Finite Group Databasebeta

← C2×C3⋊((C97⋊C3)⋊D7) #37567948

Subgroups — C2×C3⋊((C97⋊C3)⋊D7) #37567948

Order 24444.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C7×C97⋊C3C211yesmaximal, characteristic, complemented
2C3⋊((C97⋊C3)⋊D7)C212yesmaximal, direct product factor
3C2×D2037C311yesmaximal, characteristic, complemented
4C2×(C97⋊C3)⋊D7—31nomaximal
5C3×C7×C97⋊C3C2211yescharacteristic, complemented, Hall
6(C97⋊C3)⋊D7—32no—
7D2037C2×C312yescomplemented
8C2×C7×C97⋊C3—21no—
9C2×C7×C97⋊C3D311yescharacteristic, complemented
10C2×C3×C7×C97C2×C311yescharacteristic, complemented
11C2×C3⋊(D97⋊C3)—71nomaximal, Hall
12C2×D679—31noHall
13C3×C7×C97C22×C311yescharacteristic, complemented
14C7×C97⋊C3—21no—
15C7×C97⋊C3C2×D311yescharacteristic, complemented
16C2×C3×C97⋊C3D711yescharacteristic, complemented
17C3⋊(D97⋊C3)—72no—
18C2×C7×C97C3×D311yescharacteristic, complemented
19D679—32no—
20C2×D291—71no—
21C2×D97⋊C3—211no—
22C3×C97⋊C3C2×D711yescharacteristic, complemented, Hall
23C7×C97C2×C3×D311yescharacteristic, complemented, Hall
24C2×C3×C97C3×D711yescharacteristic, complemented
25D291—72no—
26C2×C97⋊C3—21no—
27C2×C97⋊C3D2111yescharacteristic, complemented
28D97⋊C3—212no—
29C2×D97—211noHall
30C3×C97C2×C3×D711yescharacteristic, complemented
31C97⋊C3—21no—
32C97⋊C3C2×D2111yescharacteristic, complemented
33C2×C3×D21—971nomaximal, Hall
34C2×C97C3×D2111yescharacteristic, complemented
35D97—212no—
36C2×C32×C7—1941no—
37C3×D21—972no—
38C97C2×C3×D2111yescharacteristic, complemented, Sylow
39C2×D21—971no—
40C2×C3×D7—2911no—
41C32×C7—1941noHall
42C2×C3×C7—1941no—
43C2×C3×C7—1941no—
44C2×C3×C7D97⋊C311yescharacteristic, complemented
45D21—972no—
46C3×D7—2912no—
47C2×C3×D3—6791noHall
48C2×D7—2911noHall
49C3×C7—1941no—
50C3×C7—1941no—
51C3×C7C2×D97⋊C311yescharacteristic, complemented
52C2×C32—1941no—
53C3×D3—6792no—
54C2×C7C3⋊(D97⋊C3)11yescharacteristic, complemented
55D7—2912no—
56C22×C3—20371no—
57C2×D3—6791no—
58C32—1941noSylow
59C7C2×C3⋊(D97⋊C3)11yescharacteristic, complemented, Sylow
60C2×C3—971no—
61C2×C3—1941no—
62C2×C3—20372no—
63C2×C3(C97⋊C3)⋊D711yescharacteristic, complemented
64D3—6792no—
65C22—20371noSylow
66C3—971no—
67C3—1941no—
68C3C2×(C97⋊C3)⋊D711yescharacteristic, complemented
69C2—20372no—
70C2C3⋊((C97⋊C3)⋊D7)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊((C97⋊C3)⋊D7)
commutator, cosocle, hypocenterC3×C7×C97C22×C3
FrattiniC1G
Fitting, socleC2×C3×C7×C97C2×C3
LCSG ▷ C3×C7×C97
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C7×C97⋊C3C2semidirect
2. C3⋊((C97⋊C3)⋊D7)C2direct (N × H)
3. C2×D2037C3semidirect
5. C3×C7×C97⋊C3C22semidirect
7. D2037C2×C3semidirect
9. C2×C7×C97⋊C3D3semidirect
10. C2×C3×C7×C97C2×C3semidirect
13. C3×C7×C97C22×C3semidirect
15. C7×C97⋊C3C2×D3semidirect
16. C2×C3×C97⋊C3D7semidirect
18. C2×C7×C97C3×D3semidirect
22. C3×C97⋊C3C2×D7semidirect
23. C7×C97C2×C3×D3semidirect
24. C2×C3×C97C3×D7semidirect
27. C2×C97⋊C3D21semidirect
30. C3×C97C2×C3×D7semidirect
32. C97⋊C3C2×D21semidirect
34. C2×C97C3×D21semidirect
38. C97C2×C3×D21semidirect
44. C2×C3×C7D97⋊C3semidirect
51. C3×C7C2×D97⋊C3semidirect
54. C2×C7C3⋊(D97⋊C3)semidirect
59. C7C2×C3⋊(D97⋊C3)semidirect
63. C2×C3(C97⋊C3)⋊D7semidirect
68. C3C2×(C97⋊C3)⋊D7semidirect
70. C2C3⋊((C97⋊C3)⋊D7)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7×C97⋊C32
C3⋊((C97⋊C3)⋊D7)2
C2×D20373
C2×(C97⋊C3)⋊D73
C2×C3⋊(D97⋊C3)7
C2×C3×D2197