Finite Group Databasebeta

← #64159

Subgroups — #64159

Order 288.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#41C211yesmaximal, characteristic, complemented
2#3828C211yesmaximal, characteristic, complemented
3#3756C211yesmaximal, characteristic, complemented
4#3755C211yesmaximal, characteristic, complemented
5#3754C211yesmaximal, characteristic, complemented
6#3753C211yesmaximal, characteristic, complemented
7C2×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#950—34nomaximal
9C32×Q8C2211yescharacteristic
10C32×D4—21no—
11C32×D4C2211yescharacteristic
12C2×C32×C4—21no—
13C2×C32×C4C2211yescharacteristic
14#638—21no—
15C4⋊(C3⋊D3)C2211yescharacteristic
16C4×C3⋊D3—21no—
17#634C2211yescharacteristic
18C3⋊(C3⋊C8)C2211yescharacteristic
19C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#41D314yescomplemented
21#235—34no—
22#216—34no—
23#215—34no—
24#214—34no—
25#213—34no—
26C2×C3⋊C8—34no—
27C22×C32—21no—
28C22×C32D411yescharacteristic
29C2×C3⋊D3—21no—
30C32×C4—21no—
31C32×C4D411yescharacteristic
32C32×C4C2311yescharacteristic
33C3⋊Dic3—21no—
34#135—91noSylow
35C3×Q8C2×D314yes—
36C3×D4—24no—
37C3×D4C2×D314yes—
38C2×C3×C4—24no—
39C2×C3×C4C2×D314yes—
40#67—64no—
41D12—34no—
42C4×D3—64no—
43Dic6—34no—
44C3⋊C8—34no—
45C3⋊C8—34no—
46C2×C32—21no—
47C2×C32—41no—
48C2×C32C2×D411yescharacteristic
49C3⋊D3—41no—
50#41—91no—
51#41C3⋊D311yescharacteristic, complemented
52Q16—91no—
53SD16—91no—
54SD16—91no—
55D8—91no—
56C2×C8—91no—
57C22×C3—24no—
58C22×C3#6714yes—
59C2×D3—64no—
60C3×C4—24no—
61C3×C4#6714yes—
62C3×C4C22×D314yes—
63Dic3—64no—
64C32#13511yescharacteristic, complemented, Sylow
65Q8—91no—
66Q8C2×C3⋊D311yescharacteristic
67D4—21no—
68D4—91no—
69D4—181no—
70D4C2×C3⋊D311yescharacteristic
71C2×C4—21no—
72C2×C4—181no—
73C2×C4C2×C3⋊D311yescharacteristic
74C8—91no—
75C8—91no—
76C2×C3—24no—
77C2×C3—44no—
78C2×C3C2×#6714yes—
79D3—124no—
80C22—21no—
81C22—181no—
82C22#63811yescharacteristic
83C4—21no—
84C4—181no—
85C4#63811yescharacteristic
86C4C22×C3⋊D311yescharacteristic
87C3#95014yescomplemented
88C2—21no—
89C2—41no—
90C2—361no—
91C2C2×#63811yescharacteristic
subgroupG/H
centerC4#638
commutator, cosocleC32×C4C23
FrattiniC4C22×C3⋊D3
FittingC32×#41C2
socleC2×C32C2×D4
hypercenter#41C3⋊D3
hypocenterC32#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C32×#41C2semidirect
2. #3828C2semidirect
3. #3756C2semidirect
4. #3755C2semidirect
5. #3754C2semidirect
6. #3753C2semidirect
7. C2×C3⋊(C3⋊C8)C2semidirect
20. C3×#41D3semidirect
51. #41C3⋊D3semidirect
64. C32#135semidirect
87. C3#950semidirect

Maximal subgroups

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

subgroupindex
C32×#412
#38282
#37562
#37552
#37542
#37532
C2×C3⋊(C3⋊C8)2
#9503