Finite Group Databasebeta

← #43244415

Subgroups — #43244415

Order 28096.

258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 258 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#28380790C211yesmaximal, characteristic, complemented
2#28380773C213yesmaximal, complemented
3#28380769C213yesmaximal, complemented
4#28380763C213yesmaximal, complemented
5C2×#20296317C213yesmaximal, complemented
6#28380750C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C439C211yesmaximal, characteristic, complemented
8#20296329C2213yescomplemented
9#20296328—23no—
10C2×Dic878C2213yescomplemented
11Q8×D439—21no—
12#20296319C2213yescomplemented
13#20296317C2213yescomplemented
14#20296317C2216yescomplemented
15#20296316C2211yescharacteristic, complemented
16#20296314C2213yescomplemented
17#20296313C2213yescomplemented
18C2×C439⋊C8C2213yescomplemented
19#41×C439—21no—
20#41×C439C2213yes—
21#41×C439C2211yescharacteristic
22C2×D4×C439—23no—
23C2×D4×C439C2213yes—
24Dic878—23no—
25Dic878C2313yes—
26D1756C2311yescharacteristic
27C22⋊D439—23no—
28C2×Dic439—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—21no—
45C4×C439—21no—
46C4×C439C2×D413yes—
47C4×C439C2411yescharacteristic
48Dic439—23no—
49C2×C439—23no—
50C2×C439—43no—
51C2×C439C22×D411yescharacteristic
52D439—41no—
53C439#57711yescharacteristic, complemented, Sylow
54#577—4391nomaximal, Sylow
552−1+4—4391no—
56H(5,𝔽2)D43911yescharacteristic, complemented
57#137—4393no—
58AGL(1,ℤ/8)—4393no—
59#135—4393no—
60C2×SD16—4393no—
61#131—4391no—
62#41—21no—
63#41—8783no—
64#41—4393no—
65#41C2×D43913yes—
66#41C2×D43911yescharacteristic
67C2×Q8—8781no—
68C2×Q8—4393no—
69C2×D4—23no—
70C2×D4C2×D43913yes—
71Q16—4393no—
72SD16—4391no—
73SD16—4393no—
74SD16—4396no—
75D8—4393no—
76M16—4393no—
77C2×C8—4393no—
78C23—23no—
79Q8—8783no—
80Q8—4393no—
81Q8C22⋊D43911yescharacteristic
82Q8C22×D43911yescharacteristic
83D4—23no—
84D4—23no—
85D4—8783no—
86D4—4391no—
87D4C22⋊D43913yes—
88D4C22×D43913yes—
89C2×C4—23no—
90C2×C4—8783no—
91C2×C4—8783no—
92C2×C4C22×D43913yes—
93C8—4391no—
94C8—4393no—
95C22—23no—
96C22—83no—
97C22—8781no—
98C22C2×C22⋊D43913yes—
99C4—21no—
100C4—8783no—
101C4C2×C22⋊D43913yes—
102C4C23×D43911yescharacteristic
103C2—23no—
104C2—43no—
105C2—17561no—
106C2C22×C22⋊D43911yescharacteristic
subgroupG/H
centerC2C22×C22⋊D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingH(5,𝔽2)×C439C2
socleC2×C439C22×D4
hypercenterH(5,𝔽2)D439
hypocenterC439#577
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. #28380790C2semidirect
2. #28380773C2semidirect
3. #28380769C2semidirect
4. #28380763C2semidirect
5. C2×#20296317C2semidirect
6. #28380750C2semidirect
7. H(5,𝔽2)×C439C2semidirect
8. #20296329C22semidirect
10. C2×Dic878C22semidirect
12. #20296319C22semidirect
13. #20296317C22semidirect
14. #20296317C22semidirect
15. #20296316C22semidirect
16. #20296314C22semidirect
17. #20296313C22semidirect
18. C2×C439⋊C8C22semidirect
53. C439#577semidirect
56. H(5,𝔽2)D439semidirect

Maximal subgroups

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

subgroupindex
#283807902
#283807732
#283807692
#283807632
C2×#202963172
#283807502
H(5,𝔽2)×C4392
#577439