Subgroups — C₃×C₁₃×#6856 #23744729

Order 9477.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	2	yes	maximal, complemented
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₁₃×#6856	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₁₃	—	3	2	no	—
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×H(3,𝔽₃)	—	3	4	no	—
7	C₃×C₁₃×H(3,𝔽₃)	—	3	18	no	—
8	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	6	yes	complemented
9	C₃²×C₉×C₁₃	—	3	2	no	—
10	C₁₃×C₃²⋊C₉	—	3	4	no	—
11	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	complemented
12	C₃×#6856	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	6	no	—
14	C₃³×C₁₃	—	3	18	no	—
15	C₃³×C₁₃	—	3	6	no	—
16	C₃³×C₁₃	—	3	6	no	—
17	C₃³×C₁₃	—	9	6	no	—
18	C₃³×C₁₃	—	9	12	no	—
19	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
20	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×H(3,𝔽₃)	—	3	18	no	—
23	C₁₃×H(3,𝔽₃)	—	3	36	no	—
24	C₃×C₉×C₁₃	—	3	6	no	—
25	C₃×C₉×C₁₃	—	9	6	no	—
26	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	2	yes	complemented
27	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	complemented
28	#6856	C₃×C₁₃	1	9	yes	direct product factor
29	C₃²×C₁₃	—	3	4	no	—
30	C₃²×C₁₃	—	3	2	no	—
31	C₃²×C₁₃	—	3	18	no	—
32	C₃²×C₁₃	—	3	4	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	—	9	9	no	—
35	C₃²×C₁₃	—	9	54	no	—
36	C₃²×C₁₃	—	9	6	no	—
37	C₃²×C₁₃	—	9	12	no	—
38	C₃²×C₁₃	AΣL(1,𝔽₂₇)	1	6	yes	—
39	C₃²×C₁₃	#732	1	6	yes	—
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	C₉×C₁₃	—	9	6	no	—
42	C₃⁴	—	3	2	no	—
43	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
44	C₃×H(3,𝔽₃)	—	3	18	no	—
45	C₃×H(3,𝔽₃)	—	3	4	no	—
46	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	6	yes	complemented
47	C₃²×C₉	—	3	2	no	—
48	C₃²⋊C₉	—	3	4	no	—
49	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	complemented
50	C₃×C₁₃	—	9	2	no	—
51	C₃×C₁₃	—	9	1	no	—
52	C₃×C₁₃	—	9	18	no	—
53	C₃×C₁₃	#6856	1	9	yes	direct product factor
54	C₃×C₁₃	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
55	C₃×C₁₃	C₃×#732	1	2	yes	—
56	C₃³	—	3	6	no	—
57	C₃³	—	3	18	no	—
58	C₃³	—	3	6	no	—
59	C₃³	—	3	6	no	—
60	C₃³	—	9	6	no	—
61	C₃³	—	9	12	no	—
62	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
63	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
64	C₃³	C₃³×C₁₃	1	1	yes	characteristic
65	H(3,𝔽₃)	—	3	18	no	—
66	H(3,𝔽₃)	—	3	36	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	—	9	6	no	—
69	C₁₃	C₃×#6856	1	1	yes	characteristic, direct product factor, Sylow
70	C₃²	—	3	4	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	3	18	no	—
73	C₃²	—	3	4	no	—
74	C₃²	—	3	2	no	—
75	C₃²	—	9	9	no	—
76	C₃²	—	9	54	no	—
77	C₃²	—	9	6	no	—
78	C₃²	—	9	12	no	—
79	C₃²	C₁₃×AΣL(1,𝔽₂₇)	1	6	yes	—
80	C₃²	C₁₃×#732	1	6	yes	—
81	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
82	C₉	—	9	6	no	—
83	C₃	—	9	2	no	—
84	C₃	—	9	1	no	—
85	C₃	—	9	18	no	—
86	C₃	C₁₃×#6856	1	9	yes	direct product factor
87	C₃	C₃×C₁₃×AΣL(1,𝔽₂₇)	1	2	yes	—
88	C₃	C₃×C₁₃×#732	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×H(3,𝔽₃)	C₃	semidirect
2. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
3. C₁₃×#6856	C₃	direct (N × H)
8. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
11. C₁₃×C₃²⋊C₉	C₃²	semidirect
12. C₃×#6856	C₁₃	direct (N × H)
26. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
27. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
28. #6856	C₃×C₁₃	direct (N × H)
46. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
49. C₃²⋊C₉	C₃²×C₁₃	semidirect
53. C₃×C₁₃	#6856	direct (N × H)
69. C₁₃	C₃×#6856	direct (N × H)
86. C₃	C₁₃×#6856	direct (N × H)

Subgroups — C3×C13×#6856 #23744729

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6856 #23744729