Subgroups — #14550804

Order 2187.

197 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6875	C₃	1	6	yes	maximal
2	#10624553	C₃	1	1	yes	maximal, characteristic
3	#10624472	C₃	1	3	yes	maximal
4	#10624467	C₃	1	1	yes	maximal, characteristic
5	#10624467	C₃	1	2	yes	maximal
6	C₃×C₂₇⋊C₃	C₃²	1	3	yes	—
7	C₃×C₂₇⋊C₃	C₃²	1	6	yes	—
8	C₃×C₉⋊C₉	C₃²	1	2	yes	—
9	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
10	C₃×C₉²	C₃²	1	1	yes	characteristic
11	#6875	—	3	18	no	—
12	#6855	—	3	3	no	—
13	C₃²×C₉	—	3	1	no	—
14	C₃²×C₉	—	3	2	no	—
15	C₃²×C₉	3₋¹⁺²	1	3	yes	—
16	C₃²×C₉	C₃³	1	1	yes	characteristic
17	C₂₇⋊C₃	—	3	6	no	—
18	C₂₇⋊C₃	—	3	6	no	—
19	C₂₇⋊C₃	—	3	6	no	—
20	C₂₇⋊C₃	—	3	3	no	—
21	C₂₇⋊C₃	3₋¹⁺²	1	18	yes	—
22	C₃×C₂₇	—	3	6	no	—
23	C₃×C₂₇	—	3	3	no	—
24	C₉⋊C₉	—	3	6	no	—
25	C₉⋊C₉	—	3	3	no	—
26	C₉²	—	3	2	no	—
27	C₉²	—	3	1	no	—
28	C₃³	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₉	—	3	3	no	—
30	C₃×C₉	—	9	3	no	—
31	C₃×C₉	—	9	3	no	—
32	C₃×C₉	—	9	6	no	—
33	C₃×C₉	—	9	1	no	—
34	C₃×C₉	—	9	2	no	—
35	C₃×C₉	C₃×3₋¹⁺²	1	6	yes	—
36	C₃×C₉	#737	1	2	yes	—
37	C₃×C₉	#737	1	3	yes	—
38	C₃×C₉	#737	1	1	yes	characteristic
39	C₂₇	—	3	18	no	—
40	C₂₇	—	9	3	no	—
41	C₃²	—	3	3	no	—
42	C₃²	#6895	1	1	yes	characteristic
43	C₃²	#6899	1	1	yes	characteristic
44	C₃²	#6900	1	2	yes	—
45	C₉	—	9	3	no	—
46	C₉	—	27	1	no	—
47	C₉	—	27	2	no	—
48	C₉	#6894	1	6	yes	—
49	C₉	#6896	1	3	yes	—
50	C₃	—	3	1	no	—
51	C₃	—	3	2	no	—
52	C₃	#10624573	1	1	yes	characteristic
53	C₃	#10624830	1	3	yes	—

	subgroup	G/H
center, socle	C₃²	#6895
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃³	C₃×3₋¹⁺²
LCS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁

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