Finite Group Databasebeta

← #19136907

Subgroups — #19136907

Order 5504.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D688C211yesmaximal, characteristic, complemented
2#14582736C212yesmaximal, complemented
3#14582734C212yesmaximal, complemented
4#14582733C211yesmaximal, characteristic, complemented
5C43×#508C211yesmaximal, characteristic, complemented
6C2×D344—21no—
7D688—21no—
8D688C2212yes—
9C43⋊C32C2212yescomplemented
10#135×C43—21no—
11Q32×C43C2211yescharacteristic, complemented
12SD32×C43—21no—
13D16×C43C2211yescharacteristic, complemented
14C2×C16×C43C2211yescharacteristic
15#41×C43—41no—
16C2×D172—41no—
17Q16×C43—21no—
18SD16×C43—41no—
19D8×C43—21no—
20C2×C8×C43D411yescharacteristic
21D344—22no—
22D344—41no—
23C16×C43D411yescharacteristic
24C16×C43C2311yescharacteristic
25C22×D43—81no—
26Q8×C43—41no—
27D4×C43—41no—
28D4×C43—81no—
29C2×C4×C43—81no—
30C2×C4×C43D811yescharacteristic
31D172—42no—
32D172—81no—
33C8×C43D811yescharacteristic
34C8×C43C2×D411yescharacteristic
35C22×C43—81no—
36C22×C43D1611yescharacteristic
37C2×D43—82no—
38C2×D43—162no—
39C4×C43—81no—
40C4×C43D1611yescharacteristic
41C4×C43C2×D811yescharacteristic
42#2263—431nomaximal, Sylow
43C2×C43—21no—
44C2×C43—161no—
45C2×C43C2×D1611yescharacteristic
46D43—162no—
47#508D4311yescharacteristic, complemented
48C2×D16—431no—
49SD64—432no—
50D32—432no—
51M64—431no—
52C43#226311yescharacteristic, complemented, Sylow
53#135—21no—
54C2×D8—861no—
55Q32C2×D4311yescharacteristic, complemented
56SD32—21no—
57D16—432no—
58D16—861no—
59D16C2×D4311yescharacteristic, complemented
60C2×C16C2×D4311yescharacteristic
61C32—432no—
62#41—41no—
63C2×D4—1721no—
64Q16—21no—
65SD16—41no—
66D8—21no—
67D8—862no—
68D8—1721no—
69C2×C8C22⋊D4311yescharacteristic
70C16C22⋊D4311yescharacteristic
71C16C22×D4311yescharacteristic
72C23—3441no—
73Q8—41no—
74D4—41no—
75D4—81no—
76D4—3441no—
77D4—1722no—
78C2×C4—81no—
79C2×C4#1062188211yescharacteristic
80C8#1062188211yescharacteristic
81C8C2×C22⋊D4311yescharacteristic
82C22—81no—
83C22—3442no—
84C22—6882no—
85C22#1306326611yescharacteristic
86C4—81no—
87C4#1306326611yescharacteristic
88C4C2×#1062188211yescharacteristic
89C2—21no—
90C2—161no—
91C2—6882no—
92C2C2×#1306326611yescharacteristic
subgroupG/H
centerC2C2×#13063266
commutatorC16×C43C23
FrattiniC16C22×D43
FittingC43×#508C2
socleC2×C43C2×D16
hypercenter#508D43
hypocenterC43#2263
LCSG ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
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×D688C2semidirect
2. #14582736C2semidirect
3. #14582734C2semidirect
4. #14582733C2semidirect
5. C43×#508C2semidirect
9. C43⋊C32C22semidirect
11. Q32×C43C22semidirect
13. D16×C43C22semidirect
47. #508D43semidirect
52. C43#2263semidirect
55. Q32C2×D43semidirect
59. D16C2×D43semidirect