Finite Group Databasebeta

← C97⋊#564 #20261490

Subgroups — C97⋊#564 #20261490

Order 6208.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690802C212yesmaximal
2#15690801C214yesmaximal
3#15690800C214yesmaximal
4#15690800C214yesmaximal
5#125×C97C211yesmaximal, characteristic
6C4⋊Dic97C2212yes—
7C4⋊Dic97C2214yes—
8C4⋊Dic97C2212yes—
9#13095490C2214yes—
10#13095490C2214yes—
11#13095490C2214yes—
12#13095490C2214yes—
13C4×Dic97C2214yes—
14C4⋊C4×C97C2212yes—
15C4⋊C4×C97C2214yes—
16C42×C97C2211yescharacteristic
17C2×C4×C97C2311yescharacteristic
18C2×C4×C97C2312yes—
19C2×C4×C97C2314yes—
20C2×Dic97C2314yes—
21C2×Dic97C2314yes—
22C22×C97C2411yescharacteristic
23C4×C97—22no—
24C4×C97—24no—
25C4×C97—21no—
26Dic97—24no—
27Dic97—24no—
28C2×C972−1+412yes—
29C2×C972−1+411yescharacteristic
30C97#56411yescharacteristic, complemented, Sylow
31#564—971nomaximal, Sylow
32#125—974no—
33#125—974no—
34#125—974no—
35#125—972no—
36#125D9711yescharacteristic
37C4⋊C4—974no—
38C4⋊C4—974no—
39C4⋊C4—974no—
40C4⋊C4—974no—
41C4⋊C4—974no—
42C4⋊C4—972no—
43C4⋊C4—972no—
44C4⋊C4C2×D9712yes—
45C4⋊C4C2×D9714yes—
46C42—974no—
47C42C2×D9711yescharacteristic
48C2×C4—974no—
49C2×C4—974no—
50C2×C4C22×D9714yes—
51C2×C4C22×D9712yes—
52C2×C4C22×D9711yescharacteristic
53C22C23×D9711yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—1944no—
58C4—1944no—
59C2#1569085712yes—
60C2#1569085811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D97
commutator, socleC22×C97C24
Fitting#125×C97C2
hypercenter#125D97
hypocenterC97#564
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C97#564semidirect