁺²	semidirect
34. C₃×C₉	C₄²⋊C₃	semidirect
39. C₄²	C₃×3₋¹⁺²	semidirect
49. C₉	C₃×C₄²⋊C₃	semidirect
56. C₃	C₉⋊(C₄²⋊C₃)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₄²⋊C₃	3
C₃×C₄²×C₉	3
C₃×C₄²⋊C₉	3
C₉⋊(C₄²⋊C₃)	3
C₃×C₉⋊A₄	4

Subgroups — C3×C9⋊(C42⋊C3) #13047780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉⋊(C₄²⋊C₃) #13047780