Finite Group Databasebeta

← C283⋊#564 #31827220

Subgroups — C283⋊#564 #31827220

Order 18112.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22583602C212yesmaximal
2#22583601C214yesmaximal
3#22583600C214yesmaximal
4#22583600C214yesmaximal
5#125×C283C211yesmaximal, characteristic
6C4⋊Dic283C2212yes—
7C4⋊Dic283C2214yes—
8C4⋊Dic283C2212yes—
9Dic283⋊C4C2214yes—
10Dic283⋊C4C2214yes—
11Dic283⋊C4C2214yes—
12Dic283⋊C4C2214yes—
13C4×Dic283C2214yes—
14C4⋊C4×C283C2212yes—
15C4⋊C4×C283C2214yes—
16C42×C283C2211yescharacteristic
17C2×Dic283C2314yes—
18C2×Dic283C2314yes—
19C2×C4×C283C2311yescharacteristic
20C2×C4×C283C2312yes—
21C2×C4×C283C2314yes—
22C22×C283C2411yescharacteristic
23C4×C283—22no—
24C4×C283—24no—
25C4×C283—21no—
26Dic283—24no—
27Dic283—24no—
28C2×C2832−1+412yes—
29C2×C2832−1+411yescharacteristic
30C283#56411yescharacteristic, complemented, Sylow
31#564—2831nomaximal, Sylow
32#125—2834no—
33#125—2834no—
34#125—2834no—
35#125—2832no—
36#125D28311yescharacteristic
37C4⋊C4—2834no—
38C4⋊C4—2834no—
39C4⋊C4—2834no—
40C4⋊C4—2834no—
41C4⋊C4—2834no—
42C4⋊C4—2832no—
43C4⋊C4—2832no—
44C4⋊C4C2×D28312yes—
45C4⋊C4C2×D28314yes—
46C42—2834no—
47C42C2×D28311yescharacteristic
48C2×C4—2834no—
49C2×C4—2834no—
50C2×C4C22×D28314yes—
51C2×C4C22×D28312yes—
52C2×C4C22×D28311yescharacteristic
53C22C23×D28311yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—5664no—
58C4—5664no—
59C2#2258365712yes—
60C2#2258365811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, prime radical, cosocleC22×C283C24
Fitting#125×C283C2
hypercenter#125D283
hypocenterC283#564
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C283#564semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225836022
#225836012
#225836002
#125×C2832
#564283