Subgroups — #14550715

Order 2187.

653 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6891	C₃	1	1	yes	maximal, characteristic
2	#10624699	C₃	1	9	yes	maximal, complemented
3	C₃×#6866	C₃	1	3	yes	maximal
4	C₃⁵	C₃²	1	1	yes	characteristic
5	C₃²×3₋¹⁺²	C₃²	1	3	yes	—
6	#6891	—	3	9	no	—
7	C₃×C₃²⋊C₉	—	3	3	no	—
8	C₃×C₃²⋊C₉	C₃²	1	9	yes	—
9	3₋¹⁺²⋊C₉	—	3	27	no	—
10	#6866	—	3	9	no	—
11	C₃⁴	—	3	3	no	—
12	C₃⁴	—	3	9	no	—
13	C₃⁴	—	9	9	no	—
14	C₃⁴	H(3,𝔽₃)	1	3	yes	—
15	C₃⁴	C₃³	1	1	yes	characteristic
16	C₃×3₋¹⁺²	—	3	6	no	—
17	C₃×3₋¹⁺²	—	3	27	no	—
18	C₃×3₋¹⁺²	H(3,𝔽₃)	1	9	yes	—
19	C₃²×C₉	—	3	3	no	—
20	C₃²×C₉	—	3	9	no	—
21	C₃²⋊C₉	—	3	27	no	—
22	C₃²⋊C₉	—	3	9	no	—
23	C₃²⋊C₉	—	3	18	no	—
24	C₃³	—	3	9	no	—
25	C₃³	—	3	3	no	—
26	C₃³	—	3	9	no	—
27	C₃³	—	9	3	no	—
28	C₃³	—	9	27	no	—
29	C₃³	—	9	6	no	—
30	C₃³	—	9	81	no	—
31	C₃³	—	9	9	no	—
32	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃³	C₃×H(3,𝔽₃)	1	3	yes	—
34	C₃³	#737	1	9	yes	—
35	3₋¹⁺²	—	3	27	no	—
36	3₋¹⁺²	—	9	18	no	—
37	C₃×C₉	—	3	9	no	—
38	C₃×C₉	—	9	9	no	—
39	C₃×C₉	—	9	9	no	—
40	C₃×C₉	—	27	9	no	—
41	C₃²	—	3	9	no	—
42	C₃²	—	3	3	no	—
43	C₃²	—	3	9	no	—
44	C₃²	—	9	9	no	—
45	C₃²	—	9	27	no	—
46	C₃²	—	9	81	no	—
47	C₃²	—	9	3	no	—
48	C₃²	—	9	6	no	—
49	C₃²	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
50	C₃²	#6893	1	3	yes	—
51	C₃²	#6893	1	9	yes	—
52	C₉	—	9	9	no	—
53	C₉	—	27	9	no	—
54	C₃	—	3	9	no	—
55	C₃	—	3	3	no	—
56	C₃	—	9	9	no	—
57	C₃	#10624564	1	1	yes	characteristic
58	C₃	#10624755	1	3	yes	—

	subgroup	G/H
center, socle	C₃²	C₃²⋊H(3,𝔽₃)
commutator, Frattini, cosocle	C₃⁴	C₃³
prime radical	C₃⁵	C₃²
LCS	G ▷ C₃⁴ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ G
LECS	G ▷ C₃⁴ ▷ C₃ ▷ C₁

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

N	H ≅ G/N	type
2. #10624699	C₃	semidirect

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