Subgroups — Dic₉⋊C₉ #66317

Order 324.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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

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