Subgroups — #14550800

Order 2187.

183 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6875	C₃	1	3	yes	maximal
2	#10624550	C₃	1	1	yes	maximal, characteristic
3	#10624472	C₃	1	3	yes	maximal
4	#10624472	C₃	1	3	yes	maximal
5	#10624467	C₃	1	3	yes	maximal
6	C₃×C₂₇⋊C₃	C₃²	1	3	yes	—
7	C₃×C₂₇⋊C₃	C₃²	1	3	yes	—
8	C₃×C₂₇⋊C₃	C₃²	1	3	yes	—
9	C₃×C₉⋊C₉	—	3	1	no	—
10	C₃×C₉⋊C₉	C₃²	1	3	yes	—
11	C₃×C₉²	C₃²	1	1	yes	characteristic
12	#6875	—	3	9	no	—
13	#6855	—	3	1	no	—
14	#6855	—	3	1	no	—
15	C₃²×C₉	—	3	3	no	—
16	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
17	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
18	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
19	C₃²×C₉	C₃³	1	1	yes	characteristic
20	C₂₇⋊C₃	—	3	6	no	—
21	C₂₇⋊C₃	—	3	6	no	—
22	C₂₇⋊C₃	—	3	3	no	—
23	C₂₇⋊C₃	—	3	3	no	—
24	C₂₇⋊C₃	—	3	6	no	—
25	C₂₇⋊C₃	3₋¹⁺²	1	9	yes	—
26	C₃×C₂₇	—	3	3	no	—
27	C₃×C₂₇	—	3	3	no	—
28	C₃×C₂₇	—	3	3	no	—
29	C₉⋊C₉	—	3	3	no	—
30	C₉⋊C₉	—	3	3	no	—
31	C₉⋊C₉	—	3	3	no	—
32	C₉⋊C₉	—	9	3	no	—
33	C₉²	—	3	3	no	—
34	C₃³	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₉	—	3	1	no	—
36	C₃×C₉	—	3	3	no	—
37	C₃×C₉	—	3	1	no	—
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	—	9	1	no	—
40	C₃×C₉	—	9	1	no	—
41	C₃×C₉	—	9	3	no	—
42	C₃×C₉	—	9	3	no	—
43	C₃×C₉	—	9	3	no	—
44	C₃×C₉	—	9	3	no	—
45	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
46	C₃×C₉	#737	1	3	yes	—
47	C₃×C₉	#737	1	3	yes	—
48	C₃×C₉	#737	1	3	yes	—
49	C₂₇	—	3	9	no	—
50	C₂₇	—	9	3	no	—
51	C₂₇	—	9	3	no	—
52	C₃²	—	3	1	no	—
53	C₃²	—	3	1	no	—
54	C₃²	—	3	1	no	—
55	C₃²	#6895	1	1	yes	characteristic
56	C₃²	#6896	1	3	yes	—
57	C₉	—	3	3	no	—
58	C₉	—	9	1	no	—
59	C₉	—	9	1	no	—
60	C₉	—	27	3	no	—
61	C₉	#6895	1	3	yes	—
62	C₉	#6896	1	3	yes	—
63	C₉	#6898	1	3	yes	—
64	C₃	—	3	3	no	—
65	C₃	#10624572	1	1	yes	characteristic
66	C₃	#10624828	1	1	yes	characteristic
67	C₃	#10624829	1	1	yes	characteristic
68	C₃	#10624830	1	1	yes	characteristic

	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

Maximal subgroups

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

subgroup	index
C₃×#6875	3
#10624550	3
#10624472	3
#10624467	3