Subgroups — C₄²×C₉⋊C₉ #13046842

Order 1296.

255 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₃²×C₄²	C₃²
commutator	C₃	C₃×C₄²×C₉
Frattini, socle, prime radical, cosocle	C₂²×C₃²	C₂²×C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄×C₉⋊C₉	C₄	direct (N × H)
11. C₄²×C₉	C₉	semidirect
16. C₉⋊C₉	C₄²	direct (N × H)
29. C₄×C₉	C₄×C₉	semidirect
37. C₄²	C₉⋊C₉	direct (N × H)
44. C₉	C₄²×C₉	semidirect
49. C₄	C₄×C₉⋊C₉	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×C₄×C₉⋊C₉	2
C₃×C₄²×C₉	3

Subgroups — C42×C9⋊C9 #13046842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₉⋊C₉ #13046842