Finite Group Databasebeta

← SD16×D229 #20301000

Subgroups — SD16×D229 #20301000

Order 7328.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D229C211yesmaximal, characteristic, complemented
2D4×D229C211yesmaximal, characteristic
3#16814655C211yesmaximal, characteristic, complemented
4#16814654C211yesmaximal, characteristic, complemented
5#16814653C211yesmaximal, characteristic, complemented
6C8×D229C211yesmaximal, characteristic, complemented
7SD16×C229C211yesmaximal, characteristic, complemented
8C22×D229—21no—
9Dic458—21no—
10Dic458C2211yescharacteristic, complemented
11D916C2211yescharacteristic
12C22⋊D229—21no—
13C4×D229—21no—
14C4×D229C2211yescharacteristic
15#14270080C2211yescharacteristic, complemented
16Q8×C229C2211yescharacteristic, complemented
17D4×C229C2211yescharacteristic
18C8×C229C2211yescharacteristic, complemented
19C22×C229—21no—
20C2×D229—21no—
21C2×D229—42no—
22C2×D229D411yescharacteristic
23C4×C229—21no—
24C4×C229C2311yescharacteristic
25Dic229—21no—
26Dic229D411yescharacteristic
27C2×C229—41no—
28C2×C229C2×D411yescharacteristic
29D229—41no—
30D229SD1612yesdirect product factor
31C229C2×SD1611yescharacteristic, complemented, Sylow
32C2×SD16—2291nomaximal, Sylow
33C2×Q8—2291no—
34C2×D4—2291no—
35SD16—2291no—
36SD16—2291no—
37SD16—2291no—
38SD16D22911yescharacteristic, direct product factor
39C2×C8—2291no—
40C23—4581no—
41Q8—4581no—
42Q8—2291no—
43Q8C2×D22911yescharacteristic, complemented
44D4—4581no—
45D4—2291no—
46D4C2×D22911yescharacteristic
47C2×C4—4581no—
48C2×C4—2291no—
49C8—2291no—
50C8C2×D22911yescharacteristic, complemented
51C22—21no—
52C22—9162no—
53C22—4581no—
54C22—2291no—
55C4—21no—
56C4—4581no—
57C4—2291no—
58C4C22×D22911yescharacteristic
59C2—41no—
60C2—9161no—
61C2—2292no—
62C2D4×D22911yescharacteristic
subgroupG/H
centerC2D4×D229
commutatorC4×C229C23
FrattiniC4C22×D229
FittingSD16×C229C2
socleC2×C229C2×D4
hypercenterSD16D229
hypocenterC229C2×SD16
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. Q8×D229C2semidirect
3. #16814655C2semidirect
4. #16814654C2semidirect
5. #16814653C2semidirect
6. C8×D229C2semidirect
7. SD16×C229C2semidirect
10. Dic458C22semidirect
15. #14270080C22semidirect
16. Q8×C229C22semidirect
18. C8×C229C22semidirect
30. D229SD16direct (N × H)
31. C229C2×SD16semidirect
38. SD16D229direct (N × H)
43. Q8C2×D229semidirect
50. C8C2×D229semidirect