Finite Group Databasebeta

← SD16×D47 #13094036

Subgroups — SD16×D47 #13094036

Order 1504.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D47C211yesmaximal, characteristic, complemented
2D4×D47C211yesmaximal, characteristic
3SD16×C47C211yesmaximal, characteristic, complemented
4#10625336C211yesmaximal, characteristic, complemented
5#10625335C211yesmaximal, characteristic, complemented
6#10625325C211yesmaximal, characteristic, complemented
7C8×D47C211yesmaximal, characteristic, complemented
8C22×D47—21no—
9Q8×C47C2211yescharacteristic, complemented
10D4×C47C2211yescharacteristic
11C22⋊D47—21no—
12D188C2211yescharacteristic
13C4×D47—21no—
14C4×D47C2211yescharacteristic
15Dic94—21no—
16Dic94C2211yescharacteristic, complemented
17C8×C47C2211yescharacteristic, complemented
18C47⋊C8C2211yescharacteristic, complemented
19C22×C47—21no—
20C2×D47—21no—
21C2×D47—42no—
22C2×D47D411yescharacteristic
23C4×C47—21no—
24C4×C47C2311yescharacteristic
25Dic47—21no—
26Dic47D411yescharacteristic
27C2×C47—41no—
28C2×C47C2×D411yescharacteristic
29D47—41no—
30D47SD1612yesdirect product factor
31C47C2×SD1611yescharacteristic, complemented, Sylow
32C2×SD16—471nomaximal, Sylow
33C2×Q8—471no—
34C2×D4—471no—
35SD16—471no—
36SD16—471no—
37SD16—471no—
38SD16D4711yescharacteristic, direct product factor
39C2×C8—471no—
40C23—941no—
41Q8—471no—
42Q8—941no—
43Q8C2×D4711yescharacteristic, complemented
44D4—471no—
45D4—941no—
46D4C2×D4711yescharacteristic
47C2×C4—471no—
48C2×C4—941no—
49C8—471no—
50C8C2×D4711yescharacteristic, complemented
51C22—21no—
52C22—471no—
53C22—941no—
54C22—1882no—
55C4—21no—
56C4—471no—
57C4—941no—
58C4C22×D4711yescharacteristic
59C2—41no—
60C2—472no—
61C2—1881no—
62C2D4×D4711yescharacteristic
subgroupG/H
centerC2D4×D47
commutator, cosocleC4×C47C23
FrattiniC4C22×D47
FittingSD16×C47C2
socleC2×C47C2×D4
prime radicalD4×D47C2
hypercenterSD16D47
hypocenterC47C2×SD16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. Q8×D47C2semidirect
3. SD16×C47C2semidirect
4. #10625336C2semidirect
5. #10625335C2semidirect
6. #10625325C2semidirect
7. C8×D47C2semidirect
9. Q8×C47C22semidirect
16. Dic94C22semidirect
17. C8×C47C22semidirect
18. C47⋊C8C22semidirect
30. D47SD16direct (N × H)
31. C47C2×SD16semidirect
38. SD16D47direct (N × H)
43. Q8C2×D47semidirect
50. C8C2×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
Q8×D472
D4×D472
SD16×C472
#106253362
#106253352
#106253252
C8×D472
C2×SD1647