Subgroups — C₉×C₉⋊C₁₆ #13046310

Order 1296.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₉²	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃⋊C₁₆	—	3	1	no	maximal
3	C₃×C₉⋊C₁₆	C₃	1	1	yes	maximal, characteristic
4	C₄×C₉²	C₄	1	1	yes	characteristic
5	C₃×C₈×C₉	—	2	1	no	—
6	C₃×C₈×C₉	D₃	1	1	yes	characteristic
7	C₃×C₈×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₉²	C₈	1	1	yes	characteristic
9	C₃×C₃⋊C₁₆	—	3	1	no	—
10	C₉×C₁₆	—	9	1	no	—
11	C₉⋊C₁₆	C₉	1	1	yes	characteristic, direct product factor
12	C₃×C₄×C₉	—	2	1	no	—
13	C₃×C₄×C₉	Dic₃	1	1	yes	characteristic
14	C₃×C₄×C₉	C₃×C₄	1	1	yes	characteristic
15	C₉²	C₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₃²×C₈	C₃×D₃	1	1	yes	characteristic
17	C₈×C₉	—	2	3	no	—
18	C₈×C₉	—	2	1	no	—
19	C₈×C₉	—	2	1	no	—
20	C₈×C₉	D₉	1	1	yes	characteristic
21	C₈×C₉	C₂×C₉	1	1	yes	characteristic
22	C₂×C₃×C₉	—	2	1	no	—
23	C₂×C₃×C₉	C₃⋊C₈	1	1	yes	characteristic
24	C₂×C₃×C₉	C₃×C₈	1	1	yes	characteristic
25	C₃×C₁₆	—	9	1	no	—
26	C₃⋊C₁₆	—	3	1	no	—
27	C₃²×C₄	C₃×Dic₃	1	1	yes	characteristic
28	C₄×C₉	—	2	3	no	—
29	C₄×C₉	—	2	1	no	—
30	C₄×C₉	—	2	1	no	—
31	C₄×C₉	Dic₉	1	1	yes	characteristic
32	C₄×C₉	C₄×C₉	1	1	yes	characteristic
33	C₃×C₉	—	2	1	no	—
34	C₃×C₉	C₃⋊C₁₆	1	1	yes	characteristic
35	C₃×C₉	C₃×C₁₆	1	1	yes	characteristic
36	C₃×C₈	—	2	1	no	—
37	C₃×C₈	C₃×D₉	1	1	yes	characteristic
38	C₃×C₈	D₃×C₉	1	1	yes	characteristic
39	C₂×C₃²	C₃×C₃⋊C₈	1	1	yes	characteristic
40	C₂×C₉	—	2	3	no	—
41	C₂×C₉	—	2	1	no	—
42	C₂×C₉	—	2	1	no	—
43	C₂×C₉	C₉⋊C₈	1	1	yes	characteristic
44	C₂×C₉	C₈×C₉	1	1	yes	characteristic
45	C₁₆	—	9	1	no	Sylow
46	C₃×C₄	—	2	1	no	—
47	C₃×C₄	C₃×Dic₉	1	1	yes	characteristic
48	C₃×C₄	C₉×Dic₃	1	1	yes	characteristic
49	C₃²	C₃×C₃⋊C₁₆	1	1	yes	characteristic
50	C₉	—	2	3	no	—
51	C₉	—	2	1	no	—
52	C₉	—	2	1	no	—
53	C₉	C₉⋊C₁₆	1	1	yes	characteristic, direct product factor
54	C₉	C₉×C₁₆	1	1	yes	characteristic, complemented
55	C₈	C₉×D₉	1	1	yes	characteristic
56	C₂×C₃	—	2	1	no	—
57	C₂×C₃	C₃×C₉⋊C₈	1	1	yes	characteristic
58	C₂×C₃	C₉×C₃⋊C₈	1	1	yes	characteristic
59	C₄	C₉×Dic₉	1	1	yes	characteristic
60	C₃	—	2	1	no	—
61	C₃	C₃×C₉⋊C₁₆	1	1	yes	characteristic
62	C₃	C₉×C₃⋊C₁₆	1	1	yes	characteristic
63	C₂	C₉×C₉⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₉	D₉
commutator, hypocenter	C₉	C₉×C₁₆
Frattini	C₃²×C₈	C₃×D₃
Fitting	C₈×C₉²	C₂
socle, prime radical	C₂×C₃²	C₃×C₃⋊C₈
cosocle	C₃×C₈×C₉	C₂×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₈×C₉

Complements

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

N	H ≅ G/N	type
11. C₉⋊C₁₆	C₉	direct (N × H)
15. C₉²	C₁₆	semidirect
53. C₉	C₉⋊C₁₆	direct (N × H)
54. C₉	C₉×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×C₉²	2
C₉×C₃⋊C₁₆	3
C₃×C₉⋊C₁₆	3

Subgroups — C9×C9⋊C16 #13046310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₉⋊C₁₆ #13046310