Finite Group Databasebeta

← #44417580

Subgroups — #44417580

Order 29248.

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#28410598C211yesmaximal, characteristic, complemented
2#28410578C213yesmaximal, complemented
3#28410577C213yesmaximal, complemented
4#28410572C213yesmaximal, complemented
5C2×#20300726C213yesmaximal, complemented
6#28410559C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C457C211yesmaximal, characteristic, complemented
8#20300742—21no—
9#20300741C2213yescomplemented
10C2×D1828C2213yescomplemented
11D4×D457—23no—
12#20300731C2211yescharacteristic, complemented
13#20300729C2213yescomplemented
14#20300728C2213yescomplemented
15#20300726C2213yescomplemented
16#20300726C2216yescomplemented
17#20300725C2213yescomplemented
18C2×#16814532C2213yescomplemented
19#41×C457—21no—
20#41×C457C2211yescharacteristic
21#41×C457C2213yescomplemented
22C2×D4×C457—23no—
23C2×D4×C457C2213yescomplemented
24C22×D457—23no—
25Dic914C2311yescharacteristic
26D1828—23no—
27D1828C2313yes—
28C22⋊D457—23no—
29C4×D457—23no—
30#16814532C2311yescharacteristic
31#16814532C2313yes—
32C23×C457—23no—
33Q8×C457D411yescharacteristic
34Q8×C457C2311yescharacteristic
35D4×C457—23no—
36D4×C457—23no—
37D4×C457D413yes—
38D4×C457C2313yes—
39C2×C4×C457—23no—
40C2×C4×C457C2313yes—
41C22×C457—23no—
42C22×C457—83no—
43C22×C457C2×D413yes—
44C2×D457—23no—
45C2×D457—83no—
46C4×C457—21no—
47C4×C457C2×D413yes—
48C4×C457C2411yescharacteristic
49Dic457—21no—
50C2×C457—23no—
51C2×C457—43no—
52C2×C457C22×D411yescharacteristic
53D457—43no—
54C457#57611yescharacteristic, complemented, Sylow
55#576—4571nomaximal, Sylow
56H(5,𝔽2)—4571no—
57H(5,𝔽2)D45711yescharacteristic, complemented
58AGL(1,ℤ/8)—4573no—
59AGL(1,ℤ/8)—4573no—
60#135—4573no—
61C2×D8—4573no—
62#131—4571no—
63#41—21no—
64#41—9141no—
65#41—4573no—
66#41C2×D45711yescharacteristic
67#41C2×D45713yescomplemented
68C2×D4—23no—
69C2×D4—9143no—
70C2×D4—4573no—
71C2×D4C2×D45713yescomplemented
72Q16—4571no—
73SD16—4573no—
74SD16—4573no—
75D8—4573no—
76D8—4576no—
77M16—4573no—
78C2×C8—4573no—
79C23—23no—
80C23—9143no—
81Q8—4571no—
82Q8C22⋊D45711yescharacteristic
83Q8C22×D45711yescharacteristic
84D4—23no—
85D4—23no—
86D4—9143no—
87D4—9143no—
88D4—4573no—
89D4C22⋊D45713yes—
90D4C22×D45713yes—
91C2×C4—23no—
92C2×C4—9143no—
93C2×C4C22×D45713yes—
94C8—4571no—
95C8—4573no—
96C22—23no—
97C22—83no—
98C22—36563no—
99C22—9143no—
100C22C2×C22⋊D45713yes—
101C4—21no—
102C4—9141no—
103C4C2×C22⋊D45713yes—
104C4C23×D45711yescharacteristic
105C2—23no—
106C2—43no—
107C2—18283no—
108C2C22×C22⋊D45711yescharacteristic
subgroupG/H
centerC2C22×C22⋊D457
commutator, cosocleC4×C457C24
FrattiniC4C23×D457
FittingH(5,𝔽2)×C457C2
socleC2×C457C22×D4
hypercenterH(5,𝔽2)D457
hypocenterC457#576
LCSG ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #28410598C2semidirect
2. #28410578C2semidirect
3. #28410577C2semidirect
4. #28410572C2semidirect
5. C2×#20300726C2semidirect
6. #28410559C2semidirect
7. H(5,𝔽2)×C457C2semidirect
9. #20300741C22semidirect
10. C2×D1828C22semidirect
12. #20300731C22semidirect
13. #20300729C22semidirect
14. #20300728C22semidirect
15. #20300726C22semidirect
16. #20300726C22semidirect
17. #20300725C22semidirect
18. C2×#16814532C22semidirect
21. #41×C457C22semidirect
23. C2×D4×C457C22semidirect
54. C457#576semidirect
57. H(5,𝔽2)D457semidirect
67. #41C2×D457semidirect
71. C2×D4C2×D457semidirect

Maximal subgroups

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

subgroupindex
#284105982
#284105782
#284105772
#284105722
C2×#203007262
#284105592
H(5,𝔽2)×C4572
#576457