Subgroups — C₇×#10624894 #19100303

Order 5103.

1148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#737	C₃	1	3	yes	maximal, complemented
2	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₇×#6893	C₃	1	24	yes	maximal, complemented
4	C₇×#6891	C₃	1	8	yes	maximal, complemented
5	C₃×C₇×C₃²⋊C₉	C₃	1	4	yes	maximal, complemented
6	#10624894	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃⁴×C₇	C₃²	1	4	yes	—
8	C₇×#737	—	3	27	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)	C₃²	1	8	yes	—
12	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
13	C₃²×C₇×C₉	C₃²	1	12	yes	complemented
14	C₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
15	C₇×C₃²⋊C₉	C₃²	1	8	yes	—
16	C₇×C₃²⋊C₉	C₃²	1	24	yes	complemented
17	C₇×C₃²⋊C₉	C₃²	1	48	yes	complemented
18	C₃×#737	C₃×C₇	1	3	yes	complemented
19	C₃²×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
20	#6893	C₃×C₇	1	24	yes	complemented
21	#6891	C₃×C₇	1	8	yes	complemented
22	C₃×C₃²⋊C₉	C₃×C₇	1	4	yes	complemented
23	C₃³×C₇	—	3	12	no	—
24	C₃³×C₇	—	3	12	no	—
25	C₃³×C₇	—	9	8	no	—
26	C₃³×C₇	C₃³	1	8	yes	—
27	C₃³×C₇	C₃³	1	4	yes	—
28	C₃³×C₇	C₃³	1	1	yes	characteristic
29	C₇×3₋¹⁺²	—	3	72	no	—
30	C₇×H(3,𝔽₃)	—	3	24	no	—
31	C₇×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
32	C₃×C₇×C₉	—	3	36	no	—
33	C₃×C₇×C₉	C₃³	1	3	yes	—
34	C₃×C₇×C₉	C₃³	1	24	yes	—
35	C₃⁴	C₃²×C₇	1	4	yes	—
36	#737	—	3	27	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)	C₃²×C₇	1	8	yes	—
40	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
41	C₃²×C₉	C₃²×C₇	1	12	yes	complemented
42	C₃²⋊C₉	C₃²×C₇	1	1	yes	characteristic
43	C₃²⋊C₉	C₃²×C₇	1	8	yes	—
44	C₃²⋊C₉	C₃²×C₇	1	24	yes	complemented
45	C₃²⋊C₉	C₃²×C₇	1	48	yes	complemented
46	C₃²×C₇	—	3	1	no	—
47	C₃²×C₇	—	3	4	no	—
48	C₃²×C₇	—	3	2	no	—
49	C₃²×C₇	—	3	8	no	—
50	C₃²×C₇	—	3	8	no	—
51	C₃²×C₇	—	3	8	no	—
52	C₃²×C₇	—	3	16	no	—
53	C₃²×C₇	—	9	36	no	—
54	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
55	C₃²×C₇	#737	1	3	yes	complemented
56	C₃²×C₇	C₃⁴	1	1	yes	characteristic
57	C₇×C₉	—	3	3	no	—
58	C₇×C₉	—	3	24	no	—
59	C₃³	—	3	12	no	—
60	C₃³	—	3	12	no	—
61	C₃³	—	9	8	no	—
62	C₃³	C₃³×C₇	1	8	yes	—
63	C₃³	C₃³×C₇	1	4	yes	—
64	C₃³	C₃³×C₇	1	1	yes	characteristic
65	3₋¹⁺²	—	3	72	no	—
66	H(3,𝔽₃)	—	3	24	no	—
67	H(3,𝔽₃)	C₇×H(3,𝔽₃)	1	9	yes	—
68	C₃×C₉	—	3	36	no	—
69	C₃×C₉	C₃³×C₇	1	3	yes	—
70	C₃×C₉	C₃³×C₇	1	24	yes	—
71	C₃×C₇	—	3	3	no	—
72	C₃×C₇	—	3	12	no	—
73	C₃×C₇	—	9	8	no	—
74	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
75	C₃×C₇	C₃×#737	1	1	yes	characteristic
76	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
77	C₃²	—	3	1	no	—
78	C₃²	—	3	4	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	8	no	—
81	C₃²	—	3	8	no	—
82	C₃²	—	3	8	no	—
83	C₃²	—	3	16	no	—
84	C₃²	—	9	36	no	—
85	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
86	C₃²	C₇×#737	1	3	yes	complemented
87	C₃²	C₃⁴×C₇	1	1	yes	characteristic
88	C₉	—	3	3	no	—
89	C₉	—	3	24	no	—
90	C₇	#10624894	1	1	yes	characteristic, direct product factor, Sylow
91	C₃	—	3	3	no	—
92	C₃	—	3	12	no	—
93	C₃	—	9	8	no	—
94	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic
95	C₃	C₃×C₇×#737	1	1	yes	characteristic
96	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
1. C₃×C₇×#737	C₃	semidirect
3. C₇×#6893	C₃	semidirect
4. C₇×#6891	C₃	semidirect
5. C₃×C₇×C₃²⋊C₉	C₃	semidirect
6. #10624894	C₇	direct (N × H)
9. C₃×C₇×3₋¹⁺²	C₃²	semidirect
13. C₃²×C₇×C₉	C₃²	semidirect
16. C₇×C₃²⋊C₉	C₃²	semidirect
17. C₇×C₃²⋊C₉	C₃²	semidirect
18. C₃×#737	C₃×C₇	semidirect
20. #6893	C₃×C₇	semidirect
21. #6891	C₃×C₇	semidirect
22. C₃×C₃²⋊C₉	C₃×C₇	semidirect
37. C₃×3₋¹⁺²	C₃²×C₇	semidirect
41. C₃²×C₉	C₃²×C₇	semidirect
44. C₃²⋊C₉	C₃²×C₇	semidirect
45. C₃²⋊C₉	C₃²×C₇	semidirect
55. C₃²×C₇	#737	semidirect
86. C₃²	C₇×#737	semidirect
90. C₇	#10624894	direct (N × H)

Subgroups — C7×#10624894 #19100303

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624894 #19100303