Finite Group Databasebeta

← C313⋊#564 #34094907

Subgroups — C313⋊#564 #34094907

Order 20032.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23756489C212yesmaximal
2#23756488C214yesmaximal
3#23756487C214yesmaximal
4#23756487C214yesmaximal
5#125×C313C211yesmaximal, characteristic
6C4⋊Dic313C2212yes—
7C4⋊Dic313C2214yes—
8C4⋊Dic313C2212yes—
9#19097540C2214yes—
10#19097540C2214yes—
11#19097540C2214yes—
12#19097540C2214yes—
13C4×Dic313C2214yes—
14C4⋊C4×C313C2212yes—
15C4⋊C4×C313C2214yes—
16C42×C313C2211yescharacteristic
17C2×Dic313C2314yes—
18C2×Dic313C2314yes—
19C2×C4×C313C2311yescharacteristic
20C2×C4×C313C2312yes—
21C2×C4×C313C2314yes—
22C22×C313C2411yescharacteristic
23C4×C313—22no—
24C4×C313—24no—
25C4×C313—21no—
26Dic313—24no—
27Dic313—24no—
28C2×C3132−1+412yes—
29C2×C3132−1+411yescharacteristic
30C313#56411yescharacteristic, complemented, Sylow
31#564—3131nomaximal, Sylow
32#125—3134no—
33#125—3134no—
34#125—3134no—
35#125—3132no—
36#125D31311yescharacteristic
37C4⋊C4—3134no—
38C4⋊C4—3134no—
39C4⋊C4—3134no—
40C4⋊C4—3134no—
41C4⋊C4—3134no—
42C4⋊C4—3132no—
43C4⋊C4—3132no—
44C4⋊C4C2×D31312yes—
45C4⋊C4C2×D31314yes—
46C42—3134no—
47C42C2×D31311yescharacteristic
48C2×C4—3134no—
49C2×C4—3134no—
50C2×C4C22×D31314yes—
51C2×C4C22×D31312yes—
52C2×C4C22×D31311yescharacteristic
53C22C23×D31311yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—6264no—
58C4—6264no—
59C2#2375654412yes—
60C2#2375654511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, prime radical, cosocleC22×C313C24
Fitting#125×C313C2
hypercenter#125D313
hypocenterC313#564
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C313#564semidirect

Maximal subgroups

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

subgroupindex
#237564892
#237564882
#237564872
#125×C3132
#564313