Finite Group Databasebeta

← #20263982

Subgroups — #20263982

Order 6368.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15691887C211yesmaximal, characteristic, complemented
2D4×D199C211yesmaximal, characteristic, complemented
3#15691873C211yesmaximal, characteristic, complemented
4D1592C211yesmaximal, characteristic, complemented
5#15691871C211yesmaximal, characteristic, complemented
6#15691869C211yesmaximal, characteristic, complemented
7SD16×C199C211yesmaximal, characteristic, complemented
8C22×D199—21no—
9D796—21no—
10D796C2211yescharacteristic
11D796C2211yescharacteristic, complemented
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—21no—
22C2×D199—42no—
23C2×D199D411yescharacteristic
24C4×C199—21no—
25C4×C199C2311yescharacteristic
26Dic199D411yescharacteristic
27C2×C199—41no—
28C2×C199C2×D411yescharacteristic
29D199—21no—
30D199—41no—
31D199—41no—
32C199AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
33AGL(1,ℤ/8)—1991nomaximal, Sylow
34#41—1991no—
35C2×D4—1991no—
36SD16—1991no—
37SD16D19911yescharacteristic, complemented
38D8—1991no—
39D8—1991no—
40M16—1991no—
41C23—3981no—
42Q8C2×D19911yescharacteristic, complemented
43D4—3981no—
44D4—3981no—
45D4—1991no—
46D4—1991no—
47D4C2×D19911yescharacteristic
48C2×C4—3981no—
49C2×C4—1991no—
50C8—1991no—
51C8C2×D19911yescharacteristic, complemented
52C22—21no—
53C22—7962no—
54C22—3981no—
55C22—3981no—
56C22—1991no—
57C4—21no—
58C4—1991no—
59C4C22×D19911yescharacteristic
60C2—41no—
61C2—7961no—
62C2—7961no—
63C2—3981no—
64C2D4×D19911yescharacteristic
subgroupG/H
centerC2D4×D199
commutatorC4×C199C23
FrattiniC4C22×D199
FittingSD16×C199C2
socleC2×C199C2×D4
hypercenterSD16D199
hypocenterC199AGL(1,ℤ/8)
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. #15691887C2semidirect
2. D4×D199C2semidirect
3. #15691873C2semidirect
4. D1592C2semidirect
5. #15691871C2semidirect
6. #15691869C2semidirect
7. SD16×C199C2semidirect
11. D796C22semidirect
15. C199⋊C8C22semidirect
16. Q8×C199C22semidirect
18. C8×C199C22semidirect
32. C199AGL(1,ℤ/8)semidirect
37. SD16D199semidirect
42. Q8C2×D199semidirect
51. C8C2×D199semidirect