Subgroups — C₇×#10624884 #19100293

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×#6900	C₃	1	9	yes	maximal, complemented
3	C₇×#6899	C₃	1	18	yes	maximal, complemented
4	C₇×#6895	C₃	1	6	yes	maximal, complemented
5	C₇×#6891	C₃	1	3	yes	maximal
6	C₇×#6887	C₃	1	3	yes	maximal, complemented
7	#10624884	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃⁴×C₇	C₃²	1	1	yes	characteristic
9	C₃×C₇×3₋¹⁺²	—	3	9	no	—
10	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
11	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
12	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
13	C₃²×C₇×C₉	C₃²	1	2	yes	—
14	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
15	C₇×C₉⋊C₉	C₃²	1	18	yes	complemented
16	C₇×C₉⋊C₉	C₃²	1	54	yes	complemented
17	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
18	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
19	C₇×C₉²	C₃²	1	9	yes	complemented
20	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
21	#6900	C₃×C₇	1	9	yes	complemented
22	#6899	C₃×C₇	1	18	yes	complemented
23	#6895	C₃×C₇	1	6	yes	complemented
24	#6891	C₃×C₇	1	3	yes	—
25	#6887	C₃×C₇	1	3	yes	complemented
26	C₃³×C₇	—	3	3	no	—
27	C₃³×C₇	—	9	3	no	—
28	C₃³×C₇	C₃³	1	2	yes	—
29	C₃³×C₇	C₃³	1	1	yes	characteristic
30	C₃³×C₇	C₃³	1	1	yes	characteristic
31	C₇×3₋¹⁺²	—	3	18	no	—
32	C₇×3₋¹⁺²	—	3	9	no	—
33	C₇×3₋¹⁺²	—	9	9	no	—
34	C₃×C₇×C₉	—	3	6	no	—
35	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	complemented
36	C₃×C₇×C₉	C₃³	1	27	yes	—
37	C₃×C₇×C₉	C₃³	1	6	yes	—
38	C₃×C₇×C₉	C₃³	1	3	yes	—
39	C₃⁴	C₃²×C₇	1	1	yes	characteristic
40	C₃×3₋¹⁺²	—	3	9	no	—
41	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
42	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
43	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
44	C₃²×C₉	C₃²×C₇	1	2	yes	—
45	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
46	C₉⋊C₉	C₃²×C₇	1	18	yes	complemented
47	C₉⋊C₉	C₃²×C₇	1	54	yes	complemented
48	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
49	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
50	C₉²	C₃²×C₇	1	9	yes	complemented
51	C₃²×C₇	—	3	3	no	—
52	C₃²×C₇	—	3	2	no	—
53	C₃²×C₇	—	3	1	no	—
54	C₃²×C₇	—	3	3	no	—
55	C₃²×C₇	—	3	6	no	—
56	C₃²×C₇	—	9	9	no	—
57	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
58	C₃²×C₇	C₃⁴	1	1	yes	characteristic
59	C₇×C₉	—	3	6	no	—
60	C₇×C₉	—	3	27	no	—
61	C₇×C₉	C₃×3₋¹⁺²	1	9	yes	—
62	C₃³	—	3	3	no	—
63	C₃³	—	9	3	no	—
64	C₃³	C₃³×C₇	1	2	yes	—
65	C₃³	C₃³×C₇	1	1	yes	characteristic
66	C₃³	C₃³×C₇	1	1	yes	characteristic
67	3₋¹⁺²	—	3	18	no	—
68	3₋¹⁺²	—	3	9	no	—
69	3₋¹⁺²	—	9	9	no	—
70	C₃×C₉	—	3	6	no	—
71	C₃×C₉	C₇×3₋¹⁺²	1	9	yes	complemented
72	C₃×C₉	C₃³×C₇	1	27	yes	—
73	C₃×C₉	C₃³×C₇	1	6	yes	—
74	C₃×C₉	C₃³×C₇	1	3	yes	—
75	C₃×C₇	—	3	3	no	—
76	C₃×C₇	—	9	1	no	—
77	C₃×C₇	—	9	2	no	—
78	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
79	C₃×C₇	3₋¹⁺⁴	1	3	yes	—
80	C₃²	—	3	3	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	3	1	no	—
83	C₃²	—	3	3	no	—
84	C₃²	—	3	6	no	—
85	C₃²	—	9	9	no	—
86	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
87	C₃²	C₃⁴×C₇	1	1	yes	characteristic
88	C₉	—	3	6	no	—
89	C₉	—	3	27	no	—
90	C₉	C₃×C₇×3₋¹⁺²	1	9	yes	—
91	C₇	#10624884	1	1	yes	characteristic, direct product factor, Sylow
92	C₃	—	3	3	no	—
93	C₃	—	9	1	no	—
94	C₃	—	9	2	no	—
95	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
96	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×#6900	C₃	semidirect
3. C₇×#6899	C₃	semidirect
4. C₇×#6895	C₃	semidirect
6. C₇×#6887	C₃	semidirect
7. #10624884	C₇	direct (N × H)
15. C₇×C₉⋊C₉	C₃²	semidirect
16. C₇×C₉⋊C₉	C₃²	semidirect
19. C₇×C₉²	C₃²	semidirect
21. #6900	C₃×C₇	semidirect
22. #6899	C₃×C₇	semidirect
23. #6895	C₃×C₇	semidirect
25. #6887	C₃×C₇	semidirect
35. C₃×C₇×C₉	3₋¹⁺²	semidirect
46. C₉⋊C₉	C₃²×C₇	semidirect
47. C₉⋊C₉	C₃²×C₇	semidirect
50. C₉²	C₃²×C₇	semidirect
71. C₃×C₉	C₇×3₋¹⁺²	semidirect
91. C₇	#10624884	direct (N × H)

Subgroups — C7×#10624884 #19100293

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624884 #19100293