Finite Group Databasebeta

← C24×#10621902 #26010481

Subgroups — C24×#10621902 #26010481

Order 11008.

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×#10621902C21120yesmaximal, direct product factor
2C24×D172C213yesmaximal, complemented
3C24×C4×D43C213yesmaximal, complemented
4C24×Q8×C43C211yesmaximal, characteristic, complemented
5C25×D43C2213yes—
6C22×#10621902C2212240yesdirect product factor
7C23×D172C221180yescomplemented
8C24×Dic43C2211yescharacteristic
9C23×C4×D43C221180yescomplemented
10C23×Q8×C43C22160yescomplemented
11C24×C4×C43C2213yes—
12C24×D43—248no—
13C24×D43C23190yes—
14C2×#10621902C2317680yesdirect product factor
15C22×D172C2311680yescomplemented
16C23×Dic43C23130yes—
17C22×C4×D43C2311680yescomplemented
18C25×C43C2311yescharacteristic
19C22×Q8×C43C231560yescomplemented
20C23×C4×C43C23190yes—
21C24×C43#41116yescomplemented
22C24×C43C24115yes—
23C23×D43—2720no—
24C23×D43C241420yes—
25C2×Q8×C43C241960yescomplemented
26C22×C4×C43C241420yes—
27C22×Dic43C241140yes—
28#10621902C2414096yesdirect product factor
29C2×D172C2412880yescomplemented
30C2×C4×D43C2412880yescomplemented
31C23×C43C2×#411120yescomplemented
32C23×C43C25135yes—
33C22×D43—21680no—
34C22×D43C251360yes—
35Q8×C43C251256yescomplemented
36C2×C4×C43C251360yes—
37C2×Dic43C251120yes—
38D172C251768yescomplemented
39C4×D43C251768yescomplemented
40C24×#41—431nomaximal, Sylow
41C22×C43C22×#411140yescomplemented
42C22×C43C26115yes—
43C2×D43—2720no—
44C2×D43C26148yes—
45C4×C43C26148yes—
46Dic43C26116yes—
47C23×#41—43120no—
48C24×Q8D4311yescharacteristic, complemented
49C24×D4—433no—
50C25×C4—433no—
51C2×C43C23×#41130yescomplemented
52C2×C43C2711yescharacteristic
53D43—248no—
54C26—433no—
55C22×#41—432240no—
56C23×Q8C2×D43160yescomplemented
57C23×D4—43180no—
58C24×C4—431no—
59C24×C4—43180no—
60C24×C4C2×D4313yes—
61C43C24×#4111yescharacteristic, complemented, Sylow
62C25—4390no—
63C25—8648no—
64C25C22×D4311yescharacteristic
65C2×#41—437680no—
66C22×Q8C22×D431560yescomplemented
67C22×D4—431680no—
68C23×C4—4330no—
69C23×C4—431680no—
70C23×C4C22×D43190yes—
71C24—43420no—
72C24—86720no—
73C24#10621902116yesdirect product factor
74C24C23×D43115yes—
75#41—434096no—
76C2×Q8C23×D431960yescomplemented
77C2×D4—432880no—
78C22×C4—43140no—
79C22×C4—432880no—
80C22×C4C23×D431420yes—
81C23—43360no—
82C23—861680no—
83C23C2×#106219021120yesdirect product factor
84C23C24×D43135yes—
85Q8C24×D431256yescomplemented
86D4—43768no—
87C2×C4—43120no—
88C2×C4—43768no—
89C2×C4C24×D431360yes—
90C22—4348no—
91C22—86720no—
92C22C22×#106219021140yesdirect product factor
93C22C25×D43115yes—
94C4—4316no—
95C4C25×D43148yes—
96C2—8648no—
97C2C23×#10621902130yesdirect product factor
98C2C26×D4311yescharacteristic
subgroupG/H
centerC25C22×D43
commutator, cosocleC2×C43C27
FrattiniC2C26×D43
FittingC24×Q8×C43C2
socleC25×C43C23
hypercenterC24×Q8D43
hypocenterC43C24×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
1. C23×#10621902C2direct (N × H)
2. C24×D172C2semidirect
3. C24×C4×D43C2semidirect
4. C24×Q8×C43C2semidirect
6. C22×#10621902C22direct (N × H)
7. C23×D172C22semidirect
9. C23×C4×D43C22semidirect
10. C23×Q8×C43C22semidirect
14. C2×#10621902C23direct (N × H)
15. C22×D172C23semidirect
17. C22×C4×D43C23semidirect
19. C22×Q8×C43C23semidirect
21. C24×C43#41semidirect
25. C2×Q8×C43C24semidirect
28. #10621902C24direct (N × H)
29. C2×D172C24semidirect
30. C2×C4×D43C24semidirect
31. C23×C43C2×#41semidirect
35. Q8×C43C25semidirect
38. D172C25semidirect
39. C4×D43C25semidirect
41. C22×C43C22×#41semidirect
48. C24×Q8D43semidirect
51. C2×C43C23×#41semidirect
56. C23×Q8C2×D43semidirect
61. C43C24×#41semidirect
66. C22×Q8C22×D43semidirect
73. C24#10621902direct (N × H)
76. C2×Q8C23×D43semidirect
83. C23C2×#10621902direct (N × H)
85. Q8C24×D43semidirect
92. C22C22×#10621902direct (N × H)
97. C2C23×#10621902direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106219022
C24×D1722
C24×C4×D432
C24×Q8×C432
C24×#4143