Subgroups — C₇×#10624912 #19100321

Order 5103.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6900	C₃	1	9	yes	maximal, complemented
2	C₇×#6898	C₃	1	9	yes	maximal, complemented
3	C₇×#6897	C₃	1	18	yes	maximal, complemented
4	C₇×#6891	C₃	1	4	yes	maximal
5	#10624912	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×3₋¹⁺²	C₃²	1	12	yes	—
8	C₇×C₉⋊C₉	C₃²	1	72	yes	complemented
9	C₇×C₃²⋊C₉	C₃²	1	24	yes	—
10	C₇×C₃²⋊C₉	C₃²	1	12	yes	—
11	C₇×C₉²	C₃²	1	9	yes	complemented
12	#6900	C₃×C₇	1	9	yes	complemented
13	#6898	C₃×C₇	1	9	yes	complemented
14	#6897	C₃×C₇	1	18	yes	complemented
15	#6891	C₃×C₇	1	4	yes	—
16	C₃³×C₇	—	9	4	no	—
17	C₃³×C₇	C₃³	1	2	yes	—
18	C₃³×C₇	C₃³	1	1	yes	characteristic
19	C₃³×C₇	C₃³	1	1	yes	characteristic
20	C₇×3₋¹⁺²	—	9	12	no	—
21	C₃×C₇×C₉	C₃³	1	36	yes	—
22	C₃⁴	C₃²×C₇	1	1	yes	characteristic
23	C₃×3₋¹⁺²	C₃²×C₇	1	12	yes	—
24	C₉⋊C₉	C₃²×C₇	1	72	yes	complemented
25	C₃²⋊C₉	C₃²×C₇	1	24	yes	—
26	C₃²⋊C₉	C₃²×C₇	1	12	yes	—
27	C₉²	C₃²×C₇	1	9	yes	complemented
28	C₃²×C₇	—	3	4	no	—
29	C₃²×C₇	—	3	8	no	—
30	C₃²×C₇	—	3	4	no	—
31	C₃²×C₇	—	9	9	no	—
32	C₃²×C₇	C₃⁴	1	1	yes	characteristic
33	C₇×C₉	—	3	36	no	—
34	C₃³	—	9	4	no	—
35	C₃³	C₃³×C₇	1	2	yes	—
36	C₃³	C₃³×C₇	1	1	yes	characteristic
37	C₃³	C₃³×C₇	1	1	yes	characteristic
38	3₋¹⁺²	—	9	12	no	—
39	C₃×C₉	C₃³×C₇	1	36	yes	—
40	C₃×C₇	—	9	1	no	—
41	C₃×C₇	—	9	2	no	—
42	C₃×C₇	—	9	1	no	—
43	C₃×C₇	3₋¹⁺⁴	1	4	yes	—
44	C₃²	—	3	4	no	—
45	C₃²	—	3	8	no	—
46	C₃²	—	3	4	no	—
47	C₃²	—	9	9	no	—
48	C₃²	C₃⁴×C₇	1	1	yes	characteristic
49	C₉	—	3	36	no	—
50	C₇	#10624912	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	9	1	no	—
52	C₃	—	9	2	no	—
53	C₃	—	9	1	no	—
54	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×#6900	C₃	semidirect
2. C₇×#6898	C₃	semidirect
3. C₇×#6897	C₃	semidirect
5. #10624912	C₇	direct (N × H)
8. C₇×C₉⋊C₉	C₃²	semidirect
11. C₇×C₉²	C₃²	semidirect
12. #6900	C₃×C₇	semidirect
13. #6898	C₃×C₇	semidirect
14. #6897	C₃×C₇	semidirect
24. C₉⋊C₉	C₃²×C₇	semidirect
27. C₉²	C₃²×C₇	semidirect
50. C₇	#10624912	direct (N × H)

Subgroups — C7×#10624912 #19100321

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624912 #19100321