Subgroups — C₇×#10624913 #19100322

Order 5103.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6898	C₃	1	18	yes	maximal, complemented
2	C₇×#6896	C₃	1	18	yes	maximal, complemented
3	C₇×#6891	C₃	1	4	yes	maximal
4	#10624913	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	C₃²	1	1	yes	characteristic
6	C₃×C₇×3₋¹⁺²	C₃²	1	12	yes	—
7	C₇×C₉⋊C₉	C₃²	1	72	yes	complemented
8	C₇×C₃²⋊C₉	C₃²	1	12	yes	—
9	C₇×C₃²⋊C₉	C₃²	1	24	yes	—
10	C₇×C₉²	C₃²	1	9	yes	complemented
11	#6898	C₃×C₇	1	18	yes	complemented
12	#6896	C₃×C₇	1	18	yes	complemented
13	#6891	C₃×C₇	1	4	yes	—
14	C₃³×C₇	—	9	4	no	—
15	C₃³×C₇	C₃³	1	2	yes	—
16	C₃³×C₇	C₃³	1	2	yes	—
17	C₇×3₋¹⁺²	—	9	12	no	—
18	C₃×C₇×C₉	C₃³	1	36	yes	—
19	C₃⁴	C₃²×C₇	1	1	yes	characteristic
20	C₃×3₋¹⁺²	C₃²×C₇	1	12	yes	—
21	C₉⋊C₉	C₃²×C₇	1	72	yes	complemented
22	C₃²⋊C₉	C₃²×C₇	1	12	yes	—
23	C₃²⋊C₉	C₃²×C₇	1	24	yes	—
24	C₉²	C₃²×C₇	1	9	yes	complemented
25	C₃²×C₇	—	3	4	no	—
26	C₃²×C₇	—	3	8	no	—
27	C₃²×C₇	—	3	4	no	—
28	C₃²×C₇	—	9	9	no	—
29	C₃²×C₇	C₃⁴	1	1	yes	characteristic
30	C₇×C₉	—	3	36	no	—
31	C₃³	—	9	4	no	—
32	C₃³	C₃³×C₇	1	2	yes	—
33	C₃³	C₃³×C₇	1	2	yes	—
34	3₋¹⁺²	—	9	12	no	—
35	C₃×C₉	C₃³×C₇	1	36	yes	—
36	C₃×C₇	—	9	2	no	—
37	C₃×C₇	—	9	2	no	—
38	C₃×C₇	3₋¹⁺⁴	1	4	yes	—
39	C₃²	—	3	4	no	—
40	C₃²	—	3	8	no	—
41	C₃²	—	3	4	no	—
42	C₃²	—	9	9	no	—
43	C₃²	C₃⁴×C₇	1	1	yes	characteristic
44	C₉	—	3	36	no	—
45	C₇	#10624913	1	1	yes	characteristic, direct product factor, Sylow
46	C₃	—	9	2	no	—
47	C₃	—	9	2	no	—
48	C₃	C₇×3₋¹⁺⁴	1	4	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
4. #10624913	C₇	direct (N × H)
7. C₇×C₉⋊C₉	C₃²	semidirect
10. C₇×C₉²	C₃²	semidirect
11. #6898	C₃×C₇	semidirect
12. #6896	C₃×C₇	semidirect
21. C₉⋊C₉	C₃²×C₇	semidirect
24. C₉²	C₃²×C₇	semidirect
45. C₇	#10624913	direct (N × H)

Subgroups — C7×#10624913 #19100322

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624913 #19100322