Finite Group Databasebeta

← C32×C4×C7×C112 #44478995

Subgroups — C32×C4×C7×C112 #44478995

Order 30492.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C7×C112C211yesmaximal, characteristic
2C3×C4×C7×C112C314yesmaximal, direct product factor
3C32×C7×C112C411yescharacteristic, direct product factor, Hall
4C2×C3×C7×C112C2×C314yes—
5C32×C4×C112C711yesmaximal, characteristic, direct product factor, Hall
6C4×C7×C112C3211yescharacteristic, direct product factor, Hall
7C32×C4×C7×C11C11112yesmaximal, direct product factor
8C3×C7×C112C3×C414yesdirect product factor
9C2×C32×C112C2×C711yescharacteristic
10C2×C7×C112C2×C3211yescharacteristic
11C3×C4×C112C3×C714yesdirect product factor
12C2×C32×C7×C11C2×C11112yes—
13C32×C112C4×C711yescharacteristic, direct product factor, Hall
14C3×C4×C7×C11C3×C11148yesdirect product factor
15C7×C112C32×C411yescharacteristic, direct product factor, Hall
16C2×C3×C112C2×C3×C714yes—
17C32×C7×C11C4×C11112yesdirect product factor
18C4×C112C32×C711yescharacteristic, direct product factor, Hall
19C2×C3×C7×C11C2×C3×C11148yes—
20C32×C4×C11C7×C11112yesdirect product factor
21C3×C112C3×C4×C714yesdirect product factor
22C4×C7×C11C32×C11112yesdirect product factor
23C32×C4×C7C11211yescharacteristic, direct product factor, Hall
24C2×C112C2×C32×C711yescharacteristic
25C3×C7×C11C3×C4×C11148yesdirect product factor
26C2×C32×C11C2×C7×C11112yes—
27C2×C7×C11C2×C32×C11112yes—
28C3×C4×C11C3×C7×C11148yesdirect product factor
29C2×C32×C7C2×C11211yescharacteristic
30C112C32×C4×C711yescharacteristic, direct product factor, Sylow
31C32×C11C4×C7×C11112yesdirect product factor
32C3×C4×C7C3×C11214yesdirect product factor
33C7×C11C32×C4×C11112yesdirect product factor
34C2×C3×C11C2×C3×C7×C11148yes—
35C32×C7C4×C11211yescharacteristic, direct product factor, Hall
36C4×C11C32×C7×C11112yesdirect product factor
37C2×C3×C7C2×C3×C11214yes—
38C32×C4C7×C11211yescharacteristic, direct product factor, Hall
39C3×C11C3×C4×C7×C11148yesdirect product factor
40C4×C7C32×C11211yescharacteristic, direct product factor, Hall
41C2×C11C2×C32×C7×C11112yes—
42C3×C7C3×C4×C11214yesdirect product factor
43C2×C32C2×C7×C11211yescharacteristic
44C2×C7C2×C32×C11211yescharacteristic
45C3×C4C3×C7×C11214yesdirect product factor
46C11C32×C4×C7×C11112yesdirect product factor
47C32C4×C7×C11211yescharacteristic, direct product factor, Sylow
48C7C32×C4×C11211yescharacteristic, direct product factor, Sylow
49C2×C3C2×C3×C7×C11214yes—
50C4C32×C7×C11211yescharacteristic, direct product factor, Sylow
51C3C3×C4×C7×C11214yesdirect product factor
52C2C2×C32×C7×C11211yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C32×C7×C112
socle, prime radicalC2×C32×C7×C112C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C4×C7×C112C3direct (N × H)
3. C32×C7×C112C4direct (N × H)
5. C32×C4×C112C7direct (N × H)
6. C4×C7×C112C32direct (N × H)
7. C32×C4×C7×C11C11direct (N × H)
8. C3×C7×C112C3×C4direct (N × H)
11. C3×C4×C112C3×C7direct (N × H)
13. C32×C112C4×C7direct (N × H)
14. C3×C4×C7×C11C3×C11direct (N × H)
15. C7×C112C32×C4direct (N × H)
17. C32×C7×C11C4×C11direct (N × H)
18. C4×C112C32×C7direct (N × H)
20. C32×C4×C11C7×C11direct (N × H)
21. C3×C112C3×C4×C7direct (N × H)
22. C4×C7×C11C32×C11direct (N × H)
23. C32×C4×C7C112direct (N × H)
25. C3×C7×C11C3×C4×C11direct (N × H)
28. C3×C4×C11C3×C7×C11direct (N × H)
30. C112C32×C4×C7direct (N × H)
31. C32×C11C4×C7×C11direct (N × H)
32. C3×C4×C7C3×C112direct (N × H)
33. C7×C11C32×C4×C11direct (N × H)
35. C32×C7C4×C112direct (N × H)
36. C4×C11C32×C7×C11direct (N × H)
38. C32×C4C7×C112direct (N × H)
39. C3×C11C3×C4×C7×C11direct (N × H)
40. C4×C7C32×C112direct (N × H)
42. C3×C7C3×C4×C112direct (N × H)
45. C3×C4C3×C7×C112direct (N × H)
46. C11C32×C4×C7×C11direct (N × H)
47. C32C4×C7×C112direct (N × H)
48. C7C32×C4×C112direct (N × H)
50. C4C32×C7×C112direct (N × H)
51. C3C3×C4×C7×C112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C7×C1122
C3×C4×C7×C1123
C32×C4×C1127
C32×C4×C7×C1111