Finite Group Databasebeta

← #46830978

Subgroups — #46830978

Order 34624.

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#31772674C211yesmaximal, characteristic, complemented
2#31772654C213yesmaximal, complemented
3#31772653C213yesmaximal, complemented
4#31772648C213yesmaximal, complemented
5C2×#22575821C213yesmaximal, complemented
6#31772635C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C541C211yesmaximal, characteristic, complemented
8#22575837—21no—
9#22575836C2213yescomplemented
10C2×D2164C2213yescomplemented
11D4×D541—23no—
12#22575826C2211yescharacteristic, complemented
13#22575824C2213yescomplemented
14#22575823C2213yescomplemented
15#22575821C2213yescomplemented
16#22575821C2216yescomplemented
17#22575820C2213yescomplemented
18C2×#16864513C2213yescomplemented
19#41×C541—21no—
20#41×C541C2211yescharacteristic
21#41×C541C2213yescomplemented
22C2×D4×C541—23no—
23C2×D4×C541C2213yescomplemented
24C22×D541—23no—
25Dic1082C2311yescharacteristic
26D2164—23no—
27D2164C2313yes—
28C22⋊D541—23no—
29C4×D541—23no—
30#16864513C2311yescharacteristic
31#16864513C2313yes—
32C23×C541—23no—
33Q8×C541D411yescharacteristic
34Q8×C541C2311yescharacteristic
35D4×C541—23no—
36D4×C541—23no—
37D4×C541D413yes—
38D4×C541C2313yes—
39C2×C4×C541—23no—
40C2×C4×C541C2313yes—
41C22×C541—23no—
42C22×C541—83no—
43C22×C541C2×D413yes—
44C2×D541—23no—
45C2×D541—83no—
46C4×C541—21no—
47C4×C541C2×D413yes—
48C4×C541C2411yescharacteristic
49Dic541—21no—
50C2×C541—23no—
51C2×C541—43no—
52C2×C541C22×D411yescharacteristic
53D541—43no—
54C541#57611yescharacteristic, complemented, Sylow
55#576—5411nomaximal, Sylow
56H(5,𝔽2)—5411no—
57H(5,𝔽2)D54111yescharacteristic, complemented
58AGL(1,ℤ/8)—5413no—
59AGL(1,ℤ/8)—5413no—
60#135—5413no—
61C2×D8—5413no—
62#131—5411no—
63#41—21no—
64#41—5413no—
65#41—10821no—
66#41C2×D54111yescharacteristic
67#41C2×D54113yescomplemented
68C2×D4—23no—
69C2×D4—5413no—
70C2×D4—10823no—
71C2×D4C2×D54113yescomplemented
72Q16—5411no—
73SD16—5413no—
74SD16—5413no—
75D8—5413no—
76D8—5416no—
77M16—5413no—
78C2×C8—5413no—
79C23—23no—
80C23—10823no—
81Q8—5411no—
82Q8C22⋊D54111yescharacteristic
83Q8C22×D54111yescharacteristic
84D4—23no—
85D4—23no—
86D4—5413no—
87D4—10823no—
88D4—10823no—
89D4C22⋊D54113yes—
90D4C22×D54113yes—
91C2×C4—23no—
92C2×C4—10823no—
93C2×C4C22×D54113yes—
94C8—5411no—
95C8—5413no—
96C22—23no—
97C22—83no—
98C22—10823no—
99C22—43283no—
100C22C2×C22⋊D54113yes—
101C4—21no—
102C4—10821no—
103C4C2×C22⋊D54113yes—
104C4C23×D54111yescharacteristic
105C2—23no—
106C2—43no—
107C2—21643no—
108C2C22×C22⋊D54111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingH(5,𝔽2)×C541C2
socleC2×C541C22×D4
hypercenterH(5,𝔽2)D541
hypocenterC541#576
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #31772674C2semidirect
2. #31772654C2semidirect
3. #31772653C2semidirect
4. #31772648C2semidirect
5. C2×#22575821C2semidirect
6. #31772635C2semidirect
7. H(5,𝔽2)×C541C2semidirect
9. #22575836C22semidirect
10. C2×D2164C22semidirect
12. #22575826C22semidirect
13. #22575824C22semidirect
14. #22575823C22semidirect
15. #22575821C22semidirect
16. #22575821C22semidirect
17. #22575820C22semidirect
18. C2×#16864513C22semidirect
21. #41×C541C22semidirect
23. C2×D4×C541C22semidirect
54. C541#576semidirect
57. H(5,𝔽2)D541semidirect
67. #41C2×D541semidirect
71. C2×D4C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726742
#317726542
#317726532
#317726482
C2×#225758212
#317726352
H(5,𝔽2)×C5412
#576541