Subgroups — C₇×#10624902 #19100311

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×#6896	C₃	1	9	yes	maximal, complemented
3	C₇×#6895	C₃	1	12	yes	maximal, complemented
4	C₇×#6891	C₃	1	2	yes	maximal
5	C₇×#6887	C₃	1	6	yes	maximal, complemented
6	C₃×C₇×C₃²⋊C₉	C₃	1	2	yes	maximal
7	#10624902	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	12	yes	—
18	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
19	C₇×C₉²	C₃²	1	9	yes	complemented
20	#6898	C₃×C₇	1	9	yes	complemented
21	#6896	C₃×C₇	1	9	yes	complemented
22	#6895	C₃×C₇	1	12	yes	complemented
23	#6891	C₃×C₇	1	2	yes	—
24	#6887	C₃×C₇	1	6	yes	complemented
25	C₃×C₃²⋊C₉	C₃×C₇	1	2	yes	—
26	C₃³×C₇	—	3	6	no	—
27	C₃³×C₇	—	9	2	no	—
28	C₃³×C₇	C₃³	1	1	yes	characteristic
29	C₃³×C₇	C₃³	1	1	yes	characteristic
30	C₃³×C₇	C₃³	1	2	yes	—
31	C₇×3₋¹⁺²	—	9	6	no	—
32	C₃×C₇×C₉	—	3	18	no	—
33	C₃×C₇×C₉	C₃³	1	6	yes	—
34	C₃×C₇×C₉	C₃³	1	18	yes	—
35	C₃×C₇×C₉	C₃³	1	12	yes	—
36	C₃⁴	C₃²×C₇	1	1	yes	characteristic
37	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
38	C₃²×C₉	C₃²×C₇	1	6	yes	—
39	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
40	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
41	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
42	C₃²⋊C₉	C₃²×C₇	1	4	yes	—
43	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
44	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
45	C₃²⋊C₉	C₃²×C₇	1	12	yes	—
46	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
47	C₉²	C₃²×C₇	1	9	yes	complemented
48	C₃²×C₇	—	3	2	no	—
49	C₃²×C₇	—	3	4	no	—
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	—	9	9	no	—
55	C₃²×C₇	#737	1	6	yes	—
56	C₃²×C₇	C₃⁴	1	1	yes	characteristic
57	C₇×C₉	—	3	6	no	—
58	C₇×C₉	—	3	12	no	—
59	C₇×C₉	—	3	18	no	—
60	C₃³	—	3	6	no	—
61	C₃³	—	9	2	no	—
62	C₃³	C₃³×C₇	1	1	yes	characteristic
63	C₃³	C₃³×C₇	1	1	yes	characteristic
64	C₃³	C₃³×C₇	1	2	yes	—
65	3₋¹⁺²	—	9	6	no	—
66	C₃×C₉	—	3	18	no	—
67	C₃×C₉	C₃³×C₇	1	6	yes	—
68	C₃×C₉	C₃³×C₇	1	18	yes	—
69	C₃×C₉	C₃³×C₇	1	12	yes	—
70	C₃×C₇	—	3	6	no	—
71	C₃×C₇	—	9	1	no	—
72	C₃×C₇	—	9	1	no	—
73	C₃×C₇	C₃×#737	1	2	yes	—
74	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
75	C₃²	—	3	2	no	—
76	C₃²	—	3	4	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	9	9	no	—
82	C₃²	C₇×#737	1	6	yes	—
83	C₃²	C₃⁴×C₇	1	1	yes	characteristic
84	C₉	—	3	6	no	—
85	C₉	—	3	12	no	—
86	C₉	—	3	18	no	—
87	C₇	#10624902	1	1	yes	characteristic, direct product factor, Sylow
88	C₃	—	3	6	no	—
89	C₃	—	9	1	no	—
90	C₃	—	9	1	no	—
91	C₃	C₃×C₇×#737	1	2	yes	—
92	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×#6896	C₃	semidirect
3. C₇×#6895	C₃	semidirect
5. C₇×#6887	C₃	semidirect
7. #10624902	C₇	direct (N × H)
11. C₇×C₉⋊C₉	C₃²	semidirect
12. C₇×C₉⋊C₉	C₃²	semidirect
19. C₇×C₉²	C₃²	semidirect
20. #6898	C₃×C₇	semidirect
21. #6896	C₃×C₇	semidirect
22. #6895	C₃×C₇	semidirect
24. #6887	C₃×C₇	semidirect
39. C₉⋊C₉	C₃²×C₇	semidirect
40. C₉⋊C₉	C₃²×C₇	semidirect
47. C₉²	C₃²×C₇	semidirect
87. C₇	#10624902	direct (N × H)

Subgroups — C7×#10624902 #19100311

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624902 #19100311