Finite Group Databasebeta

← C11×#15690926 #46803167

Subgroups — C11×#15690926 #46803167

Order 34188.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#11715913C211yesmaximal, characteristic
2C11×Dic259C311yesmaximal, characteristic, complemented, Hall
3C11×#11715913C411yescharacteristic, complemented, Hall
4C2×C7×C11×C37C2×C311yescharacteristic
5C11×Dic37⋊C3—71nomaximal, Hall
6#15690926C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C37C3×C411yescharacteristic, complemented, Hall
8C2×C11×C37⋊C3—71no—
9C11×Dic37—71noHall
10C2×#11715913C2×C1111yescharacteristic
11C11×C37⋊C3—71noHall
12Dic259C3×C1111yescharacteristic, complemented, Hall
13C11×ΓL(1,𝔽8)⋊C4—371nomaximal, Hall
14C2×C11×C37AGL(1,𝔽7)11yescharacteristic
15#11715913C4×C1111yescharacteristic, complemented, Hall
16C2×C7×C37C2×C3×C1111yescharacteristic
17C2×C11×ΓL(1,𝔽8)—371no—
18Dic37⋊C3—71noHall
19C11×C37ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
20C11×Dic7—371noHall
21C7×C37C3×C4×C1111yescharacteristic, complemented, Hall
22C11×ΓL(1,𝔽8)—371noHall
23C2×C37⋊C3—71no—
24C2×C7×C11D37⋊C311yescharacteristic
25Dic37—71noHall
26C3×C4×C11—2591noHall
27C37⋊C3—71noHall
28ΓL(1,𝔽8)⋊C4—371noHall
29C7×C11Dic37⋊C311yescharacteristic, complemented, Hall
30C2×C37C11×AGL(1,𝔽7)11yescharacteristic
31C2×C3×C11—2591no—
32C4×C11—2591noHall
33C2×ΓL(1,𝔽8)—371no—
34C37C11×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Sylow
35C3×C11—2591noHall
36Dic7—371noHall
37C2×C11#1309553711yescharacteristic
38ΓL(1,𝔽8)—371noHall
39C2×C7C11×D37⋊C311yescharacteristic
40C3×C4—2591noHall
41C11#1569092611yescharacteristic, direct product factor, Sylow
42C7C11×Dic37⋊C311yescharacteristic, complemented, Sylow
43C2×C3—2591no—
44C4—2591noSylow
45C3—2591noSylow
46C2C11×#1309553711yescharacteristic
subgroupG/H
center, hypercenterC2×C11#13095537
commutator, hypocenterC7×C37C3×C4×C11
FrattiniC2C11×#13095537
Fitting, socleC2×C7×C11×C37C2×C3
prime radicalC2×C11×#11715913C2
cosocleC2×C7×C37C2×C3×C11
LCSG ▷ C7×C37
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
2. C11×Dic259C3semidirect
3. C11×#11715913C4semidirect
6. #15690926C11direct (N × H)
7. C7×C11×C37C3×C4semidirect
12. Dic259C3×C11semidirect
15. #11715913C4×C11semidirect
19. C11×C37ΓL(1,𝔽8)⋊C4semidirect
21. C7×C37C3×C4×C11semidirect
29. C7×C11Dic37⋊C3semidirect
34. C37C11×ΓL(1,𝔽8)⋊C4semidirect
41. C11#15690926direct (N × H)
42. C7C11×Dic37⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#117159132
C11×Dic2593
C11×Dic37⋊C37
#1569092611
C11×ΓL(1,𝔽8)⋊C437