Subgroups — C₃×C₁₃×#6867 #23744837

Order 9477.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal
3	C₁₃×#6867	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	2	no	—
6	C₃²×C₉×C₁₃	—	3	1	no	—
7	C₃²×C₉×C₁₃	—	3	6	no	—
8	C₃²×C₉×C₁₃	—	3	3	no	—
9	C₃²×C₉×C₁₃	C₉	1	9	yes	complemented
10	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
11	C₁₃×C₃²⋊C₉	—	3	6	no	—
12	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
13	C₃×#6867	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	3	9	no	—
15	C₃³×C₁₃	C₃×C₉	1	3	yes	—
16	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
17	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃³×C₁₃	3₋¹⁺²	1	6	yes	—
19	C₃³×C₁₃	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₁₃	—	3	18	no	—
21	C₃×C₉×C₁₃	—	3	9	no	—
22	C₃×C₉×C₁₃	—	3	3	no	—
23	C₃×C₉×C₁₃	—	3	6	no	—
24	C₃×C₉×C₁₃	—	3	9	no	—
25	C₃×C₉×C₁₃	—	9	9	no	—
26	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	complemented
27	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
28	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
29	#6867	C₃×C₁₃	1	9	yes	direct product factor
30	C₃²×C₁₃	—	3	9	no	—
31	C₃²×C₁₃	—	3	18	no	—
32	C₃²×C₁₃	—	3	6	no	—
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	C₃²⋊C₉	1	6	yes	—
35	C₃²×C₁₃	C₃²⋊C₉	1	3	yes	—
36	C₃²×C₁₃	#731	1	9	yes	—
37	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
38	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₃²×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
40	C₉×C₁₃	—	3	9	no	—
41	C₉×C₁₃	—	9	9	no	—
42	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
43	C₃²×C₉	—	3	2	no	—
44	C₃²×C₉	—	3	1	no	—
45	C₃²×C₉	—	3	6	no	—
46	C₃²×C₉	—	3	3	no	—
47	C₃²×C₉	C₉×C₁₃	1	9	yes	complemented
48	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
49	C₃²⋊C₉	—	3	6	no	—
50	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
51	C₃×C₁₃	—	3	6	no	—
52	C₃×C₁₃	—	3	1	no	—
53	C₃×C₁₃	—	3	2	no	—
54	C₃×C₁₃	#6867	1	9	yes	direct product factor
55	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
56	C₃×C₁₃	C₃×#731	1	3	yes	—
57	C₃³	—	3	9	no	—
58	C₃³	C₃×C₉×C₁₃	1	3	yes	—
59	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
60	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃³	C₁₃×3₋¹⁺²	1	6	yes	—
62	C₃³	C₃³×C₁₃	1	1	yes	characteristic
63	C₃×C₉	—	3	18	no	—
64	C₃×C₉	—	3	9	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	3	6	no	—
67	C₃×C₉	—	3	9	no	—
68	C₃×C₉	—	9	9	no	—
69	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	complemented
70	C₁₃	C₃×#6867	1	1	yes	characteristic, direct product factor, Sylow
71	C₃²	—	3	9	no	—
72	C₃²	—	3	18	no	—
73	C₃²	—	3	6	no	—
74	C₃²	—	3	3	no	—
75	C₃²	C₁₃×C₃²⋊C₉	1	6	yes	—
76	C₃²	C₁₃×C₃²⋊C₉	1	3	yes	—
77	C₃²	C₁₃×#731	1	9	yes	—
78	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
79	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
80	C₃²	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
81	C₉	—	3	9	no	—
82	C₉	—	9	9	no	—
83	C₃	—	3	6	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	2	no	—
86	C₃	C₁₃×#6867	1	9	yes	direct product factor
87	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic
88	C₃	C₃×C₁₃×#731	1	3	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6867	C₃	direct (N × H)
9. C₃²×C₉×C₁₃	C₉	semidirect
13. C₃×#6867	C₁₃	direct (N × H)
26. C₃×C₉×C₁₃	C₃×C₉	semidirect
29. #6867	C₃×C₁₃	direct (N × H)
47. C₃²×C₉	C₉×C₁₃	semidirect
54. C₃×C₁₃	#6867	direct (N × H)
69. C₃×C₉	C₃×C₉×C₁₃	semidirect
70. C₁₃	C₃×#6867	direct (N × H)
86. C₃	C₁₃×#6867	direct (N × H)

Subgroups — C3×C13×#6867 #23744837

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6867 #23744837