Finite Group Databasebeta

← #20268594

Subgroups — #20268594

Order 6592.

268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15693067C211yesmaximal, characteristic, complemented
2#15693047C213yesmaximal, complemented
3#15693046C213yesmaximal, complemented
4#15693041C213yesmaximal, complemented
5C2×#13110090C213yesmaximal, complemented
6#15693028C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C103C211yesmaximal, characteristic, complemented
8#13110106—21no—
9#13110105C2213yescomplemented
10C2×D412C2213yescomplemented
11D4×D103—23no—
12#13110095C2211yescharacteristic, complemented
13#13110093C2213yescomplemented
14#13110092C2213yescomplemented
15#13110090C2213yescomplemented
16#13110090C2216yescomplemented
17#13110089C2213yescomplemented
18C2×C103⋊C8C2213yescomplemented
19#41×C103—21no—
20#41×C103C2211yescharacteristic
21#41×C103C2213yescomplemented
22C2×D4×C103—23no—
23C2×D4×C103C2213yescomplemented
24C23×C103—23no—
25C22×D103—23no—
26Q8×C103D411yescharacteristic
27Q8×C103C2311yescharacteristic
28D4×C103—23no—
29D4×C103—23no—
30D4×C103D413yes—
31D4×C103C2313yes—
32C2×C4×C103—23no—
33C2×C4×C103C2313yes—
34C22⋊D103—23no—
35D412—23no—
36D412C2313yes—
37C4×D103—23no—
38Dic206C2311yescharacteristic
39C103⋊C8C2311yescharacteristic
40C103⋊C8C2313yes—
41C22×C103—23no—
42C22×C103—83no—
43C22×C103C2×D413yes—
44C2×D103—23no—
45C2×D103—83no—
46C4×C103—21no—
47C4×C103C2×D413yes—
48C4×C103C2411yescharacteristic
49Dic103—21no—
50C2×C103—23no—
51C2×C103—43no—
52C2×C103C22×D411yescharacteristic
53D103—43no—
54C103#57611yescharacteristic, complemented, Sylow
55#576—1031nomaximal, Sylow
56H(5,𝔽2)—1031no—
57H(5,𝔽2)D10311yescharacteristic, complemented
58AGL(1,ℤ/8)—1033no—
59AGL(1,ℤ/8)—1033no—
60#135—1033no—
61C2×D8—1033no—
62#131—1031no—
63#41—21no—
64#41—1033no—
65#41—2061no—
66#41C2×D10311yescharacteristic
67#41C2×D10313yescomplemented
68C2×D4—23no—
69C2×D4—1033no—
70C2×D4—2063no—
71C2×D4C2×D10313yescomplemented
72Q16—1031no—
73SD16—1033no—
74SD16—1033no—
75D8—1033no—
76D8—1036no—
77M16—1033no—
78C2×C8—1033no—
79C23—23no—
80C23—2063no—
81Q8—1031no—
82Q8C22⋊D10311yescharacteristic
83Q8C22×D10311yescharacteristic
84D4—23no—
85D4—23no—
86D4—1033no—
87D4—2063no—
88D4—2063no—
89D4C22⋊D10313yes—
90D4C22×D10313yes—
91C2×C4—23no—
92C2×C4—2063no—
93C2×C4C22×D10313yes—
94C8—1031no—
95C8—1033no—
96C22—23no—
97C22—83no—
98C22—8243no—
99C22—2063no—
100C22C2×C22⋊D10313yes—
101C4—21no—
102C4—2061no—
103C4C2×C22⋊D10313yes—
104C4C23×D10311yescharacteristic
105C2—23no—
106C2—43no—
107C2—4123no—
108C2C22×C22⋊D10311yescharacteristic
subgroupG/H
centerC2C22×C22⋊D103
commutatorC4×C103C24
FrattiniC4C23×D103
FittingH(5,𝔽2)×C103C2
socleC2×C103C22×D4
hypercenterH(5,𝔽2)D103
hypocenterC103#576
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #15693067C2semidirect
2. #15693047C2semidirect
3. #15693046C2semidirect
4. #15693041C2semidirect
5. C2×#13110090C2semidirect
6. #15693028C2semidirect
7. H(5,𝔽2)×C103C2semidirect
9. #13110105C22semidirect
10. C2×D412C22semidirect
12. #13110095C22semidirect
13. #13110093C22semidirect
14. #13110092C22semidirect
15. #13110090C22semidirect
16. #13110090C22semidirect
17. #13110089C22semidirect
18. C2×C103⋊C8C22semidirect
21. #41×C103C22semidirect
23. C2×D4×C103C22semidirect
54. C103#576semidirect
57. H(5,𝔽2)D103semidirect
67. #41C2×D103semidirect
71. C2×D4C2×D103semidirect