Finite Group Databasebeta

← C23×#41×C241 #44505257

Subgroups — C23×#41×C241 #44505257

Order 30848.

6520 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×C241C2156yesmaximal, direct product factor
2C23×Q8×C241C211yesmaximal, characteristic, complemented
3C23×D4×C241C213yesmaximal, complemented
4C24×C4×C241C213yesmaximal, complemented
5C25×C241C2213yes—
6C2×#41×C241C221448yesdirect product factor
7C22×Q8×C241C22128yescomplemented
8C22×D4×C241C22184yescomplemented
9C23×C4×C241C2213yes—
10C23×C4×C241C2211yescharacteristic
11C23×C4×C241C22184yescomplemented
12C24×C241—224no—
13C24×C241C23142yes—
14C24×C241C2311yescharacteristic
15#41×C241C231512yesdirect product factor
16C2×Q8×C241C231112yescomplemented
17C2×D4×C241C231336yescomplemented
18C22×C4×C241C23142yes—
19C22×C4×C241C23114yes—
20C22×C4×C241C231336yescomplemented
21C23×C241—2168no—
22C23×C241#4118yesdirect product factor
23C23×C241C24184yes—
24C23×C241C2417yes—
25Q8×C241C24164yescomplemented
26D4×C241C241192yescomplemented
27C2×C4×C241C24128yes—
28C2×C4×C241C24184yes—
29C2×C4×C241C241192yescomplemented
30C22×C241—2168no—
31C22×C241C2×#41128yesdirect product factor
32C22×C241C25124yes—
33C22×C241C2517yes—
34C4×C241C2518yes—
35C4×C241C25124yes—
36C2×C241—224no—
37C2×C241C22×#41114yesdirect product factor
38C2×C241C2611yescharacteristic
39C241C23×#4111yescharacteristic, direct product factor, Sylow
40C23×#41C24111yesmaximal, characteristic, direct product factor, Sylow
41C22×#41C2×C241156yesdirect product factor
42C23×Q8C2×C24111yescharacteristic, complemented
43C23×D4C2×C24113yescomplemented
44C24×C4C2×C24113yescomplemented
45C25C22×C24113yes—
46C2×#41C22×C2411448yesdirect product factor
47C22×Q8C22×C241128yescomplemented
48C22×D4C22×C241184yescomplemented
49C23×C4C22×C24113yes—
50C23×C4C22×C24111yescharacteristic
51C23×C4C22×C241184yescomplemented
52C24—224no—
53C24C23×C241142yes—
54C24C23×C24111yescharacteristic
55#41C23×C2411512yesdirect product factor
56C2×Q8C23×C2411112yescomplemented
57C2×D4C23×C2411336yescomplemented
58C22×C4C23×C241114yes—
59C22×C4C23×C241142yes—
60C22×C4C23×C2411336yescomplemented
61C23—2168no—
62C23#41×C24118yesdirect product factor
63C23C24×C241184yes—
64C23C24×C24117yes—
65Q8C24×C241164yescomplemented
66D4C24×C2411192yescomplemented
67C2×C4C24×C241128yes—
68C2×C4C24×C241184yes—
69C2×C4C24×C2411192yescomplemented
70C22—2168no—
71C22C2×#41×C241128yesdirect product factor
72C22C25×C241124yes—
73C22C25×C24117yes—
74C4C25×C24118yes—
75C4C25×C241124yes—
76C2—224no—
77C2C22×#41×C241114yesdirect product factor
78C2C26×C24111yescharacteristic
subgroupG/H
centerC23×C4×C241C22
commutator, Frattini, cosocleC2C26×C241
socleC24×C241C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C4×C241 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#41×C241C2direct (N × H)
2. C23×Q8×C241C2semidirect
3. C23×D4×C241C2semidirect
4. C24×C4×C241C2semidirect
6. C2×#41×C241C22direct (N × H)
7. C22×Q8×C241C22semidirect
8. C22×D4×C241C22semidirect
11. C23×C4×C241C22semidirect
15. #41×C241C23direct (N × H)
16. C2×Q8×C241C23semidirect
17. C2×D4×C241C23semidirect
20. C22×C4×C241C23semidirect
22. C23×C241#41direct (N × H)
25. Q8×C241C24semidirect
26. D4×C241C24semidirect
29. C2×C4×C241C24semidirect
31. C22×C241C2×#41direct (N × H)
37. C2×C241C22×#41direct (N × H)
39. C241C23×#41direct (N × H)
40. C23×#41C241direct (N × H)
41. C22×#41C2×C241direct (N × H)
42. C23×Q8C2×C241semidirect
43. C23×D4C2×C241semidirect
44. C24×C4C2×C241semidirect
46. C2×#41C22×C241direct (N × H)
47. C22×Q8C22×C241semidirect
48. C22×D4C22×C241semidirect
51. C23×C4C22×C241semidirect
55. #41C23×C241direct (N × H)
56. C2×Q8C23×C241semidirect
57. C2×D4C23×C241semidirect
60. C22×C4C23×C241semidirect
62. C23#41×C241direct (N × H)
65. Q8C24×C241semidirect
66. D4C24×C241semidirect
69. C2×C4C24×C241semidirect
71. C22C2×#41×C241direct (N × H)
77. C2C22×#41×C241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×C2412
C23×Q8×C2412
C23×D4×C2412
C24×C4×C2412
C23×#41241