Finite Group Databasebeta

← C11×C22⋊#11715913 #46803296

Subgroups — C11×C22⋊#11715913 #46803296

Order 34188.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C11×C37C311yesmaximal, characteristic, complemented, Hall
2C11×#11715913—41nomaximal, Hall
3C2×C7×C11×C37—31no—
4C11×C22⋊(C37⋊C3)—71nomaximal, Hall
5C22⋊#11715913C1111yesmaximal, characteristic, direct product factor, Hall
6C7×C11×C37A411yescharacteristic, complemented, Hall
7C22×C11×C37ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
8C11×C37⋊C3—281noHall
9C22×C7×C37C3×C1111yescharacteristic, complemented, Hall
10C11×C22⋊ΓL(1,𝔽8)—371nomaximal, Hall
11C2×C11×C37—31no—
12#11715913—41noHall
13C2×C7×C37—31no—
14C22⋊(C37⋊C3)—71noHall
15C11×C37C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
16C22×C7×C11C37⋊C311yescharacteristic, complemented, Hall
17C7×C37C11×A411yescharacteristic, complemented, Hall
18C11×ΓL(1,𝔽8)—1481noHall
19C2×C7×C11—31no—
20C22×C37C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
21C11×A4—2591noHall
22C37⋊C3—281noHall
23C22⋊ΓL(1,𝔽8)—371noHall
24C7×C11C22⋊(C37⋊C3)11yescharacteristic, complemented, Hall
25C2×C37—31no—
26C22×C11#1171591311yescharacteristic, complemented, Hall
27C37C11×C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
28C3×C11—10361noHall
29C22×C7C11×C37⋊C311yescharacteristic, complemented, Hall
30C2×C11—31no—
31ΓL(1,𝔽8)—1481noHall
32C2×C7—31no—
33A4—2591noHall
34C11C22⋊#1171591311yescharacteristic, direct product factor, Sylow
35C7C11×C22⋊(C37⋊C3)11yescharacteristic, complemented, Sylow
36C22C11×#1171591311yescharacteristic, complemented, Sylow
37C3—10361noSylow
38C2—31no—
subgroupG/H
center, hypercenterC11C22⋊#11715913
commutator, cosocle, hypocenterC22×C7×C37C3×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C37C3
LCSG ▷ C22×C7×C37
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C22×C7×C11×C37C3semidirect
5. C22⋊#11715913C11direct (N × H)
6. C7×C11×C37A4semidirect
7. C22×C11×C37ΓL(1,𝔽8)semidirect
9. C22×C7×C37C3×C11semidirect
15. C11×C37C22⋊ΓL(1,𝔽8)semidirect
16. C22×C7×C11C37⋊C3semidirect
17. C7×C37C11×A4semidirect
20. C22×C37C11×ΓL(1,𝔽8)semidirect
24. C7×C11C22⋊(C37⋊C3)semidirect
26. C22×C11#11715913semidirect
27. C37C11×C22⋊ΓL(1,𝔽8)semidirect
29. C22×C7C11×C37⋊C3semidirect
34. C11C22⋊#11715913direct (N × H)
35. C7C11×C22⋊(C37⋊C3)semidirect
36. C22C11×#11715913semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C11×C373
C11×#117159134
C11×C22⋊(C37⋊C3)7
C22⋊#1171591311
C11×C22⋊ΓL(1,𝔽8)37