Finite Group Databasebeta

← #15689926

Subgroups — #15689926

Order 3008.

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#13094070C211yesmaximal, characteristic, complemented
2#13094050C213yesmaximal, complemented
3#13094049C213yesmaximal, complemented
4#13094044C213yesmaximal, complemented
5C2×#10625334C213yesmaximal, complemented
6#13094031C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C47C211yesmaximal, characteristic, complemented
8#41×C47—21no—
9#41×C47C2211yescharacteristic
10#41×C47C2213yescomplemented
11C2×D4×C47—23no—
12C2×D4×C47C2213yescomplemented
13#10625354—21no—
14D4×D47—23no—
15#10625350C2213yescomplemented
16C2×D188C2213yescomplemented
17#10625337C2211yescharacteristic, complemented
18#10625336C2213yescomplemented
19#10625335C2213yescomplemented
20#10625334C2213yescomplemented
21#10625334C2216yescomplemented
22#10625329C2213yescomplemented
23C2×C47⋊C8C2213yescomplemented
24C23×C47—23no—
25C22×D47—23no—
26Q8×C47D411yescharacteristic
27Q8×C47C2311yescharacteristic
28D4×C47—23no—
29D4×C47—23no—
30D4×C47D413yes—
31D4×C47C2313yes—
32C2×C4×C47—23no—
33C2×C4×C47C2313yes—
34C22⋊D47—23no—
35D188—23no—
36D188C2313yes—
37C4×D47—23no—
38Dic94C2311yescharacteristic
39C47⋊C8C2311yescharacteristic
40C47⋊C8C2313yes—
41C22×C47—23no—
42C22×C47—83no—
43C22×C47C2×D413yes—
44C2×D47—23no—
45C2×D47—83no—
46C4×C47—21no—
47C4×C47C2×D413yes—
48C4×C47C2411yescharacteristic
49Dic47—21no—
50C2×C47—23no—
51C2×C47—43no—
52C2×C47C22×D411yescharacteristic
53D47—43no—
54#576—471nomaximal, Sylow
55C47#57611yescharacteristic, complemented, Sylow
56H(5,𝔽2)—471no—
57H(5,𝔽2)D4711yescharacteristic, complemented
58AGL(1,ℤ/8)—473no—
59AGL(1,ℤ/8)—473no—
60#135—473no—
61C2×D8—473no—
62#131—471no—
63#41—21no—
64#41—473no—
65#41—941no—
66#41C2×D4711yescharacteristic
67#41C2×D4713yescomplemented
68C2×D4—23no—
69C2×D4—473no—
70C2×D4—943no—
71C2×D4C2×D4713yescomplemented
72Q16—471no—
73SD16—473no—
74SD16—473no—
75D8—473no—
76D8—476no—
77M16—473no—
78C2×C8—473no—
79C23—23no—
80C23—943no—
81Q8—471no—
82Q8C22⋊D4711yescharacteristic
83Q8C22×D4711yescharacteristic
84D4—23no—
85D4—23no—
86D4—473no—
87D4—943no—
88D4—943no—
89D4C22⋊D4713yes—
90D4C22×D4713yes—
91C2×C4—23no—
92C2×C4—943no—
93C2×C4C22×D4713yes—
94C8—471no—
95C8—473no—
96C22—23no—
97C22—83no—
98C22—943no—
99C22—3763no—
100C22C2×C22⋊D4713yes—
101C4—21no—
102C4—941no—
103C4C2×C22⋊D4713yes—
104C4C23×D4711yescharacteristic
105C2—23no—
106C2—43no—
107C2—1883no—
108C2C22×C22⋊D4711yescharacteristic
subgroupG/H
centerC2C22×C22⋊D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
FittingH(5,𝔽2)×C47C2
socleC2×C47C22×D4
hypercenterH(5,𝔽2)D47
hypocenterC47#576
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #13094070C2semidirect
2. #13094050C2semidirect
3. #13094049C2semidirect
4. #13094044C2semidirect
5. C2×#10625334C2semidirect
6. #13094031C2semidirect
7. H(5,𝔽2)×C47C2semidirect
10. #41×C47C22semidirect
12. C2×D4×C47C22semidirect
15. #10625350C22semidirect
16. C2×D188C22semidirect
17. #10625337C22semidirect
18. #10625336C22semidirect
19. #10625335C22semidirect
20. #10625334C22semidirect
21. #10625334C22semidirect
22. #10625329C22semidirect
23. C2×C47⋊C8C22semidirect
55. C47#576semidirect
57. H(5,𝔽2)D47semidirect
67. #41C2×D47semidirect
71. C2×D4C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940702
#130940502
#130940492
#130940442
C2×#106253342
#130940312
H(5,𝔽2)×C472
#57647