Subgroups — #14552172

Order 2187.

758 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6887	C₃	1	1	yes	maximal, characteristic
2	#10624577	C₃	1	3	yes	maximal, complemented
3	#10624576	C₃	1	3	yes	maximal, complemented
4	#10624575	C₃	1	6	yes	maximal, complemented
5	#10624573	C₃	1	3	yes	maximal, complemented
6	#10624572	C₃	1	3	yes	maximal, complemented
7	#10624566	C₃	1	9	yes	maximal
8	C₉×C₉⋊C₉	C₃	1	9	yes	maximal, complemented
9	C₉×C₃²⋊C₉	C₃	1	3	yes	maximal
10	C₃³×C₉	C₃²	1	1	yes	characteristic
11	#6887	—	3	9	no	—
12	C₃×C₉⋊C₉	C₃²	1	9	yes	—
13	C₃×C₉⋊C₉	C₃²	1	18	yes	—
14	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
15	C₃×C₉⋊C₉	C₃²	1	3	yes	—
16	C₃×C₉⋊C₉	C₃²	1	2	yes	—
17	C₃×C₃²⋊C₉	C₃²	1	9	yes	—
18	C₃×C₃²⋊C₉	C₃²	1	3	yes	—
19	C₃×C₉²	C₃²	1	9	yes	—
20	C₃×C₉²	C₃²	1	3	yes	—
21	#6855	C₃²	1	9	yes	—
22	#6855	C₃²	1	3	yes	—
23	#6855	C₃²	1	3	yes	—
24	#6855	C₃²	1	3	yes	—
25	#6855	C₃²	1	9	yes	—
26	#6855	C₃²	1	9	yes	—
27	#6855	C₃²	1	18	yes	—
28	#6855	C₃²	1	18	yes	—
29	C₃⁴	C₃³	1	1	yes	characteristic
30	C₃²×C₉	—	3	9	no	—
31	C₃²×C₉	3₋¹⁺²	1	9	yes	—
32	C₃²×C₉	C₃³	1	9	yes	—
33	C₃²×C₉	C₃³	1	9	yes	—
34	C₃²×C₉	C₃³	1	3	yes	—
35	C₃²×C₉	C₃³	1	6	yes	—
36	C₃²×C₉	C₃³	1	1	yes	characteristic
37	C₃²×C₉	C₃³	1	1	yes	characteristic
38	C₃²×C₉	C₃³	1	9	yes	—
39	C₃²×C₉	C₃³	1	1	yes	characteristic
40	C₉⋊C₉	—	3	3	no	—
41	C₉⋊C₉	—	3	9	no	—
42	C₉⋊C₉	—	3	6	no	—
43	C₉⋊C₉	—	3	54	no	—
44	C₉⋊C₉	—	3	27	no	—
45	C₃²⋊C₉	—	3	9	no	—
46	C₃²⋊C₉	—	3	27	no	—
47	C₉²	—	3	9	no	—
48	C₉²	—	3	27	no	—
49	C₃³	—	3	9	no	—
50	C₃³	—	3	3	no	—
51	C₃³	C₃×3₋¹⁺²	1	3	yes	—
52	C₃³	C₃⁴	1	1	yes	characteristic
53	C₃×C₉	—	3	9	no	—
54	C₃×C₉	—	3	18	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	3	3	no	—
57	C₃×C₉	—	3	27	no	—
58	C₃×C₉	—	3	3	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	3	9	no	—
61	C₃×C₉	—	3	9	no	—
62	C₃×C₉	—	3	9	no	—
63	C₃×C₉	—	3	9	no	—
64	C₃×C₉	—	3	18	no	—
65	C₃×C₉	—	3	18	no	—
66	C₃×C₉	—	3	18	no	—
67	C₃×C₉	—	3	9	no	—
68	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
69	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
70	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
71	C₃×C₉	#737	1	27	yes	—
72	C₃×C₉	#737	1	9	yes	—
73	C₃²	—	3	3	no	—
74	C₃²	—	3	9	no	—
75	C₃²	—	9	9	no	—
76	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
77	C₃²	C₃×#737	1	3	yes	—
78	C₃²	C₃×#737	1	9	yes	—
79	C₉	—	3	3	no	—
80	C₉	—	3	3	no	—
81	C₉	—	3	27	no	—
82	C₉	—	9	9	no	—
83	C₉	—	9	9	no	—
84	C₉	—	9	3	no	—
85	C₉	—	9	6	no	—
86	C₉	#6895	1	9	yes	—
87	C₃	—	9	3	no	—
88	C₃	C₃×#6895	1	1	yes	characteristic
89	C₃	#10624877	1	9	yes	—
90	C₃	#10624879	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃³
commutator, Frattini, socle, cosocle	C₃³	C₃⁴
prime radical	C₃⁴	C₃³
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃²×C₉ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #10624577	C₃	semidirect
3. #10624576	C₃	semidirect
4. #10624575	C₃	semidirect
5. #10624573	C₃	semidirect
6. #10624572	C₃	semidirect
8. C₉×C₉⋊C₉	C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6887	3
#10624577	3
#10624576	3
#10624575	3
#10624573	3
#10624572	3
#10624566	3
C₉×C₉⋊C₉	3
C₉×C₃²⋊C₉	3