Subgroups — C₇×#10624849 #19100258

Order 5103.

188 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	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#6883	C₃	1	3	yes	maximal, complemented
4	C₇×#6882	C₃	1	3	yes	maximal, complemented
5	C₇×#6881	C₃	1	3	yes	maximal, complemented
6	#10624849	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₇×#737	—	3	3	no	—
8	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
9	C₇×#733	C₃²	1	3	yes	—
10	C₇×#733	C₃²	1	3	yes	—
11	C₇×#732	C₃²	1	3	yes	—
12	C₇×#731	—	3	3	no	—
13	C₇×AΣL(1,𝔽₂₇)	—	3	3	no	—
14	C₇×C₉⋊C₉	—	3	1	no	—
15	C₇×C₉⋊C₉	C₃²	1	3	yes	—
16	C₇×C₃²⋊C₉	—	3	1	no	—
17	C₇×C₉²	—	3	1	no	—
18	#6908	C₃×C₇	1	3	yes	complemented
19	#6887	C₃×C₇	1	1	yes	characteristic, complemented
20	#6883	C₃×C₇	1	3	yes	complemented
21	#6882	C₃×C₇	1	3	yes	complemented
22	#6881	C₃×C₇	1	3	yes	complemented
23	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
24	C₇×3₋¹⁺²	—	3	3	no	—
25	C₇×3₋¹⁺²	—	3	3	no	—
26	C₇×3₋¹⁺²	—	9	6	no	—
27	C₇×H(3,𝔽₃)	—	3	3	no	—
28	C₃×C₇×C₉	—	3	3	no	—
29	C₃×C₇×C₉	—	3	3	no	—
30	C₃×C₇×C₉	—	9	3	no	—
31	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
32	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
33	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
34	#737	—	3	3	no	—
35	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
36	#733	C₃²×C₇	1	3	yes	—
37	#733	C₃²×C₇	1	3	yes	—
38	#732	C₃²×C₇	1	3	yes	—
39	#731	—	3	3	no	—
40	AΣL(1,𝔽₂₇)	—	3	3	no	—
41	C₉⋊C₉	—	3	1	no	—
42	C₉⋊C₉	C₃²×C₇	1	3	yes	—
43	C₃²⋊C₉	—	3	1	no	—
44	C₉²	—	3	1	no	—
45	C₃²×C₇	—	3	1	no	—
46	C₃²×C₇	—	9	1	no	—
47	C₃²×C₇	—	9	3	no	—
48	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
49	C₇×C₉	—	3	1	no	—
50	C₇×C₉	—	3	1	no	—
51	C₇×C₉	—	9	3	no	—
52	C₇×C₉	—	9	3	no	—
53	C₇×C₉	—	9	3	no	—
54	C₇×C₉	#732	1	3	yes	—
55	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
56	3₋¹⁺²	—	3	3	no	—
57	3₋¹⁺²	—	3	3	no	—
58	3₋¹⁺²	—	9	6	no	—
59	H(3,𝔽₃)	—	3	3	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	9	3	no	—
63	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
64	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
65	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
66	C₃×C₇	—	3	1	no	—
67	C₃×C₇	—	9	1	no	—
68	C₃×C₇	—	27	3	no	—
69	C₃×C₇	C₃×#732	1	1	yes	characteristic
70	C₃²	—	3	1	no	—
71	C₃²	—	9	1	no	—
72	C₃²	—	9	3	no	—
73	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
74	C₉	—	3	1	no	—
75	C₉	—	3	1	no	—
76	C₉	—	9	3	no	—
77	C₉	—	9	3	no	—
78	C₉	—	9	3	no	—
79	C₉	C₇×#732	1	3	yes	—
80	C₇	#10624849	1	1	yes	characteristic, direct product factor, Sylow
81	C₃	—	3	1	no	—
82	C₃	—	9	1	no	—
83	C₃	—	27	3	no	—
84	C₃	C₃×C₇×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₇	C₃×#732
commutator, Frattini	C₃×C₉	C₃³×C₇
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ 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. C₇×#6887	C₃	semidirect
3. C₇×#6883	C₃	semidirect
4. C₇×#6882	C₃	semidirect
5. C₇×#6881	C₃	semidirect
6. #10624849	C₇	direct (N × H)
18. #6908	C₃×C₇	semidirect
19. #6887	C₃×C₇	semidirect
20. #6883	C₃×C₇	semidirect
21. #6882	C₃×C₇	semidirect
22. #6881	C₃×C₇	semidirect
80. C₇	#10624849	direct (N × H)

Subgroups — C7×#10624849 #19100258

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624849 #19100258