Finite Group Databasebeta

← #31827268

Subgroups — #31827268

Order 18112.

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#22583656C211yesmaximal, characteristic, complemented
2#22583636C213yesmaximal, complemented
3#22583635C213yesmaximal, complemented
4#22583630C213yesmaximal, complemented
5C2×#17985377C213yesmaximal, complemented
6#22583617C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C283C211yesmaximal, characteristic, complemented
8#17985393—21no—
9#17985392C2213yescomplemented
10C2×D1132C2213yescomplemented
11D4×D283—23no—
12#17985382C2211yescharacteristic, complemented
13#17985380C2213yescomplemented
14#17985379C2213yescomplemented
15#17985377C2213yescomplemented
16#17985377C2216yescomplemented
17#17985376C2213yescomplemented
18C2×C283⋊C8C2213yescomplemented
19#41×C283—21no—
20#41×C283C2211yescharacteristic
21#41×C283C2213yescomplemented
22C2×D4×C283—23no—
23C2×D4×C283C2213yescomplemented
24C22×D283—23no—
25Dic566C2311yescharacteristic
26D1132—23no—
27D1132C2313yes—
28C22⋊D283—23no—
29C4×D283—23no—
30C283⋊C8C2311yescharacteristic
31C283⋊C8C2313yes—
32C23×C283—23no—
33Q8×C283D411yescharacteristic
34Q8×C283C2311yescharacteristic
35D4×C283—23no—
36D4×C283—23no—
37D4×C283D413yes—
38D4×C283C2313yes—
39C2×C4×C283—23no—
40C2×C4×C283C2313yes—
41C22×C283—23no—
42C22×C283—83no—
43C22×C283C2×D413yes—
44C2×D283—23no—
45C2×D283—83no—
46C4×C283—21no—
47C4×C283C2×D413yes—
48C4×C283C2411yescharacteristic
49Dic283—21no—
50C2×C283—23no—
51C2×C283—43no—
52C2×C283C22×D411yescharacteristic
53D283—43no—
54C283#57611yescharacteristic, complemented, Sylow
55#576—2831nomaximal, Sylow
56H(5,𝔽2)—2831no—
57H(5,𝔽2)D28311yescharacteristic, complemented
58AGL(1,ℤ/8)—2833no—
59AGL(1,ℤ/8)—2833no—
60#135—2833no—
61C2×D8—2833no—
62#131—2831no—
63#41—21no—
64#41—2833no—
65#41—5661no—
66#41C2×D28311yescharacteristic
67#41C2×D28313yescomplemented
68C2×D4—23no—
69C2×D4—2833no—
70C2×D4—5663no—
71C2×D4C2×D28313yescomplemented
72Q16—2831no—
73SD16—2833no—
74SD16—2833no—
75D8—2833no—
76D8—2836no—
77M16—2833no—
78C2×C8—2833no—
79C23—23no—
80C23—5663no—
81Q8—2831no—
82Q8C22⋊D28311yescharacteristic
83Q8C22×D28311yescharacteristic
84D4—23no—
85D4—23no—
86D4—2833no—
87D4—5663no—
88D4—5663no—
89D4C22⋊D28313yes—
90D4C22×D28313yes—
91C2×C4—23no—
92C2×C4—5663no—
93C2×C4C22×D28313yes—
94C8—2831no—
95C8—2833no—
96C22—23no—
97C22—83no—
98C22—5663no—
99C22—22643no—
100C22C2×C22⋊D28313yes—
101C4—21no—
102C4—5661no—
103C4C2×C22⋊D28313yes—
104C4C23×D28311yescharacteristic
105C2—23no—
106C2—43no—
107C2—11323no—
108C2C22×C22⋊D28311yescharacteristic
subgroupG/H
centerC2C22×C22⋊D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
FittingH(5,𝔽2)×C283C2
socleC2×C283C22×D4
hypercenterH(5,𝔽2)D283
hypocenterC283#576
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #22583656C2semidirect
2. #22583636C2semidirect
3. #22583635C2semidirect
4. #22583630C2semidirect
5. C2×#17985377C2semidirect
6. #22583617C2semidirect
7. H(5,𝔽2)×C283C2semidirect
9. #17985392C22semidirect
10. C2×D1132C22semidirect
12. #17985382C22semidirect
13. #17985380C22semidirect
14. #17985379C22semidirect
15. #17985377C22semidirect
16. #17985377C22semidirect
17. #17985376C22semidirect
18. C2×C283⋊C8C22semidirect
21. #41×C283C22semidirect
23. C2×D4×C283C22semidirect
54. C283#576semidirect
57. H(5,𝔽2)D283semidirect
67. #41C2×D283semidirect
71. C2×D4C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836562
#225836362
#225836352
#225836302
C2×#179853772
#225836172
H(5,𝔽2)×C2832
#576283