Finite Group Databasebeta

← #20270004

Subgroups — #20270004

Order 6752.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16809963C211yesmaximal, characteristic, complemented
2D4×D211C211yesmaximal, characteristic, complemented
3#16809949C211yesmaximal, characteristic, complemented
4D1688C211yesmaximal, characteristic, complemented
5#16809947C211yesmaximal, characteristic, complemented
6#16809945C211yesmaximal, characteristic, complemented
7SD16×C211C211yesmaximal, characteristic, complemented
8C22×D211—21no—
9D844—21no—
10D844C2211yescharacteristic
11D844C2211yescharacteristic, complemented
12C22⋊D211—21no—
13C4×D211—21no—
14C4×D211C2211yescharacteristic
15C211⋊C8C2211yescharacteristic, complemented
16Q8×C211C2211yescharacteristic, complemented
17D4×C211C2211yescharacteristic
18C8×C211C2211yescharacteristic, complemented
19C22×C211—21no—
20C2×D211—21no—
21C2×D211—21no—
22C2×D211—42no—
23C2×D211D411yescharacteristic
24C4×C211—21no—
25C4×C211C2311yescharacteristic
26Dic211D411yescharacteristic
27C2×C211—41no—
28C2×C211C2×D411yescharacteristic
29D211—21no—
30D211—41no—
31D211—41no—
32C211AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
33AGL(1,ℤ/8)—2111nomaximal, Sylow
34#41—2111no—
35C2×D4—2111no—
36SD16—2111no—
37SD16D21111yescharacteristic, complemented
38D8—2111no—
39D8—2111no—
40M16—2111no—
41C23—4221no—
42Q8C2×D21111yescharacteristic, complemented
43D4—4221no—
44D4—4221no—
45D4—2111no—
46D4—2111no—
47D4C2×D21111yescharacteristic
48C2×C4—4221no—
49C2×C4—2111no—
50C8—2111no—
51C8C2×D21111yescharacteristic, complemented
52C22—21no—
53C22—8442no—
54C22—4221no—
55C22—4221no—
56C22—2111no—
57C4—21no—
58C4—2111no—
59C4C22×D21111yescharacteristic
60C2—41no—
61C2—8441no—
62C2—8441no—
63C2—4221no—
64C2D4×D21111yescharacteristic
subgroupG/H
centerC2D4×D211
commutatorC4×C211C23
FrattiniC4C22×D211
FittingSD16×C211C2
socleC2×C211C2×D4
hypercenterSD16D211
hypocenterC211AGL(1,ℤ/8)
LCSG ▷ C4×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #16809963C2semidirect
2. D4×D211C2semidirect
3. #16809949C2semidirect
4. D1688C2semidirect
5. #16809947C2semidirect
6. #16809945C2semidirect
7. SD16×C211C2semidirect
11. D844C22semidirect
15. C211⋊C8C22semidirect
16. Q8×C211C22semidirect
18. C8×C211C22semidirect
32. C211AGL(1,ℤ/8)semidirect
37. SD16D211semidirect
42. Q8C2×D211semidirect
51. C8C2×D211semidirect