Subgroups — C₇×#10624837 #19100246

Order 5103.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6908	C₃	1	3	yes	maximal, complemented
2	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#6880	C₃	1	2	yes	maximal, complemented
4	C₇×#6879	C₃	1	1	yes	maximal, characteristic, complemented
5	C₇×#6878	C₃	1	6	yes	maximal, complemented
6	#10624837	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₇×#737	—	3	3	no	—
8	C₃²×C₇×C₉	—	3	1	no	—
9	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
10	C₇×#733	C₃²	1	6	yes	—
11	C₇×#732	C₃²	1	3	yes	—
12	C₇×#731	—	3	3	no	—
13	C₇×AΣL(1,𝔽₂₇)	—	3	3	no	—
14	C₇×C₉²	—	3	1	no	—
15	C₇×C₉²	—	3	1	no	—
16	C₇×C₉²	C₃²	1	2	yes	—
17	C₇×C₉²	C₃²	1	1	yes	characteristic
18	#6908	C₃×C₇	1	3	yes	complemented
19	C₃×C₉²	C₃×C₇	1	1	yes	characteristic, complemented
20	#6880	C₃×C₇	1	2	yes	complemented
21	#6879	C₃×C₇	1	1	yes	characteristic, complemented
22	#6878	C₃×C₇	1	6	yes	complemented
23	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
24	C₇×3₋¹⁺²	—	3	6	no	—
25	C₇×3₋¹⁺²	—	9	6	no	—
26	C₇×H(3,𝔽₃)	—	3	3	no	—
27	C₃×C₇×C₉	—	3	9	no	—
28	C₃×C₇×C₉	—	3	2	no	—
29	C₃×C₇×C₉	—	3	1	no	—
30	C₃×C₇×C₉	—	3	2	no	—
31	C₃×C₇×C₉	—	3	1	no	—
32	C₃×C₇×C₉	—	9	3	no	—
33	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
34	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
36	#737	—	3	3	no	—
37	C₃²×C₉	—	3	1	no	—
38	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
39	#733	C₃²×C₇	1	6	yes	—
40	#732	C₃²×C₇	1	3	yes	—
41	#731	—	3	3	no	—
42	AΣL(1,𝔽₂₇)	—	3	3	no	—
43	C₉²	—	3	1	no	—
44	C₉²	—	3	1	no	—
45	C₉²	C₃²×C₇	1	2	yes	—
46	C₉²	C₃²×C₇	1	1	yes	characteristic
47	C₃²×C₇	—	3	3	no	—
48	C₃²×C₇	—	3	1	no	—
49	C₃²×C₇	—	9	3	no	—
50	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₇×C₉	—	3	6	no	—
52	C₇×C₉	—	3	3	no	—
53	C₇×C₉	—	3	1	no	—
54	C₇×C₉	—	3	1	no	—
55	C₇×C₉	—	9	6	no	—
56	C₇×C₉	#732	1	2	yes	—
57	C₇×C₉	#732	1	1	yes	characteristic
58	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
59	3₋¹⁺²	—	3	6	no	—
60	3₋¹⁺²	—	9	6	no	—
61	H(3,𝔽₃)	—	3	3	no	—
62	C₃×C₉	—	3	9	no	—
63	C₃×C₉	—	3	2	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	9	3	no	—
68	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
69	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
70	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
71	C₃×C₇	—	3	1	no	—
72	C₃×C₇	—	3	3	no	—
73	C₃×C₇	—	27	3	no	—
74	C₃×C₇	C₃×#732	1	1	yes	characteristic
75	C₃²	—	3	3	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	9	3	no	—
78	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
79	C₉	—	3	6	no	—
80	C₉	—	3	3	no	—
81	C₉	—	3	1	no	—
82	C₉	—	3	1	no	—
83	C₉	—	9	6	no	—
84	C₉	C₇×#732	1	2	yes	—
85	C₉	C₇×#732	1	1	yes	characteristic
86	C₇	#10624837	1	1	yes	characteristic, direct product factor, Sylow
87	C₃	—	3	1	no	—
88	C₃	—	3	3	no	—
89	C₃	—	27	3	no	—
90	C₃	C₃×C₇×#732	1	1	yes	characteristic

	subgroup	G/H
center	C₇×C₉	#732
commutator, Frattini	C₃×C₉	C₃³×C₇
socle	C₃×C₇	C₃×#732
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₇×C₉ ◁ C₃×C₇×C₉ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#6908	C₃	semidirect
2. C₃×C₇×C₉²	C₃	semidirect
3. C₇×#6880	C₃	semidirect
4. C₇×#6879	C₃	semidirect
5. C₇×#6878	C₃	semidirect
6. #10624837	C₇	direct (N × H)
18. #6908	C₃×C₇	semidirect
19. C₃×C₉²	C₃×C₇	semidirect
20. #6880	C₃×C₇	semidirect
21. #6879	C₃×C₇	semidirect
22. #6878	C₃×C₇	semidirect
86. C₇	#10624837	direct (N × H)

Subgroups — C7×#10624837 #19100246

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624837 #19100246