Subgroups — #14550801

Order 2187.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624709	C₃	1	2	yes	maximal
2	#10624707	C₃	1	2	yes	maximal
3	#10624473	C₃	1	2	yes	maximal
4	#10624471	C₃	1	4	yes	maximal
5	#10624469	C₃	1	1	yes	maximal, characteristic
6	#10624468	C₃	1	1	yes	maximal, characteristic
7	H(3,ℤ/9)	C₃	1	1	yes	maximal, characteristic
8	C₃×C₂₇⋊C₃	C₃²	1	4	yes	—
9	C₃×C₂₇⋊C₃	C₃²	1	2	yes	—
10	C₃×C₂₇⋊C₃	C₃²	1	2	yes	—
11	C₃²×C₂₇	C₃²	1	1	yes	characteristic
12	#6887	C₃²	1	1	yes	characteristic
13	#6887	C₃²	1	1	yes	characteristic
14	#6887	C₃²	1	2	yes	—
15	#6875	—	3	6	no	—
16	C₉⋊C₂₇	—	3	6	no	—
17	C₃²×C₉	C₃³	1	1	yes	characteristic
18	C₂₇⋊C₃	—	3	4	no	—
19	C₂₇⋊C₃	—	3	4	no	—
20	C₂₇⋊C₃	—	3	4	no	—
21	C₂₇⋊C₃	—	3	4	no	—
22	C₂₇⋊C₃	—	3	4	no	—
23	C₂₇⋊C₃	—	3	2	no	—
24	C₂₇⋊C₃	3₋¹⁺²	1	6	yes	—
25	C₃×C₂₇	—	3	2	no	—
26	C₃×C₂₇	—	3	2	no	—
27	C₃×C₂₇	—	3	4	no	—
28	C₃×C₂₇	—	3	1	no	—
29	C₃×C₂₇	—	3	1	no	—
30	C₃×C₂₇	—	3	2	no	—
31	C₉⋊C₉	—	3	4	no	—
32	C₉⋊C₉	—	3	2	no	—
33	C₉⋊C₉	—	3	2	no	—
34	C₃²⋊C₉	—	3	2	no	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₃²⋊C₉	—	3	1	no	—
37	C₉²	—	3	1	no	—
38	C₉²	—	3	1	no	—
39	C₉²	3₋¹⁺²	1	6	yes	—
40	C₃³	#737	1	1	yes	characteristic
41	C₃×C₉	—	3	6	no	—
42	C₃×C₉	—	9	1	no	—
43	C₃×C₉	—	9	1	no	—
44	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
45	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
46	C₃×C₉	#737	1	1	yes	characteristic
47	C₃×C₉	#737	1	4	yes	—
48	C₃×C₉	#737	1	2	yes	—
49	C₃×C₉	#737	1	1	yes	characteristic
50	C₂₇	—	3	6	no	—
51	C₂₇	—	9	4	no	—
52	C₂₇	—	9	1	no	—
53	C₂₇	—	9	2	no	—
54	C₃²	—	9	1	no	—
55	C₃²	#6895	1	2	yes	—
56	C₃²	#6896	1	1	yes	characteristic
57	C₃²	#6898	1	1	yes	characteristic
58	C₉	—	9	6	no	—
59	C₉	—	27	1	no	—
60	C₉	—	27	1	no	—
61	C₉	#6895	1	2	yes	—
62	C₉	#6896	1	4	yes	—
63	C₉	#6896	1	1	yes	characteristic
64	C₉	#6898	1	2	yes	—
65	C₃	—	3	2	no	—
66	C₃	—	3	1	no	—
67	C₃	—	3	1	no	—
68	C₃	#10624572	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#6896
commutator, Frattini, cosocle	C₃²×C₉	C₃³
socle	C₃	#10624572
prime radical	C₃³	#737
LCS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉ ◁ 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
#10624709	3
#10624707	3
#10624473	3
#10624471	3
#10624469	3
#10624468	3
H(3,ℤ/9)	3