Finite Group Databasebeta

← C24×#6131 #16776803

Subgroups — C24×#6131 #16776803

Order 3328.

65470 conjugacy classes of subgroups; only the 32651 normal subgroups are shown.

normal subgroups only

This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 32651 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
1C23×#6131C21120yesmaximal, direct product factor
2C24×D52C213yesmaximal, complemented
3C24×C4×D13C213yesmaximal, complemented
4C24×Q8×C13C211yesmaximal, characteristic, complemented
5C25×D13C2213yes—
6C23×Q8×C13C22160yescomplemented
7C24×C4×C13C2213yes—
8C24×Dic13C2211yescharacteristic
9C22×#6131C2212240yesdirect product factor
10C23×D52C221180yescomplemented
11C23×C4×D13C221180yescomplemented
12C25×C13C2311yescharacteristic
13C24×D13—248no—
14C24×D13C23190yes—
15C22×Q8×C13C231560yescomplemented
16C23×C4×C13C23190yes—
17C23×Dic13C23130yes—
18C2×#6131C2317680yesdirect product factor
19C22×D52C2311680yescomplemented
20C22×C4×D13C2311680yescomplemented
21C24×#41—131nomaximal, Sylow
22C24×C13#41116yescomplemented
23C24×C13C24115yes—
24C23×D13—2720no—
25C23×D13C241420yes—
26C2×Q8×C13C241960yescomplemented
27C22×C4×C13C241420yes—
28C22×Dic13C241140yes—
29#6131C2414096yesdirect product factor
30C2×D52C2412880yescomplemented
31C2×C4×D13C2412880yescomplemented
32C23×#41—13120no—
33C24×Q8D1311yescharacteristic, complemented
34C24×D4—133no—
35C25×C4—133no—
36C23×C13C2×#411120yescomplemented
37C23×C13C25135yes—
38C22×D13—21680no—
39C22×D13C251360yes—
40Q8×C13C251256yescomplemented
41C2×C4×C13C251360yes—
42C2×Dic13C251120yes—
43D52C251768yescomplemented
44C4×D13C251768yescomplemented
45C26—133no—
46C22×#41—132240no—
47C23×Q8C2×D13160yescomplemented
48C23×D4—13180no—
49C24×C4—131no—
50C24×C4—13180no—
51C24×C4C2×D1313yes—
52C22×C13C22×#411140yescomplemented
53C22×C13C26115yes—
54C2×D13—2720no—
55C2×D13C26148yes—
56C4×C13C26148yes—
57Dic13C26116yes—
58C25—1390no—
59C25—2648no—
60C25C22×D1311yescharacteristic
61C2×#41—137680no—
62C22×Q8C22×D131560yescomplemented
63C22×D4—131680no—
64C23×C4—1330no—
65C23×C4—131680no—
66C23×C4C22×D13190yes—
67C2×C13C23×#41130yescomplemented
68C2×C13C2711yescharacteristic
69D13—248no—
70C24—13420no—
71C24—26720no—
72C24#6131116yesdirect product factor
73C24C23×D13115yes—
74#41—134096no—
75C2×Q8C23×D131960yescomplemented
76C2×D4—132880no—
77C22×C4—13140no—
78C22×C4—132880no—
79C22×C4C23×D131420yes—
80C13C24×#4111yescharacteristic, complemented, Sylow
81C23—13360no—
82C23—261680no—
83C23C2×#61311120yesdirect product factor
84C23C24×D13135yes—
85Q8C24×D131256yescomplemented
86D4—13768no—
87C2×C4—13120no—
88C2×C4—13768no—
89C2×C4C24×D131360yes—
90C22—1348no—
91C22—26720no—
92C22C22×#61311140yesdirect product factor
93C22C25×D13115yes—
94C4—1316no—
95C4C25×D13148yes—
96C2—2648no—
97C2C23×#6131130yesdirect product factor
98C2C26×D1311yescharacteristic
subgroupG/H
centerC25C22×D13
commutator, cosocleC2×C13C27
FrattiniC2C26×D13
FittingC24×Q8×C13C2
socleC25×C13C23
hypercenterC24×Q8D13
hypocenterC13C24×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
1. C23×#6131C2direct (N × H)
2. C24×D52C2semidirect
3. C24×C4×D13C2semidirect
4. C24×Q8×C13C2semidirect
6. C23×Q8×C13C22semidirect
9. C22×#6131C22direct (N × H)
10. C23×D52C22semidirect
11. C23×C4×D13C22semidirect
15. C22×Q8×C13C23semidirect
18. C2×#6131C23direct (N × H)
19. C22×D52C23semidirect
20. C22×C4×D13C23semidirect
22. C24×C13#41semidirect
26. C2×Q8×C13C24semidirect
29. #6131C24direct (N × H)
30. C2×D52C24semidirect
31. C2×C4×D13C24semidirect
33. C24×Q8D13semidirect
36. C23×C13C2×#41semidirect
40. Q8×C13C25semidirect
43. D52C25semidirect
44. C4×D13C25semidirect
47. C23×Q8C2×D13semidirect
52. C22×C13C22×#41semidirect
62. C22×Q8C22×D13semidirect
67. C2×C13C23×#41semidirect
72. C24#6131direct (N × H)
75. C2×Q8C23×D13semidirect
80. C13C24×#41semidirect
83. C23C2×#6131direct (N × H)
85. Q8C24×D13semidirect
92. C22C22×#6131direct (N × H)
97. C2C23×#6131direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61312
C24×D522
C24×C4×D132
C24×Q8×C132
C24×#4113