Finite Group Databasebeta

← #44541908

Subgroups — #44541908

Order 31888.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30630007C212yesmaximal, complemented
2C4×D1993C211yesmaximal, characteristic
3C2×D1993C411yescharacteristic
4C4×C1993C411yescharacteristic
5Dic1993C2211yescharacteristic
6C2×C1993C2×C411yescharacteristic
7D1993C812yescomplemented
8C1993C2×C811yescharacteristic, complemented, Sylow
9C2×C8—19931nomaximal, Sylow
10C2×C4—19931no—
11C8—19932no—
12C22—19931no—
13C4—19931no—
14C4#2254753911yescharacteristic
15C2—19932no—
16C2C2×#2254753911yescharacteristic
subgroupG/H
center, hypercenterC4#22547539
commutator, hypocenterC1993C2×C8
FrattiniC2C2×#22547539
FittingC4×C1993C4
socleC2×C1993C2×C4
prime radicalC2×D1993C4
cosocleDic1993C22
LCSG ▷ C1993
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #30630007C2semidirect
7. D1993C8semidirect
8. C1993C2×C8semidirect

Maximal subgroups

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

subgroupindex
#306300072
C4×D19932
C2×C81993