Finite Group Databasebeta

← C22×C4×C7×C31 #72183149

Subgroups — C22×C4×C7×C31 #72183149

Order 3472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C31C211yesmaximal, characteristic
2C2×C4×C7×C31C216yesmaximal, direct product factor
3C22×C7×C31C414yesdirect product factor
4C22×C7×C31C2213yes—
5C4×C7×C31C2214yesdirect product factor
6C22×C4×C31C711yesmaximal, characteristic, direct product factor, Hall
7C2×C7×C31C2×C416yesdirect product factor
8C2×C7×C31C2311yescharacteristic
9C23×C31C2×C711yescharacteristic
10C2×C4×C31C2×C716yesdirect product factor
11C7×C31C22×C411yescharacteristic, direct product factor, Hall
12C22×C31C4×C714yesdirect product factor
13C22×C31C22×C713yes—
14C4×C31C22×C714yesdirect product factor
15C22×C4×C7C3111yesmaximal, characteristic, direct product factor, Hall
16C2×C31C2×C4×C716yesdirect product factor
17C2×C31C23×C711yescharacteristic
18C23×C7C2×C3111yescharacteristic
19C2×C4×C7C2×C3116yesdirect product factor
20C31C22×C4×C711yescharacteristic, direct product factor, Sylow
21C22×C7C4×C3114yesdirect product factor
22C22×C7C22×C3113yes—
23C4×C7C22×C3114yesdirect product factor
24C22×C4C7×C3111yescharacteristic, direct product factor, Sylow
25C2×C7C2×C4×C3116yesdirect product factor
26C2×C7C23×C3111yescharacteristic
27C23C2×C7×C3111yescharacteristic
28C2×C4C2×C7×C3116yesdirect product factor
29C7C22×C4×C3111yescharacteristic, direct product factor, Sylow
30C22C4×C7×C3114yesdirect product factor
31C22C22×C7×C3113yes—
32C4C22×C7×C3114yesdirect product factor
33C2C2×C4×C7×C3116yesdirect product factor
34C2C23×C7×C3111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C7×C31
socle, prime radicalC23×C7×C31C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C31C2direct (N × H)
3. C22×C7×C31C4direct (N × H)
5. C4×C7×C31C22direct (N × H)
6. C22×C4×C31C7direct (N × H)
7. C2×C7×C31C2×C4direct (N × H)
10. C2×C4×C31C2×C7direct (N × H)
11. C7×C31C22×C4direct (N × H)
12. C22×C31C4×C7direct (N × H)
14. C4×C31C22×C7direct (N × H)
15. C22×C4×C7C31direct (N × H)
16. C2×C31C2×C4×C7direct (N × H)
19. C2×C4×C7C2×C31direct (N × H)
20. C31C22×C4×C7direct (N × H)
21. C22×C7C4×C31direct (N × H)
23. C4×C7C22×C31direct (N × H)
24. C22×C4C7×C31direct (N × H)
25. C2×C7C2×C4×C31direct (N × H)
28. C2×C4C2×C7×C31direct (N × H)
29. C7C22×C4×C31direct (N × H)
30. C22C4×C7×C31direct (N × H)
32. C4C22×C7×C31direct (N × H)
33. C2C2×C4×C7×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C312
C2×C4×C7×C312
C22×C4×C317
C22×C4×C731