Finite Group Databasebeta

← C3⋊(C3⋊(C7⋊#10596817)) #49141648

Subgroups — C3⋊(C3⋊(C7⋊#10596817)) #49141648

Order 36540.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C7×D29C211yesmaximal, characteristic
2C3⋊(C7⋊#10596817)—34nomaximal
3C32×C5×C7×C29C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C7⋊#1181))—51nomaximal, Hall
5C3×C5×C7×D29D314yes—
6C3⋊(C3⋊#10596817)—71nomaximal, Hall
7C7⋊#10596817—91noHall
8C32×C7×D29D511yescharacteristic
9C3×C5×C7×C29Dic314yescomplemented
10C32×C5×D29D711yescharacteristic
11C3⋊(C7⋊#1181)—154no—
12C5×C7×D29C3⋊D311yescharacteristic
13C32×C7×C29Dic511yescharacteristic, complemented, Hall
14C3⋊#10596817—214no—
15C32×C5×C29Dic711yescharacteristic, complemented, Hall
16C3⋊Dic105—291nomaximal, Hall
17C3×C7×D29D1514yes—
18C3⋊(C3⋊#1181)—351noHall
19C5×C7×C29C3⋊Dic311yescharacteristic, complemented, Hall
20C3×C5×D29D2114yes—
21C7⋊#1181—451noHall
22C2×C32×C5×C7—291no—
23C3×C7×C29Dic1514yescomplemented
24#10596817—631noHall
25C32×D29D3511yescharacteristic
26C3×C5×C29Dic2114yescomplemented
27Dic105—874no—
28C7×D29C3⋊D1511yescharacteristic
29C3⋊#1181—1054no—
30C32×C5×C7#118111yescharacteristic, complemented, Hall
31C5×D29C3⋊D2111yescharacteristic
32C32×C29Dic3511yescharacteristic, complemented, Hall
33C3⋊Dic21—1451noHall
34C2×C3×C5×C7—294no—
35C7×C29C3⋊Dic1511yescharacteristic, complemented, Hall
36C3⋊Dic15—2031noHall
37C3×D29D10514yes—
38C5×C29C3⋊Dic2111yescharacteristic, complemented, Hall
39Dic35—2611noHall
40C2×C32×C7—291no—
41#1181—3151noHall
42C3×C5×C7C3⋊#118114yescomplemented
43C2×C32×C5—291no—
44C3×C29Dic10514yescomplemented
45Dic21—4354no—
46C2×C5×C7—291no—
47C32×C7#1059681711yescharacteristic, complemented, Hall
48Dic15—6094no—
49D29C3⋊D10511yescharacteristic
50C32×C5C7⋊#118111yescharacteristic, complemented, Hall
51C2×C3×C7—294no—
52C3⋊Dic3—10151noHall
53C5×C7C3⋊(C3⋊#1181)11yescharacteristic, complemented, Hall
54C2×C3×C5—294no—
55C29C3⋊Dic10511yescharacteristic, complemented, Sylow
56Dic7—13051noHall
57C3×C7C3⋊#1059681714yescomplemented
58Dic5—18271noHall
59C2×C32—291no—
60C3×C5C3⋊(C7⋊#1181)14yescomplemented
61C2×C7—291no—
62Dic3—30454no—
63C2×C5—291no—
64C32C7⋊#1059681711yescharacteristic, complemented, Sylow
65C7C3⋊(C3⋊#10596817)11yescharacteristic, complemented, Sylow
66C2×C3—294no—
67C5C3⋊(C3⋊(C7⋊#1181))11yescharacteristic, complemented, Sylow
68C4—91351noSylow
69C3C3⋊(C7⋊#10596817)14yescomplemented
70C2—291no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C7×C29C4
prime radical, cosocleC32×C5×C7×D29C2
LCSG ▷ C32×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C5×C7×C29C4semidirect
9. C3×C5×C7×C29Dic3semidirect
13. C32×C7×C29Dic5semidirect
15. C32×C5×C29Dic7semidirect
19. C5×C7×C29C3⋊Dic3semidirect
23. C3×C7×C29Dic15semidirect
26. C3×C5×C29Dic21semidirect
30. C32×C5×C7#1181semidirect
32. C32×C29Dic35semidirect
35. C7×C29C3⋊Dic15semidirect
38. C5×C29C3⋊Dic21semidirect
42. C3×C5×C7C3⋊#1181semidirect
44. C3×C29Dic105semidirect
47. C32×C7#10596817semidirect
50. C32×C5C7⋊#1181semidirect
53. C5×C7C3⋊(C3⋊#1181)semidirect
55. C29C3⋊Dic105semidirect
57. C3×C7C3⋊#10596817semidirect
60. C3×C5C3⋊(C7⋊#1181)semidirect
64. C32C7⋊#10596817semidirect
65. C7C3⋊(C3⋊#10596817)semidirect
67. C5C3⋊(C3⋊(C7⋊#1181))semidirect
69. C3C3⋊(C7⋊#10596817)semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C3⋊(C7⋊#10596817)3
C3⋊(C3⋊(C7⋊#1181))5
C3⋊(C3⋊#10596817)7
C3⋊Dic10529