Finite Group Databasebeta

← C11×AGL(1,𝔽5)×#3861 #44568657

Subgroups — C11×AGL(1,𝔽5)×#3861 #44568657

Order 32340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C11×#3861C211yesmaximal, characteristic
2C72×C11×AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
3C5×C11×#3861C411yescharacteristic, complemented, Hall
4C4×C11×#3861—51nomaximal, Hall
5C72×D5×C11C2×C311yescharacteristic
6C11×AGL(1,𝔽5)×ΓL(1,𝔽8)—78nomaximal
7C2×C11×#3861—51no—
8AGL(1,𝔽5)×#3861C1111yesmaximal, characteristic, direct product factor, Hall
9C5×C72×C11C3×C411yescharacteristic, complemented, Hall
10D5×C11×ΓL(1,𝔽8)—78no—
11C4×C72×C11—51noHall
12C11×#3861AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
13C7×C11×AGL(1,𝔽5)ΓL(1,𝔽8)18yescomplemented
14D5×#3861C2×C1111yescharacteristic
15C5×C11×ΓL(1,𝔽8)—78no—
16C2×C72×C11—51no—
17C72×AGL(1,𝔽5)C3×C1111yescharacteristic, complemented, Hall
18C4×C11×ΓL(1,𝔽8)—358no—
19C7×D5×C11C2×ΓL(1,𝔽8)18yes—
20C5×#3861C4×C1111yescharacteristic, complemented, Hall
21C3×C11×AGL(1,𝔽5)—491noHall
22C4×#3861—51noHall
23C72×C11C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
24C72×D5C2×C3×C1111yescharacteristic
25C2×C11×ΓL(1,𝔽8)—358no—
26AGL(1,𝔽5)×ΓL(1,𝔽8)—78no—
27C5×C7×C11C4×ΓL(1,𝔽8)18yescomplemented
28C3×D5×C11—491no—
29C4×C7×C11—58no—
30C2×#3861—51no—
31C5×C72C3×C4×C1111yescharacteristic, complemented, Hall
32C11×ΓL(1,𝔽8)—78no—
33C11×AGL(1,𝔽5)#386111yescharacteristic, direct product factor, Hall
34D5×ΓL(1,𝔽8)—78no—
35C4×C72—51noHall
36C3×C5×C11—491noHall
37C2×C7×C11—58no—
38#3861C11×AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
39C7×AGL(1,𝔽5)C11×ΓL(1,𝔽8)18yescomplemented
40C3×C4×C11—2451noHall
41D5×C11C2×#386111yescharacteristic
42C5×ΓL(1,𝔽8)—78no—
43C2×C72—51no—
44C4×ΓL(1,𝔽8)—358no—
45C7×C11AGL(1,𝔽5)×ΓL(1,𝔽8)18yescomplemented
46C7×D5C2×C11×ΓL(1,𝔽8)18yes—
47C2×C3×C11—2451no—
48C3×AGL(1,𝔽5)—491noHall
49C5×C11C4×#386111yescharacteristic, complemented, Hall
50C72C3×C11×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
51C4×C11—51noHall
52C2×ΓL(1,𝔽8)—358no—
53C5×C7C4×C11×ΓL(1,𝔽8)18yescomplemented
54C3×C11—491noHall
55C3×D5—491no—
56C4×C7—58no—
57C2×C11—51no—
58ΓL(1,𝔽8)—78no—
59AGL(1,𝔽5)C11×#386111yescharacteristic, direct product factor, Hall
60C3×C5—491noHall
61C2×C7—58no—
62C3×C4—2451noHall
63C11AGL(1,𝔽5)×#386111yescharacteristic, direct product factor, Sylow
64D5C2×C11×#386111yescharacteristic
65C7C11×AGL(1,𝔽5)×ΓL(1,𝔽8)18yescomplemented
66C2×C3—2451no—
67C5C4×C11×#386111yescharacteristic, complemented, Sylow
68C4—51noSylow
69C3—491noSylow
70C2—51no—
subgroupG/H
center, hypercenterC11AGL(1,𝔽5)×#3861
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalD5×C11×#3861C2
cosocleC72×D5C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
2. C72×C11×AGL(1,𝔽5)C3semidirect
3. C5×C11×#3861C4semidirect
8. AGL(1,𝔽5)×#3861C11direct (N × H)
9. C5×C72×C11C3×C4semidirect
12. C11×#3861AGL(1,𝔽5)direct (N × H)
13. C7×C11×AGL(1,𝔽5)ΓL(1,𝔽8)semidirect
17. C72×AGL(1,𝔽5)C3×C11semidirect
20. C5×#3861C4×C11semidirect
23. C72×C11C3×AGL(1,𝔽5)semidirect
27. C5×C7×C11C4×ΓL(1,𝔽8)semidirect
31. C5×C72C3×C4×C11semidirect
33. C11×AGL(1,𝔽5)#3861direct (N × H)
38. #3861C11×AGL(1,𝔽5)direct (N × H)
39. C7×AGL(1,𝔽5)C11×ΓL(1,𝔽8)semidirect
45. C7×C11AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
49. C5×C11C4×#3861semidirect
50. C72C3×C11×AGL(1,𝔽5)semidirect
53. C5×C7C4×C11×ΓL(1,𝔽8)semidirect
59. AGL(1,𝔽5)C11×#3861direct (N × H)
63. C11AGL(1,𝔽5)×#3861direct (N × H)
65. C7C11×AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
67. C5C4×C11×#3861semidirect

Maximal subgroups

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

subgroupindex
D5×C11×#38612
C72×C11×AGL(1,𝔽5)3
C4×C11×#38615
C11×AGL(1,𝔽5)×ΓL(1,𝔽8)7
AGL(1,𝔽5)×#386111