Finite Group Databasebeta

← ΓL(1,𝔽8)×C11⋊#1039 #37528362

Subgroups — ΓL(1,𝔽8)×C11⋊#1039 #37528362

Order 23100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C52×C11×ΓL(1,𝔽8)C211yesmaximal, characteristic
2C7×C11⋊#1039C311yesmaximal, characteristic, complemented, Hall
3C52×C11×ΓL(1,𝔽8)C411yescharacteristic, complemented, Hall
4ΓL(1,𝔽8)×Dic55—56nomaximal
5C2×C52×C7×C11C2×C311yescharacteristic
6C3×C11⋊#1039—71nomaximal, Hall
7C2×C5×C11×ΓL(1,𝔽8)D516yes—
8ΓL(1,𝔽8)×#1039—111nomaximal, Hall
9C52×C7×C11C3×C411yescharacteristic, complemented, Hall
10C2×C3×C52×C11—71no—
11C7×Dic55—56no—
12C5×C11×ΓL(1,𝔽8)Dic516yescomplemented
13C11⋊#1039ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
14C2×C52×ΓL(1,𝔽8)D1111yescharacteristic
15ΓL(1,𝔽8)×Dic11—251noHall
16C3×C52×C11—71noHall
17C2×C5×C7×C11C3×D516yes—
18C7×#1039—111noHall
19C3×Dic55—356no—
20C2×C52×C11C2×ΓL(1,𝔽8)11yescharacteristic
21C52×ΓL(1,𝔽8)Dic1111yescharacteristic, complemented, Hall
22C2×C11×ΓL(1,𝔽8)C5⋊D511yescharacteristic
23Dic5×ΓL(1,𝔽8)—556no—
24C5×C7×C11C3×Dic516yescomplemented
25C2×C52×C7C3×D1111yescharacteristic
26C2×C3×C5×C11—76no—
27C7×Dic11—251noHall
28C3×#1039—771noHall
29C52×C11C4×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
30C11×ΓL(1,𝔽8)#103911yescharacteristic, complemented, Hall
31Dic55—56no—
32C2×C5×ΓL(1,𝔽8)D5516yes—
33C52×C7C3×Dic1111yescharacteristic, complemented, Hall
34C3×C5×C11—76no—
35C2×C7×C11C3×C5⋊D511yescharacteristic
36C2×C3×C52—71no—
37C7×Dic5—556no—
38C3×Dic11—1751noHall
39C2×C5×C11D5×ΓL(1,𝔽8)16yes—
40C5×ΓL(1,𝔽8)Dic5516yescomplemented
41#1039—111noHall
42C4×ΓL(1,𝔽8)—2751noHall
43C7×C11C3×#103911yescharacteristic, complemented, Hall
44C3×C52—71noHall
45C2×C5×C7C3×D5516yes—
46C2×C3×C11—71no—
47C3×Dic5—3856no—
48C5×C11Dic5×ΓL(1,𝔽8)16yescomplemented
49C2×C52ΓL(1,𝔽8)×D1111yescharacteristic
50Dic11—251noHall
51C2×ΓL(1,𝔽8)C5⋊D5511yescharacteristic
52C5×C7C3×Dic5516yescomplemented
53C3×C11—71noHall
54C2×C3×C5—76no—
55C4×C7—2751noHall
56C52ΓL(1,𝔽8)×Dic1111yescharacteristic, complemented, Sylow
57C2×C11ΓL(1,𝔽8)×C5⋊D511yescharacteristic
58ΓL(1,𝔽8)C11⋊#103911yescharacteristic, direct product factor, Hall
59Dic5—556no—
60C3×C5—76no—
61C2×C7C3×C5⋊D5511yescharacteristic
62C3×C4—19251noHall
63C11ΓL(1,𝔽8)×#103911yescharacteristic, complemented, Sylow
64C2×C5ΓL(1,𝔽8)×D5516yes—
65C7C3×C11⋊#103911yescharacteristic, complemented, Sylow
66C2×C3—71no—
67C5ΓL(1,𝔽8)×Dic5516yescomplemented
68C4—2751noSylow
69C3—71noSylow
70C2ΓL(1,𝔽8)×C5⋊D5511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×C5⋊D55
commutator, hypocenterC52×C7×C11C3×C4
Fitting, socle, cosocleC2×C52×C7×C11C2×C3
prime radicalC2×C52×C11×ΓL(1,𝔽8)C2
LCSG ▷ C52×C7×C11
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C7×C11⋊#1039C3semidirect
3. C52×C11×ΓL(1,𝔽8)C4semidirect
9. C52×C7×C11C3×C4semidirect
12. C5×C11×ΓL(1,𝔽8)Dic5semidirect
13. C11⋊#1039ΓL(1,𝔽8)direct (N × H)
21. C52×ΓL(1,𝔽8)Dic11semidirect
24. C5×C7×C11C3×Dic5semidirect
29. C52×C11C4×ΓL(1,𝔽8)semidirect
30. C11×ΓL(1,𝔽8)#1039semidirect
33. C52×C7C3×Dic11semidirect
40. C5×ΓL(1,𝔽8)Dic55semidirect
43. C7×C11C3×#1039semidirect
48. C5×C11Dic5×ΓL(1,𝔽8)semidirect
52. C5×C7C3×Dic55semidirect
56. C52ΓL(1,𝔽8)×Dic11semidirect
58. ΓL(1,𝔽8)C11⋊#1039direct (N × H)
63. C11ΓL(1,𝔽8)×#1039semidirect
65. C7C3×C11⋊#1039semidirect
67. C5ΓL(1,𝔽8)×Dic55semidirect

Maximal subgroups

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

subgroupindex
C2×C52×C11×ΓL(1,𝔽8)2
C7×C11⋊#10393
ΓL(1,𝔽8)×Dic555
C3×C11⋊#10397
ΓL(1,𝔽8)×#103911