Subgroups — C₃×#4169 #92249

Order 486.

138 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	C₃²×C₃⋊D₃	—	3	1	no	maximal
3	C₃×C₃⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#4169	C₃	1	3	yes	maximal, direct product factor
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	C₂×C₃	1	3	yes	complemented
10	C₃×C₃⋊D₃	—	3	3	no	—
11	C₃×C₃⋊D₃	—	3	1	no	—
12	C₃²×D₃	—	9	1	no	—
13	C₃²×D₃	—	9	2	no	—
14	C₃²×D₃	—	9	1	no	—
15	C₃⋊D₉	C₃²	1	1	yes	characteristic, complemented
16	C₃×D₉	—	9	1	no	—
17	C₃³	—	2	1	no	—
18	C₃³	—	2	3	no	—
19	C₃³	—	3	1	no	—
20	C₃³	—	3	2	no	—
21	C₃³	—	6	1	no	—
22	C₃³	—	6	2	no	—
23	C₃³	D₉	1	1	yes	characteristic, complemented
24	C₃³	C₃×D₃	1	1	yes	characteristic
25	C₃³	C₃×D₃	1	3	yes	—
26	C₃×C₉	—	2	1	no	—
27	C₃×C₉	—	2	3	no	—
28	C₃×C₉	—	3	1	no	—
29	C₃×C₉	—	6	1	no	—
30	C₃×C₉	—	6	2	no	—
31	C₃×C₉	—	6	1	no	—
32	C₃×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
33	C₂×C₃²	—	27	1	no	—
34	C₃⋊D₃	—	3	1	no	—
35	C₃×D₃	—	9	3	no	—
36	C₃×D₃	—	9	6	no	—
37	C₃×D₃	—	9	1	no	—
38	C₃×D₃	—	9	3	no	—
39	C₃×D₃	—	9	1	no	—
40	C₃×D₃	—	9	2	no	—
41	D₉	—	9	1	no	—
42	C₃²	—	2	1	no	—
43	C₃²	—	2	1	no	—
44	C₃²	—	2	2	no	—
45	C₃²	—	2	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	3	no	—
48	C₃²	—	3	6	no	—
49	C₃²	—	6	1	no	—
50	C₃²	—	6	3	no	—
51	C₃²	—	6	6	no	—
52	C₃²	—	6	2	no	—
53	C₃²	—	6	1	no	—
54	C₃²	C₃×D₉	1	1	yes	characteristic
55	C₃²	C₃×D₉	1	3	yes	complemented
56	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
57	C₃²	AGL(1,ℤ/9)	1	2	yes	—
58	C₃²	C₃²×D₃	1	1	yes	characteristic
59	C₉	—	3	1	no	—
60	C₉	—	6	1	no	—
61	C₉	—	6	3	no	—
62	C₂×C₃	—	27	3	no	—
63	C₂×C₃	—	27	1	no	—
64	D₃	—	9	1	no	—
65	D₃	—	9	1	no	—
66	D₃	—	9	2	no	—
67	C₃	—	2	1	no	—
68	C₃	—	2	1	no	—
69	C₃	—	2	2	no	—
70	C₃	—	3	3	no	—
71	C₃	—	6	3	no	—
72	C₃	#4169	1	1	yes	characteristic, direct product factor
73	C₃	C₃²×D₉	1	1	yes	characteristic
74	C₃	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
75	C₃	C₃×AGL(1,ℤ/9)	1	2	yes	—
76	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4169
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃²
Frattini	C₃²	C₃²×D₃
Fitting	C₃×C₃²⋊C₉	C₂
socle	C₃³	C₃×D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₃

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
4. #4169	C₃	direct (N × H)
7. C₃²×C₉	C₂×C₃	semidirect
9. C₃²⋊C₉	C₂×C₃	semidirect
15. C₃⋊D₉	C₃²	semidirect
23. C₃³	D₉	semidirect
32. C₃×C₉	C₂×C₃²	semidirect
55. C₃²	C₃×D₉	semidirect
72. C₃	#4169	direct (N × H)

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
C₃²×C₃⋊D₃	3
C₃×C₃⋊D₉	3
#4169	3

Subgroups — C3×#4169 #92249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4169 #92249