Finite Group Databasebeta

← C163⋊#564 #23782420

Subgroups — C163⋊#564 #23782420

Order 10432.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19104727C212yesmaximal
2#19104726C214yesmaximal
3#19104725C214yesmaximal
4#19104725C214yesmaximal
5#125×C163C211yesmaximal, characteristic
6C4⋊Dic163C2212yes—
7C4⋊Dic163C2214yes—
8C4⋊Dic163C2212yes—
9Dic163⋊C4C2214yes—
10Dic163⋊C4C2214yes—
11Dic163⋊C4C2214yes—
12Dic163⋊C4C2214yes—
13C4×Dic163C2214yes—
14C4⋊C4×C163C2212yes—
15C4⋊C4×C163C2214yes—
16C42×C163C2211yescharacteristic
17C2×Dic163C2314yes—
18C2×Dic163C2314yes—
19C2×C4×C163C2311yescharacteristic
20C2×C4×C163C2312yes—
21C2×C4×C163C2314yes—
22C22×C163C2411yescharacteristic
23C4×C163—22no—
24C4×C163—24no—
25C4×C163—21no—
26Dic163—24no—
27Dic163—24no—
28C2×C1632−1+412yes—
29C2×C1632−1+411yescharacteristic
30C163#56411yescharacteristic, complemented, Sylow
31#564—1631nomaximal, Sylow
32#125—1634no—
33#125—1634no—
34#125—1634no—
35#125—1632no—
36#125D16311yescharacteristic
37C4⋊C4—1634no—
38C4⋊C4—1634no—
39C4⋊C4—1634no—
40C4⋊C4—1634no—
41C4⋊C4—1634no—
42C4⋊C4—1632no—
43C4⋊C4—1632no—
44C4⋊C4C2×D16312yes—
45C4⋊C4C2×D16314yes—
46C42—1634no—
47C42C2×D16311yescharacteristic
48C2×C4—1634no—
49C2×C4—1634no—
50C2×C4C22×D16314yes—
51C2×C4C22×D16312yes—
52C2×C4C22×D16311yescharacteristic
53C22C23×D16311yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—3264no—
58C4—3264no—
59C2#1910478212yes—
60C2#1910478311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, prime radical, cosocleC22×C163C24
Fitting#125×C163C2
hypercenter#125D163
hypocenterC163#564
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C163#564semidirect