Finite Group Databasebeta

← SD16×D199 #20263967

Subgroups — SD16×D199 #20263967

Order 6368.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D199C211yesmaximal, characteristic, complemented
2D4×D199C211yesmaximal, characteristic
3#15691875C211yesmaximal, characteristic, complemented
4#15691874C211yesmaximal, characteristic, complemented
5#15691873C211yesmaximal, characteristic, complemented
6C8×D199C211yesmaximal, characteristic, complemented
7SD16×C199C211yesmaximal, characteristic, complemented
8C22×D199—21no—
9Dic398—21no—
10Dic398C2211yescharacteristic, complemented
11D796C2211yescharacteristic
12C22⋊D199—21no—
13C4×D199—21no—
14C4×D199C2211yescharacteristic
15C199⋊C8C2211yescharacteristic, complemented
16Q8×C199C2211yescharacteristic, complemented
17D4×C199C2211yescharacteristic
18C8×C199C2211yescharacteristic, complemented
19C22×C199—21no—
20C2×D199—21no—
21C2×D199—42no—
22C2×D199D411yescharacteristic
23C4×C199—21no—
24C4×C199C2311yescharacteristic
25Dic199—21no—
26Dic199D411yescharacteristic
27C2×C199—41no—
28C2×C199C2×D411yescharacteristic
29D199—41no—
30D199SD1612yesdirect product factor
31C199C2×SD1611yescharacteristic, complemented, Sylow
32C2×SD16—1991nomaximal, Sylow
33C2×Q8—1991no—
34C2×D4—1991no—
35SD16—1991no—
36SD16—1991no—
37SD16—1991no—
38SD16D19911yescharacteristic, direct product factor
39C2×C8—1991no—
40C23—3981no—
41Q8—3981no—
42Q8—1991no—
43Q8C2×D19911yescharacteristic, complemented
44D4—3981no—
45D4—1991no—
46D4C2×D19911yescharacteristic
47C2×C4—3981no—
48C2×C4—1991no—
49C8—1991no—
50C8C2×D19911yescharacteristic, complemented
51C22—21no—
52C22—7962no—
53C22—3981no—
54C22—1991no—
55C4—21no—
56C4—3981no—
57C4—1991no—
58C4C22×D19911yescharacteristic
59C2—41no—
60C2—7961no—
61C2—1992no—
62C2D4×D19911yescharacteristic
subgroupG/H
centerC2D4×D199
commutatorC4×C199C23
FrattiniC4C22×D199
FittingSD16×C199C2
socleC2×C199C2×D4
hypercenterSD16D199
hypocenterC199C2×SD16
LCSG ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. Q8×D199C2semidirect
3. #15691875C2semidirect
4. #15691874C2semidirect
5. #15691873C2semidirect
6. C8×D199C2semidirect
7. SD16×C199C2semidirect
10. Dic398C22semidirect
15. C199⋊C8C22semidirect
16. Q8×C199C22semidirect
18. C8×C199C22semidirect
30. D199SD16direct (N × H)
31. C199C2×SD16semidirect
38. SD16D199direct (N × H)
43. Q8C2×D199semidirect
50. C8C2×D199semidirect