Subgroups — C₇×#10624911 #19100320

Order 5103.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6899	C₃	1	18	yes	maximal, complemented
2	C₇×#6897	C₃	1	9	yes	maximal, complemented
3	C₇×#6896	C₃	1	9	yes	maximal, complemented
4	C₇×#6891	C₃	1	2	yes	maximal
5	C₇×#6891	C₃	1	2	yes	maximal
6	#10624911	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃⁴×C₇	C₃²	1	1	yes	characteristic
8	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
9	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
10	C₇×C₉⋊C₉	C₃²	1	72	yes	complemented
11	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
13	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
14	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
15	C₇×C₃²⋊C₉	C₃²	1	12	yes	—
16	C₇×C₉²	C₃²	1	9	yes	complemented
17	#6899	C₃×C₇	1	18	yes	complemented
18	#6897	C₃×C₇	1	9	yes	complemented
19	#6896	C₃×C₇	1	9	yes	complemented
20	#6891	C₃×C₇	1	2	yes	—
21	#6891	C₃×C₇	1	2	yes	—
22	C₃³×C₇	—	9	2	no	—
23	C₃³×C₇	—	9	2	no	—
24	C₃³×C₇	C₃³	1	1	yes	characteristic
25	C₃³×C₇	C₃³	1	2	yes	—
26	C₃³×C₇	C₃³	1	1	yes	characteristic
27	C₇×3₋¹⁺²	—	9	6	no	—
28	C₇×3₋¹⁺²	—	9	6	no	—
29	C₃×C₇×C₉	C₃³	1	18	yes	—
30	C₃×C₇×C₉	C₃³	1	18	yes	—
31	C₃⁴	C₃²×C₇	1	1	yes	characteristic
32	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
33	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
34	C₉⋊C₉	C₃²×C₇	1	72	yes	complemented
35	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
36	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
37	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
38	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
39	C₃²⋊C₉	C₃²×C₇	1	12	yes	—
40	C₉²	C₃²×C₇	1	9	yes	complemented
41	C₃²×C₇	—	3	2	no	—
42	C₃²×C₇	—	3	2	no	—
43	C₃²×C₇	—	3	2	no	—
44	C₃²×C₇	—	3	2	no	—
45	C₃²×C₇	—	3	2	no	—
46	C₃²×C₇	—	3	4	no	—
47	C₃²×C₇	—	3	2	no	—
48	C₃²×C₇	—	9	9	no	—
49	C₃²×C₇	C₃⁴	1	1	yes	characteristic
50	C₇×C₉	—	3	18	no	—
51	C₇×C₉	—	3	18	no	—
52	C₃³	—	9	2	no	—
53	C₃³	—	9	2	no	—
54	C₃³	C₃³×C₇	1	1	yes	characteristic
55	C₃³	C₃³×C₇	1	2	yes	—
56	C₃³	C₃³×C₇	1	1	yes	characteristic
57	3₋¹⁺²	—	9	6	no	—
58	3₋¹⁺²	—	9	6	no	—
59	C₃×C₉	C₃³×C₇	1	18	yes	—
60	C₃×C₉	C₃³×C₇	1	18	yes	—
61	C₃×C₇	—	9	1	no	—
62	C₃×C₇	—	9	2	no	—
63	C₃×C₇	—	9	1	no	—
64	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
65	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
66	C₃²	—	3	2	no	—
67	C₃²	—	3	2	no	—
68	C₃²	—	3	2	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	4	no	—
72	C₃²	—	3	2	no	—
73	C₃²	—	9	9	no	—
74	C₃²	C₃⁴×C₇	1	1	yes	characteristic
75	C₉	—	3	18	no	—
76	C₉	—	3	18	no	—
77	C₇	#10624911	1	1	yes	characteristic, direct product factor, Sylow
78	C₃	—	9	1	no	—
79	C₃	—	9	2	no	—
80	C₃	—	9	1	no	—
81	C₃	C₇×3₋¹⁺⁴	1	2	yes	—
82	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×#6899	C₃	semidirect
2. C₇×#6897	C₃	semidirect
3. C₇×#6896	C₃	semidirect
6. #10624911	C₇	direct (N × H)
10. C₇×C₉⋊C₉	C₃²	semidirect
16. C₇×C₉²	C₃²	semidirect
17. #6899	C₃×C₇	semidirect
18. #6897	C₃×C₇	semidirect
19. #6896	C₃×C₇	semidirect
34. C₉⋊C₉	C₃²×C₇	semidirect
40. C₉²	C₃²×C₇	semidirect
77. C₇	#10624911	direct (N × H)

Subgroups — C7×#10624911 #19100320

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624911 #19100320