Finite Group Databasebeta

← C23×C3×C7 #4287

Subgroups — C23×C3×C7 #4287

Order 168.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C7C217yesmaximal, direct product factor
2C23×C7C311yesmaximal, characteristic, direct product factor, Hall
3C2×C3×C7C2217yesdirect product factor
4C22×C7C2×C317yesdirect product factor
5C23×C3C711yesmaximal, characteristic, direct product factor, Hall
6C3×C7C2311yescharacteristic, direct product factor, Hall
7C2×C7C22×C317yesdirect product factor
8C22×C3C2×C717yesdirect product factor
9C23C3×C711yescharacteristic, direct product factor, Sylow
10C7C23×C311yescharacteristic, direct product factor, Sylow
11C2×C3C22×C717yesdirect product factor
12C22C2×C3×C717yesdirect product factor
13C3C23×C711yescharacteristic, direct product factor, Sylow
14C2C22×C3×C717yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C7C2direct (N × H)
2. C23×C7C3direct (N × H)
3. C2×C3×C7C22direct (N × H)
4. C22×C7C2×C3direct (N × H)
5. C23×C3C7direct (N × H)
6. C3×C7C23direct (N × H)
7. C2×C7C22×C3direct (N × H)
8. C22×C3C2×C7direct (N × H)
9. C23C3×C7direct (N × H)
10. C7C23×C3direct (N × H)
11. C2×C3C22×C7direct (N × H)
12. C22C2×C3×C7direct (N × H)
13. C3C23×C7direct (N × H)
14. C2C22×C3×C7direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C72
C23×C73
C23×C37