Finite Group Databasebeta

← #46830983

Subgroups — #46830983

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#31772674C211yesmaximal, characteristic, complemented
2#31772659C213yesmaximal, complemented
3#31772653C213yesmaximal, complemented
4#31772648C213yesmaximal, complemented
5C2×#22575823C213yesmaximal, complemented
6#31772635C211yesmaximal, characteristic, complemented
72−1+4×C541C211yesmaximal, characteristic, complemented
8#22575837—21no—
9#22575836C2213yes—
10C2×D2164C2213yes—
11D4×D541—23no—
12#22575826C2213yescomplemented
13#22575824C2211yescharacteristic, complemented
14#22575823C2213yescomplemented
15#22575823C2216yescomplemented
16#22575821C2213yescomplemented
17#22575820C2213yescomplemented
18C2×#16864513C2213yescomplemented
19#41×C541—23no—
20#41×C541C2211yescharacteristic
21#41×C541C2213yescomplemented
22C2×Q8×C541—21no—
23C2×Q8×C541C2213yescomplemented
24C22×D541—23no—
25Dic1082C2311yescharacteristic
26D2164—23no—
27D2164C2313yes—
28C22⋊D541—23no—
29C4×D541—23no—
30#16864513C2311yescharacteristic
31#16864513C2313yes—
32Q8×C541—23no—
33Q8×C541D411yescharacteristic
34Q8×C541C2313yes—
35D4×C541—23no—
36D4×C541D413yes—
37D4×C541C2311yescharacteristic
38C2×C4×C541—23no—
39C2×C4×C541—23no—
40C2×C4×C541C2313yes—
41C22×C541—21no—
42C22×C541C2×D413yes—
43C2×D541—23no—
44C2×D541—83no—
45C4×C541—23no—
46C4×C541C2×D413yes—
47C4×C541C2411yescharacteristic
48Dic541—21no—
49C2×C541—23no—
50C2×C541—41no—
51C2×C541C22×D411yescharacteristic
52D541—43no—
53C541#57711yescharacteristic, complemented, Sylow
54#577—5411nomaximal, Sylow
552−1+4D54111yescharacteristic, complemented
56H(5,𝔽2)—5411no—
57#137—5413no—
58AGL(1,ℤ/8)—5413no—
59#135—5413no—
60C2×SD16—5413no—
61#131—5411no—
62#41—23no—
63#41—5413no—
64#41—10821no—
65#41C2×D54111yescharacteristic
66#41C2×D54113yescomplemented
67C2×Q8—21no—
68C2×Q8C2×D54113yescomplemented
69C2×D4—5413no—
70C2×D4—10823no—
71Q16—5413no—
72SD16—5413no—
73SD16—5416no—
74SD16—5411no—
75D8—5413no—
76M16—5413no—
77C2×C8—5413no—
78C23—10823no—
79Q8—23no—
80Q8—5411no—
81Q8C22⋊D54111yescharacteristic
82Q8C22×D54113yes—
83D4—23no—
84D4—5413no—
85D4—10823no—
86D4—10823no—
87D4C22⋊D54113yes—
88D4C22×D54111yescharacteristic
89C2×C4—23no—
90C2×C4—23no—
91C2×C4—10823no—
92C2×C4C22×D54113yes—
93C8—5411no—
94C8—5413no—
95C22—21no—
96C22—10823no—
97C22—43283no—
98C22C2×C22⋊D54113yes—
99C4—23no—
100C4—10821no—
101C4C2×C22⋊D54113yes—
102C4C23×D54111yescharacteristic
103C2—23no—
104C2—41no—
105C2—21643no—
106C2C22×C22⋊D54111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting2−1+4×C541C2
socleC2×C541C22×D4
hypercenter2−1+4D541
hypocenterC541#577
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #31772674C2semidirect
2. #31772659C2semidirect
3. #31772653C2semidirect
4. #31772648C2semidirect
5. C2×#22575823C2semidirect
6. #31772635C2semidirect
7. 2−1+4×C541C2semidirect
12. #22575826C22semidirect
13. #22575824C22semidirect
14. #22575823C22semidirect
15. #22575823C22semidirect
16. #22575821C22semidirect
17. #22575820C22semidirect
18. C2×#16864513C22semidirect
21. #41×C541C22semidirect
23. C2×Q8×C541C22semidirect
53. C541#577semidirect
55. 2−1+4D541semidirect
66. #41C2×D541semidirect
68. C2×Q8C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726742
#317726592
#317726532
#317726482
C2×#225758232
#317726352
2−1+4×C5412
#577541