Finite Group Databasebeta

← SD16×D269 #22575465

Subgroups — SD16×D269 #22575465

Order 8608.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D269C211yesmaximal, characteristic, complemented
2D4×D269C211yesmaximal, characteristic
3#16864391C211yesmaximal, characteristic, complemented
4#16864390C211yesmaximal, characteristic, complemented
5#16864389C211yesmaximal, characteristic, complemented
6C8×D269C211yesmaximal, characteristic, complemented
7SD16×C269C211yesmaximal, characteristic, complemented
8C22×D269—21no—
9Dic538—21no—
10Dic538C2211yescharacteristic, complemented
11D1076C2211yescharacteristic
12C22⋊D269—21no—
13C4×D269—21no—
14C4×D269C2211yescharacteristic
15#14524130C2211yescharacteristic, complemented
16Q8×C269C2211yescharacteristic, complemented
17D4×C269C2211yescharacteristic
18C8×C269C2211yescharacteristic, complemented
19C22×C269—21no—
20C2×D269—21no—
21C2×D269—42no—
22C2×D269D411yescharacteristic
23C4×C269—21no—
24C4×C269C2311yescharacteristic
25Dic269—21no—
26Dic269D411yescharacteristic
27C2×C269—41no—
28C2×C269C2×D411yescharacteristic
29D269—41no—
30D269SD1612yesdirect product factor
31C269C2×SD1611yescharacteristic, complemented, Sylow
32C2×SD16—2691nomaximal, Sylow
33C2×Q8—2691no—
34C2×D4—2691no—
35SD16—2691no—
36SD16—2691no—
37SD16—2691no—
38SD16D26911yescharacteristic, direct product factor
39C2×C8—2691no—
40C23—5381no—
41Q8—2691no—
42Q8—5381no—
43Q8C2×D26911yescharacteristic, complemented
44D4—2691no—
45D4—5381no—
46D4C2×D26911yescharacteristic
47C2×C4—2691no—
48C2×C4—5381no—
49C8—2691no—
50C8C2×D26911yescharacteristic, complemented
51C22—21no—
52C22—2691no—
53C22—5381no—
54C22—10762no—
55C4—21no—
56C4—2691no—
57C4—5381no—
58C4C22×D26911yescharacteristic
59C2—41no—
60C2—2692no—
61C2—10761no—
62C2D4×D26911yescharacteristic
subgroupG/H
centerC2D4×D269
commutatorC4×C269C23
FrattiniC4C22×D269
FittingSD16×C269C2
socleC2×C269C2×D4
hypercenterSD16D269
hypocenterC269C2×SD16
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. Q8×D269C2semidirect
3. #16864391C2semidirect
4. #16864390C2semidirect
5. #16864389C2semidirect
6. C8×D269C2semidirect
7. SD16×C269C2semidirect
10. Dic538C22semidirect
15. #14524130C22semidirect
16. Q8×C269C22semidirect
18. C8×C269C22semidirect
30. D269SD16direct (N × H)
31. C269C2×SD16semidirect
38. SD16D269direct (N × H)
43. Q8C2×D269semidirect
50. C8C2×D269semidirect