Subgroups — (C₉⋊C₈)⋊C₉ #10619496

Order 648.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃⋊C₈	—	3	1	no	maximal
3	C₃×C₉⋊C₈	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉⋊C₉	C₄	1	1	yes	characteristic
5	C₃×C₄×C₉	—	2	1	no	—
6	C₃×C₄×C₉	D₃	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂×C₃	1	1	yes	characteristic
8	C₉⋊C₉	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₃⋊C₈	—	3	1	no	—
10	C₈×C₉	—	9	1	no	—
11	C₉⋊C₈	C₉	1	1	yes	characteristic, complemented
12	C₂×C₃×C₉	—	2	1	no	—
13	C₂×C₃×C₉	Dic₃	1	1	yes	characteristic
14	C₂×C₃×C₉	C₃×C₄	1	1	yes	characteristic
15	C₃²×C₄	C₃×D₃	1	1	yes	characteristic
16	C₄×C₉	—	2	1	no	—
17	C₄×C₉	—	3	1	no	—
18	C₄×C₉	—	6	1	no	—
19	C₄×C₉	C₂×C₉	1	1	yes	characteristic
20	C₃×C₉	—	2	1	no	—
21	C₃×C₉	C₃⋊C₈	1	1	yes	characteristic
22	C₃×C₉	C₃×C₈	1	1	yes	characteristic
23	C₃×C₈	—	9	1	no	—
24	C₃⋊C₈	—	3	1	no	—
25	C₂×C₃²	C₃×Dic₃	1	1	yes	characteristic
26	C₂×C₉	—	2	1	no	—
27	C₂×C₉	—	3	1	no	—
28	C₂×C₉	—	6	1	no	—
29	C₂×C₉	C₄×C₉	1	1	yes	characteristic
30	C₃×C₄	—	2	1	no	—
31	C₃×C₄	D₃×C₉	1	1	yes	characteristic
32	C₃×C₄	AGL(1,ℤ/9)	1	1	yes	characteristic
33	C₃²	C₃×C₃⋊C₈	1	1	yes	characteristic
34	C₉	—	2	1	no	—
35	C₉	—	3	1	no	—
36	C₉	—	6	1	no	—
37	C₉	C₈×C₉	1	1	yes	characteristic, complemented
38	C₈	—	9	1	no	Sylow
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	C₉×Dic₃	1	1	yes	characteristic
41	C₂×C₃	3₋¹⁺²⋊C₄	1	1	yes	characteristic
42	C₄	D₉⋊C₉	1	1	yes	characteristic
43	C₃	—	2	1	no	—
44	C₃	C₉×C₃⋊C₈	1	1	yes	characteristic
45	C₃	3₋¹⁺²⋊C₈	1	1	yes	characteristic
46	C₂	Dic₉⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	AGL(1,ℤ/9)
commutator, hypocenter	C₉	C₈×C₉
Frattini	C₃²×C₄	C₃×D₃
Fitting	C₄×C₉⋊C₉	C₂
socle, prime radical	C₂×C₃²	C₃×Dic₃
cosocle	C₃×C₄×C₉	C₂×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
8. C₉⋊C₉	C₈	semidirect
11. C₉⋊C₈	C₉	semidirect
37. C₉	C₈×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₉⋊C₉	2
C₉×C₃⋊C₈	3
C₃×C₉⋊C₈	3

Subgroups — (C9⋊C8)⋊C9 #10619496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₉⋊C₈)⋊C₉ #10619496