Subgroups — C₇×#10624863 #19100272

Order 5103.

944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉×3₋¹⁺²	C₃	1	27	yes	maximal, complemented
3	C₇×#6887	C₃	1	9	yes	maximal, complemented
4	C₃×C₇×C₃²⋊C₉	C₃	1	3	yes	maximal
5	#10624863	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×3₋¹⁺²	C₉	1	27	yes	complemented
8	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
9	C₃²×C₇×C₉	C₃²	1	9	yes	—
10	C₃²×C₇×C₉	C₃²	1	3	yes	—
11	C₇×C₉⋊C₉	C₃²	1	54	yes	complemented
12	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
13	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
14	C₇×C₉²	C₃²	1	27	yes	complemented
15	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
16	C₉×3₋¹⁺²	C₃×C₇	1	27	yes	complemented
17	#6887	C₃×C₇	1	9	yes	complemented
18	C₃×C₃²⋊C₉	C₃×C₇	1	3	yes	—
19	C₃³×C₇	—	9	3	no	—
20	C₃³×C₇	C₃×C₉	1	9	yes	—
21	C₃³×C₇	C₃³	1	1	yes	characteristic
22	C₃³×C₇	C₃³	1	3	yes	—
23	C₇×3₋¹⁺²	C₃×C₉	1	81	yes	complemented
24	C₃×C₇×C₉	—	9	9	no	—
25	C₃×C₇×C₉	C₃×C₉	1	27	yes	complemented
26	C₃×C₇×C₉	C₃³	1	27	yes	—
27	C₃×C₇×C₉	C₃³	1	9	yes	—
28	C₃⁴	C₃²×C₇	1	1	yes	characteristic
29	C₃×3₋¹⁺²	C₇×C₉	1	27	yes	complemented
30	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
31	C₃²×C₉	C₃²×C₇	1	9	yes	—
32	C₃²×C₉	C₃²×C₇	1	3	yes	—
33	C₉⋊C₉	C₃²×C₇	1	54	yes	complemented
34	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
35	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
36	C₉²	C₃²×C₇	1	27	yes	complemented
37	C₃²×C₇	—	3	3	no	—
38	C₃²×C₇	—	3	3	no	—
39	C₃²×C₇	—	3	6	no	—
40	C₃²×C₇	—	9	9	no	—
41	C₃²×C₇	C₃²×C₉	1	3	yes	—
42	C₃²×C₇	C₃²×C₉	1	9	yes	—
43	C₃²×C₇	C₃⁴	1	1	yes	characteristic
44	C₇×C₉	—	3	27	no	—
45	C₇×C₉	C₃²×C₉	1	27	yes	—
46	C₃³	—	9	3	no	—
47	C₃³	C₃×C₇×C₉	1	9	yes	—
48	C₃³	C₃³×C₇	1	1	yes	characteristic
49	C₃³	C₃³×C₇	1	3	yes	—
50	3₋¹⁺²	C₃×C₇×C₉	1	81	yes	complemented
51	C₃×C₉	—	9	9	no	—
52	C₃×C₉	C₃×C₇×C₉	1	27	yes	complemented
53	C₃×C₉	C₃³×C₇	1	27	yes	—
54	C₃×C₉	C₃³×C₇	1	9	yes	—
55	C₃×C₇	—	3	9	no	—
56	C₃×C₇	—	3	3	no	—
57	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
58	C₃×C₇	3₋¹⁺⁴	1	3	yes	—
59	C₃²	—	3	3	no	—
60	C₃²	—	3	3	no	—
61	C₃²	—	3	6	no	—
62	C₃²	—	9	9	no	—
63	C₃²	C₃²×C₇×C₉	1	3	yes	—
64	C₃²	C₃²×C₇×C₉	1	9	yes	—
65	C₃²	C₃⁴×C₇	1	1	yes	characteristic
66	C₉	—	3	27	no	—
67	C₉	C₃²×C₇×C₉	1	27	yes	—
68	C₇	#10624863	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	—	3	9	no	—
70	C₃	—	3	3	no	—
71	C₃	C₃³×C₇×C₉	1	1	yes	characteristic
72	C₃	C₇×3₋¹⁺⁴	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×C₉×3₋¹⁺²	C₃	semidirect
3. C₇×#6887	C₃	semidirect
5. #10624863	C₇	direct (N × H)
7. C₃×C₇×3₋¹⁺²	C₉	semidirect
11. C₇×C₉⋊C₉	C₃²	semidirect
14. C₇×C₉²	C₃²	semidirect
16. C₉×3₋¹⁺²	C₃×C₇	semidirect
17. #6887	C₃×C₇	semidirect
23. C₇×3₋¹⁺²	C₃×C₉	semidirect
25. C₃×C₇×C₉	C₃×C₉	semidirect
29. C₃×3₋¹⁺²	C₇×C₉	semidirect
33. C₉⋊C₉	C₃²×C₇	semidirect
36. C₉²	C₃²×C₇	semidirect
50. 3₋¹⁺²	C₃×C₇×C₉	semidirect
52. C₃×C₉	C₃×C₇×C₉	semidirect
68. C₇	#10624863	direct (N × H)

Subgroups — C7×#10624863 #19100272

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624863 #19100272