Finite Group Databasebeta

← C3⋊(C3⋊(C7⋊#10596814)) #49141643

Subgroups — C3⋊(C3⋊(C7⋊#10596814)) #49141643

Order 36540.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×D145C211yesmaximal, characteristic
2C3⋊(C7⋊#10596814)—34nomaximal
3C32×C5×C7×C29C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C7⋊#1181))—51nomaximal, Hall
5C3×C7×D145D314yes—
6C3⋊(C3⋊#10596814)—71nomaximal, Hall
7C7⋊#10596814—91noHall
8C32×C7×D29—51no—
9C3×C5×C7×C29Dic314yescomplemented
10C32×D145D711yescharacteristic
11C3⋊(C7⋊#1181)—154no—
12C7×D145C3⋊D311yescharacteristic
13C32×C7×C29AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C3⋊#10596814—214no—
15C32×C5×C29Dic711yescharacteristic, complemented, Hall
16C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))—291nomaximal, Hall
17C3×C7×D29—54no—
18C3⋊(C3⋊#1181)—351noHall
19C5×C7×C29C3⋊Dic311yescharacteristic, complemented, Hall
20C3×D145D2114yes—
21C7⋊#1181—451noHall
22C32×C7×D5—291no—
23C3×C7×C29ΓL(1,𝔽16)14yescomplemented
24#10596814—631noHall
25C32×D29—51no—
26C3×C5×C29Dic2114yescomplemented
27C3⋊(C7⋊AGL(1,𝔽5))—874no—
28C7×D29—51no—
29C3⋊#1181—1054no—
30C32×C5×C7#118111yescharacteristic, complemented, Hall
31D145C3⋊D2111yescharacteristic
32C32×C29C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
33C3⋊Dic21—1451noHall
34C3×C7×D5—294no—
35C7×C29C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
36C3⋊ΓL(1,𝔽16)—2031noHall
37C3×D29—54no—
38C5×C29C3⋊Dic2111yescharacteristic, complemented, Hall
39C7⋊AGL(1,𝔽5)—2611noHall
40C2×C32×C7—1451no—
41#1181—3151noHall
42C3×C5×C7C3⋊#118114yescomplemented
43C32×D5—291no—
44C3×C29C3⋊(C7⋊AGL(1,𝔽5))14yescomplemented
45Dic21—4354no—
46C7×D5—291no—
47C32×C7#1059681411yescharacteristic, complemented, Hall
48ΓL(1,𝔽16)—6094no—
49D29—51no—
50C32×C5C7⋊#118111yescharacteristic, complemented, Hall
51C2×C3×C7—1454no—
52C3⋊Dic3—10151noHall
53C5×C7C3⋊(C3⋊#1181)11yescharacteristic, complemented, Hall
54C3×D5—294no—
55C29C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))11yescharacteristic, complemented, Sylow
56Dic7—13051noHall
57C3×C7C3⋊#1059681414yescomplemented
58AGL(1,𝔽5)—18271noHall
59C2×C32—1451no—
60C3×C5C3⋊(C7⋊#1181)14yescomplemented
61C2×C7—1451no—
62Dic3—30454no—
63D5—291no—
64C32C7⋊#1059681411yescharacteristic, complemented, Sylow
65C7C3⋊(C3⋊#10596814)11yescharacteristic, complemented, Sylow
66C2×C3—1454no—
67C5C3⋊(C3⋊(C7⋊#1181))11yescharacteristic, complemented, Sylow
68C4—91351noSylow
69C3C3⋊(C7⋊#10596814)14yescomplemented
70C2—1451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C7×C29C4
prime radical, cosocleC32×C7×D145C2
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×C29AGL(1,𝔽5)semidirect
15. C32×C5×C29Dic7semidirect
19. C5×C7×C29C3⋊Dic3semidirect
23. C3×C7×C29ΓL(1,𝔽16)semidirect
26. C3×C5×C29Dic21semidirect
30. C32×C5×C7#1181semidirect
32. C32×C29C7⋊AGL(1,𝔽5)semidirect
35. C7×C29C3⋊ΓL(1,𝔽16)semidirect
38. C5×C29C3⋊Dic21semidirect
42. C3×C5×C7C3⋊#1181semidirect
44. C3×C29C3⋊(C7⋊AGL(1,𝔽5))semidirect
47. C32×C7#10596814semidirect
50. C32×C5C7⋊#1181semidirect
53. C5×C7C3⋊(C3⋊#1181)semidirect
55. C29C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))semidirect
57. C3×C7C3⋊#10596814semidirect
60. C3×C5C3⋊(C7⋊#1181)semidirect
64. C32C7⋊#10596814semidirect
65. C7C3⋊(C3⋊#10596814)semidirect
67. C5C3⋊(C3⋊(C7⋊#1181))semidirect
69. C3C3⋊(C7⋊#10596814)semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1452
C3⋊(C7⋊#10596814)3
C3⋊(C3⋊(C7⋊#1181))5
C3⋊(C3⋊#10596814)7
C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))29