Finite Group Databasebeta

← #64127

Subgroups — #64127

Order 288.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3832C211yesmaximal, characteristic
2Q8×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×Q16C211yesmaximal, characteristic, complemented
4#3756C211yesmaximal, characteristic, complemented
5#3755C211yesmaximal, characteristic, complemented
6#3744C211yesmaximal, characteristic, complemented
7#3743C211yesmaximal, characteristic, complemented
8#918—34nomaximal
9C32×Q8C2211yescharacteristic
10C32×Q8C2211yescharacteristic
11C4⋊(C3⋊D3)—21no—
12C4⋊(C3⋊D3)C2211yescharacteristic
13C4×C3⋊D3—21no—
14C4×C3⋊D3—21no—
15C4×C3⋊D3C2211yescharacteristic
16#634—21no—
17#634C2211yescharacteristic
18C32×C8C2211yescharacteristic
19C3⋊(C3⋊C8)C2211yescharacteristic
20#239—34no—
21D3×Q8—34no—
22C3×Q16D314yescomplemented
23#216—34no—
24#215—34no—
25#204—34no—
26ΓL(1,𝔽25)—34no—
27C2×C3⋊D3—21no—
28C2×C3⋊D3D411yescharacteristic
29C32×C4—21no—
30C32×C4—21no—
31C32×C4C2311yescharacteristic
32C3⋊Dic3—21no—
33C3⋊Dic3D411yescharacteristic
34#137—91noSylow
35C3×Q8C2×D314yes—
36C3×Q8C2×D314yes—
37D12—34no—
38D12—64no—
39C4×D3—34no—
40C4×D3—64no—
41C4×D3—64no—
42Dic6—34no—
43Dic6—64no—
44C3×C8C2×D314yes—
45C3⋊C8—34no—
46C2×C32C2×D411yescharacteristic
47C3⋊D3—21no—
48C3⋊D3—41no—
49#41—91no—
50C2×Q8—91no—
51Q16—91no—
52Q16C3⋊D311yescharacteristic, complemented
53SD16—91no—
54SD16—91no—
55M16—91no—
56C2×D3—34no—
57C2×D3—64no—
58C3×C4—24no—
59C3×C4—24no—
60C3×C4C22×D314yes—
61Dic3—34no—
62Dic3—64no—
63C32#13711yescharacteristic, complemented, Sylow
64Q8—91no—
65Q8—181no—
66Q8C2×C3⋊D311yescharacteristic
67Q8C2×C3⋊D311yescharacteristic
68D4—91no—
69D4—181no—
70C2×C4—91no—
71C2×C4—181no—
72C2×C4—181no—
73C8—91no—
74C8C2×C3⋊D311yescharacteristic
75C2×C3D3×D414yes—
76D3—64no—
77D3—124no—
78C22—91no—
79C22—181no—
80C4—21no—
81C4—21no—
82C4—91no—
83C4—181no—
84C4C22×C3⋊D311yescharacteristic
85C3#91814yescomplemented
86C2—181no—
87C2—361no—
88C2D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2D4×C3⋊D3
commutator, cosocleC32×C4C23
FrattiniC4C22×C3⋊D3
FittingC32×Q16C2
socleC2×C32C2×D4
prime radical#3832C2
hypercenterQ16C3⋊D3
hypocenterC32#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ Q16

Complements

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

NH ≅ G/Ntype
2. Q8×C3⋊D3C2semidirect
3. C32×Q16C2semidirect
4. #3756C2semidirect
5. #3755C2semidirect
6. #3744C2semidirect
7. #3743C2semidirect
22. C3×Q16D3semidirect
52. Q16C3⋊D3semidirect
63. C32#137semidirect
85. C3#918semidirect

Maximal subgroups

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

subgroupindex
#38322
Q8×C3⋊D32
C32×Q162
#37562
#37552
#37442
#37432
#9183