Subgroups — C₇×#10624906 #19100315

Order 5103.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6898	C₃	1	9	yes	maximal, complemented
2	C₇×#6897	C₃	1	9	yes	maximal, complemented
3	C₇×#6894	C₃	1	12	yes	maximal, complemented
4	C₇×#6891	C₃	1	2	yes	maximal
5	C₇×C₉×3₋¹⁺²	C₃	1	6	yes	maximal, complemented
6	C₃×C₇×C₃²⋊C₉	C₃	1	2	yes	maximal
7	#10624906	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃⁴×C₇	C₃²	1	1	yes	characteristic
9	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
10	C₃²×C₇×C₉	C₃²	1	6	yes	—
11	C₇×C₉⋊C₉	C₃²	1	36	yes	complemented
12	C₇×C₉⋊C₉	C₃²	1	36	yes	complemented
13	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
14	C₇×C₃²⋊C₉	C₃²	1	4	yes	—
15	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
16	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
17	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
19	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
20	C₇×C₉²	C₃²	1	9	yes	complemented
21	#6898	C₃×C₇	1	9	yes	complemented
22	#6897	C₃×C₇	1	9	yes	complemented
23	#6894	C₃×C₇	1	12	yes	complemented
24	#6891	C₃×C₇	1	2	yes	—
25	C₉×3₋¹⁺²	C₃×C₇	1	6	yes	complemented
26	C₃×C₃²⋊C₉	C₃×C₇	1	2	yes	—
27	C₃³×C₇	—	3	6	no	—
28	C₃³×C₇	—	9	2	no	—
29	C₃³×C₇	C₃³	1	1	yes	characteristic
30	C₃³×C₇	C₃³	1	1	yes	characteristic
31	C₃³×C₇	C₃³	1	2	yes	—
32	C₇×3₋¹⁺²	—	3	18	no	—
33	C₃×C₇×C₉	—	9	6	no	—
34	C₃×C₇×C₉	C₃³	1	6	yes	—
35	C₃×C₇×C₉	C₃³	1	18	yes	—
36	C₃×C₇×C₉	C₃³	1	12	yes	—
37	C₃⁴	C₃²×C₇	1	1	yes	characteristic
38	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
39	C₃²×C₉	C₃²×C₇	1	6	yes	—
40	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
41	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
42	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
43	C₃²⋊C₉	C₃²×C₇	1	4	yes	—
44	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
45	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
46	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
47	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
48	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
49	C₉²	C₃²×C₇	1	9	yes	complemented
50	C₃²×C₇	—	3	2	no	—
51	C₃²×C₇	—	3	2	no	—
52	C₃²×C₇	—	3	2	no	—
53	C₃²×C₇	—	3	2	no	—
54	C₃²×C₇	—	3	2	no	—
55	C₃²×C₇	—	3	2	no	—
56	C₃²×C₇	—	3	2	no	—
57	C₃²×C₇	—	9	9	no	—
58	C₃²×C₇	#737	1	6	yes	—
59	C₃²×C₇	C₃⁴	1	1	yes	characteristic
60	C₇×C₉	—	3	18	no	—
61	C₇×C₉	—	3	6	no	—
62	C₇×C₉	—	3	12	no	—
63	C₃³	—	3	6	no	—
64	C₃³	—	9	2	no	—
65	C₃³	C₃³×C₇	1	1	yes	characteristic
66	C₃³	C₃³×C₇	1	1	yes	characteristic
67	C₃³	C₃³×C₇	1	2	yes	—
68	3₋¹⁺²	—	3	18	no	—
69	C₃×C₉	—	9	6	no	—
70	C₃×C₉	C₃³×C₇	1	6	yes	—
71	C₃×C₉	C₃³×C₇	1	18	yes	—
72	C₃×C₉	C₃³×C₇	1	12	yes	—
73	C₃×C₇	—	3	6	no	—
74	C₃×C₇	—	9	1	no	—
75	C₃×C₇	—	9	1	no	—
76	C₃×C₇	C₃×#737	1	2	yes	—
77	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	3	2	no	—
83	C₃²	—	3	2	no	—
84	C₃²	—	3	2	no	—
85	C₃²	—	9	9	no	—
86	C₃²	C₇×#737	1	6	yes	—
87	C₃²	C₃⁴×C₇	1	1	yes	characteristic
88	C₉	—	3	18	no	—
89	C₉	—	3	6	no	—
90	C₉	—	3	12	no	—
91	C₇	#10624906	1	1	yes	characteristic, direct product factor, Sylow
92	C₃	—	3	6	no	—
93	C₃	—	9	1	no	—
94	C₃	—	9	1	no	—
95	C₃	C₃×C₇×#737	1	2	yes	—
96	C₃	C₇×3₋¹⁺⁴	1	2	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
1. C₇×#6898	C₃	semidirect
2. C₇×#6897	C₃	semidirect
3. C₇×#6894	C₃	semidirect
5. C₇×C₉×3₋¹⁺²	C₃	semidirect
7. #10624906	C₇	direct (N × H)
11. C₇×C₉⋊C₉	C₃²	semidirect
12. C₇×C₉⋊C₉	C₃²	semidirect
20. C₇×C₉²	C₃²	semidirect
21. #6898	C₃×C₇	semidirect
22. #6897	C₃×C₇	semidirect
23. #6894	C₃×C₇	semidirect
25. C₉×3₋¹⁺²	C₃×C₇	semidirect
40. C₉⋊C₉	C₃²×C₇	semidirect
41. C₉⋊C₉	C₃²×C₇	semidirect
49. C₉²	C₃²×C₇	semidirect
91. C₇	#10624906	direct (N × H)

Subgroups — C7×#10624906 #19100315

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624906 #19100315