Finite Group Databasebeta

← #43244407

Subgroups — #43244407

Order 28096.

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#28380789C211yesmaximal, characteristic, complemented
2#28380769C213yesmaximal, complemented
3#28380768C213yesmaximal, complemented
4#28380763C213yesmaximal, complemented
5C2×#20296314C213yesmaximal, complemented
6#28380750C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C439C211yesmaximal, characteristic, complemented
8#20296330—21no—
9#20296329C2213yescomplemented
10C2×D1756C2213yescomplemented
11D4×D439—23no—
12#20296319C2211yescharacteristic, complemented
13#20296317C2213yescomplemented
14#20296316C2213yescomplemented
15#20296314C2213yescomplemented
16#20296314C2216yescomplemented
17#20296313C2213yescomplemented
18C2×C439⋊C8C2213yescomplemented
19#41×C439—21no—
20#41×C439C2211yescharacteristic
21#41×C439C2213yescomplemented
22C2×D4×C439—23no—
23C2×D4×C439C2213yescomplemented
24C22×D439—23no—
25Dic878C2311yescharacteristic
26D1756—23no—
27D1756C2313yes—
28C22⋊D439—23no—
29C4×D439—23no—
30C439⋊C8C2311yescharacteristic
31C439⋊C8C2313yes—
32C23×C439—23no—
33Q8×C439D411yescharacteristic
34Q8×C439C2311yescharacteristic
35D4×C439—23no—
36D4×C439—23no—
37D4×C439D413yes—
38D4×C439C2313yes—
39C2×C4×C439—23no—
40C2×C4×C439C2313yes—
41C22×C439—23no—
42C22×C439—83no—
43C22×C439C2×D413yes—
44C2×D439—23no—
45C2×D439—83no—
46C4×C439—21no—
47C4×C439C2×D413yes—
48C4×C439C2411yescharacteristic
49Dic439—21no—
50C2×C439—23no—
51C2×C439—43no—
52C2×C439C22×D411yescharacteristic
53D439—43no—
54C439#57611yescharacteristic, complemented, Sylow
55#576—4391nomaximal, Sylow
56H(5,𝔽2)—4391no—
57H(5,𝔽2)D43911yescharacteristic, complemented
58AGL(1,ℤ/8)—4393no—
59AGL(1,ℤ/8)—4393no—
60#135—4393no—
61C2×D8—4393no—
62#131—4391no—
63#41—21no—
64#41—8781no—
65#41—4393no—
66#41C2×D43911yescharacteristic
67#41C2×D43913yescomplemented
68C2×D4—23no—
69C2×D4—8783no—
70C2×D4—4393no—
71C2×D4C2×D43913yescomplemented
72Q16—4391no—
73SD16—4393no—
74SD16—4393no—
75D8—4393no—
76D8—4396no—
77M16—4393no—
78C2×C8—4393no—
79C23—23no—
80C23—8783no—
81Q8—4391no—
82Q8C22⋊D43911yescharacteristic
83Q8C22×D43911yescharacteristic
84D4—23no—
85D4—23no—
86D4—8783no—
87D4—8783no—
88D4—4393no—
89D4C22⋊D43913yes—
90D4C22×D43913yes—
91C2×C4—23no—
92C2×C4—8783no—
93C2×C4C22×D43913yes—
94C8—4391no—
95C8—4393no—
96C22—23no—
97C22—83no—
98C22—8783no—
99C22—35123no—
100C22C2×C22⋊D43913yes—
101C4—21no—
102C4—8781no—
103C4C2×C22⋊D43913yes—
104C4C23×D43911yescharacteristic
105C2—23no—
106C2—43no—
107C2—17563no—
108C2C22×C22⋊D43911yescharacteristic
subgroupG/H
centerC2C22×C22⋊D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingH(5,𝔽2)×C439C2
socleC2×C439C22×D4
hypercenterH(5,𝔽2)D439
hypocenterC439#576
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #28380789C2semidirect
2. #28380769C2semidirect
3. #28380768C2semidirect
4. #28380763C2semidirect
5. C2×#20296314C2semidirect
6. #28380750C2semidirect
7. H(5,𝔽2)×C439C2semidirect
9. #20296329C22semidirect
10. C2×D1756C22semidirect
12. #20296319C22semidirect
13. #20296317C22semidirect
14. #20296316C22semidirect
15. #20296314C22semidirect
16. #20296314C22semidirect
17. #20296313C22semidirect
18. C2×C439⋊C8C22semidirect
21. #41×C439C22semidirect
23. C2×D4×C439C22semidirect
54. C439#576semidirect
57. H(5,𝔽2)D439semidirect
67. #41C2×D439semidirect
71. C2×D4C2×D439semidirect

Maximal subgroups

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

subgroupindex
#283807892
#283807692
#283807682
#283807632
C2×#202963142
#283807502
H(5,𝔽2)×C4392
#576439