Finite Group Databasebeta

← C22×#13108049 #20265589

Subgroups — C22×#13108049 #20265589

Order 6464.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13108049C216yesmaximal, direct product factor
2C22×C8×C101C211yesmaximal, characteristic
3#13108049C2214yesdirect product factor
4C22×C4×C101C411yescharacteristic
5C2×C8×C101C413yes—
6C2×C8×C101C2213yes—
7C23×C101C811yescharacteristic
8C2×C4×C101C813yes—
9C2×C4×C101C2×C413yes—
10C8×C101C2×C413yes—
11C8×C101C2311yescharacteristic
12C22×C101C1614yescomplemented
13C22×C101C2×C813yes—
14C4×C101C2×C813yes—
15C4×C101C22×C411yescharacteristic
16C2×C101C2×C1616yescomplemented
17C2×C101C22×C811yescharacteristic
18C101C22×C1611yescharacteristic, complemented, Sylow
19C22×C16—1011nomaximal, Sylow
20C22×C8D10111yescharacteristic
21C2×C16—1016no—
22C22×C4Dic10111yescharacteristic
23C2×C8Dic10113yes—
24C2×C8C2×D10113yes—
25C16—1014no—
26C23#1171757911yescharacteristic
27C2×C4#1171757913yes—
28C2×C4C2×Dic10113yes—
29C8C2×Dic10113yes—
30C8C22×D10111yescharacteristic
31C22#1310804914yesdirect product factor
32C22C2×#1171757913yes—
33C4C2×#1171757913yes—
34C4C22×Dic10111yescharacteristic
35C2C2×#1310804916yesdirect product factor
36C2C22×#1171757911yescharacteristic
subgroupG/H
center, hypercenterC22×C8D101
commutator, hypocenterC101C22×C16
FrattiniC8C22×D101
FittingC22×C8×C101C2
socleC23×C101C8
LCSG ▷ C101
UCSC1 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#13108049C2direct (N × H)
3. #13108049C22direct (N × H)
12. C22×C101C16semidirect
16. C2×C101C2×C16semidirect
18. C101C22×C16semidirect
31. C22#13108049direct (N × H)
35. C2C2×#13108049direct (N × H)