Finite Group Databasebeta

← C11⋊C5×C22⋊#3861 #44568613

Subgroups — C11⋊C5×C22⋊#3861 #44568613

Order 32340.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C72×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
2C11⋊C5×#3861—41nomaximal, Hall
3C11×C22⋊#3861C511yesmaximal, characteristic, complemented, Hall
4C2×C72×C11⋊C5—31no—
5C11⋊C5×C22⋊ΓL(1,𝔽8)—78nomaximal
6C5×C22⋊#3861—111nomaximal, Hall
7C72×C11⋊C5A411yescharacteristic, complemented, Hall
8C22×C72×C11C3×C511yescharacteristic, complemented, Hall
9C11×#3861—41noHall
10C22×C7×C11⋊C5ΓL(1,𝔽8)18yescomplemented
11ΓL(1,𝔽8)×C11⋊C5—288no—
12C2×C72×C11—31no—
13C22×C5×C72—111noHall
14C11×C22⋊ΓL(1,𝔽8)—78no—
15C2×C7×C11⋊C5—38no—
16C5×#3861—441noHall
17A4×C11⋊C5—491noHall
18C22⋊#3861C11⋊C511yescharacteristic, direct product factor, Hall
19C72×C11C5×A411yescharacteristic, complemented, Hall
20C2×C5×C72—331no—
21C5×C22⋊ΓL(1,𝔽8)—778no—
22C7×C11⋊C5C22⋊ΓL(1,𝔽8)18yescomplemented
23C22×C7×C11C5×ΓL(1,𝔽8)18yescomplemented
24C5×C72—111noHall
25C11×ΓL(1,𝔽8)—288no—
26C22×C11⋊C5#386111yescharacteristic, complemented, Hall
27C22×C72C3×C11⋊C511yescharacteristic, complemented, Hall
28C3×C11⋊C5—1961noHall
29C2×C7×C11—38no—
30#3861—41noHall
31C22×C5×C7—118no—
32C11×A4—491noHall
33C2×C11⋊C5—31no—
34C5×ΓL(1,𝔽8)—3088no—
35C2×C72—31no—
36C22⋊ΓL(1,𝔽8)—78no—
37C7×C11C5×C22⋊ΓL(1,𝔽8)18yescomplemented
38C2×C5×C7—338no—
39C5×A4—5391noHall
40C11⋊C5C22⋊#386111yescharacteristic, direct product factor, Hall
41C72A4×C11⋊C511yescharacteristic, complemented, Sylow
42C22×C11C5×#386111yescharacteristic, complemented, Hall
43C5×C7—118no—
44C3×C11—1961noHall
45C22×C7ΓL(1,𝔽8)×C11⋊C518yescomplemented
46C2×C11—31no—
47ΓL(1,𝔽8)—288no—
48C22×C5—111noHall
49C3×C5—21561noHall
50C2×C7—38no—
51A4—491noHall
52C11C5×C22⋊#386111yescharacteristic, complemented, Sylow
53C2×C5—331no—
54C7C11⋊C5×C22⋊ΓL(1,𝔽8)18yescomplemented
55C5—111noSylow
56C22C11⋊C5×#386111yescharacteristic, complemented, Sylow
57C3—1961noSylow
58C2—31no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C72×C11C3×C5
LCSG ▷ C22×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C22×C72×C11⋊C5C3semidirect
3. C11×C22⋊#3861C5semidirect
7. C72×C11⋊C5A4semidirect
8. C22×C72×C11C3×C5semidirect
10. C22×C7×C11⋊C5ΓL(1,𝔽8)semidirect
18. C22⋊#3861C11⋊C5direct (N × H)
19. C72×C11C5×A4semidirect
22. C7×C11⋊C5C22⋊ΓL(1,𝔽8)semidirect
23. C22×C7×C11C5×ΓL(1,𝔽8)semidirect
26. C22×C11⋊C5#3861semidirect
27. C22×C72C3×C11⋊C5semidirect
37. C7×C11C5×C22⋊ΓL(1,𝔽8)semidirect
40. C11⋊C5C22⋊#3861direct (N × H)
41. C72A4×C11⋊C5semidirect
42. C22×C11C5×#3861semidirect
45. C22×C7ΓL(1,𝔽8)×C11⋊C5semidirect
52. C11C5×C22⋊#3861semidirect
54. C7C11⋊C5×C22⋊ΓL(1,𝔽8)semidirect
56. C22C11⋊C5×#3861semidirect

Maximal subgroups

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

subgroupindex
C22×C72×C11⋊C53
C11⋊C5×#38614
C11×C22⋊#38615
C11⋊C5×C22⋊ΓL(1,𝔽8)7
C5×C22⋊#386111