Finite Group Databasebeta

← C157⋊#564 #23758028

Subgroups — C157⋊#564 #23758028

Order 10048.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19097763C212yesmaximal
2#19097762C214yesmaximal
3#19097761C214yesmaximal
4#19097761C214yesmaximal
5#125×C157C211yesmaximal, characteristic
6C4⋊Dic157C2212yes—
7C4⋊Dic157C2214yes—
8C4⋊Dic157C2212yes—
9#14578933C2214yes—
10#14578933C2214yes—
11#14578933C2214yes—
12#14578933C2214yes—
13C4×Dic157C2214yes—
14C4⋊C4×C157C2212yes—
15C4⋊C4×C157C2214yes—
16C42×C157C2211yescharacteristic
17C2×Dic157C2314yes—
18C2×Dic157C2314yes—
19C2×C4×C157C2311yescharacteristic
20C2×C4×C157C2312yes—
21C2×C4×C157C2314yes—
22C22×C157C2411yescharacteristic
23C4×C157—22no—
24C4×C157—24no—
25C4×C157—21no—
26Dic157—24no—
27Dic157—24no—
28C2×C1572−1+412yes—
29C2×C1572−1+411yescharacteristic
30C157#56411yescharacteristic, complemented, Sylow
31#564—1571nomaximal, Sylow
32#125—1574no—
33#125—1574no—
34#125—1574no—
35#125—1572no—
36#125D15711yescharacteristic
37C4⋊C4—1574no—
38C4⋊C4—1574no—
39C4⋊C4—1574no—
40C4⋊C4—1574no—
41C4⋊C4—1574no—
42C4⋊C4—1572no—
43C4⋊C4—1572no—
44C4⋊C4C2×D15712yes—
45C4⋊C4C2×D15714yes—
46C42—1574no—
47C42C2×D15711yescharacteristic
48C2×C4—1574no—
49C2×C4—1574no—
50C2×C4C22×D15714yes—
51C2×C4C22×D15712yes—
52C2×C4C22×D15711yescharacteristic
53C22C23×D15711yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—3144no—
58C4—3144no—
59C2#1909781812yes—
60C2#1909781911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D157
commutator, socle, prime radical, cosocleC22×C157C24
Fitting#125×C157C2
hypercenter#125D157
hypocenterC157#564
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C157#564semidirect