Finite Group Databasebeta

← C22×C3×C4×C7 #66735

Subgroups — C22×C3×C4×C7 #66735

Order 336.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C7C211yesmaximal, characteristic
2C2×C3×C4×C7C216yesmaximal, direct product factor
3C22×C4×C7C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C7C414yesdirect product factor
5C22×C3×C7C2213yes—
6C3×C4×C7C2214yesdirect product factor
7C23×C7C2×C311yescharacteristic
8C2×C4×C7C2×C316yesdirect product factor
9C22×C3×C4C711yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C7C2×C416yesdirect product factor
11C2×C3×C7C2311yescharacteristic
12C22×C7C3×C414yesdirect product factor
13C22×C7C22×C313yes—
14C4×C7C22×C314yesdirect product factor
15C23×C3C2×C711yescharacteristic
16C2×C3×C4C2×C716yesdirect product factor
17C3×C7C22×C411yescharacteristic, direct product factor, Hall
18C22×C4C3×C711yescharacteristic, direct product factor, Sylow
19C2×C7C2×C3×C416yesdirect product factor
20C2×C7C23×C311yescharacteristic
21C22×C3C4×C714yesdirect product factor
22C22×C3C22×C713yes—
23C3×C4C22×C714yesdirect product factor
24C23C2×C3×C711yescharacteristic
25C2×C4C2×C3×C716yesdirect product factor
26C7C22×C3×C411yescharacteristic, direct product factor, Sylow
27C2×C3C2×C4×C716yesdirect product factor
28C2×C3C23×C711yescharacteristic
29C22C3×C4×C714yesdirect product factor
30C22C22×C3×C713yes—
31C4C22×C3×C714yesdirect product factor
32C3C22×C4×C711yescharacteristic, direct product factor, Sylow
33C2C2×C3×C4×C716yesdirect product factor
34C2C23×C3×C711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C7
socle, prime radicalC23×C3×C7C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C7C2direct (N × H)
3. C22×C4×C7C3direct (N × H)
4. C22×C3×C7C4direct (N × H)
6. C3×C4×C7C22direct (N × H)
8. C2×C4×C7C2×C3direct (N × H)
9. C22×C3×C4C7direct (N × H)
10. C2×C3×C7C2×C4direct (N × H)
12. C22×C7C3×C4direct (N × H)
14. C4×C7C22×C3direct (N × H)
16. C2×C3×C4C2×C7direct (N × H)
17. C3×C7C22×C4direct (N × H)
18. C22×C4C3×C7direct (N × H)
19. C2×C7C2×C3×C4direct (N × H)
21. C22×C3C4×C7direct (N × H)
23. C3×C4C22×C7direct (N × H)
25. C2×C4C2×C3×C7direct (N × H)
26. C7C22×C3×C4direct (N × H)
27. C2×C3C2×C4×C7direct (N × H)
29. C22C3×C4×C7direct (N × H)
31. C4C22×C3×C7direct (N × H)
32. C3C22×C4×C7direct (N × H)
33. C2C2×C3×C4×C7direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C72
C2×C3×C4×C72
C22×C4×C73
C22×C3×C47