Finite Group Databasebeta

← C3×C41×D97 #37558784

Subgroups — C3×C41×D97 #37558784

Order 23862.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C41×C97C211yesmaximal, characteristic, complemented, Hall
2C41×D97C311yesmaximal, characteristic, direct product factor, Hall
3C41×C97C2×C311yescharacteristic, complemented, Hall
4C3×D97C4111yesmaximal, characteristic, direct product factor, Hall
5C3×C97C2×C4111yescharacteristic, complemented, Hall
6C2×C3×C41—971nomaximal, Hall
7D97C3×C4111yescharacteristic, direct product factor, Hall
8C3×C41D9711yescharacteristic, direct product factor, Hall
9C97C2×C3×C4111yescharacteristic, complemented, Sylow
10C2×C41—971noHall
11C41C3×D9711yescharacteristic, direct product factor, Sylow
12C2×C3—971noHall
13C3C41×D9711yescharacteristic, direct product factor, Sylow
14C2—971noSylow
subgroupG/H
center, hypercenterC3×C41D97
commutator, cosocle, hypocenterC97C2×C3×C41
FrattiniC1G
Fitting, socleC3×C41×C97C2
LCSG ▷ C97
UCSC1 ◁ C3×C41

Complements

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

NH ≅ G/Ntype
1. C3×C41×C97C2semidirect
2. C41×D97C3direct (N × H)
3. C41×C97C2×C3semidirect
4. C3×D97C41direct (N × H)
5. C3×C97C2×C41semidirect
7. D97C3×C41direct (N × H)
8. C3×C41D97direct (N × H)
9. C97C2×C3×C41semidirect
11. C41C3×D97direct (N × H)
13. C3C41×D97direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C41×C972
C41×D973
C3×D9741
C2×C3×C4197