Finite Group Databasebeta

← C7×C3⋊(C3⋊#63122) #30655683

Subgroups — C7×C3⋊(C3⋊#63122) #30655683

Order 16380.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×D65C211yesmaximal, characteristic
2C7×C3⋊#63122—34nomaximal
3C32×C5×C7×C13C411yescharacteristic, complemented, Hall
4C7×C3⋊(C3⋊#261)—51nomaximal, Hall
5C3×C7×D65D314yes—
6C3⋊(C3⋊#63122)C711yesmaximal, characteristic, direct product factor, Hall
7C7×#63122—91noHall
8C32×C7×D13—51no—
9C3×C5×C7×C13Dic314yescomplemented
10C7×C3⋊ΓL(1,𝔽16)—131nomaximal, Hall
11C32×D65C2×C711yescharacteristic
12C7×C3⋊#261—154no—
13C7×D65C3⋊D311yescharacteristic
14C32×C7×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
15C3⋊#63122—34no—
16C32×C7×D5—131no—
17C32×C5×C13C4×C711yescharacteristic, complemented, Hall
18C3×C7×D13—54no—
19C3⋊(C3⋊#261)—51noHall
20C5×C7×C13C3⋊Dic311yescharacteristic, complemented, Hall
21C7×ΓL(1,𝔽16)—394no—
22C3×D65D3×C714yes—
23C7×#261—451noHall
24C32×C5×C7#26111yescharacteristic, complemented, Hall
25C3×C7×C13ΓL(1,𝔽16)14yescomplemented
26#63122—91noHall
27C7×C3⋊Dic3—651noHall
28C32×D13—51no—
29C3×C7×D5—134no—
30C3×C5×C13C7×Dic314yescomplemented
31C7×D13—51no—
32C3⋊ΓL(1,𝔽16)—131noHall
33C3⋊#261—154no—
34C7×AGL(1,𝔽5)—1171noHall
35D65C7×C3⋊D311yescharacteristic
36C2×C32×C7—651no—
37C32×C13C7×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C3×C5×C7C3⋊#26114yescomplemented
39C7×C13C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
40C32×D5—131no—
41C7×Dic3—1954no—
42C3×D13—54no—
43C7×D5—131no—
44C5×C13C7×C3⋊Dic311yescharacteristic, complemented, Hall
45C32×C7#6312211yescharacteristic, complemented, Hall
46ΓL(1,𝔽16)—394no—
47#261—451noHall
48C32×C5C7×#26111yescharacteristic, complemented, Hall
49C2×C3×C7—654no—
50C3×C13C7×ΓL(1,𝔽16)14yescomplemented
51C3⋊Dic3—651noHall
52C5×C7C3⋊(C3⋊#261)11yescharacteristic, complemented, Hall
53C3×D5—134no—
54C4×C7—5851noHall
55D13—51no—
56C3×C7C3⋊#6312214yescomplemented
57AGL(1,𝔽5)—1171noHall
58C2×C32—651no—
59C3×C5C7×C3⋊#26114yescomplemented
60C2×C7—651no—
61C13C7×C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
62Dic3—1954no—
63D5—131no—
64C32C7×#6312211yescharacteristic, complemented, Sylow
65C7C3⋊(C3⋊#63122)11yescharacteristic, direct product factor, Sylow
66C2×C3—654no—
67C5C7×C3⋊(C3⋊#261)11yescharacteristic, complemented, Sylow
68C4—5851noSylow
69C3C7×C3⋊#6312214yescomplemented
70C2—651no—
subgroupG/H
center, hypercenterC7C3⋊(C3⋊#63122)
commutator, hypocenterC32×C5×C13C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC32×C7×D65C2
cosocleC32×D65C2×C7
LCSG ▷ C32×C5×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
3. C32×C5×C7×C13C4semidirect
6. C3⋊(C3⋊#63122)C7direct (N × H)
9. C3×C5×C7×C13Dic3semidirect
14. C32×C7×C13AGL(1,𝔽5)semidirect
17. C32×C5×C13C4×C7semidirect
20. C5×C7×C13C3⋊Dic3semidirect
24. C32×C5×C7#261semidirect
25. C3×C7×C13ΓL(1,𝔽16)semidirect
30. C3×C5×C13C7×Dic3semidirect
37. C32×C13C7×AGL(1,𝔽5)semidirect
38. C3×C5×C7C3⋊#261semidirect
39. C7×C13C3⋊ΓL(1,𝔽16)semidirect
44. C5×C13C7×C3⋊Dic3semidirect
45. C32×C7#63122semidirect
48. C32×C5C7×#261semidirect
50. C3×C13C7×ΓL(1,𝔽16)semidirect
52. C5×C7C3⋊(C3⋊#261)semidirect
56. C3×C7C3⋊#63122semidirect
59. C3×C5C7×C3⋊#261semidirect
61. C13C7×C3⋊ΓL(1,𝔽16)semidirect
64. C32C7×#63122semidirect
65. C7C3⋊(C3⋊#63122)direct (N × H)
67. C5C7×C3⋊(C3⋊#261)semidirect
69. C3C7×C3⋊#63122semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D652
C7×C3⋊#631223
C7×C3⋊(C3⋊#261)5
C3⋊(C3⋊#63122)7
C7×C3⋊ΓL(1,𝔽16)13