Finite Group Databasebeta

← D3×SD32 #4913

Subgroups — D3×SD32 #4913

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q16C211yesmaximal, characteristic, complemented
2D3×D8C211yesmaximal, characteristic
3C3×SD32C211yesmaximal, characteristic, complemented
4#828C211yesmaximal, characteristic, complemented
5#827C211yesmaximal, characteristic, complemented
6#800C211yesmaximal, characteristic, complemented
7D3×C16C211yesmaximal, characteristic, complemented
8C2×SD32—31nomaximal, Sylow
9D3×Q8—21no—
10D3×D4—21no—
11C3×Q16C2211yescharacteristic, complemented
12C3×D8C2211yescharacteristic
13#216—21no—
14#213—21no—
15Dic12C2211yescharacteristic, complemented
16D24C2211yescharacteristic
17D3×C8C2211yescharacteristic
18C3×C16C2211yescharacteristic, complemented
19C3⋊C16C2211yescharacteristic, complemented
20C2×Q16—31no—
21C2×D8—31no—
22SD32—31no—
23SD32—31no—
24SD32—31no—
25SD32D311yescharacteristic, direct product factor
26C2×C16—31no—
27C22×D3—41no—
28C3×Q8—21no—
29C3×D4—21no—
30#67—41no—
31D12—21no—
32C4×D3—41no—
33C4×D3D411yescharacteristic
34Dic6—21no—
35Dic6—41no—
36C3×C8C2311yescharacteristic
37C3⋊C8D411yescharacteristic
38C2×Q8—61no—
39C2×D4—61no—
40Q16—31no—
41Q16—61no—
42Q16C2×D311yescharacteristic, complemented
43D8—31no—
44D8—61no—
45D8C2×D311yescharacteristic
46C2×C8—31no—
47C16—31no—
48C16C2×D311yescharacteristic, complemented
49C22×C3—41no—
50C2×D3—41no—
51C2×D3—82no—
52C2×D3D811yescharacteristic
53C3×C4—41no—
54C3×C4C2×D411yescharacteristic
55Dic3—41no—
56Dic3D811yescharacteristic
57C23—121no—
58Q8—21no—
59Q8—61no—
60Q8—121no—
61D4—21no—
62D4—61no—
63D4—121no—
64C2×C4—31no—
65C2×C4—121no—
66C8—31no—
67C8C22×D311yescharacteristic
68C2×C3—81no—
69C2×C3C2×D811yescharacteristic
70D3—81no—
71D3SD3212yesdirect product factor
72C22—31no—
73C22—41no—
74C22—121no—
75C22—242no—
76C4—31no—
77C4—41no—
78C4—121no—
79C4D3×D411yescharacteristic
80C3C2×SD3211yescharacteristic, complemented, Sylow
81C2—32no—
82C2—81no—
83C2—241no—
84C2D3×D811yescharacteristic
subgroupG/H
centerC2D3×D8
commutator, cosocleC3×C8C23
FrattiniC8C22×D3
FittingC3×SD32C2
socleC2×C3C2×D8
prime radicalD3×D8C2
hypercenterSD32D3
hypocenterC3C2×SD32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. D3×Q16C2semidirect
3. C3×SD32C2semidirect
4. #828C2semidirect
5. #827C2semidirect
6. #800C2semidirect
7. D3×C16C2semidirect
11. C3×Q16C22semidirect
15. Dic12C22semidirect
18. C3×C16C22semidirect
19. C3⋊C16C22semidirect
25. SD32D3direct (N × H)
42. Q16C2×D3semidirect
48. C16C2×D3semidirect
71. D3SD32direct (N × H)
80. C3C2×SD32semidirect

Maximal subgroups

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

subgroupindex
D3×Q162
D3×D82
C3×SD322
#8282
#8272
#8002
D3×C162
C2×SD323