Finite Group Databasebeta

← C24×C13×#41 #15749436

Subgroups — C24×C13×#41 #15749436

Order 3328.

65470 conjugacy classes of subgroups; only the 59038 normal subgroups are shown.

normal subgroups only

This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 59038 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×C13×#41C21120yesmaximal, direct product factor
2C24×Q8×C13C211yesmaximal, characteristic, complemented
3C24×D4×C13C213yesmaximal, complemented
4C25×C4×C13C213yesmaximal, complemented
5C26×C13C2213yes—
6C22×C13×#41C2212240yesdirect product factor
7C23×Q8×C13C22160yescomplemented
8C23×D4×C13C221180yescomplemented
9C24×C4×C13C2213yes—
10C24×C4×C13C2211yescharacteristic
11C24×C4×C13C221180yescomplemented
12C25×C13—248no—
13C25×C13C23190yes—
14C25×C13C2311yescharacteristic
15C2×C13×#41C2317680yesdirect product factor
16C22×Q8×C13C231560yescomplemented
17C22×D4×C13C2311680yescomplemented
18C23×C4×C13C23190yes—
19C23×C4×C13C23130yes—
20C23×C4×C13C2311680yescomplemented
21C24×#41C1311yesmaximal, characteristic, direct product factor, Sylow
22C24×C13—2720no—
23C24×C13#41116yesdirect product factor
24C24×C13C241420yes—
25C24×C13C24115yes—
26C13×#41C2414096yesdirect product factor
27C2×Q8×C13C241960yescomplemented
28C2×D4×C13C2412880yescomplemented
29C22×C4×C13C241140yes—
30C22×C4×C13C241420yes—
31C22×C4×C13C2412880yescomplemented
32C23×#41C2×C131120yesdirect product factor
33C24×Q8C2×C1311yescharacteristic, complemented
34C24×D4C2×C1313yescomplemented
35C25×C4C2×C1313yescomplemented
36C23×C13—21680no—
37C23×C13C2×#411120yesdirect product factor
38C23×C13C251360yes—
39C23×C13C25135yes—
40Q8×C13C251256yescomplemented
41D4×C13C251768yescomplemented
42C2×C4×C13C251120yes—
43C2×C4×C13C251360yes—
44C2×C4×C13C251768yescomplemented
45C26C22×C1313yes—
46C22×#41C22×C1312240yesdirect product factor
47C23×Q8C22×C13160yescomplemented
48C23×D4C22×C131180yescomplemented
49C24×C4C22×C1311yescharacteristic
50C24×C4C22×C1313yes—
51C24×C4C22×C131180yescomplemented
52C22×C13—2720no—
53C22×C13C22×#411140yesdirect product factor
54C22×C13C26148yes—
55C22×C13C26115yes—
56C4×C13C26116yes—
57C4×C13C26148yes—
58C25—248no—
59C25C23×C13190yes—
60C25C23×C1311yescharacteristic
61C2×#41C23×C1317680yesdirect product factor
62C22×Q8C23×C131560yescomplemented
63C22×D4C23×C1311680yescomplemented
64C23×C4C23×C13130yes—
65C23×C4C23×C13190yes—
66C23×C4C23×C1311680yescomplemented
67C2×C13—248no—
68C2×C13C23×#41130yesdirect product factor
69C2×C13C2711yescharacteristic
70C24—2720no—
71C24C13×#41116yesdirect product factor
72C24C24×C131420yes—
73C24C24×C13115yes—
74#41C24×C1314096yesdirect product factor
75C2×Q8C24×C131960yescomplemented
76C2×D4C24×C1312880yescomplemented
77C22×C4C24×C131140yes—
78C22×C4C24×C131420yes—
79C22×C4C24×C1312880yescomplemented
80C13C24×#4111yescharacteristic, direct product factor, Sylow
81C23—21680no—
82C23C2×C13×#411120yesdirect product factor
83C23C25×C131360yes—
84C23C25×C13135yes—
85Q8C25×C131256yescomplemented
86D4C25×C131768yescomplemented
87C2×C4C25×C131120yes—
88C2×C4C25×C131360yes—
89C2×C4C25×C131768yescomplemented
90C22—2720no—
91C22C22×C13×#411140yesdirect product factor
92C22C26×C13148yes—
93C22C26×C13115yes—
94C4C26×C13116yes—
95C4C26×C13148yes—
96C2—248no—
97C2C23×C13×#41130yesdirect product factor
98C2C27×C1311yescharacteristic
subgroupG/H
centerC24×C4×C13C22
commutator, Frattini, cosocleC2C27×C13
socleC25×C13C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C13×#41C2direct (N × H)
2. C24×Q8×C13C2semidirect
3. C24×D4×C13C2semidirect
4. C25×C4×C13C2semidirect
6. C22×C13×#41C22direct (N × H)
7. C23×Q8×C13C22semidirect
8. C23×D4×C13C22semidirect
11. C24×C4×C13C22semidirect
15. C2×C13×#41C23direct (N × H)
16. C22×Q8×C13C23semidirect
17. C22×D4×C13C23semidirect
20. C23×C4×C13C23semidirect
21. C24×#41C13direct (N × H)
23. C24×C13#41direct (N × H)
26. C13×#41C24direct (N × H)
27. C2×Q8×C13C24semidirect
28. C2×D4×C13C24semidirect
31. C22×C4×C13C24semidirect
32. C23×#41C2×C13direct (N × H)
33. C24×Q8C2×C13semidirect
34. C24×D4C2×C13semidirect
35. C25×C4C2×C13semidirect
37. C23×C13C2×#41direct (N × H)
40. Q8×C13C25semidirect
41. D4×C13C25semidirect
44. C2×C4×C13C25semidirect
46. C22×#41C22×C13direct (N × H)
47. C23×Q8C22×C13semidirect
48. C23×D4C22×C13semidirect
51. C24×C4C22×C13semidirect
53. C22×C13C22×#41direct (N × H)
61. C2×#41C23×C13direct (N × H)
62. C22×Q8C23×C13semidirect
63. C22×D4C23×C13semidirect
66. C23×C4C23×C13semidirect
68. C2×C13C23×#41direct (N × H)
71. C24C13×#41direct (N × H)
74. #41C24×C13direct (N × H)
75. C2×Q8C24×C13semidirect
76. C2×D4C24×C13semidirect
79. C22×C4C24×C13semidirect
80. C13C24×#41direct (N × H)
82. C23C2×C13×#41direct (N × H)
85. Q8C25×C13semidirect
86. D4C25×C13semidirect
89. C2×C4C25×C13semidirect
91. C22C22×C13×#41direct (N × H)
97. C2C23×C13×#41direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C13×#412
C24×Q8×C132
C24×D4×C132
C25×C4×C132
C24×#4113