Subgroups — C₇×#10624886 #19100295

Order 5103.

728 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×#6895	C₃	1	9	yes	maximal, complemented
3	C₇×#6894	C₃	1	27	yes	maximal, complemented
4	C₃×C₇×C₃²⋊C₉	C₃	1	3	yes	maximal
5	#10624886	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×3₋¹⁺²	—	3	9	no	—
8	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
9	C₃²×C₇×C₉	C₃²	1	3	yes	—
10	C₃²×C₇×C₉	C₃²	1	9	yes	—
11	C₇×C₉⋊C₉	C₃²	1	81	yes	complemented
12	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
13	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
14	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
15	#6895	C₃×C₇	1	9	yes	complemented
16	#6894	C₃×C₇	1	27	yes	complemented
17	C₃×C₃²⋊C₉	C₃×C₇	1	3	yes	—
18	C₃³×C₇	—	9	3	no	—
19	C₃³×C₇	3₋¹⁺²	1	9	yes	—
20	C₃³×C₇	C₃³	1	1	yes	characteristic
21	C₃³×C₇	C₃³	1	3	yes	—
22	C₇×3₋¹⁺²	—	3	27	no	—
23	C₃×C₇×C₉	—	3	9	no	—
24	C₃×C₇×C₉	—	9	9	no	—
25	C₃×C₇×C₉	C₃³	1	27	yes	—
26	C₃×C₇×C₉	C₃³	1	9	yes	—
27	C₃⁴	C₃²×C₇	1	1	yes	characteristic
28	C₃×3₋¹⁺²	—	3	9	no	—
29	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
30	C₃²×C₉	C₃²×C₇	1	3	yes	—
31	C₃²×C₉	C₃²×C₇	1	9	yes	—
32	C₉⋊C₉	C₃²×C₇	1	81	yes	complemented
33	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
34	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
35	C₃²×C₇	—	3	3	no	—
36	C₃²×C₇	—	3	3	no	—
37	C₃²×C₇	—	3	6	no	—
38	C₃²×C₇	—	9	9	no	—
39	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
40	C₃²×C₇	C₃×3₋¹⁺²	1	9	yes	—
41	C₃²×C₇	C₃⁴	1	1	yes	characteristic
42	C₇×C₉	—	3	9	no	—
43	C₇×C₉	—	3	27	no	—
44	C₃³	—	9	3	no	—
45	C₃³	C₇×3₋¹⁺²	1	9	yes	—
46	C₃³	C₃³×C₇	1	1	yes	characteristic
47	C₃³	C₃³×C₇	1	3	yes	—
48	3₋¹⁺²	—	3	27	no	—
49	C₃×C₉	—	3	9	no	—
50	C₃×C₉	—	9	9	no	—
51	C₃×C₉	C₃³×C₇	1	27	yes	—
52	C₃×C₉	C₃³×C₇	1	9	yes	—
53	C₃×C₇	—	3	9	no	—
54	C₃×C₇	—	3	3	no	—
55	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
56	C₃×C₇	3₋¹⁺⁴	1	3	yes	—
57	C₃²	—	3	3	no	—
58	C₃²	—	3	3	no	—
59	C₃²	—	3	6	no	—
60	C₃²	—	9	9	no	—
61	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
62	C₃²	C₃×C₇×3₋¹⁺²	1	9	yes	—
63	C₃²	C₃⁴×C₇	1	1	yes	characteristic
64	C₉	—	3	9	no	—
65	C₉	—	3	27	no	—
66	C₇	#10624886	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	3	9	no	—
68	C₃	—	3	3	no	—
69	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
70	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×#6895	C₃	semidirect
3. C₇×#6894	C₃	semidirect
5. #10624886	C₇	direct (N × H)
11. C₇×C₉⋊C₉	C₃²	semidirect
15. #6895	C₃×C₇	semidirect
16. #6894	C₃×C₇	semidirect
32. C₉⋊C₉	C₃²×C₇	semidirect
66. C₇	#10624886	direct (N × H)

Subgroups — C7×#10624886 #19100295

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624886 #19100295