Finite Group Databasebeta

← C42×C7×C11×C17 #72198528

Subgroups — C42×C7×C11×C17 #72198528

Order 20944.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C11×C17C213yesmaximal
2C42×C11×C17C711yesmaximal, characteristic, direct product factor, Hall
3C22×C7×C11×C17C2211yescharacteristic
4C4×C7×C11×C17C416yesdirect product factor
5C2×C7×C11×C17C2×C413yes—
6C42×C7×C17C1111yesmaximal, characteristic, direct product factor, Hall
7C2×C4×C11×C17C2×C713yes—
8C7×C11×C17C4211yescharacteristic, direct product factor, Hall
9C42×C7×C11C1711yesmaximal, characteristic, direct product factor, Hall
10C2×C4×C7×C17C2×C1113yes—
11C22×C11×C17C22×C711yescharacteristic
12C4×C11×C17C4×C716yesdirect product factor
13C2×C4×C7×C11C2×C1713yes—
14C22×C7×C17C22×C1111yescharacteristic
15C4×C7×C17C4×C1116yesdirect product factor
16C2×C11×C17C2×C4×C713yes—
17C22×C7×C11C22×C1711yescharacteristic
18C4×C7×C11C4×C1716yesdirect product factor
19C42×C17C7×C1111yescharacteristic, direct product factor, Hall
20C2×C7×C17C2×C4×C1113yes—
21C11×C17C42×C711yescharacteristic, direct product factor, Hall
22C42×C11C7×C1711yescharacteristic, direct product factor, Hall
23C2×C7×C11C2×C4×C1713yes—
24C2×C4×C17C2×C7×C1113yes—
25C7×C17C42×C1111yescharacteristic, direct product factor, Hall
26C42×C7C11×C1711yescharacteristic, direct product factor, Hall
27C2×C4×C11C2×C7×C1713yes—
28C7×C11C42×C1711yescharacteristic, direct product factor, Hall
29C22×C17C22×C7×C1111yescharacteristic
30C4×C17C4×C7×C1116yesdirect product factor
31C2×C4×C7C2×C11×C1713yes—
32C22×C11C22×C7×C1711yescharacteristic
33C4×C11C4×C7×C1716yesdirect product factor
34C2×C17C2×C4×C7×C1113yes—
35C22×C7C22×C11×C1711yescharacteristic
36C4×C7C4×C11×C1716yesdirect product factor
37C2×C11C2×C4×C7×C1713yes—
38C17C42×C7×C1111yescharacteristic, direct product factor, Sylow
39C42C7×C11×C1711yescharacteristic, direct product factor, Sylow
40C2×C7C2×C4×C11×C1713yes—
41C11C42×C7×C1711yescharacteristic, direct product factor, Sylow
42C2×C4C2×C7×C11×C1713yes—
43C7C42×C11×C1711yescharacteristic, direct product factor, Sylow
44C22C22×C7×C11×C1711yescharacteristic
45C4C4×C7×C11×C1716yesdirect product factor
46C2C2×C4×C7×C11×C1713yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C7×C11×C17
socle, prime radicalC22×C7×C11×C17C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C42×C11×C17C7direct (N × H)
4. C4×C7×C11×C17C4direct (N × H)
6. C42×C7×C17C11direct (N × H)
8. C7×C11×C17C42direct (N × H)
9. C42×C7×C11C17direct (N × H)
12. C4×C11×C17C4×C7direct (N × H)
15. C4×C7×C17C4×C11direct (N × H)
18. C4×C7×C11C4×C17direct (N × H)
19. C42×C17C7×C11direct (N × H)
21. C11×C17C42×C7direct (N × H)
22. C42×C11C7×C17direct (N × H)
25. C7×C17C42×C11direct (N × H)
26. C42×C7C11×C17direct (N × H)
28. C7×C11C42×C17direct (N × H)
30. C4×C17C4×C7×C11direct (N × H)
33. C4×C11C4×C7×C17direct (N × H)
36. C4×C7C4×C11×C17direct (N × H)
38. C17C42×C7×C11direct (N × H)
39. C42C7×C11×C17direct (N × H)
41. C11C42×C7×C17direct (N × H)
43. C7C42×C11×C17direct (N × H)
45. C4C4×C7×C11×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C11×C172
C42×C11×C177
C42×C7×C1711
C42×C7×C1117