Finite Group Databasebeta

← C32×C7⋊(Dic11⋊C5) #28357482

Subgroups — C32×C7⋊(Dic11⋊C5) #28357482

Order 13860.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C7×C11⋊C5C211yesmaximal, characteristic
2C3×C7⋊(Dic11⋊C5)C314yesmaximal, direct product factor
3C32×C7×C11⋊C5C411yescharacteristic, complemented, Hall
4C32×Dic77C511yesmaximal, characteristic, complemented, Hall
5C2×C3×C7×C11⋊C5C2×C314yes—
6C32×Dic11⋊C5—71nomaximal, Hall
7C7⋊(Dic11⋊C5)C3211yescharacteristic, direct product factor, Hall
8C2×C32×C7×C11C2×C511yescharacteristic
9C32×C5×Dic7—111nomaximal, Hall
10C3×C7×C11⋊C5C3×C414yescomplemented
11C2×C32×C11⋊C5D711yescharacteristic
12C3×Dic77C3×C514yescomplemented
13C2×C7×C11⋊C5C2×C3211yescharacteristic
14C32×C7×C11C4×C511yescharacteristic, complemented, Hall
15C3×Dic11⋊C5—74no—
16C2×C32×C5×C7—111no—
17C32×C11⋊C5Dic711yescharacteristic, complemented, Hall
18C2×C3×C7×C11C2×C3×C514yes—
19C3×C5×Dic7—114no—
20C32×Dic11—71noHall
21C7×C11⋊C5C32×C411yescharacteristic, complemented, Hall
22C2×C3×C11⋊C5C3×D714yes—
23C32×C5×C7—111noHall
24Dic77C32×C511yescharacteristic, complemented, Hall
25C32×Dic7—111noHall
26C3×C7×C11C3×C4×C514yescomplemented
27Dic11⋊C5—71noHall
28C2×C3×C5×C7—114no—
29C2×C32×C11C5×D711yescharacteristic
30C32×C4×C5—771noHall
31C3×C11⋊C5C3×Dic714yescomplemented
32C2×C7×C11C2×C32×C511yescharacteristic
33C5×Dic7—111noHall
34C3×Dic11—74no—
35C2×C32×C7AGL(1,𝔽11)11yescharacteristic
36C2×C11⋊C5C32×D711yescharacteristic
37C3×C5×C7—114no—
38C32×C11C5×Dic711yescharacteristic, complemented, Hall
39C2×C32×C5—111no—
40C3×Dic7—114no—
41C7×C11C32×C4×C511yescharacteristic, complemented, Hall
42C2×C5×C7—111no—
43C2×C3×C11C3×C5×D714yes—
44C32×C7Dic11⋊C511yescharacteristic, complemented, Hall
45C3×C4×C5—774no—
46C11⋊C5C32×Dic711yescharacteristic, complemented, Hall
47C32×C5—111noHall
48Dic11—71noHall
49C2×C3×C7C3×AGL(1,𝔽11)14yes—
50C32×C4—771noHall
51C5×C7—111noHall
52C3×C11C3×C5×Dic714yescomplemented
53C2×C3×C5—114no—
54Dic7—111noHall
55C2×C11C32×C5×D711yescharacteristic
56C3×C7C3×Dic11⋊C514yescomplemented
57C4×C5—771noHall
58C2×C32C7⋊AGL(1,𝔽11)11yescharacteristic
59C3×C5—114no—
60C2×C7C32×AGL(1,𝔽11)11yescharacteristic
61C3×C4—774no—
62C11C32×C5×Dic711yescharacteristic, complemented, Sylow
63C2×C5—111no—
64C32C7⋊(Dic11⋊C5)11yescharacteristic, direct product factor, Sylow
65C7C32×Dic11⋊C511yescharacteristic, complemented, Sylow
66C2×C3C3×C7⋊AGL(1,𝔽11)14yes—
67C5—111noSylow
68C4—771noSylow
69C3C3×C7⋊(Dic11⋊C5)14yesdirect product factor
70C2C32×C7⋊AGL(1,𝔽11)11yescharacteristic
subgroupG/H
center, hypercenterC2×C32C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C32×C4×C5
FrattiniC2C32×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C32×C7×C11C2×C5
prime radicalC2×C32×C7×C11⋊C5C2
cosocleC2×C7×C11C2×C32×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C32

Complements

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

NH ≅ G/Ntype
2. C3×C7⋊(Dic11⋊C5)C3direct (N × H)
3. C32×C7×C11⋊C5C4semidirect
4. C32×Dic77C5semidirect
7. C7⋊(Dic11⋊C5)C32direct (N × H)
10. C3×C7×C11⋊C5C3×C4semidirect
12. C3×Dic77C3×C5semidirect
14. C32×C7×C11C4×C5semidirect
17. C32×C11⋊C5Dic7semidirect
21. C7×C11⋊C5C32×C4semidirect
24. Dic77C32×C5semidirect
26. C3×C7×C11C3×C4×C5semidirect
31. C3×C11⋊C5C3×Dic7semidirect
38. C32×C11C5×Dic7semidirect
41. C7×C11C32×C4×C5semidirect
44. C32×C7Dic11⋊C5semidirect
46. C11⋊C5C32×Dic7semidirect
52. C3×C11C3×C5×Dic7semidirect
56. C3×C7C3×Dic11⋊C5semidirect
62. C11C32×C5×Dic7semidirect
64. C32C7⋊(Dic11⋊C5)direct (N × H)
65. C7C32×Dic11⋊C5semidirect
69. C3C3×C7⋊(Dic11⋊C5)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C7×C11⋊C52
C3×C7⋊(Dic11⋊C5)3
C32×Dic775
C32×Dic11⋊C57
C32×C5×Dic711