Finite Group Databasebeta

← C22×C4⋊#87604 #20261797

Subgroups — C22×C4⋊#87604 #20261797

Order 6208.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#87604C212yesmaximal
2C2×C4⋊#87604C2112yesmaximal, direct product factor
3C22×C4×D97C211yesmaximal, characteristic
4C22×#87604—28no—
5C22×#87604C22112yes—
6C4⋊#87604C22116yesdirect product factor
7C23×D97C2211yescharacteristic
8C22×Dic97C411yescharacteristic, complemented
9C2×C4×D97C416yescomplemented
10C2×C4×D97C2216yes—
11C22×C4×C97C411yescharacteristic, complemented
12C23×C97C2×C411yescharacteristic
13C22×D97C2×C413yes—
14C22×D97D414yes—
15C22×D97Q814yes—
16C22×D97C2313yes—
17C2×#87604—224no—
18C2×#87604C2318yes—
19C2×C4×C97C2×C416yescomplemented
20C2×Dic97C2×C416yescomplemented
21C4×D97C2×C4112yescomplemented
22C4×D97C2314yes—
23C22×C97C4⋊C414yescomplemented
24C22×C97C22×C413yes—
25C2×D97C4⋊C4112yescomplemented
26C2×D97C22×C413yes—
27C2×D97C2×D416yes—
28C2×D97C2×Q816yes—
29C2×D97C2411yescharacteristic
30#87604—28no—
31C4×C97C22×C414yescomplemented
32Dic97C22×C414yescomplemented
33C2×C97C2×C4⋊C416yescomplemented
34C2×C97C23×C411yescharacteristic
35D97C2×C4⋊C416yescomplemented
36D97C22×D411yescharacteristic
37D97C22×Q811yescharacteristic
38C97C22×C4⋊C411yescharacteristic, complemented, Sylow
39C22×C4⋊C4—971nomaximal, Sylow
40C23×C4—971no—
41C23×C4—972no—
42C2×C4⋊C4—9712no—
43C24—971no—
44C22×C4—971no—
45C22×C4—976no—
46C22×C4—976no—
47C22×C4—9712no—
48C22×C4—1948no—
49C22×C4#8760411yescharacteristic, complemented
50C4⋊C4—9716no—
51C23—974no—
52C23—974no—
53C23—973no—
54C23—973no—
55C23C2×#8760411yescharacteristic
56C2×C4—976no—
57C2×C4—974no—
58C2×C4—9712no—
59C2×C4—978no—
60C2×C4—19424no—
61C2×C4C2×#8760416yescomplemented
62C22—976no—
63C22—9712no—
64C22—976no—
65C22—971no—
66C22—973no—
67C22C4⋊#8760414yesdirect product factor
68C22C22×#8760413yes—
69C4—974no—
70C4—1948no—
71C4C22×#8760414yescomplemented
72C2—971no—
73C2—976no—
74C2—971no—
75C2C2×C4⋊#8760416yesdirect product factor
76C2C23×#8760411yescharacteristic
subgroupG/H
centerC23C2×#87604
commutatorC2×C97C23×C4
FrattiniC2C23×#87604
FittingC22×C4×C97C4
socleC23×C97C2×C4
hypercenterC22×C4#87604
hypocenterC97C22×C4⋊C4
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#87604C2direct (N × H)
6. C4⋊#87604C22direct (N × H)
8. C22×Dic97C4semidirect
9. C2×C4×D97C4semidirect
11. C22×C4×C97C4semidirect
19. C2×C4×C97C2×C4semidirect
20. C2×Dic97C2×C4semidirect
21. C4×D97C2×C4semidirect
23. C22×C97C4⋊C4semidirect
25. C2×D97C4⋊C4semidirect
31. C4×C97C22×C4semidirect
32. Dic97C22×C4semidirect
33. C2×C97C2×C4⋊C4semidirect
35. D97C2×C4⋊C4semidirect
38. C97C22×C4⋊C4semidirect
49. C22×C4#87604semidirect
61. C2×C4C2×#87604semidirect
67. C22C4⋊#87604direct (N × H)
71. C4C22×#87604semidirect
75. C2C2×C4⋊#87604direct (N × H)