Finite Group Databasebeta

← #42119862

Subgroups — #42119862

Order 27584.

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#28352235C211yesmaximal, characteristic, complemented
2#28352215C213yesmaximal, complemented
3#28352214C213yesmaximal, complemented
4#28352209C213yesmaximal, complemented
5C2×#20293785C213yesmaximal, complemented
6#28352196C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C431C211yesmaximal, characteristic, complemented
8#20293801—21no—
9#20293800C2213yescomplemented
10C2×D1724C2213yescomplemented
11D4×D431—23no—
12#20293790C2211yescharacteristic, complemented
13#20293788C2213yescomplemented
14#20293787C2213yescomplemented
15#20293785C2213yescomplemented
16#20293785C2216yescomplemented
17#20293784C2213yescomplemented
18C2×C431⋊C8C2213yescomplemented
19#41×C431—21no—
20#41×C431C2211yescharacteristic
21#41×C431C2213yescomplemented
22C2×D4×C431—23no—
23C2×D4×C431C2213yescomplemented
24C22×D431—23no—
25Dic862C2311yescharacteristic
26D1724—23no—
27D1724C2313yes—
28C22⋊D431—23no—
29C4×D431—23no—
30C431⋊C8C2311yescharacteristic
31C431⋊C8C2313yes—
32C23×C431—23no—
33Q8×C431D411yescharacteristic
34Q8×C431C2311yescharacteristic
35D4×C431—23no—
36D4×C431—23no—
37D4×C431D413yes—
38D4×C431C2313yes—
39C2×C4×C431—23no—
40C2×C4×C431C2313yes—
41C22×C431—23no—
42C22×C431—83no—
43C22×C431C2×D413yes—
44C2×D431—23no—
45C2×D431—83no—
46C4×C431—21no—
47C4×C431C2×D413yes—
48C4×C431C2411yescharacteristic
49Dic431—21no—
50C2×C431—23no—
51C2×C431—43no—
52C2×C431C22×D411yescharacteristic
53D431—43no—
54C431#57611yescharacteristic, complemented, Sylow
55#576—4311nomaximal, Sylow
56H(5,𝔽2)—4311no—
57H(5,𝔽2)D43111yescharacteristic, complemented
58AGL(1,ℤ/8)—4313no—
59AGL(1,ℤ/8)—4313no—
60#135—4313no—
61C2×D8—4313no—
62#131—4311no—
63#41—21no—
64#41—8621no—
65#41—4313no—
66#41C2×D43111yescharacteristic
67#41C2×D43113yescomplemented
68C2×D4—23no—
69C2×D4—8623no—
70C2×D4—4313no—
71C2×D4C2×D43113yescomplemented
72Q16—4311no—
73SD16—4313no—
74SD16—4313no—
75D8—4313no—
76D8—4316no—
77M16—4313no—
78C2×C8—4313no—
79C23—23no—
80C23—8623no—
81Q8—4311no—
82Q8C22⋊D43111yescharacteristic
83Q8C22×D43111yescharacteristic
84D4—23no—
85D4—23no—
86D4—8623no—
87D4—8623no—
88D4—4313no—
89D4C22⋊D43113yes—
90D4C22×D43113yes—
91C2×C4—23no—
92C2×C4—8623no—
93C2×C4C22×D43113yes—
94C8—4311no—
95C8—4313no—
96C22—23no—
97C22—83no—
98C22—8623no—
99C22—34483no—
100C22C2×C22⋊D43113yes—
101C4—21no—
102C4—8621no—
103C4C2×C22⋊D43113yes—
104C4C23×D43111yescharacteristic
105C2—23no—
106C2—43no—
107C2—17243no—
108C2C22×C22⋊D43111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D431
commutator, cosocleC4×C431C24
FrattiniC4C23×D431
FittingH(5,𝔽2)×C431C2
socleC2×C431C22×D4
hypercenterH(5,𝔽2)D431
hypocenterC431#576
LCSG ▷ C4×C431 ▷ C2×C431 ▷ C431
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #28352235C2semidirect
2. #28352215C2semidirect
3. #28352214C2semidirect
4. #28352209C2semidirect
5. C2×#20293785C2semidirect
6. #28352196C2semidirect
7. H(5,𝔽2)×C431C2semidirect
9. #20293800C22semidirect
10. C2×D1724C22semidirect
12. #20293790C22semidirect
13. #20293788C22semidirect
14. #20293787C22semidirect
15. #20293785C22semidirect
16. #20293785C22semidirect
17. #20293784C22semidirect
18. C2×C431⋊C8C22semidirect
21. #41×C431C22semidirect
23. C2×D4×C431C22semidirect
54. C431#576semidirect
57. H(5,𝔽2)D431semidirect
67. #41C2×D431semidirect
71. C2×D4C2×D431semidirect

Maximal subgroups

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

subgroupindex
#283522352
#283522152
#283522142
#283522092
C2×#202937852
#283521962
H(5,𝔽2)×C4312
#576431