Finite Group Databasebeta

← C2×#11758187 #14519849

Subgroups — C2×#11758187 #14519849

Order 1952.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92418C211yesmaximal, characteristic
2#11758187C212yesmaximal, direct product factor
3C2×C4×C61C411yescharacteristic
4#92418C411yescharacteristic
5#92418C2211yescharacteristic
6C22×C61C811yescharacteristic
7C4×C61C811yescharacteristic
8C4×C61C2×C411yescharacteristic
9C2×C61C1612yescomplemented
10C2×C61C2×C811yescharacteristic
11C61C2×C1611yescharacteristic, complemented, Sylow
12C2×C16—611nomaximal, Sylow
13C2×C8—611no—
14C16—612no—
15C2×C4#692311yescharacteristic
16C8—611no—
17C8—611no—
18C22#9242011yescharacteristic
19C4#9242011yescharacteristic
20C4C2×#692311yescharacteristic
21C2#1175818712yesdirect product factor
22C2C2×#9242011yescharacteristic
subgroupG/H
center, hypercenterC2×C4#6923
commutator, hypocenterC61C2×C16
FrattiniC4C2×#6923
FittingC2×C4×C61C4
socle, prime radicalC22×C61C8
cosocle#92418C22
LCSG ▷ C61
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11758187C2direct (N × H)
9. C2×C61C16semidirect
11. C61C2×C16semidirect
21. C2#11758187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#924182
#117581872
C2×C1661