Subgroups — C₇×#10624883 #19100292

Order 5103.

926 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
3	C₇×#6891	C₃	1	9	yes	maximal, complemented
4	C₃×C₇×C₃²⋊C₉	C₃	1	3	yes	maximal, complemented
5	#10624883	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	3	yes	—
7	C₃⁴×C₇	C₃²	1	1	yes	characteristic
8	C₃×C₇×3₋¹⁺²	C₃²	1	27	yes	complemented
9	C₃×C₇×H(3,𝔽₃)	—	3	9	no	—
10	C₃×C₇×H(3,𝔽₃)	C₃²	1	9	yes	—
11	C₃²×C₇×C₉	C₃²	1	9	yes	complemented
12	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
13	C₇×C₃²⋊C₉	C₃²	1	18	yes	complemented
14	C₇×C₃²⋊C₉	C₃²	1	54	yes	complemented
15	C₃²×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
16	C₉⋊H(3,𝔽₃)	C₃×C₇	1	27	yes	complemented
17	#6891	C₃×C₇	1	9	yes	complemented
18	C₃×C₃²⋊C₉	C₃×C₇	1	3	yes	complemented
19	C₃³×C₇	—	3	9	no	—
20	C₃³×C₇	—	9	1	no	—
21	C₃³×C₇	—	9	3	no	—
22	C₃³×C₇	—	9	2	no	—
23	C₃³×C₇	—	9	6	no	—
24	C₃³×C₇	3₋¹⁺²	1	9	yes	complemented
25	C₃³×C₇	C₃³	1	9	yes	—
26	C₃³×C₇	C₃³	1	1	yes	characteristic
27	C₃³×C₇	C₃³	1	3	yes	—
28	C₇×3₋¹⁺²	—	9	27	no	—
29	C₇×H(3,𝔽₃)	—	3	27	no	—
30	C₃×C₇×C₉	—	9	9	no	—
31	C₃×C₇×C₉	C₃³	1	27	yes	—
32	C₃⁴	C₃²×C₇	1	3	yes	—
33	C₃⁴	C₃²×C₇	1	1	yes	characteristic
34	C₃×3₋¹⁺²	C₃²×C₇	1	27	yes	complemented
35	C₃×H(3,𝔽₃)	—	3	9	no	—
36	C₃×H(3,𝔽₃)	C₃²×C₇	1	9	yes	—
37	C₃²×C₉	C₃²×C₇	1	9	yes	complemented
38	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
39	C₃²⋊C₉	C₃²×C₇	1	18	yes	complemented
40	C₃²⋊C₉	C₃²×C₇	1	54	yes	complemented
41	C₃²×C₇	—	3	3	no	—
42	C₃²×C₇	—	3	1	no	—
43	C₃²×C₇	—	3	2	no	—
44	C₃²×C₇	—	3	6	no	—
45	C₃²×C₇	—	3	9	no	—
46	C₃²×C₇	—	3	9	no	—
47	C₃²×C₇	—	3	18	no	—
48	C₃²×C₇	—	9	9	no	—
49	C₃²×C₇	—	9	27	no	—
50	C₃²×C₇	C₃×3₋¹⁺²	1	9	yes	—
51	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
52	C₃²×C₇	C₃⁴	1	1	yes	characteristic
53	C₇×C₉	—	3	27	no	—
54	C₃³	—	3	9	no	—
55	C₃³	—	9	1	no	—
56	C₃³	—	9	3	no	—
57	C₃³	—	9	2	no	—
58	C₃³	—	9	6	no	—
59	C₃³	C₇×3₋¹⁺²	1	9	yes	complemented
60	C₃³	C₃³×C₇	1	9	yes	—
61	C₃³	C₃³×C₇	1	1	yes	characteristic
62	C₃³	C₃³×C₇	1	3	yes	—
63	3₋¹⁺²	—	9	27	no	—
64	H(3,𝔽₃)	—	3	27	no	—
65	C₃×C₉	—	9	9	no	—
66	C₃×C₉	C₃³×C₇	1	27	yes	—
67	C₃×C₇	—	3	3	no	—
68	C₃×C₇	—	3	9	no	—
69	C₃×C₇	—	9	9	no	—
70	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
71	C₃×C₇	H(5,𝔽₃)	1	1	yes	characteristic
72	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
73	C₃²	—	3	3	no	—
74	C₃²	—	3	1	no	—
75	C₃²	—	3	2	no	—
76	C₃²	—	3	6	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	18	no	—
80	C₃²	—	9	9	no	—
81	C₃²	—	9	27	no	—
82	C₃²	C₃×C₇×3₋¹⁺²	1	9	yes	—
83	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
84	C₃²	C₃⁴×C₇	1	1	yes	characteristic
85	C₉	—	3	27	no	—
86	C₇	#10624883	1	1	yes	characteristic, direct product factor, Sylow
87	C₃	—	3	3	no	—
88	C₃	—	3	9	no	—
89	C₃	—	9	9	no	—
90	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
91	C₃	C₇×H(5,𝔽₃)	1	1	yes	characteristic
92	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
2. C₇×C₉⋊H(3,𝔽₃)	C₃	semidirect
3. C₇×#6891	C₃	semidirect
4. C₃×C₇×C₃²⋊C₉	C₃	semidirect
5. #10624883	C₇	direct (N × H)
8. C₃×C₇×3₋¹⁺²	C₃²	semidirect
11. C₃²×C₇×C₉	C₃²	semidirect
13. C₇×C₃²⋊C₉	C₃²	semidirect
14. C₇×C₃²⋊C₉	C₃²	semidirect
16. C₉⋊H(3,𝔽₃)	C₃×C₇	semidirect
17. #6891	C₃×C₇	semidirect
18. C₃×C₃²⋊C₉	C₃×C₇	semidirect
24. C₃³×C₇	3₋¹⁺²	semidirect
34. C₃×3₋¹⁺²	C₃²×C₇	semidirect
37. C₃²×C₉	C₃²×C₇	semidirect
39. C₃²⋊C₉	C₃²×C₇	semidirect
40. C₃²⋊C₉	C₃²×C₇	semidirect
59. C₃³	C₇×3₋¹⁺²	semidirect
86. C₇	#10624883	direct (N × H)

Subgroups — C7×#10624883 #19100292

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624883 #19100292