Finite Group Databasebeta

← #14583700

Subgroups — #14583700

Order 2752.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#13063370C212yesmaximal, complemented
2#13063351C212yesmaximal, complemented
3#13063349C214yesmaximal, complemented
4#13063347C211yesmaximal, characteristic, complemented
5#13063344C212yesmaximal, complemented
6D8×D43C212yesmaximal, complemented
7#13063331C211yesmaximal, characteristic, complemented
8C2×D8×C43C211yesmaximal, characteristic, complemented
9C2×D4×C43C2212yescomplemented
10C2×C22⋊D43—24no—
11#10621900—22no—
12#10621900C2214yescomplemented
13D4×D43—22no—
14D4×D43C2214yescomplemented
15#10621898C2211yescharacteristic
16#10621898C2212yescomplemented
17D8×C43C2212yescomplemented
18D8×C43C2212yescomplemented
19C2×C8×C43C2211yescharacteristic, complemented
20#10621883C2214yescomplemented
21#10621882C2214yescomplemented
22#10621877C2211yescharacteristic, complemented
23Dic172C2211yescharacteristic, complemented
24D344C2211yescharacteristic, complemented
25#10621873C2212yescomplemented
26#10621872C2212yescomplemented
27C8×D43C2212yescomplemented
28C23×C43—22no—
29C22×D43—24no—
30D4×C43—22no—
31D4×C43C2314yes—
32C2×C4×C43C2311yescharacteristic
33C22⋊D43—22no—
34C22⋊D43—24no—
35C22⋊D43—24no—
36C22⋊D43D412yes—
37C2×Dic43—24no—
38D172D411yescharacteristic
39D172C2312yes—
40C4×D43—22no—
41C4×D43C2312yes—
42Dic86D411yescharacteristic
43Dic86C2312yes—
44C8×C43C2311yescharacteristic
45C8×C43C2311yescharacteristic
46C43⋊C8C2312yes—
47C22×C43—24no—
48C22×C43—82no—
49C22×C43C2×D411yescharacteristic
50C2×D43—22no—
51C2×D43—84no—
52C2×D43C2×D412yes—
53C4×C43C2×D411yescharacteristic
54C4×C43C2411yescharacteristic
55Dic43—22no—
56Dic43C2×D412yes—
57C2×C43—21no—
58C2×C43—44no—
59C2×C43C22×D411yescharacteristic
60D43—22no—
61D43—42no—
62#576—431nomaximal, Sylow
63C43#57611yescharacteristic, complemented, Sylow
64H(5,𝔽2)—432no—
65AGL(1,ℤ/8)—432no—
66AGL(1,ℤ/8)—434no—
67#135—432no—
68#135—431no—
69C2×D8—432no—
70C2×D8D4311yescharacteristic, complemented
71#131—431no—
72#41—431no—
73#41—434no—
74#41—432no—
75#41—862no—
76C2×D4—434no—
77C2×D4—862no—
78C2×D4—864no—
79C2×D4C2×D4312yescomplemented
80Q16—431no—
81SD16—434no—
82SD16—432no—
83D8—434no—
84D8—431no—
85D8C2×D4312yescomplemented
86D8C2×D4312yescomplemented
87M16—431no—
88M16—432no—
89C2×C8—432no—
90C2×C8C2×D4311yescharacteristic, complemented
91C23—22no—
92C23—864no—
93Q8—431no—
94Q8—432no—
95D4—22no—
96D4—432no—
97D4—431no—
98D4—432no—
99D4—864no—
100D4—864no—
101D4—862no—
102D4C22×D4314yes—
103C2×C4—432no—
104C2×C4—864no—
105C2×C4—862no—
106C2×C4C22×D4311yescharacteristic
107C8—432no—
108C8C22×D4311yescharacteristic
109C8C22×D4311yescharacteristic
110C22—24no—
111C22—82no—
112C22—432no—
113C22—862no—
114C22—3444no—
115C22D4×D4311yescharacteristic
116C4—432no—
117C4—862no—
118C4D4×D4311yescharacteristic
119C4C23×D4311yescharacteristic
120C2—21no—
121C2—44no—
122C2—862no—
123C2—1722no—
124C2C2×D4×D4311yescharacteristic
subgroupG/H
centerC2C2×D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
FittingC2×D8×C43C2
socleC2×C43C22×D4
hypercenterC2×D8D43
hypocenterC43#576
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #13063370C2semidirect
2. #13063351C2semidirect
3. #13063349C2semidirect
4. #13063347C2semidirect
5. #13063344C2semidirect
6. D8×D43C2semidirect
7. #13063331C2semidirect
8. C2×D8×C43C2semidirect
9. C2×D4×C43C22semidirect
12. #10621900C22semidirect
14. D4×D43C22semidirect
16. #10621898C22semidirect
17. D8×C43C22semidirect
18. D8×C43C22semidirect
19. C2×C8×C43C22semidirect
20. #10621883C22semidirect
21. #10621882C22semidirect
22. #10621877C22semidirect
23. Dic172C22semidirect
24. D344C22semidirect
25. #10621873C22semidirect
26. #10621872C22semidirect
27. C8×D43C22semidirect
63. C43#576semidirect
70. C2×D8D43semidirect
79. C2×D4C2×D43semidirect
85. D8C2×D43semidirect
86. D8C2×D43semidirect
90. C2×C8C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633702
#130633512
#130633492
#130633472
#130633442
D8×D432
#130633312
C2×D8×C432
#57643