Finite Group Databasebeta

← #20259926

Subgroups — #20259926

Order 6176.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690556C211yesmaximal, characteristic, complemented
2D4×D193C211yesmaximal, characteristic, complemented
3#15690542C211yesmaximal, characteristic, complemented
4D1544C211yesmaximal, characteristic, complemented
5#15690540C211yesmaximal, characteristic, complemented
6#15690538C211yesmaximal, characteristic, complemented
7SD16×C193C211yesmaximal, characteristic, complemented
8C22×D193—21no—
9D772—21no—
10D772C2211yescharacteristic
11D772C2211yescharacteristic, complemented
12C22⋊D193—21no—
13C4×D193—21no—
14C4×D193C2211yescharacteristic
15#13095393C2211yescharacteristic, complemented
16Q8×C193C2211yescharacteristic, complemented
17D4×C193C2211yescharacteristic
18C8×C193C2211yescharacteristic, complemented
19C22×C193—21no—
20C2×D193—21no—
21C2×D193—21no—
22C2×D193—42no—
23C2×D193D411yescharacteristic
24C4×C193—21no—
25C4×C193C2311yescharacteristic
26Dic193D411yescharacteristic
27C2×C193—41no—
28C2×C193C2×D411yescharacteristic
29D193—21no—
30D193—41no—
31D193—41no—
32C193AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
33AGL(1,ℤ/8)—1931nomaximal, Sylow
34#41—1931no—
35C2×D4—1931no—
36SD16—1931no—
37SD16D19311yescharacteristic, complemented
38D8—1931no—
39D8—1931no—
40M16—1931no—
41C23—3861no—
42Q8C2×D19311yescharacteristic, complemented
43D4—3861no—
44D4—3861no—
45D4—1931no—
46D4—1931no—
47D4C2×D19311yescharacteristic
48C2×C4—3861no—
49C2×C4—1931no—
50C8—1931no—
51C8C2×D19311yescharacteristic, complemented
52C22—21no—
53C22—7722no—
54C22—3861no—
55C22—3861no—
56C22—1931no—
57C4—21no—
58C4—1931no—
59C4C22×D19311yescharacteristic
60C2—41no—
61C2—7721no—
62C2—7721no—
63C2—3861no—
64C2D4×D19311yescharacteristic
subgroupG/H
centerC2D4×D193
commutatorC4×C193C23
FrattiniC4C22×D193
FittingSD16×C193C2
socleC2×C193C2×D4
hypercenterSD16D193
hypocenterC193AGL(1,ℤ/8)
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #15690556C2semidirect
2. D4×D193C2semidirect
3. #15690542C2semidirect
4. D1544C2semidirect
5. #15690540C2semidirect
6. #15690538C2semidirect
7. SD16×C193C2semidirect
11. D772C22semidirect
15. #13095393C22semidirect
16. Q8×C193C22semidirect
18. C8×C193C22semidirect
32. C193AGL(1,ℤ/8)semidirect
37. SD16D193semidirect
42. Q8C2×D193semidirect
51. C8C2×D193semidirect