Finite Group Databasebeta

← C7×C3⋊(C3⋊#10596815) #49141640

Subgroups — C7×C3⋊(C3⋊#10596815) #49141640

Order 36540.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×D145C211yesmaximal, characteristic
2C7×C3⋊#10596815—34nomaximal
3C32×C5×C7×C29C411yescharacteristic, complemented, Hall
4C7×C3⋊(C3⋊#1181)—51nomaximal, Hall
5C3×C7×D145D314yes—
6C3⋊(C3⋊#10596815)C711yesmaximal, characteristic, direct product factor, Hall
7C7×#10596815—91noHall
8C32×C7×D29—51no—
9C3×C5×C7×C29Dic314yescomplemented
10C32×D145C2×C711yescharacteristic
11C7×C3⋊#1181—154no—
12C7×D145C3⋊D311yescharacteristic
13C32×C7×C29AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C3⋊#10596815—34no—
15C32×C5×C29C4×C711yescharacteristic, complemented, Hall
16C7×C3⋊ΓL(1,𝔽16)—291nomaximal, Hall
17C3×C7×D29—54no—
18C3⋊(C3⋊#1181)—51noHall
19C5×C7×C29C3⋊Dic311yescharacteristic, complemented, Hall
20C3×D145D3×C714yes—
21C7×#1181—451noHall
22C32×C7×D5—291no—
23C3×C7×C29ΓL(1,𝔽16)14yescomplemented
24#10596815—91noHall
25C32×D29—51no—
26C3×C5×C29C7×Dic314yescomplemented
27C7×ΓL(1,𝔽16)—874no—
28C7×D29—51no—
29C3⋊#1181—154no—
30C32×C5×C7#118111yescharacteristic, complemented, Hall
31D145C7×C3⋊D311yescharacteristic
32C32×C29C7×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
33C7×C3⋊Dic3—1451noHall
34C3×C7×D5—294no—
35C7×C29C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
36C3⋊ΓL(1,𝔽16)—291noHall
37C3×D29—54no—
38C5×C29C7×C3⋊Dic311yescharacteristic, complemented, Hall
39C7×AGL(1,𝔽5)—2611noHall
40C2×C32×C7—1451no—
41#1181—451noHall
42C3×C5×C7C3⋊#118114yescomplemented
43C32×D5—291no—
44C3×C29C7×ΓL(1,𝔽16)14yescomplemented
45C7×Dic3—4354no—
46C7×D5—291no—
47C32×C7#1059681511yescharacteristic, complemented, Hall
48ΓL(1,𝔽16)—874no—
49D29—51no—
50C32×C5C7×#118111yescharacteristic, complemented, Hall
51C2×C3×C7—1454no—
52C3⋊Dic3—1451noHall
53C5×C7C3⋊(C3⋊#1181)11yescharacteristic, complemented, Hall
54C3×D5—294no—
55C29C7×C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
56C4×C7—13051noHall
57C3×C7C3⋊#1059681514yescomplemented
58AGL(1,𝔽5)—2611noHall
59C2×C32—1451no—
60C3×C5C7×C3⋊#118114yescomplemented
61C2×C7—1451no—
62Dic3—4354no—
63D5—291no—
64C32C7×#1059681511yescharacteristic, complemented, Sylow
65C7C3⋊(C3⋊#10596815)11yescharacteristic, direct product factor, Sylow
66C2×C3—1454no—
67C5C7×C3⋊(C3⋊#1181)11yescharacteristic, complemented, Sylow
68C4—13051noSylow
69C3C7×C3⋊#1059681514yescomplemented
70C2—1451no—
subgroupG/H
center, hypercenterC7C3⋊(C3⋊#10596815)
commutator, hypocenterC32×C5×C29C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C7×D145C2
cosocleC32×D145C2×C7
LCSG ▷ C32×C5×C29
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
3. C32×C5×C7×C29C4semidirect
6. C3⋊(C3⋊#10596815)C7direct (N × H)
9. C3×C5×C7×C29Dic3semidirect
13. C32×C7×C29AGL(1,𝔽5)semidirect
15. C32×C5×C29C4×C7semidirect
19. C5×C7×C29C3⋊Dic3semidirect
23. C3×C7×C29ΓL(1,𝔽16)semidirect
26. C3×C5×C29C7×Dic3semidirect
30. C32×C5×C7#1181semidirect
32. C32×C29C7×AGL(1,𝔽5)semidirect
35. C7×C29C3⋊ΓL(1,𝔽16)semidirect
38. C5×C29C7×C3⋊Dic3semidirect
42. C3×C5×C7C3⋊#1181semidirect
44. C3×C29C7×ΓL(1,𝔽16)semidirect
47. C32×C7#10596815semidirect
50. C32×C5C7×#1181semidirect
53. C5×C7C3⋊(C3⋊#1181)semidirect
55. C29C7×C3⋊ΓL(1,𝔽16)semidirect
57. C3×C7C3⋊#10596815semidirect
60. C3×C5C7×C3⋊#1181semidirect
64. C32C7×#10596815semidirect
65. C7C3⋊(C3⋊#10596815)direct (N × H)
67. C5C7×C3⋊(C3⋊#1181)semidirect
69. C3C7×C3⋊#10596815semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1452
C7×C3⋊#105968153
C7×C3⋊(C3⋊#1181)5
C3⋊(C3⋊#10596815)7
C7×C3⋊ΓL(1,𝔽16)29