Subgroups — C₇×#10624885 #19100294

Order 5103.

716 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×#6896	C₃	1	27	yes	maximal, complemented
3	C₇×#6895	C₃	1	6	yes	maximal, complemented
4	C₇×#6891	C₃	1	3	yes	maximal
5	C₇×#6887	C₃	1	3	yes	maximal, complemented
6	#10624885	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃⁴×C₇	C₃²	1	1	yes	characteristic
8	C₃×C₇×3₋¹⁺²	—	3	9	no	—
9	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
10	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
11	C₃²×C₇×C₉	C₃²	1	2	yes	—
12	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
13	C₇×C₉⋊C₉	C₃²	1	18	yes	complemented
14	C₇×C₉⋊C₉	C₃²	1	54	yes	complemented
15	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
16	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
17	C₇×C₉²	C₃²	1	9	yes	complemented
18	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
19	#6896	C₃×C₇	1	27	yes	complemented
20	#6895	C₃×C₇	1	6	yes	complemented
21	#6891	C₃×C₇	1	3	yes	—
22	#6887	C₃×C₇	1	3	yes	complemented
23	C₃³×C₇	—	3	3	no	—
24	C₃³×C₇	—	9	3	no	—
25	C₃³×C₇	C₃³	1	3	yes	—
26	C₃³×C₇	C₃³	1	1	yes	characteristic
27	C₇×3₋¹⁺²	—	3	27	no	—
28	C₇×3₋¹⁺²	—	9	9	no	—
29	C₃×C₇×C₉	—	3	6	no	—
30	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	complemented
31	C₃×C₇×C₉	C₃³	1	27	yes	—
32	C₃×C₇×C₉	C₃³	1	6	yes	—
33	C₃×C₇×C₉	C₃³	1	3	yes	—
34	C₃⁴	C₃²×C₇	1	1	yes	characteristic
35	C₃×3₋¹⁺²	—	3	9	no	—
36	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
37	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
38	C₃²×C₉	C₃²×C₇	1	2	yes	—
39	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
40	C₉⋊C₉	C₃²×C₇	1	18	yes	complemented
41	C₉⋊C₉	C₃²×C₇	1	54	yes	complemented
42	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
43	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
44	C₉²	C₃²×C₇	1	9	yes	complemented
45	C₃²×C₇	—	3	3	no	—
46	C₃²×C₇	—	3	3	no	—
47	C₃²×C₇	—	3	3	no	—
48	C₃²×C₇	—	3	6	no	—
49	C₃²×C₇	—	9	9	no	—
50	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
51	C₃²×C₇	C₃⁴	1	1	yes	characteristic
52	C₇×C₉	—	3	6	no	—
53	C₇×C₉	—	3	27	no	—
54	C₇×C₉	C₃×3₋¹⁺²	1	9	yes	—
55	C₃³	—	3	3	no	—
56	C₃³	—	9	3	no	—
57	C₃³	C₃³×C₇	1	3	yes	—
58	C₃³	C₃³×C₇	1	1	yes	characteristic
59	3₋¹⁺²	—	3	27	no	—
60	3₋¹⁺²	—	9	9	no	—
61	C₃×C₉	—	3	6	no	—
62	C₃×C₉	C₇×3₋¹⁺²	1	9	yes	complemented
63	C₃×C₉	C₃³×C₇	1	27	yes	—
64	C₃×C₉	C₃³×C₇	1	6	yes	—
65	C₃×C₉	C₃³×C₇	1	3	yes	—
66	C₃×C₇	—	3	3	no	—
67	C₃×C₇	—	9	3	no	—
68	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
69	C₃×C₇	3₋¹⁺⁴	1	3	yes	—
70	C₃²	—	3	3	no	—
71	C₃²	—	3	3	no	—
72	C₃²	—	3	3	no	—
73	C₃²	—	3	6	no	—
74	C₃²	—	9	9	no	—
75	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
76	C₃²	C₃⁴×C₇	1	1	yes	characteristic
77	C₉	—	3	6	no	—
78	C₉	—	3	27	no	—
79	C₉	C₃×C₇×3₋¹⁺²	1	9	yes	—
80	C₇	#10624885	1	1	yes	characteristic, direct product factor, Sylow
81	C₃	—	3	3	no	—
82	C₃	—	9	3	no	—
83	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
84	C₃	C₇×3₋¹⁺⁴	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×#6896	C₃	semidirect
3. C₇×#6895	C₃	semidirect
5. C₇×#6887	C₃	semidirect
6. #10624885	C₇	direct (N × H)
13. C₇×C₉⋊C₉	C₃²	semidirect
14. C₇×C₉⋊C₉	C₃²	semidirect
17. C₇×C₉²	C₃²	semidirect
19. #6896	C₃×C₇	semidirect
20. #6895	C₃×C₇	semidirect
22. #6887	C₃×C₇	semidirect
30. C₃×C₇×C₉	3₋¹⁺²	semidirect
40. C₉⋊C₉	C₃²×C₇	semidirect
41. C₉⋊C₉	C₃²×C₇	semidirect
44. C₉²	C₃²×C₇	semidirect
62. C₃×C₉	C₇×3₋¹⁺²	semidirect
80. C₇	#10624885	direct (N × H)

Subgroups — C7×#10624885 #19100294

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624885 #19100294