Finite Group Databasebeta

← #34094963

Subgroups — #34094963

Order 20032.

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#23756544C211yesmaximal, characteristic, complemented
2#23756527C213yesmaximal, complemented
3#23756523C213yesmaximal, complemented
4#23756517C213yesmaximal, complemented
5C2×#19097549C213yesmaximal, complemented
6#23756504C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C313C211yesmaximal, characteristic, complemented
8#19097561C2213yescomplemented
9#19097560—23no—
10C2×Dic626C2213yescomplemented
11Q8×D313—21no—
12#19097551C2213yescomplemented
13#19097549C2213yescomplemented
14#19097549C2216yescomplemented
15#19097548C2211yescharacteristic, complemented
16#19097546C2213yescomplemented
17#19097545C2213yescomplemented
18C2×#14578809C2213yescomplemented
19#41×C313—21no—
20#41×C313C2213yes—
21#41×C313C2211yescharacteristic
22C2×D4×C313—23no—
23C2×D4×C313C2213yes—
24Dic626—23no—
25Dic626C2313yes—
26D1252C2311yescharacteristic
27C22⋊D313—23no—
28C2×Dic313—23no—
29C4×D313—23no—
30#14578809C2311yescharacteristic
31#14578809C2313yes—
32C23×C313—23no—
33Q8×C313D411yescharacteristic
34Q8×C313C2311yescharacteristic
35D4×C313—23no—
36D4×C313—23no—
37D4×C313D413yes—
38D4×C313C2313yes—
39C2×C4×C313—23no—
40C2×C4×C313C2313yes—
41C22×C313—23no—
42C22×C313—83no—
43C22×C313C2×D413yes—
44C2×D313—21no—
45C4×C313—21no—
46C4×C313C2×D413yes—
47C4×C313C2411yescharacteristic
48Dic313—23no—
49C2×C313—23no—
50C2×C313—43no—
51C2×C313C22×D411yescharacteristic
52D313—41no—
53C313#57711yescharacteristic, complemented, Sylow
54#577—3131nomaximal, Sylow
552−1+4—3131no—
56H(5,𝔽2)D31311yescharacteristic, complemented
57#137—3133no—
58AGL(1,ℤ/8)—3133no—
59#135—3133no—
60C2×SD16—3133no—
61#131—3131no—
62#41—21no—
63#41—3133no—
64#41—6263no—
65#41C2×D31313yes—
66#41C2×D31311yescharacteristic
67C2×Q8—3133no—
68C2×Q8—6261no—
69C2×D4—23no—
70C2×D4C2×D31313yes—
71Q16—3133no—
72SD16—3131no—
73SD16—3133no—
74SD16—3136no—
75D8—3133no—
76M16—3133no—
77C2×C8—3133no—
78C23—23no—
79Q8—3133no—
80Q8—6263no—
81Q8C22⋊D31311yescharacteristic
82Q8C22×D31311yescharacteristic
83D4—23no—
84D4—23no—
85D4—3131no—
86D4—6263no—
87D4C22⋊D31313yes—
88D4C22×D31313yes—
89C2×C4—23no—
90C2×C4—6263no—
91C2×C4—6263no—
92C2×C4C22×D31313yes—
93C8—3131no—
94C8—3133no—
95C22—23no—
96C22—83no—
97C22—6261no—
98C22C2×C22⋊D31313yes—
99C4—21no—
100C4—6263no—
101C4C2×C22⋊D31313yes—
102C4C23×D31311yescharacteristic
103C2—23no—
104C2—43no—
105C2—12521no—
106C2C22×C22⋊D31311yescharacteristic
subgroupG/H
centerC2C22×C22⋊D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
FittingH(5,𝔽2)×C313C2
socleC2×C313C22×D4
hypercenterH(5,𝔽2)D313
hypocenterC313#577
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #23756544C2semidirect
2. #23756527C2semidirect
3. #23756523C2semidirect
4. #23756517C2semidirect
5. C2×#19097549C2semidirect
6. #23756504C2semidirect
7. H(5,𝔽2)×C313C2semidirect
8. #19097561C22semidirect
10. C2×Dic626C22semidirect
12. #19097551C22semidirect
13. #19097549C22semidirect
14. #19097549C22semidirect
15. #19097548C22semidirect
16. #19097546C22semidirect
17. #19097545C22semidirect
18. C2×#14578809C22semidirect
53. C313#577semidirect
56. H(5,𝔽2)D313semidirect

Maximal subgroups

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

subgroupindex
#237565442
#237565272
#237565232
#237565172
C2×#190975492
#237565042
H(5,𝔽2)×C3132
#577313