Finite Group Databasebeta

← C24×#1161 #14267680

Subgroups — C24×#1161 #14267680

Order 1792.

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
1C24×C7×Q8C211yesmaximal, characteristic, complemented
2C23×#1161C21120yesmaximal, direct product factor
3C24×D28C213yesmaximal, complemented
4C24×C4×D7C213yesmaximal, complemented
5C25×D7C2213yes—
6C23×C7×Q8C22160yescomplemented
7C24×C4×C7C2213yes—
8C24×Dic7C2211yescharacteristic
9C22×#1161C2212240yesdirect product factor
10C23×D28C221180yescomplemented
11C23×C4×D7C221180yescomplemented
12C24×#41—71nomaximal, Sylow
13C25×C7C2311yescharacteristic
14C24×D7—248no—
15C24×D7C23190yes—
16C22×C7×Q8C231560yescomplemented
17C23×C4×C7C23190yes—
18C23×Dic7C23130yes—
19C2×#1161C2317680yesdirect product factor
20C22×D28C2311680yescomplemented
21C22×C4×D7C2311680yescomplemented
22C23×#41—7120no—
23C24×Q8D711yescharacteristic, complemented
24C24×D4—73no—
25C25×C4—73no—
26C24×C7#41116yescomplemented
27C24×C7C24115yes—
28C23×D7—2720no—
29C23×D7C241420yes—
30C2×C7×Q8C241960yescomplemented
31C22×C4×C7C241420yes—
32C22×Dic7C241140yes—
33#1161C2414096yesdirect product factor
34C2×D28C2412880yescomplemented
35C2×C4×D7C2412880yescomplemented
36C26—73no—
37C22×#41—72240no—
38C23×Q8C2×D7160yescomplemented
39C23×D4—7180no—
40C24×C4—71no—
41C24×C4—7180no—
42C24×C4C2×D713yes—
43C23×C7C2×#411120yescomplemented
44C23×C7C25135yes—
45C22×D7—21680no—
46C22×D7C251360yes—
47C7×Q8C251256yescomplemented
48C2×C4×C7C251360yes—
49C2×Dic7C251120yes—
50D28C251768yescomplemented
51C4×D7C251768yescomplemented
52C25—790no—
53C25—1448no—
54C25C22×D711yescharacteristic
55C2×#41—77680no—
56C22×Q8C22×D71560yescomplemented
57C22×D4—71680no—
58C23×C4—730no—
59C23×C4—71680no—
60C23×C4C22×D7190yes—
61C22×C7C22×#411140yescomplemented
62C22×C7C26115yes—
63C2×D7—2720no—
64C2×D7C26148yes—
65C4×C7C26148yes—
66Dic7C26116yes—
67C24—7420no—
68C24—14720no—
69C24#1161116yesdirect product factor
70C24C23×D7115yes—
71#41—74096no—
72C2×Q8C23×D71960yescomplemented
73C2×D4—72880no—
74C22×C4—7140no—
75C22×C4—72880no—
76C22×C4C23×D71420yes—
77C2×C7C23×#41130yescomplemented
78C2×C7C2711yescharacteristic
79D7—248no—
80C23—7360no—
81C23—141680no—
82C23C2×#11611120yesdirect product factor
83C23C24×D7135yes—
84Q8C24×D71256yescomplemented
85D4—7768no—
86C2×C4—7120no—
87C2×C4—7768no—
88C2×C4C24×D71360yes—
89C7C24×#4111yescharacteristic, complemented, Sylow
90C22—748no—
91C22—14720no—
92C22C22×#11611140yesdirect product factor
93C22C25×D7115yes—
94C4—716no—
95C4C25×D7148yes—
96C2—1448no—
97C2C23×#1161130yesdirect product factor
98C2C26×D711yescharacteristic
subgroupG/H
centerC25C22×D7
commutator, cosocleC2×C7C27
FrattiniC2C26×D7
FittingC24×C7×Q8C2
socleC25×C7C23
hypercenterC24×Q8D7
hypocenterC7C24×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C25 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
1. C24×C7×Q8C2semidirect
2. C23×#1161C2direct (N × H)
3. C24×D28C2semidirect
4. C24×C4×D7C2semidirect
6. C23×C7×Q8C22semidirect
9. C22×#1161C22direct (N × H)
10. C23×D28C22semidirect
11. C23×C4×D7C22semidirect
16. C22×C7×Q8C23semidirect
19. C2×#1161C23direct (N × H)
20. C22×D28C23semidirect
21. C22×C4×D7C23semidirect
23. C24×Q8D7semidirect
26. C24×C7#41semidirect
30. C2×C7×Q8C24semidirect
33. #1161C24direct (N × H)
34. C2×D28C24semidirect
35. C2×C4×D7C24semidirect
38. C23×Q8C2×D7semidirect
43. C23×C7C2×#41semidirect
47. C7×Q8C25semidirect
50. D28C25semidirect
51. C4×D7C25semidirect
56. C22×Q8C22×D7semidirect
61. C22×C7C22×#41semidirect
69. C24#1161direct (N × H)
72. C2×Q8C23×D7semidirect
77. C2×C7C23×#41semidirect
82. C23C2×#1161direct (N × H)
84. Q8C24×D7semidirect
89. C7C24×#41semidirect
92. C22C22×#1161direct (N × H)
97. C2C23×#1161direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C7×Q82
C23×#11612
C24×D282
C24×C4×D72
C24×#417