Finite Group Databasebeta

← #46830986

Subgroups — #46830986

Order 34624.

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#31772675C211yesmaximal, characteristic, complemented
2#31772658C213yesmaximal, complemented
3#31772654C213yesmaximal, complemented
4#31772648C213yesmaximal, complemented
5C2×#22575824C213yesmaximal, complemented
6#31772635C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C541C211yesmaximal, characteristic, complemented
8#22575836C2213yescomplemented
9#22575835—23no—
10C2×Dic1082C2213yescomplemented
11Q8×D541—21no—
12#22575826C2213yescomplemented
13#22575824C2213yescomplemented
14#22575824C2216yescomplemented
15#22575823C2211yescharacteristic, complemented
16#22575821C2213yescomplemented
17#22575820C2213yescomplemented
18C2×#16864513C2213yescomplemented
19#41×C541—21no—
20#41×C541C2213yes—
21#41×C541C2211yescharacteristic
22C2×D4×C541—23no—
23C2×D4×C541C2213yes—
24Dic1082—23no—
25Dic1082C2313yes—
26D2164C2311yescharacteristic
27C22⋊D541—23no—
28C2×Dic541—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—21no—
45C4×C541—21no—
46C4×C541C2×D413yes—
47C4×C541C2411yescharacteristic
48Dic541—23no—
49C2×C541—23no—
50C2×C541—43no—
51C2×C541C22×D411yescharacteristic
52D541—41no—
53C541#57711yescharacteristic, complemented, Sylow
54#577—5411nomaximal, Sylow
552−1+4—5411no—
56H(5,𝔽2)D54111yescharacteristic, complemented
57#137—5413no—
58AGL(1,ℤ/8)—5413no—
59#135—5413no—
60C2×SD16—5413no—
61#131—5411no—
62#41—21no—
63#41—5413no—
64#41—10823no—
65#41C2×D54113yes—
66#41C2×D54111yescharacteristic
67C2×Q8—5413no—
68C2×Q8—10821no—
69C2×D4—23no—
70C2×D4C2×D54113yes—
71Q16—5413no—
72SD16—5411no—
73SD16—5413no—
74SD16—5416no—
75D8—5413no—
76M16—5413no—
77C2×C8—5413no—
78C23—23no—
79Q8—5413no—
80Q8—10823no—
81Q8C22⋊D54111yescharacteristic
82Q8C22×D54111yescharacteristic
83D4—23no—
84D4—23no—
85D4—5411no—
86D4—10823no—
87D4C22⋊D54113yes—
88D4C22×D54113yes—
89C2×C4—23no—
90C2×C4—10823no—
91C2×C4—10823no—
92C2×C4C22×D54113yes—
93C8—5411no—
94C8—5413no—
95C22—23no—
96C22—83no—
97C22—10821no—
98C22C2×C22⋊D54113yes—
99C4—21no—
100C4—10823no—
101C4C2×C22⋊D54113yes—
102C4C23×D54111yescharacteristic
103C2—23no—
104C2—43no—
105C2—21641no—
106C2C22×C22⋊D54111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingH(5,𝔽2)×C541C2
socleC2×C541C22×D4
hypercenterH(5,𝔽2)D541
hypocenterC541#577
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. #31772675C2semidirect
2. #31772658C2semidirect
3. #31772654C2semidirect
4. #31772648C2semidirect
5. C2×#22575824C2semidirect
6. #31772635C2semidirect
7. H(5,𝔽2)×C541C2semidirect
8. #22575836C22semidirect
10. C2×Dic1082C22semidirect
12. #22575826C22semidirect
13. #22575824C22semidirect
14. #22575824C22semidirect
15. #22575823C22semidirect
16. #22575821C22semidirect
17. #22575820C22semidirect
18. C2×#16864513C22semidirect
53. C541#577semidirect
56. H(5,𝔽2)D541semidirect

Maximal subgroups

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

subgroupindex
#317726752
#317726582
#317726542
#317726482
C2×#225758242
#317726352
H(5,𝔽2)×C5412
#577541