Finite Group Databasebeta

← C3⋊(C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))) #44568864

Subgroups — C3⋊(C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))) #44568864

Order 32340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×D5×C11C211yesmaximal, characteristic
2C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))—31nomaximal, Hall
3C3×C5×C72×C11C411yescharacteristic, complemented, Hall
4C3⋊(C7⋊Dic77)—51nomaximal, Hall
5C72×D5×C11D311yescharacteristic
6C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))—78nomaximal
7C2×C3×C72×C11—51no—
8C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))—111nomaximal, Hall
9C5×C72×C11Dic311yescharacteristic, complemented, Hall
10C3×C7×D5×C11D718yes—
11C7⋊Dic77—151noHall
12C3×C72×C11AGL(1,𝔽5)11yescharacteristic, complemented, Hall
13C7⋊(C11⋊AGL(1,𝔽5))—218no—
14C3×C72×D5D1111yescharacteristic
15C3×C5×C7×C11Dic718yescomplemented
16C2×C72×C11—51no—
17C7⋊(C7⋊AGL(1,𝔽5))—331noHall
18Dic231—358no—
19C7×D5×C11D2118yes—
20C3×C5×C72Dic1111yescharacteristic, complemented, Hall
21C3⋊(C11⋊AGL(1,𝔽5))—491noHall
22C3⋊(C7⋊Dic7)—551noHall
23C72×C11ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
24C72×D5D3311yescharacteristic
25C2×C3×C7×C11—58no—
26C3⋊(C7⋊AGL(1,𝔽5))—778no—
27C5×C7×C11Dic2118yescomplemented
28C3×D5×C11C7⋊D711yescharacteristic
29Dic77—1058no—
30C2×C3×C72—51no—
31C5×C72Dic3311yescharacteristic, complemented, Hall
32C3×C7×C11C7⋊AGL(1,𝔽5)18yescomplemented
33C11⋊AGL(1,𝔽5)—1471noHall
34C3×C7×D5D7718yes—
35C7⋊Dic7—1651noHall
36C3×C5×C11C7⋊Dic711yescharacteristic, complemented, Hall
37C2×C7×C11—58no—
38C3×C72C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
39C7⋊AGL(1,𝔽5)—2318no—
40Dic33—2451noHall
41D5×C11C3⋊(C7⋊D7)11yescharacteristic
42C3×C5×C7Dic7718yescomplemented
43C2×C72—51no—
44Dic21—3858no—
45C7×C11C3⋊(C7⋊AGL(1,𝔽5))18yescomplemented
46C7×D5D23118yes—
47C2×C3×C11—51no—
48ΓL(1,𝔽16)—5391noHall
49C5×C11C3⋊(C7⋊Dic7)11yescharacteristic, complemented, Hall
50C72C3⋊(C11⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
51Dic11—7351noHall
52C2×C3×C7—58no—
53C5×C7Dic23118yescomplemented
54C3×C11C7⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Hall
55C3×D5C7⋊D7711yescharacteristic
56Dic7—11558no—
57C2×C11—51no—
58C3×C7C7⋊(C11⋊AGL(1,𝔽5))18yescomplemented
59AGL(1,𝔽5)—16171noHall
60C3×C5C7⋊Dic7711yescharacteristic, complemented, Hall
61C2×C7—58no—
62Dic3—26951noHall
63C11C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))11yescharacteristic, complemented, Sylow
64D5C3⋊(C7⋊D77)11yescharacteristic
65C7C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))18yescomplemented
66C2×C3—51no—
67C5C3⋊(C7⋊Dic77)11yescharacteristic, complemented, Sylow
68C4—80851noSylow
69C3C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))11yescharacteristic, complemented, Sylow
70C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C72×C11C4
prime radical, cosocleC3×C72×D5×C11C2
LCSG ▷ C3×C5×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×C5×C72×C11C4semidirect
9. C5×C72×C11Dic3semidirect
12. C3×C72×C11AGL(1,𝔽5)semidirect
15. C3×C5×C7×C11Dic7semidirect
20. C3×C5×C72Dic11semidirect
23. C72×C11ΓL(1,𝔽16)semidirect
27. C5×C7×C11Dic21semidirect
31. C5×C72Dic33semidirect
32. C3×C7×C11C7⋊AGL(1,𝔽5)semidirect
36. C3×C5×C11C7⋊Dic7semidirect
38. C3×C72C11⋊AGL(1,𝔽5)semidirect
42. C3×C5×C7Dic77semidirect
45. C7×C11C3⋊(C7⋊AGL(1,𝔽5))semidirect
49. C5×C11C3⋊(C7⋊Dic7)semidirect
50. C72C3⋊(C11⋊AGL(1,𝔽5))semidirect
53. C5×C7Dic231semidirect
54. C3×C11C7⋊(C7⋊AGL(1,𝔽5))semidirect
58. C3×C7C7⋊(C11⋊AGL(1,𝔽5))semidirect
60. C3×C5C7⋊Dic77semidirect
63. C11C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))semidirect
65. C7C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))semidirect
67. C5C3⋊(C7⋊Dic77)semidirect
69. C3C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D5×C112
C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))3
C3⋊(C7⋊Dic77)5
C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))7
C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))11