Finite Group Databasebeta

← C11⋊#14523608 #37528510

Subgroups — C11⋊#14523608 #37528510

Order 23100.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×(C5⋊D5)⋊ΓL(1,𝔽8)C211yesmaximal, characteristic
2C7⋊(C11⋊#1043)C311yesmaximal, characteristic, complemented, Hall
3C11×C7⋊(C52⋊C3)C411yescharacteristic, complemented, Hall
4C7×C11×C5⋊D5C2×C311yescharacteristic
5C11⋊(#1043⋊C3)—71nomaximal, Hall
6#14523608—111nomaximal, Hall
7C52×C7×C11C3×C411yescharacteristic, complemented, Hall
8C11×(C5⋊D5)⋊C3—141no—
9C7⋊(C11⋊AGL(1,𝔽5))—152no—
10C11⋊#1043—71noHall
11(C5⋊D5)⋊ΓL(1,𝔽8)D1111yescharacteristic
12C11⋊(ΓL(1,𝔽8)⋊C4)—251nomaximal, Hall
13C11×C52⋊C3—141noHall
14C7×D5×C11—152no—
15C7⋊#1043—111noHall
16C11×C5⋊D5AGL(1,𝔽7)11yescharacteristic
17C7⋊(C52⋊C3)Dic1111yescharacteristic, complemented, Hall
18C2×C11×ΓL(1,𝔽8)—251no—
19C5×C7×C11—32no—
20C7×C5⋊D5C3×D1111yescharacteristic
21Dic77—251noHall
22#1043⋊C3—771noHall
23C52×C11ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
24C11×ΓL(1,𝔽8)—1001noHall
25C11⋊AGL(1,𝔽5)—1052no—
26C52×C7C3×Dic1111yescharacteristic, complemented, Hall
27C2×C7×C11—251no—
28(C5⋊D5)⋊C3—141no—
29C7⋊AGL(1,𝔽5)—1652no—
30C3×Dic11—1751noHall
31D5×C11—152no—
32#1043—771noHall
33ΓL(1,𝔽8)⋊C4—2751noHall
34C7×C11#1043⋊C311yescharacteristic, complemented, Hall
35C52⋊C3—141noHall
36C7×D5—152no—
37C2×C3×C11—3501no—
38C5×C11—32no—
39C5⋊D5C11⋊AGL(1,𝔽7)11yescharacteristic
40Dic11—1751noHall
41C2×ΓL(1,𝔽8)—251no—
42C5×C7—32no—
43C3×C11—7001noHall
44Dic7—2751noHall
45C52C11⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Sylow
46C2×C11—251no—
47ΓL(1,𝔽8)—1001noHall
48AGL(1,𝔽5)—11552no—
49C2×C7—251no—
50C3×C4—19251noHall
51C11#1452360811yescharacteristic, complemented, Sylow
52D5—152no—
53C7C11⋊(#1043⋊C3)11yescharacteristic, complemented, Sylow
54C2×C3—3501no—
55C5—32no—
56C4—19251noSylow
57C3—7001noSylow
58C2—251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C7×C11C3×C4
prime radicalC11×(C5⋊D5)⋊ΓL(1,𝔽8)C2
cosocleC7×C11×C5⋊D5C2×C3
LCSG ▷ C52×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
2. C7⋊(C11⋊#1043)C3semidirect
3. C11×C7⋊(C52⋊C3)C4semidirect
7. C52×C7×C11C3×C4semidirect
17. C7⋊(C52⋊C3)Dic11semidirect
23. C52×C11ΓL(1,𝔽8)⋊C4semidirect
26. C52×C7C3×Dic11semidirect
34. C7×C11#1043⋊C3semidirect
45. C52C11⋊(ΓL(1,𝔽8)⋊C4)semidirect
51. C11#14523608semidirect
53. C7C11⋊(#1043⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C11×(C5⋊D5)⋊ΓL(1,𝔽8)2
C7⋊(C11⋊#1043)3
C11⋊(#1043⋊C3)7
#1452360811
C11⋊(ΓL(1,𝔽8)⋊C4)25