Finite Group Databasebeta

← C5×C11×C22⋊#3861 #44568927

Subgroups — C5×C11×C22⋊#3861 #44568927

Order 32340.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C72×C11C311yesmaximal, characteristic, complemented, Hall
2C5×C11×#3861—41nomaximal, Hall
3C11×C22⋊#3861C511yesmaximal, characteristic, direct product factor, Hall
4C2×C5×C72×C11—31no—
5C5×C11×C22⋊ΓL(1,𝔽8)—78nomaximal
6C5×C22⋊#3861C1111yesmaximal, characteristic, direct product factor, Hall
7C5×C72×C11A411yescharacteristic, complemented, Hall
8C22×C72×C11C3×C511yescharacteristic, complemented, Hall
9C11×#3861—41noHall
10C22×C5×C7×C11ΓL(1,𝔽8)18yescomplemented
11C5×C11×ΓL(1,𝔽8)—288no—
12C2×C72×C11—31no—
13C22×C5×C72C3×C1111yescharacteristic, complemented, Hall
14C11×C22⋊ΓL(1,𝔽8)—78no—
15C2×C5×C7×C11—38no—
16C5×#3861—41noHall
17C5×C11×A4—491noHall
18C22⋊#3861C5×C1111yescharacteristic, direct product factor, Hall
19C72×C11C5×A411yescharacteristic, complemented, Hall
20C2×C5×C72—31no—
21C5×C22⋊ΓL(1,𝔽8)—78no—
22C5×C7×C11C22⋊ΓL(1,𝔽8)18yescomplemented
23C22×C7×C11C5×ΓL(1,𝔽8)18yescomplemented
24C5×C72C11×A411yescharacteristic, complemented, Hall
25C11×ΓL(1,𝔽8)—288no—
26C22×C5×C11#386111yescharacteristic, complemented, Hall
27C22×C72C3×C5×C1111yescharacteristic, complemented, Hall
28C3×C5×C11—1961noHall
29C2×C7×C11—38no—
30#3861—41noHall
31C22×C5×C7C11×ΓL(1,𝔽8)18yescomplemented
32C11×A4—491noHall
33C2×C5×C11—31no—
34C5×ΓL(1,𝔽8)—288no—
35C2×C72—31no—
36C22⋊ΓL(1,𝔽8)—78no—
37C7×C11C5×C22⋊ΓL(1,𝔽8)18yescomplemented
38C2×C5×C7—38no—
39C5×A4—491noHall
40C5×C11C22⋊#386111yescharacteristic, direct product factor, Hall
41C72C5×C11×A411yescharacteristic, complemented, Sylow
42C22×C11C5×#386111yescharacteristic, complemented, Hall
43C5×C7C11×C22⋊ΓL(1,𝔽8)18yescomplemented
44C3×C11—1961noHall
45C22×C7C5×C11×ΓL(1,𝔽8)18yescomplemented
46C2×C11—31no—
47ΓL(1,𝔽8)—288no—
48C22×C5C11×#386111yescharacteristic, complemented, Hall
49C3×C5—1961noHall
50C2×C7—38no—
51A4—491noHall
52C11C5×C22⋊#386111yescharacteristic, direct product factor, Sylow
53C2×C5—31no—
54C7C5×C11×C22⋊ΓL(1,𝔽8)18yescomplemented
55C5C11×C22⋊#386111yescharacteristic, direct product factor, Sylow
56C22C5×C11×#386111yescharacteristic, complemented, Sylow
57C3—1961noSylow
58C2—31no—
subgroupG/H
center, hypercenterC5×C11C22⋊#3861
commutator, cosocle, hypocenterC22×C72C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C72×C11C3
LCSG ▷ C22×C72
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C22×C5×C72×C11C3semidirect
3. C11×C22⋊#3861C5direct (N × H)
6. C5×C22⋊#3861C11direct (N × H)
7. C5×C72×C11A4semidirect
8. C22×C72×C11C3×C5semidirect
10. C22×C5×C7×C11ΓL(1,𝔽8)semidirect
13. C22×C5×C72C3×C11semidirect
18. C22⋊#3861C5×C11direct (N × H)
19. C72×C11C5×A4semidirect
22. C5×C7×C11C22⋊ΓL(1,𝔽8)semidirect
23. C22×C7×C11C5×ΓL(1,𝔽8)semidirect
24. C5×C72C11×A4semidirect
26. C22×C5×C11#3861semidirect
27. C22×C72C3×C5×C11semidirect
31. C22×C5×C7C11×ΓL(1,𝔽8)semidirect
37. C7×C11C5×C22⋊ΓL(1,𝔽8)semidirect
40. C5×C11C22⋊#3861direct (N × H)
41. C72C5×C11×A4semidirect
42. C22×C11C5×#3861semidirect
43. C5×C7C11×C22⋊ΓL(1,𝔽8)semidirect
45. C22×C7C5×C11×ΓL(1,𝔽8)semidirect
48. C22×C5C11×#3861semidirect
52. C11C5×C22⋊#3861direct (N × H)
54. C7C5×C11×C22⋊ΓL(1,𝔽8)semidirect
55. C5C11×C22⋊#3861direct (N × H)
56. C22C5×C11×#3861semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C72×C113
C5×C11×#38614
C11×C22⋊#38615
C5×C11×C22⋊ΓL(1,𝔽8)7
C5×C22⋊#386111