Finite Group Databasebeta

← D3×SD16 #913

Subgroups — D3×SD16 #913

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8C211yesmaximal, characteristic, complemented
2D3×D4C211yesmaximal, characteristic
3C3×SD16C211yesmaximal, characteristic, complemented
4#215C211yesmaximal, characteristic, complemented
5#214C211yesmaximal, characteristic, complemented
6#204C211yesmaximal, characteristic, complemented
7D3×C8C211yesmaximal, characteristic, complemented
8C2×SD16—31nomaximal, Sylow
9C22×D3—21no—
10C3×Q8C2211yescharacteristic, complemented
11C3×D4C2211yescharacteristic
12#67—21no—
13D12C2211yescharacteristic
14C4×D3—21no—
15C4×D3C2211yescharacteristic
16Dic6—21no—
17Dic6C2211yescharacteristic, complemented
18C3×C8C2211yescharacteristic, complemented
19C3⋊C8C2211yescharacteristic, complemented
20C2×Q8—31no—
21C2×D4—31no—
22SD16—31no—
23SD16—31no—
24SD16—31no—
25SD16D311yescharacteristic, direct product factor
26C2×C8—31no—
27C22×C3—21no—
28C2×D3—21no—
29C2×D3—42no—
30C2×D3D411yescharacteristic
31C3×C4—21no—
32C3×C4C2311yescharacteristic
33Dic3—21no—
34Dic3D411yescharacteristic
35C23—61no—
36Q8—31no—
37Q8—61no—
38Q8C2×D311yescharacteristic, complemented
39D4—31no—
40D4—61no—
41D4C2×D311yescharacteristic
42C2×C4—31no—
43C2×C4—61no—
44C8—31no—
45C8C2×D311yescharacteristic, complemented
46C2×C3—41no—
47C2×C3C2×D411yescharacteristic
48D3—41no—
49D3SD1612yesdirect product factor
50C22—21no—
51C22—31no—
52C22—61no—
53C22—122no—
54C4—21no—
55C4—31no—
56C4—61no—
57C4C22×D311yescharacteristic
58C3C2×SD1611yescharacteristic, complemented, Sylow
59C2—32no—
60C2—41no—
61C2—121no—
62C2D3×D411yescharacteristic
subgroupG/H
centerC2D3×D4
commutator, cosocleC3×C4C23
FrattiniC4C22×D3
FittingC3×SD16C2
socleC2×C3C2×D4
prime radicalD3×D4C2
hypercenterSD16D3
hypocenterC3C2×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. D3×Q8C2semidirect
3. C3×SD16C2semidirect
4. #215C2semidirect
5. #214C2semidirect
6. #204C2semidirect
7. D3×C8C2semidirect
10. C3×Q8C22semidirect
17. Dic6C22semidirect
18. C3×C8C22semidirect
19. C3⋊C8C22semidirect
25. SD16D3direct (N × H)
38. Q8C2×D3semidirect
45. C8C2×D3semidirect
49. D3SD16direct (N × H)
58. C3C2×SD16semidirect

Maximal subgroups

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

subgroupindex
D3×Q82
D3×D42
C3×SD162
#2152
#2142
#2042
D3×C82
C2×SD163