Subgroups — C₃×C₇×#6887 #19100267

Order 5103.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
2	C₇×#6887	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₇×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃×C₇×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃×C₇×C₉²	C₃	1	3	yes	maximal, complemented
6	C₃×#6887	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃⁴×C₇	C₃²	1	1	yes	characteristic
8	C₃²×C₇×C₉	C₉	1	27	yes	complemented
9	C₃²×C₇×C₉	C₃²	1	9	yes	—
10	C₃²×C₇×C₉	C₃²	1	2	yes	—
11	C₃²×C₇×C₉	C₃²	1	9	yes	—
12	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
13	C₇×C₉⋊C₉	C₃²	1	54	yes	complemented
14	C₇×C₃²⋊C₉	C₃²	1	27	yes	—
15	C₇×C₉²	C₃²	1	27	yes	complemented
16	C₃³×C₉	C₃×C₇	1	1	yes	characteristic
17	#6887	C₃×C₇	1	27	yes	direct product factor
18	C₃×C₉⋊C₉	C₃×C₇	1	6	yes	complemented
19	C₃×C₃²⋊C₉	C₃×C₇	1	3	yes	—
20	C₃×C₉²	C₃×C₇	1	3	yes	complemented
21	C₃³×C₇	—	3	9	no	—
22	C₃³×C₇	C₃×C₉	1	9	yes	—
23	C₃³×C₇	C₃³	1	3	yes	—
24	C₃³×C₇	C₃³	1	1	yes	characteristic
25	C₃×C₇×C₉	—	3	27	no	—
26	C₃×C₇×C₉	C₃×C₉	1	18	yes	—
27	C₃×C₇×C₉	C₃×C₉	1	9	yes	—
28	C₃×C₇×C₉	C₃×C₉	1	81	yes	complemented
29	C₃×C₇×C₉	C₃³	1	27	yes	—
30	C₃×C₇×C₉	C₃³	1	3	yes	—
31	C₃×C₇×C₉	C₃³	1	6	yes	—
32	C₃⁴	C₃²×C₇	1	1	yes	characteristic
33	C₃²×C₉	C₇×C₉	1	27	yes	complemented
34	C₃²×C₉	C₃²×C₇	1	9	yes	—
35	C₃²×C₉	C₃²×C₇	1	2	yes	—
36	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
37	C₃²×C₉	C₃²×C₇	1	9	yes	—
38	C₉⋊C₉	C₃²×C₇	1	54	yes	complemented
39	C₃²⋊C₉	C₃²×C₇	1	27	yes	—
40	C₉²	C₃²×C₇	1	27	yes	complemented
41	C₃²×C₇	—	3	9	no	—
42	C₃²×C₇	—	3	27	no	—
43	C₃²×C₇	C₃²×C₉	1	9	yes	—
44	C₃²×C₇	C₃²×C₉	1	3	yes	—
45	C₃²×C₇	#737	1	9	yes	—
46	C₃²×C₇	C₃⁴	1	1	yes	characteristic
47	C₇×C₉	—	3	27	no	—
48	C₇×C₉	C₃²×C₉	1	18	yes	—
49	C₇×C₉	C₃²×C₉	1	9	yes	—
50	C₃³	—	3	9	no	—
51	C₃³	C₃×C₇×C₉	1	9	yes	—
52	C₃³	C₃³×C₇	1	3	yes	—
53	C₃³	C₃³×C₇	1	1	yes	characteristic
54	C₃×C₉	—	3	27	no	—
55	C₃×C₉	C₃×C₇×C₉	1	18	yes	—
56	C₃×C₉	C₃×C₇×C₉	1	9	yes	—
57	C₃×C₉	C₃×C₇×C₉	1	81	yes	complemented
58	C₃×C₉	C₃³×C₇	1	27	yes	—
59	C₃×C₉	C₃³×C₇	1	3	yes	—
60	C₃×C₉	C₃³×C₇	1	6	yes	—
61	C₃×C₇	—	3	9	no	—
62	C₃×C₇	#6887	1	9	yes	direct product factor
63	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
64	C₃×C₇	C₃×#737	1	3	yes	—
65	C₃²	—	3	27	no	—
66	C₃²	—	3	9	no	—
67	C₃²	C₃²×C₇×C₉	1	9	yes	—
68	C₃²	C₃²×C₇×C₉	1	3	yes	—
69	C₃²	C₇×#737	1	9	yes	—
70	C₃²	C₃⁴×C₇	1	1	yes	characteristic
71	C₉	—	3	27	no	—
72	C₉	C₃²×C₇×C₉	1	9	yes	—
73	C₉	C₃²×C₇×C₉	1	18	yes	—
74	C₇	C₃×#6887	1	1	yes	characteristic, direct product factor, Sylow
75	C₃	—	3	9	no	—
76	C₃	C₇×#6887	1	9	yes	direct product factor
77	C₃	C₃³×C₇×C₉	1	1	yes	characteristic
78	C₃	C₃×C₇×#737	1	3	yes	—

	subgroup	G/H
center	C₃²×C₇×C₉	C₃²
commutator	C₃	C₃³×C₇×C₉
Frattini	C₃²	C₃⁴×C₇
socle	C₃³×C₇	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#6887	C₃	direct (N × H)
3. C₃×C₇×C₉⋊C₉	C₃	semidirect
5. C₃×C₇×C₉²	C₃	semidirect
6. C₃×#6887	C₇	direct (N × H)
8. C₃²×C₇×C₉	C₉	semidirect
13. C₇×C₉⋊C₉	C₃²	semidirect
15. C₇×C₉²	C₃²	semidirect
17. #6887	C₃×C₇	direct (N × H)
18. C₃×C₉⋊C₉	C₃×C₇	semidirect
20. C₃×C₉²	C₃×C₇	semidirect
28. C₃×C₇×C₉	C₃×C₉	semidirect
33. C₃²×C₉	C₇×C₉	semidirect
38. C₉⋊C₉	C₃²×C₇	semidirect
40. C₉²	C₃²×C₇	semidirect
57. C₃×C₉	C₃×C₇×C₉	semidirect
62. C₃×C₇	#6887	direct (N × H)
74. C₇	C₃×#6887	direct (N × H)
76. C₃	C₇×#6887	direct (N × H)

Subgroups — C3×C7×#6887 #19100267

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6887 #19100267