Finite Group Databasebeta

← C11⋊C5×C22⋊#3862 #44568614

Subgroups — C11⋊C5×C22⋊#3862 #44568614

Order 32340.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C72×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
2C11⋊C5×#3862—41nomaximal, Hall
3C11×C22⋊#3862C511yesmaximal, characteristic, complemented, Hall
4C2×C72×C11⋊C5—31no—
5C11⋊C5×C22⋊ΓL(1,𝔽8)—72nomaximal
6C5×C22⋊#3862—111nomaximal, Hall
7C72×C11⋊C5A411yescharacteristic, complemented, Hall
8C22×C72×C11C3×C511yescharacteristic, complemented, Hall
9C11×#3862—41noHall
10C22×C7×C11⋊C5—32no—
11C22×C7×C11⋊C5ΓL(1,𝔽8)12yescomplemented
12ΓL(1,𝔽8)×C11⋊C5—282no—
13C2×C72×C11—31no—
14C22×C5×C72—111noHall
15C11×C22⋊ΓL(1,𝔽8)—72no—
16C2×C7×C11⋊C5—36no—
17C2×C7×C11⋊C5—32no—
18C5×#3862—441noHall
19A4×C11⋊C5—491noHall
20C22⋊#3862C11⋊C511yescharacteristic, direct product factor, Hall
21C72×C11C5×A411yescharacteristic, complemented, Hall
22C2×C5×C72—331no—
23C5×C22⋊ΓL(1,𝔽8)—772no—
24C7×C11⋊C5—32no—
25C7×C11⋊C5C22⋊ΓL(1,𝔽8)12yescomplemented
26C22×C7×C11—32no—
27C22×C7×C11C5×ΓL(1,𝔽8)12yescomplemented
28C5×C72—111noHall
29C11×ΓL(1,𝔽8)—282no—
30C22×C11⋊C5#386211yescharacteristic, complemented, Hall
31C22×C72C3×C11⋊C511yescharacteristic, complemented, Hall
32C3×C11⋊C5—1961noHall
33C2×C7×C11—36no—
34C2×C7×C11—32no—
35#3862—41noHall
36C22×C5×C7—112no—
37C22×C5×C7—332no—
38C11×A4—491noHall
39C2×C11⋊C5—31no—
40C5×ΓL(1,𝔽8)—3082no—
41C2×C72—31no—
42C22⋊ΓL(1,𝔽8)—72no—
43C7×C11—32no—
44C7×C11C5×C22⋊ΓL(1,𝔽8)12yescomplemented
45C2×C5×C7—332no—
46C2×C5×C7—336no—
47C5×A4—5391noHall
48C11⋊C5C22⋊#386211yescharacteristic, direct product factor, Hall
49C72A4×C11⋊C511yescharacteristic, complemented, Sylow
50C22×C11C5×#386211yescharacteristic, complemented, Hall
51C5×C7—112no—
52C5×C7—332no—
53C3×C11—1961noHall
54C22×C7—32no—
55C22×C7ΓL(1,𝔽8)×C11⋊C512yescomplemented
56C2×C11—31no—
57ΓL(1,𝔽8)—282no—
58C22×C5—111noHall
59C3×C5—21561noHall
60C2×C7—36no—
61C2×C7—32no—
62A4—491noHall
63C11C5×C22⋊#386211yescharacteristic, complemented, Sylow
64C2×C5—331no—
65C7—32no—
66C7C11⋊C5×C22⋊ΓL(1,𝔽8)12yescomplemented
67C5—111noSylow
68C22C11⋊C5×#386211yescharacteristic, complemented, Sylow
69C3—1961noSylow
70C2—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⋊#3862C5semidirect
7. C72×C11⋊C5A4semidirect
8. C22×C72×C11C3×C5semidirect
11. C22×C7×C11⋊C5ΓL(1,𝔽8)semidirect
20. C22⋊#3862C11⋊C5direct (N × H)
21. C72×C11C5×A4semidirect
25. C7×C11⋊C5C22⋊ΓL(1,𝔽8)semidirect
27. C22×C7×C11C5×ΓL(1,𝔽8)semidirect
30. C22×C11⋊C5#3862semidirect
31. C22×C72C3×C11⋊C5semidirect
44. C7×C11C5×C22⋊ΓL(1,𝔽8)semidirect
48. C11⋊C5C22⋊#3862direct (N × H)
49. C72A4×C11⋊C5semidirect
50. C22×C11C5×#3862semidirect
55. C22×C7ΓL(1,𝔽8)×C11⋊C5semidirect
63. C11C5×C22⋊#3862semidirect
66. C7C11⋊C5×C22⋊ΓL(1,𝔽8)semidirect
68. C22C11⋊C5×#3862semidirect

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×#38624
C11×C22⋊#38625
C11⋊C5×C22⋊ΓL(1,𝔽8)7
C5×C22⋊#386211