Subgroups — #14552195

Order 2187.

1274 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6891	C₃	1	2	yes	maximal
2	C₃²×C₃²⋊C₉	C₃	1	2	yes	maximal
3	#10624569	C₃	1	9	yes	maximal, complemented
4	#10624568	C₃	1	9	yes	maximal, complemented
5	#10624558	C₃	1	18	yes	maximal, complemented
6	C₃⁵	C₃²	1	1	yes	characteristic
7	C₃²×3₋¹⁺²	C₃²	1	6	yes	—
8	C₃³×C₉	C₃²	1	6	yes	—
9	#6891	—	3	18	no	—
10	C₃×C₃²⋊C₉	—	3	18	no	—
11	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
13	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
15	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
16	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
17	#6855	C₃²	1	81	yes	complemented
18	C₃⁴	—	3	18	no	—
19	C₃⁴	—	9	6	no	—
20	C₃⁴	H(3,𝔽₃)	1	9	yes	—
21	C₃⁴	C₃³	1	1	yes	characteristic
22	C₃⁴	C₃³	1	1	yes	characteristic
23	C₃⁴	C₃³	1	2	yes	—
24	C₃×3₋¹⁺²	—	3	18	no	—
25	C₃×3₋¹⁺²	—	3	54	no	—
26	C₃²×C₉	—	3	18	no	—
27	C₃²×C₉	—	9	18	no	—
28	C₃²×C₉	C₃³	1	18	yes	—
29	C₃²×C₉	C₃³	1	18	yes	—
30	C₃²⋊C₉	—	3	18	no	—
31	C₃²⋊C₉	—	3	18	no	—
32	C₃²⋊C₉	—	3	18	no	—
33	C₃²⋊C₉	—	3	18	no	—
34	C₃²⋊C₉	—	3	18	no	—
35	C₃²⋊C₉	—	3	18	no	—
36	C₃³	—	3	6	no	—
37	C₃³	—	3	6	no	—
38	C₃³	—	3	6	no	—
39	C₃³	—	3	6	no	—
40	C₃³	—	3	6	no	—
41	C₃³	—	3	6	no	—
42	C₃³	—	3	6	no	—
43	C₃³	—	3	54	no	—
44	C₃³	—	9	18	no	—
45	C₃³	—	9	81	no	—
46	C₃³	C₃×H(3,𝔽₃)	1	3	yes	—
47	C₃³	C₃×H(3,𝔽₃)	1	3	yes	—
48	C₃³	C₃×H(3,𝔽₃)	1	6	yes	—
49	C₃³	#737	1	18	yes	—
50	C₃³	C₃⁴	1	1	yes	characteristic
51	3₋¹⁺²	—	9	54	no	—
52	C₃×C₉	—	3	18	no	—
53	C₃×C₉	—	3	18	no	—
54	C₃×C₉	—	3	54	no	—
55	C₃×C₉	—	3	54	no	—
56	C₃×C₉	—	9	54	no	—
57	C₃²	—	3	6	no	—
58	C₃²	—	3	6	no	—
59	C₃²	—	3	6	no	—
60	C₃²	—	3	54	no	—
61	C₃²	—	3	6	no	—
62	C₃²	—	3	6	no	—
63	C₃²	—	3	6	no	—
64	C₃²	—	3	6	no	—
65	C₃²	—	9	81	no	—
66	C₃²	—	9	9	no	—
67	C₃²	—	9	9	no	—
68	C₃²	#6893	1	18	yes	—
69	C₃²	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
70	C₃²	C₃×#737	1	6	yes	—
71	C₃²	3₋¹⁺⁴	1	6	yes	—
72	C₉	—	9	18	no	—
73	C₉	—	9	18	no	—
74	C₃	—	3	18	no	—
75	C₃	—	9	3	no	—
76	C₃	—	9	3	no	—
77	C₃	C₃×#6893	1	2	yes	—
78	C₃	#10624881	1	2	yes	—
79	C₃	#10624906	1	9	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃³	C₃⁴
prime radical	C₃⁵	C₃²
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #10624569	C₃	semidirect
4. #10624568	C₃	semidirect
5. #10624558	C₃	semidirect
17. #6855	C₃²	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6891	3
C₃²×C₃²⋊C₉	3
#10624569	3
#10624568	3
#10624558	3