Finite Group Databasebeta

← C7×#10624889 #19100298

Subgroups — C7×#10624889 #19100298

Order 5103.

620 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 440 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×#6897C3118yesmaximal, complemented
2C7×#6896C319yesmaximal, complemented
3C7×#6894C316yesmaximal, complemented
4C7×#6891C312yesmaximal
5C7×#6891C311yesmaximal, characteristic
6C7×C9×3−1+2C313yesmaximal, complemented
7C3×C7×C32⋊C9C311yesmaximal, characteristic
8#10624889C711yesmaximal, characteristic, direct product factor, Sylow
9C34×C7C3211yescharacteristic
10C3×C7×3−1+2C3213yes—
11C3×C7×3−1+2C3216yes—
12C32×C7×C9C3211yescharacteristic
13C32×C7×C9C3212yes—
14C7×C9⋊C9C32118yescomplemented
15C7×C9⋊C9C32154yescomplemented
16C7×C32⋊C9C3213yes—
17C7×C32⋊C9C3216yes—
18C7×C32⋊C9C3216yes—
19C7×C32⋊C9C3213yes—
20C7×C32⋊C9C3216yes—
21C7×C32⋊C9C32112yes—
22C7×C92C3219yescomplemented
23#6897C3×C7118yescomplemented
24#6896C3×C719yescomplemented
25#6894C3×C716yescomplemented
26#6891C3×C712yes—
27#6891C3×C711yescharacteristic
28C9×3−1+2C3×C713yescomplemented
29C3×C32⋊C9C3×C711yescharacteristic
30C33×C7—33no—
31C33×C7—91no—
32C33×C7—92no—
33C33×C7C3312yes—
34C33×C7C3311yescharacteristic
35C33×C7C3311yescharacteristic
36C7×3−1+2—39no—
37C7×3−1+2—96no—
38C3×C7×C9—91no—
39C3×C7×C9—92no—
40C3×C7×C9C3313yes—
41C3×C7×C9C3319yes—
42C3×C7×C9C33118yes—
43C3×C7×C9C3316yes—
44C34C32×C711yescharacteristic
45C3×3−1+2C32×C713yes—
46C3×3−1+2C32×C716yes—
47C32×C9C32×C711yescharacteristic
48C32×C9C32×C712yes—
49C9⋊C9C32×C7118yescomplemented
50C9⋊C9C32×C7154yescomplemented
51C32⋊C9C32×C713yes—
52C32⋊C9C32×C716yes—
53C32⋊C9C32×C716yes—
54C32⋊C9C32×C713yes—
55C32⋊C9C32×C716yes—
56C32⋊C9C32×C7112yes—
57C92C32×C719yescomplemented
58C32×C7—31no—
59C32×C7—32no—
60C32×C7—32no—
61C32×C7—31no—
62C32×C7—32no—
63C32×C7—32no—
64C32×C7—34no—
65C32×C7—31no—
66C32×C7—99no—
67C32×C7#73713yes—
68C32×C7C3411yescharacteristic
69C7×C9—39no—
70C7×C9—33no—
71C7×C9—36no—
72C7×C9—318no—
73C33—33no—
74C33—91no—
75C33—92no—
76C33C33×C712yes—
77C33C33×C711yescharacteristic
78C33C33×C711yescharacteristic
793−1+2—39no—
803−1+2—96no—
81C3×C9—91no—
82C3×C9—92no—
83C3×C9C33×C713yes—
84C3×C9C33×C719yes—
85C3×C9C33×C7118yes—
86C3×C9C33×C716yes—
87C3×C7—33no—
88C3×C7—91no—
89C3×C7—92no—
90C3×C7C3×#73711yescharacteristic
91C3×C73−1+411yescharacteristic
92C3×C73−1+412yes—
93C32—31no—
94C32—32no—
95C32—32no—
96C32—31no—
97C32—32no—
98C32—32no—
99C32—34no—
100C32—31no—
101C32—99no—
102C32C7×#73713yes—
103C32C34×C711yescharacteristic
104C9—39no—
105C9—33no—
106C9—36no—
107C9—318no—
108C7#1062488911yescharacteristic, direct product factor, Sylow
109C3—33no—
110C3—91no—
111C3—92no—
112C3C3×C7×#73711yescharacteristic
113C3C7×3−1+411yescharacteristic
114C3C7×3−1+412yes—
subgroupG/H
center, socleC32×C7C34
commutator, FrattiniC32C34×C7
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#6897C3semidirect
2. C7×#6896C3semidirect
3. C7×#6894C3semidirect
6. C7×C9×3−1+2C3semidirect
8. #10624889C7direct (N × H)
14. C7×C9⋊C9C32semidirect
15. C7×C9⋊C9C32semidirect
22. C7×C92C32semidirect
23. #6897C3×C7semidirect
24. #6896C3×C7semidirect
25. #6894C3×C7semidirect
28. C9×3−1+2C3×C7semidirect
49. C9⋊C9C32×C7semidirect
50. C9⋊C9C32×C7semidirect
57. C92C32×C7semidirect
108. C7#10624889direct (N × H)