Subgroups — C₃⋊#4169 #92292

Order 486.

177 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₃)	—	3	1	no	maximal
3	C₃⋊(C₃⋊D₉)	C₃	1	1	yes	maximal, characteristic, complemented
4	#4169	—	3	3	no	maximal
5	C₃⁴	D₃	1	1	yes	characteristic
6	C₃²×C₉	—	2	1	no	—
7	C₃²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃²⋊C₉	—	2	3	no	—
9	C₃²⋊C₉	D₃	1	3	yes	complemented
10	C₃⋊(C₃⋊D₃)	—	3	1	no	—
11	C₃×C₃⋊D₃	—	9	3	no	—
12	C₃×C₃⋊D₃	—	9	6	no	—
13	C₃×C₃⋊D₃	—	9	3	no	—
14	C₃×C₃⋊D₃	—	9	1	no	—
15	C₃⋊D₉	—	3	3	no	—
16	C₃⋊D₉	—	9	3	no	—
17	C₃³	—	2	3	no	—
18	C₃³	—	2	1	no	—
19	C₃³	—	3	3	no	—
20	C₃³	—	3	6	no	—
21	C₃³	D₉	1	3	yes	complemented
22	C₃³	C₃×D₃	1	1	yes	characteristic
23	C₃³	C₃⋊D₃	1	1	yes	characteristic
24	C₃×C₉	—	2	3	no	—
25	C₃×C₉	—	3	3	no	—
26	C₃×C₉	—	6	3	no	—
27	C₃×C₉	C₃×D₃	1	3	yes	complemented
28	C₃⋊D₃	—	9	3	no	—
29	C₃⋊D₃	—	9	3	no	—
30	C₃⋊D₃	—	9	6	no	—
31	C₃⋊D₃	—	9	1	no	—
32	C₃×D₃	—	27	9	no	—
33	C₃×D₃	—	27	1	no	—
34	C₃×D₃	—	27	2	no	—
35	C₃×D₃	—	27	1	no	—
36	D₉	—	27	3	no	—
37	C₃²	—	2	3	no	—
38	C₃²	—	2	1	no	—
39	C₃²	—	3	9	no	—
40	C₃²	—	3	1	no	—
41	C₃²	—	3	2	no	—
42	C₃²	—	6	9	no	—
43	C₃²	—	6	1	no	—
44	C₃²	—	6	2	no	—
45	C₃²	C₃×D₉	1	3	yes	—
46	C₃²	(C₃⋊D₃)⋊C₃	1	3	yes	—
47	C₃²	AGL(1,ℤ/9)	1	6	yes	—
48	C₃²	C₃⋊D₉	1	1	yes	characteristic, complemented
49	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
50	C₉	—	3	3	no	—
51	C₉	—	6	3	no	—
52	C₂×C₃	—	81	1	no	—
53	D₃	—	27	9	no	—
54	D₃	—	27	1	no	—
55	D₃	—	27	1	no	—
56	D₃	—	27	2	no	—
57	C₃	—	3	1	no	—
58	C₃	—	6	3	no	—
59	C₃	—	6	1	no	—
60	C₃	#4169	1	9	yes	complemented
61	C₃	C₃×C₃⋊D₉	1	1	yes	characteristic
62	C₃	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
63	C₃	C₃⋊AGL(1,ℤ/9)	1	2	yes	—
64	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃²×C₉	C₂×C₃
Frattini	C₃²	C₃×C₃⋊D₃
Fitting	C₃×C₃²⋊C₉	C₂
socle	C₃³	C₃×D₃
LCS	G ▷ C₃²×C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊C₉	C₂	semidirect
3. C₃⋊(C₃⋊D₉)	C₃	semidirect
7. C₃²×C₉	C₂×C₃	semidirect
9. C₃²⋊C₉	D₃	semidirect
21. C₃³	D₉	semidirect
27. C₃×C₉	C₃×D₃	semidirect
48. C₃²	C₃⋊D₉	semidirect
60. C₃	#4169	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊C₉	2
C₃×C₃⋊(C₃⋊D₃)	3
C₃⋊(C₃⋊D₉)	3
#4169	3

Subgroups — C3⋊#4169 #92292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#4169 #92292