Finite Group Databasebeta

← C7×((C11⋊D11)⋊C3)⋊D3 #44479090

Subgroups — C7×((C11⋊D11)⋊C3)⋊D3 #44479090

Order 30492.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C3⋊#10624391C212yesmaximal, complemented
2C3×C7×(C11⋊D11)⋊C3C211yesmaximal, characteristic, complemented
3C7×D33⋊D11—31nomaximal
4C7×#10624391⋊C2—33nomaximal
5C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
6C7×C11×D33—32no—
7C3×C7×C11⋊D11D311yescharacteristic, complemented
8C7×(C11⋊D11)⋊C3D313yescomplemented
9C7×#10624391—36no—
10((C11⋊D11)⋊C3)⋊D3C711yesmaximal, characteristic, direct product factor, Hall
11C7×D112—91noHall
12C7×C112⋊C3C2×D313yescomplemented
13C3×C7×C112C2×D311yescharacteristic, complemented
14C3⋊#10624391C2×C712yescomplemented
15C3×(C11⋊D11)⋊C3C2×C711yescharacteristic, complemented
16C7×C11⋊D11C3⋊D311yescharacteristic, complemented
17C7×C11×D11—92no—
18D33⋊D11—31no—
19#10624391⋊C2—33no—
20C3×C112⋊C3C22×C711yescharacteristic, complemented, Hall
21D3×C7×D11—332no—
22C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
23C11×D33—32no—
24C3×C11⋊D11D3×C711yescharacteristic, complemented
25(C11⋊D11)⋊C3D3×C713yescomplemented
26#10624391—36no—
27D112—91noHall
28C7×D33—32no—
29D3×C7×C11—332no—
30C3×C7×D11—332no—
31C3×C7×D11—661no—
32C3×C112C2×D3×C711yescharacteristic, complemented
33C112⋊C3C2×D3×C713yescomplemented
34C2×C7×D11—992no—
35C2×C7×C3⋊D3—1211nomaximal, Hall
36C11⋊D11C7×C3⋊D311yescharacteristic, complemented
37C11×D11—92no—
38C3×C7×C11—32no—
39C3×C7×C11—61no—
40C2×C7×C11—992no—
41C7×D11—92no—
42C7×D11—332no—
43C7×D11—661no—
44D3×D11—332no—
45C2×C32×C7—1211no—
46C7×C3⋊D3—1212no—
47C112C2×C7×C3⋊D311yescharacteristic, complemented, Sylow
48C2×D3×C7—3631no—
49C2×D3×C7—3633no—
50C7×C11—32no—
51C7×C11—61no—
52D33—32no—
53C3×D11—332no—
54C3×D11—661no—
55D3×C11—332no—
56C32×C7—1211noHall
57C2×D11—992no—
58C2×C3×C7—1213no—
59C2×C3×C7—1211no—
60D3×C7—332no—
61D3×C7—3636no—
62C2×C3⋊D3—1211noHall
63C3×C11—32no—
64C3×C11—61no—
65C22×C7—10891noHall
66C2×C11—992no—
67D11—92no—
68D11—332no—
69D11—661no—
70C3×C7—1213no—
71C3×C7#10624391⋊C211yescharacteristic, complemented
72C2×C32—1211no—
73C3⋊D3—1212no—
74C2×C7—992no—
75C2×C7—1211no—
76C2×D3—3631no—
77C2×D3—3633no—
78C11—32no—
79C11—61no—
80C32—1211noSylow
81C7((C11⋊D11)⋊C3)⋊D311yescharacteristic, direct product factor, Sylow
82C2×C3—1213no—
83C2×C3—1211no—
84D3—332no—
85D3—3636no—
86C22—10891noSylow
87C3—1213no—
88C3C7×#10624391⋊C211yescharacteristic, complemented
89C2—992no—
90C2—1211no—
subgroupG/H
center, hypercenterC7((C11⋊D11)⋊C3)⋊D3
commutator, cosocle, hypocenterC3×C112⋊C3C22×C7
FrattiniC1G
Fitting, socleC3×C7×C112C2×D3
LCSG ▷ C3×C112⋊C3
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C3⋊#10624391C2semidirect
2. C3×C7×(C11⋊D11)⋊C3C2semidirect
5. C3×C7×C112⋊C3C22semidirect
7. C3×C7×C11⋊D11D3semidirect
8. C7×(C11⋊D11)⋊C3D3semidirect
10. ((C11⋊D11)⋊C3)⋊D3C7direct (N × H)
12. C7×C112⋊C3C2×D3semidirect
13. C3×C7×C112C2×D3semidirect
14. C3⋊#10624391C2×C7semidirect
15. C3×(C11⋊D11)⋊C3C2×C7semidirect
16. C7×C11⋊D11C3⋊D3semidirect
20. C3×C112⋊C3C22×C7semidirect
22. C7×C112C2×C3⋊D3semidirect
24. C3×C11⋊D11D3×C7semidirect
25. (C11⋊D11)⋊C3D3×C7semidirect
32. C3×C112C2×D3×C7semidirect
33. C112⋊C3C2×D3×C7semidirect
36. C11⋊D11C7×C3⋊D3semidirect
47. C112C2×C7×C3⋊D3semidirect
71. C3×C7#10624391⋊C2semidirect
81. C7((C11⋊D11)⋊C3)⋊D3direct (N × H)
88. C3C7×#10624391⋊C2semidirect

Maximal subgroups

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

subgroupindex
C7×C3⋊#106243912
C3×C7×(C11⋊D11)⋊C32
C7×D33⋊D113
C7×#10624391⋊C23
((C11⋊D11)⋊C3)⋊D37
C2×C7×C3⋊D3121