Finite Group Databasebeta

← C193⋊#564 #27136014

Subgroups — C193⋊#564 #27136014

Order 12352.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20259891C212yesmaximal
2#20259890C214yesmaximal
3#20259889C214yesmaximal
4#20259889C214yesmaximal
5#125×C193C211yesmaximal, characteristic
6C4⋊Dic193C2212yes—
7C4⋊Dic193C2214yes—
8C4⋊Dic193C2212yes—
9#15690534C2214yes—
10#15690534C2214yes—
11#15690534C2214yes—
12#15690534C2214yes—
13C4×Dic193C2214yes—
14C4⋊C4×C193C2212yes—
15C4⋊C4×C193C2214yes—
16C42×C193C2211yescharacteristic
17C2×Dic193C2314yes—
18C2×Dic193C2314yes—
19C2×C4×C193C2311yescharacteristic
20C2×C4×C193C2312yes—
21C2×C4×C193C2314yes—
22C22×C193C2411yescharacteristic
23C4×C193—22no—
24C4×C193—24no—
25C4×C193—21no—
26Dic193—24no—
27Dic193—24no—
28C2×C1932−1+412yes—
29C2×C1932−1+411yescharacteristic
30C193#56411yescharacteristic, complemented, Sylow
31#564—1931nomaximal, Sylow
32#125—1934no—
33#125—1934no—
34#125—1934no—
35#125—1932no—
36#125D19311yescharacteristic
37C4⋊C4—1934no—
38C4⋊C4—1934no—
39C4⋊C4—1934no—
40C4⋊C4—1934no—
41C4⋊C4—1934no—
42C4⋊C4—1932no—
43C4⋊C4—1932no—
44C4⋊C4C2×D19312yes—
45C4⋊C4C2×D19314yes—
46C42—1934no—
47C42C2×D19311yescharacteristic
48C2×C4—1934no—
49C2×C4—1934no—
50C2×C4C22×D19314yes—
51C2×C4C22×D19312yes—
52C2×C4C22×D19311yescharacteristic
53C22C23×D19311yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—3864no—
58C4—3864no—
59C2#2025994612yes—
60C2#2025994711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D193
commutator, socle, prime radical, cosocleC22×C193C24
Fitting#125×C193C2
hypercenter#125D193
hypocenterC193#564
LCSG ▷ C22×C193 ▷ C193
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C193#564semidirect

Maximal subgroups

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

subgroupindex
#202598912
#202598902
#202598892
#125×C1932
#564193