Subgroups — C₇×#10624930 #19100339

Order 5103.

1118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×3₋¹⁺⁴	C₃	1	2	yes	maximal, complemented
2	C₇×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×#6909	C₃	1	24	yes	maximal, complemented
5	C₃×C₇×AΣL(1,𝔽₂₇)	C₃	1	12	yes	maximal, complemented
6	#10624930	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃⁴×C₇	C₃²	1	4	yes	complemented
8	C₇×#737	—	3	18	no	—
9	C₃×C₇×3₋¹⁺²	C₃²	1	24	yes	complemented
10	C₃×C₇×H(3,𝔽₃)	—	3	9	no	—
11	C₃×C₇×H(3,𝔽₃)	—	3	9	no	—
12	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
13	C₃×C₇×H(3,𝔽₃)	C₃²	1	8	yes	complemented
14	C₃×C₇×H(3,𝔽₃)	C₃²	1	12	yes	complemented
15	C₇×AΣL(1,𝔽₂₇)	C₃²	1	9	yes	complemented
16	C₇×AΣL(1,𝔽₂₇)	C₃²	1	72	yes	complemented
17	3₋¹⁺⁴	C₃×C₇	1	2	yes	complemented
18	H(5,𝔽₃)	C₃×C₇	1	1	yes	characteristic, complemented
19	C₃²×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic, complemented
20	#6909	C₃×C₇	1	24	yes	complemented
21	C₃×AΣL(1,𝔽₂₇)	C₃×C₇	1	12	yes	complemented
22	C₃³×C₇	—	3	12	no	—
23	C₃³×C₇	—	3	12	no	—
24	C₃³×C₇	—	9	12	no	—
25	C₃³×C₇	C₃³	1	1	yes	characteristic
26	C₃³×C₇	C₃³	1	8	yes	—
27	C₃³×C₇	C₃³	1	4	yes	—
28	C₇×3₋¹⁺²	—	3	48	no	—
29	C₇×3₋¹⁺²	C₃³	1	18	yes	—
30	C₇×H(3,𝔽₃)	—	3	24	no	—
31	C₇×H(3,𝔽₃)	—	3	24	no	—
32	C₇×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
33	C₇×H(3,𝔽₃)	C₃³	1	9	yes	—
34	C₃×C₇×C₉	—	3	24	no	—
35	C₃⁴	C₃²×C₇	1	4	yes	complemented
36	#737	—	3	18	no	—
37	C₃×3₋¹⁺²	C₃²×C₇	1	24	yes	complemented
38	C₃×H(3,𝔽₃)	—	3	9	no	—
39	C₃×H(3,𝔽₃)	—	3	9	no	—
40	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
41	C₃×H(3,𝔽₃)	C₃²×C₇	1	8	yes	complemented
42	C₃×H(3,𝔽₃)	C₃²×C₇	1	12	yes	complemented
43	AΣL(1,𝔽₂₇)	C₃²×C₇	1	9	yes	complemented
44	AΣL(1,𝔽₂₇)	C₃²×C₇	1	72	yes	complemented
45	C₃²×C₇	—	3	3	no	—
46	C₃²×C₇	—	3	1	no	—
47	C₃²×C₇	—	3	8	no	—
48	C₃²×C₇	—	3	9	no	—
49	C₃²×C₇	—	9	4	no	—
50	C₃²×C₇	—	9	36	no	—
51	C₃²×C₇	—	9	8	no	—
52	C₃²×C₇	—	27	12	no	—
53	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
54	C₃²×C₇	C₃⁴	1	1	yes	characteristic
55	C₇×C₉	—	3	18	no	—
56	C₃³	—	3	12	no	—
57	C₃³	—	3	12	no	—
58	C₃³	—	9	12	no	—
59	C₃³	C₃³×C₇	1	1	yes	characteristic
60	C₃³	C₃³×C₇	1	8	yes	—
61	C₃³	C₃³×C₇	1	4	yes	—
62	3₋¹⁺²	—	3	48	no	—
63	3₋¹⁺²	C₃³×C₇	1	18	yes	—
64	H(3,𝔽₃)	—	3	24	no	—
65	H(3,𝔽₃)	—	3	24	no	—
66	H(3,𝔽₃)	C₇×H(3,𝔽₃)	1	9	yes	—
67	H(3,𝔽₃)	C₃³×C₇	1	9	yes	—
68	C₃×C₉	—	3	24	no	—
69	C₃×C₇	—	3	3	no	—
70	C₃×C₇	—	3	1	no	—
71	C₃×C₇	—	3	12	no	—
72	C₃×C₇	—	9	8	no	—
73	C₃×C₇	—	9	9	no	—
74	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
75	C₃²	—	3	3	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	8	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	9	4	no	—
80	C₃²	—	9	36	no	—
81	C₃²	—	9	8	no	—
82	C₃²	—	27	12	no	—
83	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
84	C₃²	C₃⁴×C₇	1	1	yes	characteristic
85	C₉	—	3	18	no	—
86	C₇	#10624930	1	1	yes	characteristic, direct product factor, Sylow
87	C₃	—	3	1	no	—
88	C₃	—	3	3	no	—
89	C₃	—	3	12	no	—
90	C₃	—	9	8	no	—
91	C₃	—	9	9	no	—
92	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₇	C₃²×H(3,𝔽₃)
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ C₃×C₇×H(3,𝔽₃) ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×3₋¹⁺⁴	C₃	semidirect
2. C₇×H(5,𝔽₃)	C₃	semidirect
3. C₃²×C₇×H(3,𝔽₃)	C₃	semidirect
4. C₇×#6909	C₃	semidirect
5. C₃×C₇×AΣL(1,𝔽₂₇)	C₃	semidirect
6. #10624930	C₇	direct (N × H)
7. C₃⁴×C₇	C₃²	semidirect
9. C₃×C₇×3₋¹⁺²	C₃²	semidirect
13. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
14. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
15. C₇×AΣL(1,𝔽₂₇)	C₃²	semidirect
16. C₇×AΣL(1,𝔽₂₇)	C₃²	semidirect
17. 3₋¹⁺⁴	C₃×C₇	semidirect
18. H(5,𝔽₃)	C₃×C₇	semidirect
19. C₃²×H(3,𝔽₃)	C₃×C₇	semidirect
20. #6909	C₃×C₇	semidirect
21. C₃×AΣL(1,𝔽₂₇)	C₃×C₇	semidirect
35. C₃⁴	C₃²×C₇	semidirect
37. C₃×3₋¹⁺²	C₃²×C₇	semidirect
41. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
42. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
43. AΣL(1,𝔽₂₇)	C₃²×C₇	semidirect
44. AΣL(1,𝔽₂₇)	C₃²×C₇	semidirect
86. C₇	#10624930	direct (N × H)

Subgroups — C7×#10624930 #19100339

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624930 #19100339