Subgroups — #14550874

Order 2187.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#733	C₃	1	3	yes	maximal
2	#10624550	C₃	1	1	yes	maximal, characteristic
3	#10624495	C₃	1	3	yes	maximal
4	#10624491	C₃	1	3	yes	maximal
5	#10624482	C₃	1	3	yes	maximal
6	C₃×#733	C₃²	1	3	yes	—
7	C₉×3₋¹⁺²	—	3	3	no	—
8	C₃×C₉⋊C₉	—	3	1	no	—
9	C₃×C₉⋊C₉	—	3	1	no	—
10	C₃×C₉²	C₃²	1	1	yes	characteristic
11	3₋¹⁺²⋊C₉	—	3	3	no	—
12	3₋¹⁺²⋊C₉	—	3	3	no	—
13	#6868	C₃²	1	3	yes	—
14	#6868	C₃²	1	3	yes	—
15	#6855	—	3	1	no	—
16	#6855	C₃²	1	3	yes	—
17	C₃×3₋¹⁺²	—	3	3	no	—
18	C₃²×C₉	—	3	3	no	—
19	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃²×C₉	C₃³	1	1	yes	characteristic
23	#733	—	3	9	no	—
24	C₉⋊C₉	—	9	3	no	—
25	C₉⋊C₉	—	9	3	no	—
26	C₉⋊C₉	—	9	6	no	—
27	C₃²⋊C₉	—	3	3	no	—
28	C₃²⋊C₉	—	3	3	no	—
29	C₉²	—	3	3	no	—
30	C₉²	—	9	3	no	—
31	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
32	3₋¹⁺²	—	3	9	no	—
33	3₋¹⁺²	—	9	6	no	—
34	C₃×C₉	—	3	1	no	—
35	C₃×C₉	—	3	1	no	—
36	C₃×C₉	—	3	3	no	—
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	—	3	3	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	—	9	3	no	—
46	C₃×C₉	—	9	3	no	—
47	C₃×C₉	—	9	3	no	—
48	C₃×C₉	#732	1	3	yes	—
49	C₃²	—	3	1	no	—
50	C₃²	—	3	1	no	—
51	C₃²	—	3	1	no	—
52	C₃²	C₃×#732	1	1	yes	characteristic
53	C₃²	#6908	1	3	yes	—
54	C₉	—	3	3	no	—
55	C₉	—	3	3	no	—
56	C₉	—	3	3	no	—
57	C₉	—	9	1	no	—
58	C₉	—	9	9	no	—
59	C₉	—	27	3	no	—
60	C₉	—	27	3	no	—
61	C₉	—	27	3	no	—
62	C₃	—	3	3	no	—
63	C₃	#10624585	1	1	yes	characteristic
64	C₃	#10624840	1	1	yes	characteristic
65	C₃	#10624850	1	1	yes	characteristic
66	C₃	#10624850	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²	C₃×#732
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃³	C₃×H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

Maximal subgroups

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

subgroup	index
C₉×#733	3
#10624550	3
#10624495	3
#10624491	3
#10624482	3