Finite Group Databasebeta

← C22×#15690909 #27159027

Subgroups — C22×#15690909 #27159027

Order 12416.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15690909C216yesmaximal, direct product factor
2C22×#13095523C211yesmaximal, characteristic
3#15690909C2214yesdirect product factor
4C2×#13095523C413yes—
5C2×#13095523C2213yes—
6C22×#11715897C411yescharacteristic
7#13095523C2×C413yes—
8#13095523C2311yescharacteristic
9C2×#11715897C813yes—
10C2×#11715897C2×C413yes—
11C22×Dic97C811yescharacteristic
12C23×C97C1611yescharacteristic
13C2×Dic97C1613yes—
14C2×Dic97C2×C813yes—
15#11715897C2×C813yes—
16#11715897C22×C411yescharacteristic
17C22×C97C3214yescomplemented
18C22×C97C2×C1613yes—
19Dic97C2×C1613yes—
20Dic97C22×C811yescharacteristic
21C2×C97C2×C3216yescomplemented
22C2×C97C22×C1611yescharacteristic
23C22×C32—971nomaximal, Sylow
24C97C22×C3211yescharacteristic, complemented, Sylow
25C22×C16—971no—
26C2×C32—976no—
27C22×C8—971no—
28C2×C16—973no—
29C2×C16—973no—
30C32—974no—
31C22×C4—971no—
32C2×C8—973no—
33C2×C8—973no—
34C16—971no—
35C16—973no—
36C23#1309552511yescharacteristic
37C2×C4—973no—
38C2×C4—973no—
39C8—971no—
40C8—973no—
41C22#1569090914yesdirect product factor
42C22C2×#1309552513yes—
43C4—971no—
44C4—973no—
45C2C2×#1569090916yesdirect product factor
46C2C22×#1309552511yescharacteristic
subgroupG/H
center, hypercenterC23#13095525
commutator, hypocenterC97C22×C32
FrattiniC2C22×#13095525
Fitting, socle, prime radicalC23×C97C16
cosocle#13095523C23
LCSG ▷ C97
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#15690909C2direct (N × H)
3. #15690909C22direct (N × H)
17. C22×C97C32semidirect
21. C2×C97C2×C32semidirect
24. C97C22×C32semidirect
41. C22#15690909direct (N × H)
45. C2C2×#15690909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156909092
C22×#130955232
C22×C3297