Subgroups — #611⋊C₃ #6225

Order 216.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
3	3₋¹⁺²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#67	—	3	1	no	maximal
5	#611	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×3₋¹⁺²	—	2	1	no	—
7	C₂×3₋¹⁺²	C₂²	1	1	yes	characteristic
8	AGL(1,ℤ/9)	—	2	1	no	—
9	C₂²×C₃²	D₃	1	1	yes	characteristic
10	C₂×C₃×D₃	—	3	1	no	—
11	C₃×Dic₃	—	3	1	no	—
12	C₂²×C₉	—	2	1	no	—
13	C₂²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₉	C₂×C₃	1	1	yes	characteristic, complemented
15	Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
16	3₋¹⁺²	D₄	1	1	yes	characteristic, complemented, Sylow
17	C₃×D₄	—	9	1	no	—
18	#67	—	3	1	no	—
19	C₂×C₃²	—	2	1	no	—
20	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
21	C₃×D₃	—	6	1	no	—
22	C₂×C₉	—	2	2	no	—
23	C₂×C₉	—	2	1	no	—
24	C₂×C₉	—	2	1	no	—
25	C₂×C₉	C₂²×C₃	1	1	yes	characteristic
26	D₉	—	2	1	no	—
27	C₂²×C₃	—	3	1	no	—
28	C₂²×C₃	—	9	1	no	—
29	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
30	C₂×D₃	—	3	1	no	—
31	C₃×C₄	—	9	1	no	—
32	Dic₃	—	3	1	no	—
33	C₃²	#67	1	1	yes	characteristic
34	C₉	—	2	1	no	—
35	C₉	C₃×D₄	1	1	yes	characteristic, complemented
36	D₄	—	9	1	no	Sylow
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	—	3	1	no	—
39	C₂×C₃	—	6	1	no	—
40	C₂×C₃	—	18	1	no	—
41	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
42	D₃	—	6	1	no	—
43	C₂²	—	9	1	no	—
44	C₂²	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
45	C₄	—	9	1	no	—
46	C₃	—	3	1	no	—
47	C₃	C₃×#67	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	18	1	no	—
50	C₂	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×AGL(1,ℤ/9)
commutator, cosocle	C₂×C₉	C₂²×C₃
Frattini, socle	C₂×C₃	C₂×C₃×D₃
Fitting	C₂²×3₋¹⁺²	C₂
hypercenter	C₂²	AGL(1,ℤ/9)
hypocenter	C₉	C₃×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×3₋¹⁺²	C₂	semidirect
2. C₂×AGL(1,ℤ/9)	C₂	semidirect
3. 3₋¹⁺²⋊C₄	C₂	semidirect
5. #611	C₃	semidirect
13. C₂²×C₉	C₂×C₃	semidirect
14. C₂×D₉	C₂×C₃	semidirect
15. Dic₉	C₂×C₃	semidirect
16. 3₋¹⁺²	D₄	semidirect
35. C₉	C₃×D₄	semidirect
44. C₂²	AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×3₋¹⁺²	2
C₂×AGL(1,ℤ/9)	2
3₋¹⁺²⋊C₄	2
C₃×#67	3
#611	3

Subgroups — #611⋊C3 #6225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #611⋊C₃ #6225