Finite Group Databasebeta

← C7×#10624851 #19100260

Subgroups — C7×#10624851 #19100260

Order 5103.

200 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#6913C312yesmaximal, complemented
2C7×#6911C311yesmaximal, characteristic, complemented
3C7×#6900C311yesmaximal, characteristic, complemented
4C7×#6883C312yesmaximal, complemented
5C7×#6881C314yesmaximal, complemented
6C7×#6879C311yesmaximal, characteristic, complemented
7C7×#6878C312yesmaximal, complemented
8#10624851C711yesmaximal, characteristic, direct product factor, Sylow
9C7×#737—32no—
10C3×C7×3−1+2—31no—
11C3×C7×3−1+2C3211yescharacteristic
12C3×C7×H(3,𝔽3)—31no—
13C7×#733C3214yescomplemented
14C7×#732—32no—
15C7×#732C3212yes—
16C7×#732C3211yescharacteristic
17C7×#732C3212yescomplemented
18C7×#731—32no—
19C7×AΣL(1,𝔽27)—32no—
20C7×C9⋊C9—32no—
21C7×C9⋊C9C3212yescomplemented
22C7×C92C3211yescharacteristic, complemented
23#6913C3×C712yescomplemented
24#6911C3×C711yescharacteristic, complemented
25#6900C3×C711yescharacteristic, complemented
26#6883C3×C712yescomplemented
27#6881C3×C714yescomplemented
28#6879C3×C711yescharacteristic, complemented
29#6878C3×C712yescomplemented
30C33×C7—91no—
31C33×C7H(3,𝔽3)11yescharacteristic
32C7×3−1+2—34no—
33C7×3−1+2—91no—
34C7×3−1+2—93no—
35C7×3−1+2—94no—
36C7×H(3,𝔽3)—32no—
37C7×H(3,𝔽3)—32no—
38C7×H(3,𝔽3)—31no—
39C7×H(3,𝔽3)—92no—
40C3×C7×C9—31no—
41C3×C7×C9—32no—
42C3×C7×C9—92no—
43C3×C7×C9H(3,𝔽3)12yes—
44C3×C7×C9C3311yescharacteristic
45#737—32no—
46C3×3−1+2—31no—
47C3×3−1+2C32×C711yescharacteristic
48C3×H(3,𝔽3)—31no—
49#733C32×C714yescomplemented
50#732—32no—
51#732C32×C712yes—
52#732C32×C711yescharacteristic
53#732C32×C712yescomplemented
54#731—32no—
55AΣL(1,𝔽27)—32no—
56C9⋊C9—32no—
57C9⋊C9C32×C712yescomplemented
58C92C32×C711yescharacteristic, complemented
59C32×C7—31no—
60C32×C7—91no—
61C32×C7—92no—
62C32×C7—92no—
63C32×C7—91no—
64C32×C7—273no—
65C32×C7C3×H(3,𝔽3)11yescharacteristic
66C7×C9—33no—
67C7×C9—32no—
68C7×C9—31no—
69C7×C9—92no—
70C7×C9—94no—
71C33—91no—
72C33C7×H(3,𝔽3)11yescharacteristic
733−1+2—34no—
743−1+2—91no—
753−1+2—93no—
763−1+2—94no—
77H(3,𝔽3)—32no—
78H(3,𝔽3)—32no—
79H(3,𝔽3)—31no—
80H(3,𝔽3)—92no—
81C3×C9—31no—
82C3×C9—32no—
83C3×C9—92no—
84C3×C9C7×H(3,𝔽3)12yes—
85C3×C9C33×C711yescharacteristic
86C3×C7—31no—
87C3×C7—91no—
88C3×C7—272no—
89C3×C7—272no—
90C3×C7—271no—
91C3×C7#691111yescharacteristic
92C32—31no—
93C32—91no—
94C32—92no—
95C32—92no—
96C32—91no—
97C32—273no—
98C32C3×C7×H(3,𝔽3)11yescharacteristic
99C9—33no—
100C9—32no—
101C9—31no—
102C9—92no—
103C9—94no—
104C7#1062485111yescharacteristic, direct product factor, Sylow
105C3—31no—
106C3—91no—
107C3—272no—
108C3—271no—
109C3—272no—
110C3C7×#691111yescharacteristic
subgroupG/H
center, socleC3×C7#6911
commutator, FrattiniC3×C9C33×C7
LCSG ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1
UCSC1 ◁ C3×C7 ◁ C32×C7 ◁ C3×C7×3−1+2 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#6913C3semidirect
2. C7×#6911C3semidirect
3. C7×#6900C3semidirect
4. C7×#6883C3semidirect
5. C7×#6881C3semidirect
6. C7×#6879C3semidirect
7. C7×#6878C3semidirect
8. #10624851C7direct (N × H)
13. C7×#733C32semidirect
17. C7×#732C32semidirect
21. C7×C9⋊C9C32semidirect
22. C7×C92C32semidirect
23. #6913C3×C7semidirect
24. #6911C3×C7semidirect
25. #6900C3×C7semidirect
26. #6883C3×C7semidirect
27. #6881C3×C7semidirect
28. #6879C3×C7semidirect
29. #6878C3×C7semidirect
49. #733C32×C7semidirect
53. #732C32×C7semidirect
57. C9⋊C9C32×C7semidirect
58. C92C32×C7semidirect
104. C7#10624851direct (N × H)