Finite Group Databasebeta

← C11×#13097586 #31798220

Subgroups — C11×#13097586 #31798220

Order 17556.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#87704C211yesmaximal, characteristic
2C11×C19×Dic7C311yesmaximal, characteristic, complemented, Hall
3C11×#87704C411yescharacteristic, complemented, Hall
4C2×C7×C11×C19C2×C311yescharacteristic
5C4×C11×C19⋊C3—71nomaximal, Hall
6#13097586C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C19C3×C411yescharacteristic, complemented, Hall
8C2×C11×C19⋊C3—71no—
9C11×ΓL(1,𝔽8)⋊C4—191nomaximal, Hall
10C4×C11×C19—71noHall
11C2×#87704C2×C1111yescharacteristic
12C11×C19⋊C3—71noHall
13C19×Dic7C3×C1111yescharacteristic, complemented, Hall
14C2×C11×ΓL(1,𝔽8)—191no—
15C2×C11×C19AGL(1,𝔽7)11yescharacteristic
16#87704C4×C1111yescharacteristic, complemented, Hall
17C11×Dic7C19⋊C311yescharacteristic, complemented, Hall
18C2×C7×C19C2×C3×C1111yescharacteristic
19C11×ΓL(1,𝔽8)—191noHall
20C4×C19⋊C3—71noHall
21C11×C19ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
22C2×C7×C11C2×C19⋊C311yescharacteristic
23C7×C19C3×C4×C1111yescharacteristic, complemented, Hall
24C3×C4×C11—1331noHall
25C2×C19⋊C3—71no—
26ΓL(1,𝔽8)⋊C4—191noHall
27C7×C11C4×C19⋊C311yescharacteristic, complemented, Hall
28C4×C19—71noHall
29C2×C3×C11—1331no—
30C19⋊C3—71noHall
31C4×C11—71noHall
32C2×ΓL(1,𝔽8)—191no—
33C2×C19C11×AGL(1,𝔽7)11yescharacteristic
34C3×C11—1331noHall
35Dic7C11×C19⋊C311yescharacteristic, complemented, Hall
36C2×C11#1171632511yescharacteristic
37ΓL(1,𝔽8)—191noHall
38C19C11×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Sylow
39C2×C7C2×C11×C19⋊C311yescharacteristic
40C3×C4—1331noHall
41C11#1309758611yescharacteristic, direct product factor, Sylow
42C7C4×C11×C19⋊C311yescharacteristic, complemented, Sylow
43C2×C3—1331no—
44C4—71noSylow
45C3—1331noSylow
46C2C11×#1171632511yescharacteristic
subgroupG/H
center, hypercenterC2×C11#11716325
commutator, hypocenterC7×C19C3×C4×C11
FrattiniC2C11×#11716325
Fitting, socleC2×C7×C11×C19C2×C3
prime radicalC2×C11×#87704C2
cosocleC2×C7×C19C2×C3×C11
LCSG ▷ C7×C19
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
2. C11×C19×Dic7C3semidirect
3. C11×#87704C4semidirect
6. #13097586C11direct (N × H)
7. C7×C11×C19C3×C4semidirect
13. C19×Dic7C3×C11semidirect
16. #87704C4×C11semidirect
17. C11×Dic7C19⋊C3semidirect
21. C11×C19ΓL(1,𝔽8)⋊C4semidirect
23. C7×C19C3×C4×C11semidirect
27. C7×C11C4×C19⋊C3semidirect
35. Dic7C11×C19⋊C3semidirect
38. C19C11×ΓL(1,𝔽8)⋊C4semidirect
41. C11#13097586direct (N × H)
42. C7C4×C11×C19⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#877042
C11×C19×Dic73
C4×C11×C19⋊C37
#1309758611
C11×ΓL(1,𝔽8)⋊C419