Subgroups — C₃×#4183 #92320

Order 486.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×AΣL(1,𝔽₂₇)	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×C₃⋊D₃	—	3	1	no	maximal
3	C₃×AGL(1,ℤ/9)	—	3	2	no	maximal
4	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	maximal
5	#4183	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃⁴	D₃	1	1	yes	characteristic, complemented
7	C₃×3₋¹⁺²	D₃	1	2	yes	complemented
8	C₃×H(3,𝔽₃)	D₃	1	1	yes	characteristic, complemented
9	AΣL(1,𝔽₂₇)	—	2	1	no	—
10	AΣL(1,𝔽₂₇)	—	2	2	no	—
11	AΣL(1,𝔽₂₇)	—	2	1	no	—
12	AΣL(1,𝔽₂₇)	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₃⋊D₃	—	3	1	no	—
14	C₃×C₃⋊D₃	—	3	2	no	—
15	C₃×C₃⋊D₃	—	3	1	no	—
16	C₃×C₃⋊D₃	—	3	1	no	—
17	C₃²×D₃	—	9	3	no	—
18	C₃²×D₃	—	9	1	no	—
19	AGL(1,ℤ/9)	—	3	4	no	—
20	AGL(1,ℤ/9)	—	3	2	no	—
21	(C₃⋊D₃)⋊C₃	—	3	2	no	—
22	(C₃⋊D₃)⋊C₃	—	3	1	no	—
23	C₃×D₉	—	3	2	no	—
24	C₃³	—	2	1	no	—
25	C₃³	—	3	3	no	—
26	C₃³	—	3	2	no	—
27	C₃³	—	3	1	no	—
28	C₃³	—	3	1	no	—
29	C₃³	—	6	3	no	—
30	C₃³	C₃×D₃	1	1	yes	characteristic, complemented
31	C₃³	C₃⋊D₃	1	1	yes	characteristic
32	3₋¹⁺²	—	2	2	no	—
33	3₋¹⁺²	—	3	4	no	—
34	3₋¹⁺²	C₃×D₃	1	2	yes	complemented
35	H(3,𝔽₃)	—	2	1	no	—
36	H(3,𝔽₃)	—	3	2	no	—
37	H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic, complemented
38	C₃×C₉	—	3	2	no	—
39	C₂×C₃²	—	27	1	no	—
40	C₃⋊D₃	—	3	1	no	—
41	C₃⋊D₃	—	3	1	no	—
42	C₃×D₃	—	9	3	no	—
43	C₃×D₃	—	9	6	no	—
44	C₃×D₃	—	9	3	no	—
45	C₃×D₃	—	9	1	no	—
46	C₃×D₃	—	9	2	no	—
47	C₃×D₃	—	9	1	no	—
48	C₃×D₃	—	27	1	no	—
49	D₉	—	3	2	no	—
50	C₃²	—	3	3	no	—
51	C₃²	—	3	1	no	—
52	C₃²	—	3	1	no	—
53	C₃²	—	3	6	no	—
54	C₃²	—	3	3	no	—
55	C₃²	—	3	1	no	—
56	C₃²	—	6	1	no	—
57	C₃²	—	6	3	no	—
58	C₃²	—	6	6	no	—
59	C₃²	—	6	3	no	—
60	C₃²	—	6	1	no	—
61	C₃²	—	6	1	no	—
62	C₃²	—	9	1	no	—
63	C₃²	—	18	1	no	—
64	C₃²	#272	1	1	yes	characteristic
65	C₃²	#272	1	2	yes	—
66	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
67	C₉	—	3	2	no	—
68	C₉	—	6	2	no	—
69	C₂×C₃	—	27	2	no	—
70	C₂×C₃	—	27	1	no	—
71	C₂×C₃	—	27	1	no	—
72	D₃	—	9	3	no	—
73	D₃	—	9	1	no	—
74	D₃	—	27	1	no	—
75	C₃	—	2	1	no	—
76	C₃	—	3	3	no	—
77	C₃	—	3	2	no	—
78	C₃	—	3	1	no	—
79	C₃	—	6	3	no	—
80	C₃	—	9	1	no	—
81	C₃	—	18	1	no	—
82	C₃	#4183	1	1	yes	characteristic, direct product factor
83	C₃	C₃×#272	1	1	yes	characteristic
84	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4183
commutator, cosocle, hypocenter	AΣL(1,𝔽₂₇)	C₂×C₃
Frattini	C₃²	C₃×C₃⋊D₃
Fitting	C₃×AΣL(1,𝔽₂₇)	C₂
socle	C₃²	#272
LCS	G ▷ AΣL(1,𝔽₂₇)
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×AΣL(1,𝔽₂₇)	C₂	semidirect
5. #4183	C₃	direct (N × H)
6. C₃⁴	D₃	semidirect
7. C₃×3₋¹⁺²	D₃	semidirect
8. C₃×H(3,𝔽₃)	D₃	semidirect
12. AΣL(1,𝔽₂₇)	C₂×C₃	semidirect
30. C₃³	C₃×D₃	semidirect
34. 3₋¹⁺²	C₃×D₃	semidirect
37. H(3,𝔽₃)	C₃×D₃	semidirect
82. C₃	#4183	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×AΣL(1,𝔽₂₇)	2
C₃²×C₃⋊D₃	3
C₃×AGL(1,ℤ/9)	3
C₃×(C₃⋊D₃)⋊C₃	3
#4183	3

Subgroups — C3×#4183 #92320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4183 #92320