Finite Group Databasebeta

← C3⋊(C7⋊(C7⋊(Dic11⋊C5))) #44568469

Subgroups — C3⋊(C7⋊(C7⋊(Dic11⋊C5))) #44568469

Order 32340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C72×C11⋊C5C211yesmaximal, characteristic
2C7⋊(C7⋊(Dic11⋊C5))—31nomaximal, Hall
3C3×C72×C11⋊C5C411yescharacteristic, complemented, Hall
4C3⋊(C7⋊Dic77)C511yesmaximal, characteristic, complemented, Hall
5C2×C72×C11⋊C5D311yescharacteristic
6C3⋊(C7⋊(Dic11⋊C5))—78nomaximal
7C2×C3×C72×C11C2×C511yescharacteristic
8C5×C3⋊(C7⋊Dic7)—111nomaximal, Hall
9C72×C11⋊C5Dic311yescharacteristic, complemented, Hall
10C2×C3×C7×C11⋊C5D718yes—
11C7⋊Dic77—31noHall
12C3×C72×C11C4×C511yescharacteristic, complemented, Hall
13C7⋊(Dic11⋊C5)—218no—
14C2×C3×C5×C72—111no—
15C3×C7×C11⋊C5Dic718yescomplemented
16C2×C72×C11C5×D311yescharacteristic
17C5×C7⋊Dic7—331noHall
18Dic231—78no—
19C2×C7×C11⋊C5D2118yes—
20C3×C5×C72—111noHall
21C3⋊(Dic11⋊C5)—491noHall
22C3⋊(C7⋊Dic7)—111noHall
23C72×C11C5×Dic311yescharacteristic, complemented, Hall
24C2×C5×C72—111no—
25C2×C3×C7×C11C5×D718yes—
26C5×Dic21—778no—
27C7×C11⋊C5Dic2118yescomplemented
28C2×C3×C11⋊C5C7⋊D711yescharacteristic
29Dic77—218no—
30C2×C3×C72AGL(1,𝔽11)11yescharacteristic
31C5×C72—111noHall
32C3×C7×C11C5×Dic718yescomplemented
33Dic11⋊C5—1471noHall
34C2×C3×C5×C7—118no—
35C7⋊Dic7—331noHall
36C3×C11⋊C5C7⋊Dic711yescharacteristic, complemented, Hall
37C2×C7×C11C5×D2118yes—
38C3×C72Dic11⋊C511yescharacteristic, complemented, Hall
39C5×Dic7—2318no—
40Dic33—491noHall
41C2×C11⋊C5C3⋊(C7⋊D7)11yescharacteristic
42C3×C5×C7—118no—
43C2×C72C3⋊AGL(1,𝔽11)11yescharacteristic
44Dic21—778no—
45C7×C11C5×Dic2118yescomplemented
46C2×C5×C7—118no—
47C2×C3×C11C5×C7⋊D711yescharacteristic
48C5×Dic3—5391noHall
49C11⋊C5C3⋊(C7⋊Dic7)11yescharacteristic, complemented, Hall
50C72C3⋊(Dic11⋊C5)11yescharacteristic, complemented, Sylow
51Dic11—1471noHall
52C2×C3×C7C7⋊AGL(1,𝔽11)18yes—
53C5×C7—118no—
54C3×C11C5×C7⋊Dic711yescharacteristic, complemented, Hall
55C2×C3×C5—111no—
56Dic7—2318no—
57C2×C11C5×C3⋊(C7⋊D7)11yescharacteristic
58C3×C7C7⋊(Dic11⋊C5)18yescomplemented
59C4×C5—16171noHall
60C3×C5—111noHall
61C2×C7C3⋊(C7⋊AGL(1,𝔽11))18yes—
62Dic3—5391noHall
63C11C5×C3⋊(C7⋊Dic7)11yescharacteristic, complemented, Sylow
64C2×C5—111no—
65C7C3⋊(C7⋊(Dic11⋊C5))18yescomplemented
66C2×C3C7⋊(C7⋊AGL(1,𝔽11))11yescharacteristic
67C5—111noSylow
68C4—16171noSylow
69C3C7⋊(C7⋊(Dic11⋊C5))11yescharacteristic, complemented, Sylow
70C2C3⋊(C7⋊(C7⋊AGL(1,𝔽11)))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊(C7⋊(C7⋊AGL(1,𝔽11)))
commutator, hypocenterC3×C72×C11C4×C5
Fitting, socle, cosocleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
LCSG ▷ C3×C72×C11
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C3×C72×C11⋊C5C4semidirect
4. C3⋊(C7⋊Dic77)C5semidirect
9. C72×C11⋊C5Dic3semidirect
12. C3×C72×C11C4×C5semidirect
15. C3×C7×C11⋊C5Dic7semidirect
23. C72×C11C5×Dic3semidirect
27. C7×C11⋊C5Dic21semidirect
32. C3×C7×C11C5×Dic7semidirect
36. C3×C11⋊C5C7⋊Dic7semidirect
38. C3×C72Dic11⋊C5semidirect
45. C7×C11C5×Dic21semidirect
49. C11⋊C5C3⋊(C7⋊Dic7)semidirect
50. C72C3⋊(Dic11⋊C5)semidirect
54. C3×C11C5×C7⋊Dic7semidirect
58. C3×C7C7⋊(Dic11⋊C5)semidirect
63. C11C5×C3⋊(C7⋊Dic7)semidirect
65. C7C3⋊(C7⋊(Dic11⋊C5))semidirect
69. C3C7⋊(C7⋊(Dic11⋊C5))semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C72×C11⋊C52
C7⋊(C7⋊(Dic11⋊C5))3
C3⋊(C7⋊Dic77)5
C3⋊(C7⋊(Dic11⋊C5))7
C5×C3⋊(C7⋊Dic7)11