Subgroups — C₃×#10624574 #14552162

Order 2187.

1178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉⋊C₉	C₃	1	4	yes	maximal
2	#10624574	C₃	1	27	yes	maximal, direct product factor
3	C₃×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃×#6855	C₃	1	2	yes	maximal
5	C₃×#6855	C₃	1	2	yes	maximal
6	C₃×#6855	C₃	1	4	yes	maximal
7	C₃³×C₉	C₃²	1	1	yes	characteristic
8	C₃³×C₉	C₃²	1	2	yes	—
9	C₃³×C₉	C₃²	1	4	yes	—
10	C₃³×C₉	C₃²	1	2	yes	—
11	C₃³×C₉	C₃²	1	4	yes	—
12	C₃×C₉⋊C₉	—	3	36	no	—
13	C₃×C₉⋊C₉	C₃²	1	36	yes	—
14	#6855	C₃²	1	9	yes	—
15	#6855	C₃²	1	18	yes	—
16	#6855	C₃²	1	18	yes	—
17	#6855	C₃²	1	36	yes	—
18	C₃⁴	C₃³	1	1	yes	characteristic
19	C₃²×C₉	—	3	12	no	—
20	C₃²×C₉	—	3	12	no	—
21	C₃²×C₉	—	3	12	no	—
22	C₃²×C₉	—	3	12	no	—
23	C₃²×C₉	—	3	12	no	—
24	C₃²×C₉	—	3	6	no	—
25	C₃²×C₉	—	3	6	no	—
26	C₃²×C₉	—	3	6	no	—
27	C₃²×C₉	—	3	6	no	—
28	C₃²×C₉	—	3	6	no	—
29	C₃²×C₉	—	3	12	no	—
30	C₃²×C₉	—	3	6	no	—
31	C₃²×C₉	—	3	24	no	—
32	C₃²×C₉	—	3	12	no	—
33	C₃²×C₉	3₋¹⁺²	1	36	yes	—
34	C₃²×C₉	C₃³	1	3	yes	—
35	C₃²×C₉	C₃³	1	6	yes	—
36	C₃²×C₉	C₃³	1	12	yes	—
37	C₃²×C₉	C₃³	1	6	yes	—
38	C₃²×C₉	C₃³	1	12	yes	—
39	C₉⋊C₉	—	3	108	no	—
40	C₃³	C₃×3₋¹⁺²	1	12	yes	—
41	C₃³	#737	1	6	yes	—
42	C₃³	#737	1	12	yes	—
43	C₃³	#737	1	3	yes	—
44	C₃³	#737	1	6	yes	—
45	C₃³	C₃⁴	1	1	yes	characteristic
46	C₃×C₉	—	3	12	no	—
47	C₃×C₉	—	3	12	no	—
48	C₃×C₉	—	3	12	no	—
49	C₃×C₉	—	3	108	no	—
50	C₃×C₉	—	3	12	no	—
51	C₃×C₉	—	3	12	no	—
52	C₃×C₉	—	3	6	no	—
53	C₃×C₉	—	3	6	no	—
54	C₃×C₉	—	3	6	no	—
55	C₃×C₉	—	3	6	no	—
56	C₃×C₉	—	3	6	no	—
57	C₃×C₉	—	3	12	no	—
58	C₃×C₉	—	3	6	no	—
59	C₃×C₉	—	3	24	no	—
60	C₃×C₉	—	3	12	no	—
61	C₃×C₉	—	9	18	no	—
62	C₃×C₉	—	9	9	no	—
63	C₃×C₉	—	9	18	no	—
64	C₃×C₉	—	9	36	no	—
65	C₃×C₉	C₃×3₋¹⁺²	1	36	yes	—
66	C₃²	#6894	1	36	yes	—
67	C₃²	#6896	1	18	yes	—
68	C₃²	#6897	1	9	yes	—
69	C₃²	#6898	1	18	yes	—
70	C₃²	#6899	1	36	yes	—
71	C₃²	C₃²×3₋¹⁺²	1	4	yes	—
72	C₃²	C₃×#737	1	2	yes	—
73	C₃²	C₃×#737	1	4	yes	—
74	C₃²	C₃×#737	1	1	yes	characteristic
75	C₃²	C₃×#737	1	2	yes	—
76	C₉	—	3	36	no	—
77	C₉	—	9	6	no	—
78	C₉	—	9	3	no	—
79	C₉	—	9	6	no	—
80	C₉	—	9	12	no	—
81	C₃	#10624574	1	27	yes	direct product factor
82	C₃	C₃×#6894	1	4	yes	—
83	C₃	C₃×#6896	1	2	yes	—
84	C₃	C₃×#6897	1	1	yes	characteristic
85	C₃	C₃×#6898	1	2	yes	—
86	C₃	C₃×#6899	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #10624574	C₃	direct (N × H)
81. C₃	#10624574	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₉⋊C₉	3
#10624574	3
C₃×#6855	3

Subgroups — C3×#10624574 #14552162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624574 #14552162