Subgroups — C₃×C₇×#6900 #19100287

Order 5103.

1076 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×3₋¹⁺²	C₃	1	4	yes	maximal
2	C₇×#6900	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₇×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
4	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#6900	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×3₋¹⁺²	—	3	36	no	—
8	C₃×C₇×3₋¹⁺²	C₃²	1	36	yes	—
9	C₃²×C₇×C₉	C₃²	1	8	yes	—
10	C₃²×C₇×C₉	C₃²	1	4	yes	—
11	C₇×C₉⋊C₉	C₃²	1	72	yes	complemented
12	C₇×C₉²	C₃²	1	9	yes	complemented
13	C₃²×3₋¹⁺²	C₃×C₇	1	4	yes	—
14	#6900	C₃×C₇	1	27	yes	direct product factor
15	C₃×C₉⋊C₉	C₃×C₇	1	8	yes	complemented
16	C₃×C₉²	C₃×C₇	1	1	yes	characteristic, complemented
17	C₃³×C₇	—	3	12	no	—
18	C₃³×C₇	C₃³	1	3	yes	—
19	C₃³×C₇	C₃³	1	1	yes	characteristic
20	C₇×3₋¹⁺²	—	3	108	no	—
21	C₃×C₇×C₉	—	3	24	no	—
22	C₃×C₇×C₉	3₋¹⁺²	1	36	yes	complemented
23	C₃×C₇×C₉	C₃³	1	24	yes	—
24	C₃×C₇×C₉	C₃³	1	12	yes	—
25	C₃⁴	C₃²×C₇	1	1	yes	characteristic
26	C₃×3₋¹⁺²	—	3	36	no	—
27	C₃×3₋¹⁺²	C₃²×C₇	1	36	yes	—
28	C₃²×C₉	C₃²×C₇	1	8	yes	—
29	C₃²×C₉	C₃²×C₇	1	4	yes	—
30	C₉⋊C₉	C₃²×C₇	1	72	yes	complemented
31	C₉²	C₃²×C₇	1	9	yes	complemented
32	C₃²×C₇	—	3	12	no	—
33	C₃²×C₇	—	9	9	no	—
34	C₃²×C₇	C₃×3₋¹⁺²	1	12	yes	—
35	C₃²×C₇	C₃⁴	1	1	yes	characteristic
36	C₇×C₉	—	3	24	no	—
37	C₇×C₉	C₃×3₋¹⁺²	1	36	yes	complemented
38	C₃³	—	3	12	no	—
39	C₃³	C₃³×C₇	1	3	yes	—
40	C₃³	C₃³×C₇	1	1	yes	characteristic
41	3₋¹⁺²	—	3	108	no	—
42	C₃×C₉	—	3	24	no	—
43	C₃×C₉	C₇×3₋¹⁺²	1	36	yes	complemented
44	C₃×C₉	C₃³×C₇	1	24	yes	—
45	C₃×C₉	C₃³×C₇	1	12	yes	—
46	C₃×C₇	—	9	3	no	—
47	C₃×C₇	#6900	1	9	yes	direct product factor
48	C₃×C₇	C₃²×3₋¹⁺²	1	4	yes	—
49	C₃²	—	3	12	no	—
50	C₃²	—	9	9	no	—
51	C₃²	C₃×C₇×3₋¹⁺²	1	12	yes	—
52	C₃²	C₃⁴×C₇	1	1	yes	characteristic
53	C₉	—	3	24	no	—
54	C₉	C₃×C₇×3₋¹⁺²	1	36	yes	complemented
55	C₇	C₃×#6900	1	1	yes	characteristic, direct product factor, Sylow
56	C₃	—	9	3	no	—
57	C₃	C₇×#6900	1	9	yes	direct product factor
58	C₃	C₃²×C₇×3₋¹⁺²	1	4	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. C₇×#6900	C₃	direct (N × H)
3. C₃×C₇×C₉⋊C₉	C₃	semidirect
4. C₃×C₇×C₉²	C₃	semidirect
5. C₃×#6900	C₇	direct (N × H)
11. C₇×C₉⋊C₉	C₃²	semidirect
12. C₇×C₉²	C₃²	semidirect
14. #6900	C₃×C₇	direct (N × H)
15. C₃×C₉⋊C₉	C₃×C₇	semidirect
16. C₃×C₉²	C₃×C₇	semidirect
22. C₃×C₇×C₉	3₋¹⁺²	semidirect
30. C₉⋊C₉	C₃²×C₇	semidirect
31. C₉²	C₃²×C₇	semidirect
37. C₇×C₉	C₃×3₋¹⁺²	semidirect
43. C₃×C₉	C₇×3₋¹⁺²	semidirect
47. C₃×C₇	#6900	direct (N × H)
54. C₉	C₃×C₇×3₋¹⁺²	semidirect
55. C₇	C₃×#6900	direct (N × H)
57. C₃	C₇×#6900	direct (N × H)

Subgroups — C3×C7×#6900 #19100287

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6900 #19100287