Finite Group Databasebeta

← C2×C3×#19104441 #44528019

Subgroups — C2×C3×#19104441 #44528019

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#19104441C211yesmaximal, characteristic, direct product factor, Hall
2C2×#19104441C313yesmaximal, direct product factor
3C2×C3×C7×C13×C19C311yesmaximal, characteristic, complemented
4#19104441C2×C313yesdirect product factor
5C3×C7×C13×C19C2×C311yescharacteristic, complemented
6C2×C3×#10625203—71nomaximal, Hall
7C2×C7×C13×C19C3211yescharacteristic, complemented, Hall
8C2×C3×#87705—131nomaximal, Hall
9C3×#10625203—71noHall
10C7×C13×C19C2×C3211yescharacteristic, complemented, Hall
11C2×C3×#63270—191nomaximal, Hall
12C2×C3×C13×C19ΓL(1,𝔽8)11yescharacteristic, complemented
13C2×#10625203—73no—
14C3×#87705—131noHall
15C3×#63270—191noHall
16C2×C3×C7×C19C13⋊C311yescharacteristic, complemented
17C2×#87705—133no—
18C3×C13×C19C2×ΓL(1,𝔽8)11yescharacteristic, complemented
19#10625203—73no—
20C2×C3×C7×C13C19⋊C311yescharacteristic, complemented
21C2×#63270—193no—
22C2×C13×C19C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
23C3×C7×C19C2×C13⋊C311yescharacteristic, complemented
24#87705—133no—
25C2×C3×C19⋊C3—911noHall
26C3×C7×C13C2×C19⋊C311yescharacteristic, complemented
27#63270—193no—
28C2×C7×C19C3×C13⋊C311yescharacteristic, complemented, Hall
29C13×C19C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
30C2×C3×C13⋊C3—1331noHall
31C2×C7×C13C3×C19⋊C311yescharacteristic, complemented, Hall
32C3×C19⋊C3—911noHall
33C7×C19C2×C3×C13⋊C311yescharacteristic, complemented, Hall
34C2×C3×ΓL(1,𝔽8)—2471noHall
35C3×C13⋊C3—1331noHall
36C2×C3×C19#6327011yescharacteristic, complemented
37C2×C19⋊C3—913no—
38C7×C13C2×C3×C19⋊C311yescharacteristic, complemented, Hall
39C2×C3×C13#8770511yescharacteristic, complemented
40C2×C13⋊C3—1333no—
41C3×ΓL(1,𝔽8)—2471noHall
42C3×C19C2×#6327011yescharacteristic, complemented
43C19⋊C3—913no—
44C2×C3×C7#1062520311yescharacteristic, complemented
45C2×ΓL(1,𝔽8)—2473no—
46C3×C13C2×#8770511yescharacteristic, complemented
47C13⋊C3—1333no—
48C2×C19C3×#6327011yescharacteristic, complemented, Hall
49C2×C13C3×#8770511yescharacteristic, complemented, Hall
50C3×C7C2×#1062520311yescharacteristic, complemented
51ΓL(1,𝔽8)—2473no—
52C19C2×C3×#6327011yescharacteristic, complemented, Sylow
53C2×C32—17291noHall
54C2×C7C3×#1062520311yescharacteristic, complemented, Hall
55C13C2×C3×#8770511yescharacteristic, complemented, Sylow
56C32—17291noSylow
57C7C2×C3×#1062520311yescharacteristic, complemented, Sylow
58C2×C3—17293no—
59C2×C3#1910444111yescharacteristic, direct product factor
60C3—17293no—
61C3C2×#1910444111yescharacteristic, direct product factor
62C2C3×#1910444111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3#19104441
commutator, cosocle, hypocenterC7×C13×C19C2×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C13×C19C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#19104441C2direct (N × H)
2. C2×#19104441C3direct (N × H)
3. C2×C3×C7×C13×C19C3semidirect
4. #19104441C2×C3direct (N × H)
5. C3×C7×C13×C19C2×C3semidirect
7. C2×C7×C13×C19C32semidirect
10. C7×C13×C19C2×C32semidirect
12. C2×C3×C13×C19ΓL(1,𝔽8)semidirect
16. C2×C3×C7×C19C13⋊C3semidirect
18. C3×C13×C19C2×ΓL(1,𝔽8)semidirect
20. C2×C3×C7×C13C19⋊C3semidirect
22. C2×C13×C19C3×ΓL(1,𝔽8)semidirect
23. C3×C7×C19C2×C13⋊C3semidirect
26. C3×C7×C13C2×C19⋊C3semidirect
28. C2×C7×C19C3×C13⋊C3semidirect
29. C13×C19C2×C3×ΓL(1,𝔽8)semidirect
31. C2×C7×C13C3×C19⋊C3semidirect
33. C7×C19C2×C3×C13⋊C3semidirect
36. C2×C3×C19#63270semidirect
38. C7×C13C2×C3×C19⋊C3semidirect
39. C2×C3×C13#87705semidirect
42. C3×C19C2×#63270semidirect
44. C2×C3×C7#10625203semidirect
46. C3×C13C2×#87705semidirect
48. C2×C19C3×#63270semidirect
49. C2×C13C3×#87705semidirect
50. C3×C7C2×#10625203semidirect
52. C19C2×C3×#63270semidirect
54. C2×C7C3×#10625203semidirect
55. C13C2×C3×#87705semidirect
57. C7C2×C3×#10625203semidirect
59. C2×C3#19104441direct (N × H)
61. C3C2×#19104441direct (N × H)
62. C2C3×#19104441direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#191044412
C2×#191044413
C2×C3×C7×C13×C193
C2×C3×#106252037
C2×C3×#8770513
C2×C3×#6327019