Finite Group Databasebeta

← #49183518

Subgroups — #49183518

Order 37952.

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#34039331C211yesmaximal, characteristic, complemented
2#34039311C213yesmaximal, complemented
3#34039310C213yesmaximal, complemented
4#34039305C213yesmaximal, complemented
5C2×#23748718C213yesmaximal, complemented
6#34039292C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C593C211yesmaximal, characteristic, complemented
8#23748734—21no—
9#23748733C2213yescomplemented
10C2×D2372C2213yescomplemented
11D4×D593—23no—
12#23748723C2211yescharacteristic, complemented
13#23748721C2213yescomplemented
14#23748720C2213yescomplemented
15#23748718C2213yescomplemented
16#23748718C2216yescomplemented
17#23748717C2213yescomplemented
18C2×#18011654C2213yescomplemented
19#41×C593—21no—
20#41×C593C2211yescharacteristic
21#41×C593C2213yescomplemented
22C2×D4×C593—23no—
23C2×D4×C593C2213yescomplemented
24C22×D593—23no—
25Dic1186C2311yescharacteristic
26D2372—23no—
27D2372C2313yes—
28C22⋊D593—23no—
29C4×D593—23no—
30#18011654C2311yescharacteristic
31#18011654C2313yes—
32C23×C593—23no—
33Q8×C593D411yescharacteristic
34Q8×C593C2311yescharacteristic
35D4×C593—23no—
36D4×C593—23no—
37D4×C593D413yes—
38D4×C593C2313yes—
39C2×C4×C593—23no—
40C2×C4×C593C2313yes—
41C22×C593—23no—
42C22×C593—83no—
43C22×C593C2×D413yes—
44C2×D593—23no—
45C2×D593—83no—
46C4×C593—21no—
47C4×C593C2×D413yes—
48C4×C593C2411yescharacteristic
49Dic593—21no—
50C2×C593—23no—
51C2×C593—43no—
52C2×C593C22×D411yescharacteristic
53D593—43no—
54C593#57611yescharacteristic, complemented, Sylow
55#576—5931nomaximal, Sylow
56H(5,𝔽2)—5931no—
57H(5,𝔽2)D59311yescharacteristic, complemented
58AGL(1,ℤ/8)—5933no—
59AGL(1,ℤ/8)—5933no—
60#135—5933no—
61C2×D8—5933no—
62#131—5931no—
63#41—21no—
64#41—5933no—
65#41—11861no—
66#41C2×D59311yescharacteristic
67#41C2×D59313yescomplemented
68C2×D4—23no—
69C2×D4—5933no—
70C2×D4—11863no—
71C2×D4C2×D59313yescomplemented
72Q16—5931no—
73SD16—5933no—
74SD16—5933no—
75D8—5933no—
76D8—5936no—
77M16—5933no—
78C2×C8—5933no—
79C23—23no—
80C23—11863no—
81Q8—5931no—
82Q8C22⋊D59311yescharacteristic
83Q8C22×D59311yescharacteristic
84D4—23no—
85D4—23no—
86D4—5933no—
87D4—11863no—
88D4—11863no—
89D4C22⋊D59313yes—
90D4C22×D59313yes—
91C2×C4—23no—
92C2×C4—11863no—
93C2×C4C22×D59313yes—
94C8—5931no—
95C8—5933no—
96C22—23no—
97C22—83no—
98C22—47443no—
99C22—11863no—
100C22C2×C22⋊D59313yes—
101C4—21no—
102C4—11861no—
103C4C2×C22⋊D59313yes—
104C4C23×D59311yescharacteristic
105C2—23no—
106C2—43no—
107C2—23723no—
108C2C22×C22⋊D59311yescharacteristic
subgroupG/H
centerC2C22×C22⋊D593
commutator, cosocleC4×C593C24
FrattiniC4C23×D593
FittingH(5,𝔽2)×C593C2
socleC2×C593C22×D4
hypercenterH(5,𝔽2)D593
hypocenterC593#576
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #34039331C2semidirect
2. #34039311C2semidirect
3. #34039310C2semidirect
4. #34039305C2semidirect
5. C2×#23748718C2semidirect
6. #34039292C2semidirect
7. H(5,𝔽2)×C593C2semidirect
9. #23748733C22semidirect
10. C2×D2372C22semidirect
12. #23748723C22semidirect
13. #23748721C22semidirect
14. #23748720C22semidirect
15. #23748718C22semidirect
16. #23748718C22semidirect
17. #23748717C22semidirect
18. C2×#18011654C22semidirect
21. #41×C593C22semidirect
23. C2×D4×C593C22semidirect
54. C593#576semidirect
57. H(5,𝔽2)D593semidirect
67. #41C2×D593semidirect
71. C2×D4C2×D593semidirect

Maximal subgroups

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

subgroupindex
#340393312
#340393112
#340393102
#340393052
C2×#237487182
#340392922
H(5,𝔽2)×C5932
#576593