Finite Group Databasebeta

← C3×C7⋊(C7⋊(C11⋊AGL(1,𝔽5))) #44568816

Subgroups — C3×C7⋊(C7⋊(C11⋊AGL(1,𝔽5))) #44568816

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)))C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C11C411yescharacteristic, complemented, Hall
4C3×C7⋊Dic77—51nomaximal, Hall
5C72×D5×C11C2×C311yescharacteristic
6C3×C7⋊(C11⋊AGL(1,𝔽5))—78nomaximal
7C2×C3×C72×C11—51no—
8C3×C7⋊(C7⋊AGL(1,𝔽5))—111nomaximal, Hall
9C5×C72×C11C3×C411yescharacteristic, complemented, Hall
10C3×C7×D5×C11D718yes—
11C7⋊Dic77—51noHall
12C3×C72×C11AGL(1,𝔽5)11yescharacteristic, complemented, Hall
13C7⋊(C11⋊AGL(1,𝔽5))—78no—
14C3×C72×D5D1111yescharacteristic
15C3×C5×C7×C11Dic718yescomplemented
16C2×C72×C11—51no—
17C7⋊(C7⋊AGL(1,𝔽5))—111noHall
18C3×Dic77—358no—
19C7×D5×C11C3×D718yes—
20C3×C5×C72Dic1111yescharacteristic, complemented, Hall
21C3×C11⋊AGL(1,𝔽5)—491noHall
22C3×C7⋊Dic7—551noHall
23C72×C11C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
24C72×D5C3×D1111yescharacteristic
25C2×C3×C7×C11—58no—
26C3×C7⋊AGL(1,𝔽5)—778no—
27C5×C7×C11C3×Dic718yescomplemented
28C3×D5×C11C7⋊D711yescharacteristic
29Dic77—358no—
30C2×C3×C72—51no—
31C5×C72C3×Dic1111yescharacteristic, complemented, Hall
32C3×C7×C11C7⋊AGL(1,𝔽5)18yescomplemented
33C11⋊AGL(1,𝔽5)—491noHall
34C3×C7×D5D7718yes—
35C7⋊Dic7—551noHall
36C3×C5×C11C7⋊Dic711yescharacteristic, complemented, Hall
37C2×C7×C11—58no—
38C3×C72C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
39C7⋊AGL(1,𝔽5)—778no—
40C3×Dic11—2451noHall
41D5×C11C3×C7⋊D711yescharacteristic
42C3×C5×C7Dic7718yescomplemented
43C2×C72—51no—
44C3×Dic7—3858no—
45C7×C11C3×C7⋊AGL(1,𝔽5)18yescomplemented
46C7×D5C3×D7718yes—
47C2×C3×C11—51no—
48C3×AGL(1,𝔽5)—5391noHall
49C5×C11C3×C7⋊Dic711yescharacteristic, complemented, Hall
50C72C3×C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
51Dic11—2451noHall
52C2×C3×C7—58no—
53C5×C7C3×Dic7718yescomplemented
54C3×C11C7⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Hall
55C3×D5C7⋊D7711yescharacteristic
56Dic7—3858no—
57C2×C11—51no—
58C3×C7C7⋊(C11⋊AGL(1,𝔽5))18yescomplemented
59AGL(1,𝔽5)—5391noHall
60C3×C5C7⋊Dic7711yescharacteristic, complemented, Hall
61C2×C7—58no—
62C3×C4—26951noHall
63C11C3×C7⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
64D5C3×C7⋊D7711yescharacteristic
65C7C3×C7⋊(C11⋊AGL(1,𝔽5))18yescomplemented
66C2×C3—51no—
67C5C3×C7⋊Dic7711yescharacteristic, complemented, Sylow
68C4—26951noSylow
69C3C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))11yescharacteristic, direct product factor, Sylow
70C2—51no—
subgroupG/H
center, hypercenterC3C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))
commutator, hypocenterC5×C72×C11C3×C4
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C72×D5×C11C2
cosocleC72×D5×C11C2×C3
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))C3direct (N × H)
3. C3×C5×C72×C11C4semidirect
9. C5×C72×C11C3×C4semidirect
12. C3×C72×C11AGL(1,𝔽5)semidirect
15. C3×C5×C7×C11Dic7semidirect
20. C3×C5×C72Dic11semidirect
23. C72×C11C3×AGL(1,𝔽5)semidirect
27. C5×C7×C11C3×Dic7semidirect
31. C5×C72C3×Dic11semidirect
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⋊Dic7semidirect
50. C72C3×C11⋊AGL(1,𝔽5)semidirect
53. C5×C7C3×Dic77semidirect
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⋊Dic77semidirect
69. C3C7⋊(C7⋊(C11⋊AGL(1,𝔽5)))direct (N × H)

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⋊Dic775
C3×C7⋊(C11⋊AGL(1,𝔽5))7
C3×C7⋊(C7⋊AGL(1,𝔽5))11