Subgroups — C₃×C₇×#6891 #19100275

Order 5103.

2636 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₇×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
3	C₇×#6891	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₇×C₃²⋊C₉	C₃	1	9	yes	maximal, complemented
5	C₃×#6891	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	—	3	9	no	—
7	C₃⁴×C₇	—	3	27	no	—
8	C₃⁴×C₇	C₃²	1	9	yes	—
9	C₃⁴×C₇	C₃²	1	1	yes	characteristic
10	C₃⁴×C₇	C₃²	1	3	yes	—
11	C₃×C₇×3₋¹⁺²	—	3	27	no	—
12	C₃×C₇×3₋¹⁺²	C₃²	1	27	yes	complemented
13	C₃²×C₇×C₉	C₃²	1	9	yes	complemented
14	C₇×C₃²⋊C₉	C₃²	1	81	yes	complemented
15	C₃⁵	C₃×C₇	1	1	yes	characteristic
16	C₃²×3₋¹⁺²	C₃×C₇	1	3	yes	complemented
17	#6891	C₃×C₇	1	27	yes	direct product factor
18	C₃×C₃²⋊C₉	C₃×C₇	1	9	yes	complemented
19	C₃³×C₇	—	3	243	no	—
20	C₃³×C₇	—	3	27	no	—
21	C₃³×C₇	—	3	9	no	—
22	C₃³×C₇	—	3	9	no	—
23	C₃³×C₇	—	3	18	no	—
24	C₃³×C₇	—	3	81	no	—
25	C₃³×C₇	H(3,𝔽₃)	1	9	yes	—
26	C₃³×C₇	3₋¹⁺²	1	27	yes	complemented
27	C₃³×C₇	C₃³	1	3	yes	—
28	C₃³×C₇	C₃³	1	9	yes	—
29	C₃³×C₇	C₃³	1	1	yes	characteristic
30	C₇×3₋¹⁺²	—	3	81	no	—
31	C₃×C₇×C₉	—	3	27	no	—
32	C₃×C₇×C₉	C₃³	1	27	yes	complemented
33	C₃⁴	—	3	9	no	—
34	C₃⁴	—	3	27	no	—
35	C₃⁴	C₃²×C₇	1	9	yes	—
36	C₃⁴	C₃²×C₇	1	1	yes	characteristic
37	C₃⁴	C₃²×C₇	1	3	yes	—
38	C₃×3₋¹⁺²	—	3	27	no	—
39	C₃×3₋¹⁺²	C₃²×C₇	1	27	yes	complemented
40	C₃²×C₉	C₃²×C₇	1	9	yes	complemented
41	C₃²⋊C₉	C₃²×C₇	1	81	yes	complemented
42	C₃²×C₇	—	3	243	no	—
43	C₃²×C₇	—	3	9	no	—
44	C₃²×C₇	—	3	9	no	—
45	C₃²×C₇	—	3	18	no	—
46	C₃²×C₇	—	3	27	no	—
47	C₃²×C₇	—	3	81	no	—
48	C₃²×C₇	C₃×H(3,𝔽₃)	1	9	yes	—
49	C₃²×C₇	C₃×H(3,𝔽₃)	1	3	yes	—
50	C₃²×C₇	C₃×3₋¹⁺²	1	9	yes	—
51	C₃²×C₇	C₃×3₋¹⁺²	1	27	yes	complemented
52	C₃²×C₇	C₃⁴	1	1	yes	characteristic
53	C₇×C₉	—	3	27	no	—
54	C₃³	—	3	243	no	—
55	C₃³	—	3	27	no	—
56	C₃³	—	3	9	no	—
57	C₃³	—	3	9	no	—
58	C₃³	—	3	18	no	—
59	C₃³	—	3	81	no	—
60	C₃³	C₇×H(3,𝔽₃)	1	9	yes	—
61	C₃³	C₇×3₋¹⁺²	1	27	yes	complemented
62	C₃³	C₃³×C₇	1	3	yes	—
63	C₃³	C₃³×C₇	1	9	yes	—
64	C₃³	C₃³×C₇	1	1	yes	characteristic
65	3₋¹⁺²	—	3	81	no	—
66	C₃×C₉	—	3	27	no	—
67	C₃×C₉	C₃³×C₇	1	27	yes	complemented
68	C₃×C₇	—	3	9	no	—
69	C₃×C₇	—	3	27	no	—
70	C₃×C₇	#6891	1	9	yes	direct product factor
71	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
72	C₃×C₇	C₃²×3₋¹⁺²	1	3	yes	—
73	C₃²	—	3	243	no	—
74	C₃²	—	3	27	no	—
75	C₃²	—	3	81	no	—
76	C₃²	—	3	9	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	3	18	no	—
79	C₃²	C₃×C₇×H(3,𝔽₃)	1	9	yes	—
80	C₃²	C₃×C₇×H(3,𝔽₃)	1	3	yes	—
81	C₃²	C₃×C₇×3₋¹⁺²	1	9	yes	—
82	C₃²	C₃×C₇×3₋¹⁺²	1	27	yes	complemented
83	C₃²	C₃⁴×C₇	1	1	yes	characteristic
84	C₉	—	3	27	no	—
85	C₇	C₃×#6891	1	1	yes	characteristic, direct product factor, Sylow
86	C₃	—	3	9	no	—
87	C₃	—	3	27	no	—
88	C₃	C₇×#6891	1	9	yes	direct product factor
89	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic
90	C₃	C₃²×C₇×3₋¹⁺²	1	3	yes	—

	subgroup	G/H
center, socle	C₃³×C₇	C₃³
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇×3₋¹⁺²	C₃	semidirect
3. C₇×#6891	C₃	direct (N × H)
4. C₃×C₇×C₃²⋊C₉	C₃	semidirect
5. C₃×#6891	C₇	direct (N × H)
12. C₃×C₇×3₋¹⁺²	C₃²	semidirect
13. C₃²×C₇×C₉	C₃²	semidirect
14. C₇×C₃²⋊C₉	C₃²	semidirect
16. C₃²×3₋¹⁺²	C₃×C₇	semidirect
17. #6891	C₃×C₇	direct (N × H)
18. C₃×C₃²⋊C₉	C₃×C₇	semidirect
26. C₃³×C₇	3₋¹⁺²	semidirect
32. C₃×C₇×C₉	C₃³	semidirect
39. C₃×3₋¹⁺²	C₃²×C₇	semidirect
40. C₃²×C₉	C₃²×C₇	semidirect
41. C₃²⋊C₉	C₃²×C₇	semidirect
51. C₃²×C₇	C₃×3₋¹⁺²	semidirect
61. C₃³	C₇×3₋¹⁺²	semidirect
67. C₃×C₉	C₃³×C₇	semidirect
70. C₃×C₇	#6891	direct (N × H)
82. C₃²	C₃×C₇×3₋¹⁺²	semidirect
85. C₇	C₃×#6891	direct (N × H)
88. C₃	C₇×#6891	direct (N × H)

Subgroups — C3×C7×#6891 #19100275

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6891 #19100275