Finite Group Databasebeta

← #20245700

Subgroups — #20245700

Order 6016.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D752C211yesmaximal, characteristic, complemented
2#15688960C212yesmaximal, complemented
3#15688958C212yesmaximal, complemented
4#15688957C211yesmaximal, characteristic, complemented
5C47×#508C211yesmaximal, characteristic, complemented
6C2×D376—21no—
7D752—21no—
8D752C2212yes—
9C47⋊C32C2212yescomplemented
10#135×C47—21no—
11Q32×C47C2211yescharacteristic, complemented
12SD32×C47—21no—
13D16×C47C2211yescharacteristic, complemented
14C2×C16×C47C2211yescharacteristic
15#41×C47—41no—
16C2×D188—41no—
17Q16×C47—21no—
18SD16×C47—41no—
19D8×C47—21no—
20C2×C8×C47D411yescharacteristic
21D376—22no—
22D376—41no—
23C16×C47D411yescharacteristic
24C16×C47C2311yescharacteristic
25C22×D47—81no—
26Q8×C47—41no—
27D4×C47—41no—
28D4×C47—81no—
29C2×C4×C47—81no—
30C2×C4×C47D811yescharacteristic
31D188—42no—
32D188—81no—
33C8×C47D811yescharacteristic
34C8×C47C2×D411yescharacteristic
35C22×C47—81no—
36C22×C47D1611yescharacteristic
37C2×D47—82no—
38C2×D47—162no—
39C4×C47—81no—
40C4×C47D1611yescharacteristic
41C4×C47C2×D811yescharacteristic
42#2263—471nomaximal, Sylow
43C2×C47—21no—
44C2×C47—161no—
45C2×C47C2×D1611yescharacteristic
46D47—162no—
47#508D4711yescharacteristic, complemented
48C2×D16—471no—
49SD64—472no—
50D32—472no—
51M64—471no—
52C47#226311yescharacteristic, complemented, Sylow
53#135—21no—
54C2×D8—941no—
55Q32C2×D4711yescharacteristic, complemented
56SD32—21no—
57D16—472no—
58D16—941no—
59D16C2×D4711yescharacteristic, complemented
60C2×C16C2×D4711yescharacteristic
61C32—472no—
62#41—41no—
63C2×D4—1881no—
64Q16—21no—
65SD16—41no—
66D8—21no—
67D8—942no—
68D8—1881no—
69C2×C8C22⋊D4711yescharacteristic
70C16C22⋊D4711yescharacteristic
71C16C22×D4711yescharacteristic
72C23—3761no—
73Q8—41no—
74D4—41no—
75D4—81no—
76D4—3761no—
77D4—1882no—
78C2×C4—81no—
79C2×C4#1062533411yescharacteristic
80C8#1062533411yescharacteristic
81C8C2×C22⋊D4711yescharacteristic
82C22—81no—
83C22—3762no—
84C22—7522no—
85C22#1309396511yescharacteristic
86C4—81no—
87C4#1309396511yescharacteristic
88C4C2×#1062533411yescharacteristic
89C2—21no—
90C2—161no—
91C2—7522no—
92C2C2×#1309396511yescharacteristic
subgroupG/H
centerC2C2×#13093965
commutatorC16×C47C23
FrattiniC16C22×D47
FittingC47×#508C2
socleC2×C47C2×D16
hypercenter#508D47
hypocenterC47#2263
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #508

Complements

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

NH ≅ G/Ntype
1. C2×D752C2semidirect
2. #15688960C2semidirect
3. #15688958C2semidirect
4. #15688957C2semidirect
5. C47×#508C2semidirect
9. C47⋊C32C22semidirect
11. Q32×C47C22semidirect
13. D16×C47C22semidirect
47. #508D47semidirect
52. C47#2263semidirect
55. Q32C2×D47semidirect
59. D16C2×D47semidirect