Finite Group Databasebeta

← #23782477

Subgroups — #23782477

Order 10432.

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#19104782C211yesmaximal, characteristic, complemented
2#19104781C211yesmaximal, characteristic, complemented
3#19104768C213yesmaximal, complemented
4#19104763C213yesmaximal, complemented
5#19104757C213yesmaximal, complemented
6C2×#14579688C213yesmaximal, complemented
7#131×C163C211yesmaximal, characteristic, complemented
8#14579700—21no—
9#14579699C2213yes—
10#14579699C2213yescomplemented
11#14579698—23no—
12C2×Dic326C2213yescomplemented
13Q8×D163—21no—
14C2×D652C2213yes—
15D4×D163—23no—
16Dic652C2213yescomplemented
17#14579688C2216yescomplemented
18#14579688C2213yescomplemented
19#14579688C2211yescharacteristic, complemented
20D1304C2213yescomplemented
21#41×C163C2211yescharacteristic
22M16×C163C2213yescomplemented
23C2×C8×C163C2213yescomplemented
24C22×D163—23no—
25Dic326—23no—
26Dic326C2313yes—
27Dic326C2311yescharacteristic
28D652—23no—
29D652C2311yescharacteristic
30D652C2313yes—
31C22⋊D163—23no—
32C22⋊D163—23no—
33C2×Dic163—23no—
34C4×D163—23no—
35C4×D163—23no—
36Q8×C163D411yescharacteristic
37D4×C163D413yes—
38C2×C4×C163C2313yes—
39C8×C163C2311yescharacteristic
40C8×C163C2313yes—
41C22×C163C2×D413yes—
42C2×D163—21no—
43C2×D163—23no—
44C2×D163—83no—
45C4×C163C2×D413yes—
46C4×C163C2411yescharacteristic
47Dic163—21no—
48Dic163—23no—
49C2×C163—23no—
50C2×C163C22×D411yescharacteristic
51D163—41no—
52D163—43no—
53C163#57711yescharacteristic, complemented, Sylow
54#577—1631nomaximal, Sylow
552−1+4—1631no—
56H(5,𝔽2)—1631no—
57#137—1633no—
58AGL(1,ℤ/8)—1633no—
59#135—1633no—
60C2×SD16—1633no—
61#131D16311yescharacteristic, complemented
62#41—3261no—
63#41—3263no—
64#41—1633no—
65#41—1633no—
66#41C2×D16311yescharacteristic
67C2×Q8—3261no—
68C2×Q8—1633no—
69C2×D4—3263no—
70C2×D4—1633no—
71Q16—1633no—
72SD16—1633no—
73SD16—1636no—
74SD16—1631no—
75D8—1633no—
76M16C2×D16313yescomplemented
77C2×C8C2×D16313yescomplemented
78C23—3263no—
79Q8—3263no—
80Q8—1633no—
81Q8—1631no—
82Q8D65211yescharacteristic
83D4—3263no—
84D4—3263no—
85D4—3263no—
86D4—1631no—
87D4—1633no—
88D4D65213yes—
89C2×C4—3263no—
90C2×C4—3263no—
91C2×C4—3263no—
92C2×C4C22×D16313yes—
93C8C22×D16311yescharacteristic
94C8C22×D16313yes—
95C22—13043no—
96C22—3261no—
97C22—3263no—
98C22C2×D65213yes—
99C4—3261no—
100C4—3263no—
101C4C2×D65213yes—
102C4C23×D16311yescharacteristic
103C2—23no—
104C2—6523no—
105C2—6521no—
106C2C22×D65211yescharacteristic
subgroupG/H
centerC2C22×D652
commutator, cosocleC4×C163C24
FrattiniC4C23×D163
Fitting#131×C163C2
socleC2×C163C22×D4
hypercenter#131D163
hypocenterC163#577
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ #41 ◁ #131

Complements

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

NH ≅ G/Ntype
1. #19104782C2semidirect
2. #19104781C2semidirect
3. #19104768C2semidirect
4. #19104763C2semidirect
5. #19104757C2semidirect
6. C2×#14579688C2semidirect
7. #131×C163C2semidirect
10. #14579699C22semidirect
12. C2×Dic326C22semidirect
16. Dic652C22semidirect
17. #14579688C22semidirect
18. #14579688C22semidirect
19. #14579688C22semidirect
20. D1304C22semidirect
22. M16×C163C22semidirect
23. C2×C8×C163C22semidirect
53. C163#577semidirect
61. #131D163semidirect
76. M16C2×D163semidirect
77. C2×C8C2×D163semidirect