Finite Group Databasebeta

← C2×#1057 #6121

Subgroups — C2×#1057 #6121

Order 208.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic13C211yesmaximal, characteristic
2#1057C212yesmaximal, direct product factor
3C22×C13C411yescharacteristic
4Dic13C411yescharacteristic
5Dic13C2211yescharacteristic
6C2×C13C812yescomplemented
7C2×C13C2×C411yescharacteristic
8C2×C8—131nomaximal, Sylow
9C13C2×C811yescharacteristic, complemented, Sylow
10C2×C4—131no—
11C8—132no—
12C22#26111yescharacteristic
13C4—131no—
14C4—131no—
15C2#105712yesdirect product factor
16C2C2×#26111yescharacteristic
subgroupG/H
center, hypercenterC22#261
commutator, hypocenterC13C2×C8
FrattiniC2C2×#261
Fitting, socle, prime radicalC22×C13C4
cosocleDic13C22
LCSG ▷ C13
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #1057C2direct (N × H)
6. C2×C13C8semidirect
9. C13C2×C8semidirect
15. C2#1057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Dic132
#10572
C2×C813