Finite Group Databasebeta

← C22×C4×C11×C71 #72190836

Subgroups — C22×C4×C11×C71 #72190836

Order 12496.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×C71C211yesmaximal, characteristic
2C2×C4×C11×C71C216yesmaximal, direct product factor
3C22×C11×C71C414yesdirect product factor
4C22×C11×C71C2213yes—
5C4×C11×C71C2214yesdirect product factor
6C2×C11×C71C2×C416yesdirect product factor
7C2×C11×C71C2311yescharacteristic
8C22×C4×C71C1111yesmaximal, characteristic, direct product factor, Hall
9C11×C71C22×C411yescharacteristic, direct product factor, Hall
10C23×C71C2×C1111yescharacteristic
11C2×C4×C71C2×C1116yesdirect product factor
12C22×C71C4×C1114yesdirect product factor
13C22×C71C22×C1113yes—
14C4×C71C22×C1114yesdirect product factor
15C22×C4×C11C7111yesmaximal, characteristic, direct product factor, Hall
16C2×C71C2×C4×C1116yesdirect product factor
17C2×C71C23×C1111yescharacteristic
18C23×C11C2×C7111yescharacteristic
19C2×C4×C11C2×C7116yesdirect product factor
20C71C22×C4×C1111yescharacteristic, direct product factor, Sylow
21C22×C11C4×C7114yesdirect product factor
22C22×C11C22×C7113yes—
23C4×C11C22×C7114yesdirect product factor
24C2×C11C2×C4×C7116yesdirect product factor
25C2×C11C23×C7111yescharacteristic
26C22×C4C11×C7111yescharacteristic, direct product factor, Sylow
27C11C22×C4×C7111yescharacteristic, direct product factor, Sylow
28C23C2×C11×C7111yescharacteristic
29C2×C4C2×C11×C7116yesdirect product factor
30C22C4×C11×C7114yesdirect product factor
31C22C22×C11×C7113yes—
32C4C22×C11×C7114yesdirect product factor
33C2C2×C4×C11×C7116yesdirect product factor
34C2C23×C11×C7111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C11×C71
socle, prime radicalC23×C11×C71C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×C71C2direct (N × H)
3. C22×C11×C71C4direct (N × H)
5. C4×C11×C71C22direct (N × H)
6. C2×C11×C71C2×C4direct (N × H)
8. C22×C4×C71C11direct (N × H)
9. C11×C71C22×C4direct (N × H)
11. C2×C4×C71C2×C11direct (N × H)
12. C22×C71C4×C11direct (N × H)
14. C4×C71C22×C11direct (N × H)
15. C22×C4×C11C71direct (N × H)
16. C2×C71C2×C4×C11direct (N × H)
19. C2×C4×C11C2×C71direct (N × H)
20. C71C22×C4×C11direct (N × H)
21. C22×C11C4×C71direct (N × H)
23. C4×C11C22×C71direct (N × H)
24. C2×C11C2×C4×C71direct (N × H)
26. C22×C4C11×C71direct (N × H)
27. C11C22×C4×C71direct (N × H)
29. C2×C4C2×C11×C71direct (N × H)
30. C22C4×C11×C71direct (N × H)
32. C4C22×C11×C71direct (N × H)
33. C2C2×C4×C11×C71direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×C712
C2×C4×C11×C712
C22×C4×C7111
C22×C4×C1171