Finite Group Databasebeta

← #50306693

Subgroups — #50306693

Order 38336.

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#34062761C211yesmaximal, characteristic, complemented
2#34062741C213yesmaximal, complemented
3#34062740C213yesmaximal, complemented
4#34062735C213yesmaximal, complemented
5C2×#23751063C213yesmaximal, complemented
6#34062722C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C599C211yesmaximal, characteristic, complemented
8#23751079—21no—
9#23751078C2213yescomplemented
10C2×D2396C2213yescomplemented
11D4×D599—23no—
12#23751068C2211yescharacteristic, complemented
13#23751066C2213yescomplemented
14#23751065C2213yescomplemented
15#23751063C2213yescomplemented
16#23751063C2216yescomplemented
17#23751062C2213yescomplemented
18C2×C599⋊C8C2213yescomplemented
19#41×C599—21no—
20#41×C599C2211yescharacteristic
21#41×C599C2213yescomplemented
22C2×D4×C599—23no—
23C2×D4×C599C2213yescomplemented
24C22×D599—23no—
25Dic1198C2311yescharacteristic
26D2396—23no—
27D2396C2313yes—
28C22⋊D599—23no—
29C4×D599—23no—
30C599⋊C8C2311yescharacteristic
31C599⋊C8C2313yes—
32C23×C599—23no—
33Q8×C599D411yescharacteristic
34Q8×C599C2311yescharacteristic
35D4×C599—23no—
36D4×C599—23no—
37D4×C599D413yes—
38D4×C599C2313yes—
39C2×C4×C599—23no—
40C2×C4×C599C2313yes—
41C22×C599—23no—
42C22×C599—83no—
43C22×C599C2×D413yes—
44C2×D599—23no—
45C2×D599—83no—
46C4×C599—21no—
47C4×C599C2×D413yes—
48C4×C599C2411yescharacteristic
49Dic599—21no—
50C2×C599—23no—
51C2×C599—43no—
52C2×C599C22×D411yescharacteristic
53D599—43no—
54C599#57611yescharacteristic, complemented, Sylow
55#576—5991nomaximal, Sylow
56H(5,𝔽2)—5991no—
57H(5,𝔽2)D59911yescharacteristic, complemented
58AGL(1,ℤ/8)—5993no—
59AGL(1,ℤ/8)—5993no—
60#135—5993no—
61C2×D8—5993no—
62#131—5991no—
63#41—21no—
64#41—5993no—
65#41—11981no—
66#41C2×D59911yescharacteristic
67#41C2×D59913yescomplemented
68C2×D4—23no—
69C2×D4—5993no—
70C2×D4—11983no—
71C2×D4C2×D59913yescomplemented
72Q16—5991no—
73SD16—5993no—
74SD16—5993no—
75D8—5993no—
76D8—5996no—
77M16—5993no—
78C2×C8—5993no—
79C23—23no—
80C23—11983no—
81Q8—5991no—
82Q8C22⋊D59911yescharacteristic
83Q8C22×D59911yescharacteristic
84D4—23no—
85D4—23no—
86D4—5993no—
87D4—11983no—
88D4—11983no—
89D4C22⋊D59913yes—
90D4C22×D59913yes—
91C2×C4—23no—
92C2×C4—11983no—
93C2×C4C22×D59913yes—
94C8—5991no—
95C8—5993no—
96C22—23no—
97C22—83no—
98C22—11983no—
99C22—47923no—
100C22C2×C22⋊D59913yes—
101C4—21no—
102C4—11981no—
103C4C2×C22⋊D59913yes—
104C4C23×D59911yescharacteristic
105C2—23no—
106C2—43no—
107C2—23963no—
108C2C22×C22⋊D59911yescharacteristic
subgroupG/H
centerC2C22×C22⋊D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
FittingH(5,𝔽2)×C599C2
socleC2×C599C22×D4
hypercenterH(5,𝔽2)D599
hypocenterC599#576
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #34062761C2semidirect
2. #34062741C2semidirect
3. #34062740C2semidirect
4. #34062735C2semidirect
5. C2×#23751063C2semidirect
6. #34062722C2semidirect
7. H(5,𝔽2)×C599C2semidirect
9. #23751078C22semidirect
10. C2×D2396C22semidirect
12. #23751068C22semidirect
13. #23751066C22semidirect
14. #23751065C22semidirect
15. #23751063C22semidirect
16. #23751063C22semidirect
17. #23751062C22semidirect
18. C2×C599⋊C8C22semidirect
21. #41×C599C22semidirect
23. C2×D4×C599C22semidirect
54. C599#576semidirect
57. H(5,𝔽2)D599semidirect
67. #41C2×D599semidirect
71. C2×D4C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627612
#340627412
#340627402
#340627352
C2×#237510632
#340627222
H(5,𝔽2)×C5992
#576599