Finite Group Databasebeta

← #20261538

Subgroups — #20261538

Order 6208.

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#15690856C211yesmaximal, characteristic, complemented
2#15690836C213yesmaximal, complemented
3#15690835C213yesmaximal, complemented
4#15690830C213yesmaximal, complemented
5C2×#13095496C213yesmaximal, complemented
6#15690817C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C97C211yesmaximal, characteristic, complemented
8#13095512—21no—
9#13095511C2213yescomplemented
10C2×D388C2213yescomplemented
11D4×D97—23no—
12#13095501C2211yescharacteristic, complemented
13#13095499C2213yescomplemented
14#13095498C2213yescomplemented
15#13095496C2213yescomplemented
16#13095496C2216yescomplemented
17#13095495C2213yescomplemented
18C2×#11715895C2213yescomplemented
19#41×C97—21no—
20#41×C97C2211yescharacteristic
21#41×C97C2213yescomplemented
22C2×D4×C97—23no—
23C2×D4×C97C2213yescomplemented
24C23×C97—23no—
25C22×D97—23no—
26Q8×C97D411yescharacteristic
27Q8×C97C2311yescharacteristic
28D4×C97—23no—
29D4×C97—23no—
30D4×C97D413yes—
31D4×C97C2313yes—
32C2×C4×C97—23no—
33C2×C4×C97C2313yes—
34C22⋊D97—23no—
35D388—23no—
36D388C2313yes—
37C4×D97—23no—
38Dic194C2311yescharacteristic
39#11715895C2311yescharacteristic
40#11715895C2313yes—
41C22×C97—23no—
42C22×C97—83no—
43C22×C97C2×D413yes—
44C2×D97—23no—
45C2×D97—83no—
46C4×C97—21no—
47C4×C97C2×D413yes—
48C4×C97C2411yescharacteristic
49Dic97—21no—
50C2×C97—23no—
51C2×C97—43no—
52C2×C97C22×D411yescharacteristic
53D97—43no—
54C97#57611yescharacteristic, complemented, Sylow
55#576—971nomaximal, Sylow
56H(5,𝔽2)—971no—
57H(5,𝔽2)D9711yescharacteristic, complemented
58AGL(1,ℤ/8)—973no—
59AGL(1,ℤ/8)—973no—
60#135—973no—
61C2×D8—973no—
62#131—971no—
63#41—21no—
64#41—973no—
65#41—1941no—
66#41C2×D9711yescharacteristic
67#41C2×D9713yescomplemented
68C2×D4—23no—
69C2×D4—973no—
70C2×D4—1943no—
71C2×D4C2×D9713yescomplemented
72Q16—971no—
73SD16—973no—
74SD16—973no—
75D8—973no—
76D8—976no—
77M16—973no—
78C2×C8—973no—
79C23—23no—
80C23—1943no—
81Q8—971no—
82Q8C22⋊D9711yescharacteristic
83Q8C22×D9711yescharacteristic
84D4—23no—
85D4—23no—
86D4—973no—
87D4—1943no—
88D4—1943no—
89D4C22⋊D9713yes—
90D4C22×D9713yes—
91C2×C4—23no—
92C2×C4—1943no—
93C2×C4C22×D9713yes—
94C8—971no—
95C8—973no—
96C22—23no—
97C22—83no—
98C22—7763no—
99C22—1943no—
100C22C2×C22⋊D9713yes—
101C4—21no—
102C4—1941no—
103C4C2×C22⋊D9713yes—
104C4C23×D9711yescharacteristic
105C2—23no—
106C2—43no—
107C2—3883no—
108C2C22×C22⋊D9711yescharacteristic
subgroupG/H
centerC2C22×C22⋊D97
commutatorC4×C97C24
FrattiniC4C23×D97
FittingH(5,𝔽2)×C97C2
socleC2×C97C22×D4
hypercenterH(5,𝔽2)D97
hypocenterC97#576
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #15690856C2semidirect
2. #15690836C2semidirect
3. #15690835C2semidirect
4. #15690830C2semidirect
5. C2×#13095496C2semidirect
6. #15690817C2semidirect
7. H(5,𝔽2)×C97C2semidirect
9. #13095511C22semidirect
10. C2×D388C22semidirect
12. #13095501C22semidirect
13. #13095499C22semidirect
14. #13095498C22semidirect
15. #13095496C22semidirect
16. #13095496C22semidirect
17. #13095495C22semidirect
18. C2×#11715895C22semidirect
21. #41×C97C22semidirect
23. C2×D4×C97C22semidirect
54. C97#576semidirect
57. H(5,𝔽2)D97semidirect
67. #41C2×D97semidirect
71. C2×D4C2×D97semidirect