Finite Group Databasebeta

← C2×C43×#585 #19132410

Subgroups — C2×C43×#585 #19132410

Order 5504.

5956 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#585C2132yesmaximal, direct product factor
2C2×2−1+4×C43C216yesmaximal, complemented
3C2×H(5,𝔽2)×C43C2110yesmaximal, complemented
4C22×#41×C43C2115yesmaximal, complemented
52−1+4×C43C22196yescomplemented
6H(5,𝔽2)×C43C221160yescomplemented
7C2×#41×C43C22120yescomplemented
8C2×#41×C43C22160yescomplemented
9C2×#41×C43C221240yescomplemented
10C22×Q8×C43C22115yescomplemented
11C22×D4×C43C22145yescomplemented
12C23×C4×C43C22115yescomplemented
13C24×C43C23115yes—
14#41×C43C231160yescomplemented
15#41×C43C231480yescomplemented
16C2×Q8×C43C23120yes—
17C2×Q8×C43C231120yescomplemented
18C2×D4×C43C23160yes—
19C2×D4×C43C231360yescomplemented
20C22×C4×C43C23145yes—
21C22×C4×C43C23115yes—
22C22×C4×C43C231120yescomplemented
23C23×C43—430no—
24C23×C43C24115yes—
25C23×C43C24160yes—
26Q8×C43C24180yes—
27D4×C43C241240yes—
28C2×C4×C43C24115yes—
29C2×C4×C43C24160yes—
30C2×C4×C43C241180yes—
31C2×C4×C43C2411yescharacteristic
32C22×C43—230no—
33C22×C43—460no—
34C22×C43C25130yes—
35C22×C43C2511yescharacteristic
36C4×C43C2512yes—
37C4×C43C25130yes—
38C2×#585C4311yesmaximal, characteristic, direct product factor, Sylow
39C2×C43—230no—
40C2×C43#58512yesdirect product factor
41C2×C43C2611yescharacteristic
42#585C2×C43132yesdirect product factor
43C2×2−1+4C2×C4316yescomplemented
44C2×H(5,𝔽2)C2×C43110yescomplemented
45C22×#41C2×C43115yescomplemented
46C43C2×#58511yescharacteristic, direct product factor, Sylow
472−1+4C22×C43196yescomplemented
48H(5,𝔽2)C22×C431160yescomplemented
49C2×#41C22×C43120yescomplemented
50C2×#41C22×C43160yescomplemented
51C2×#41C22×C431240yescomplemented
52C22×Q8C22×C43115yescomplemented
53C22×D4C22×C43145yescomplemented
54C23×C4C22×C43115yescomplemented
55C24C23×C43115yes—
56#41C23×C431160yescomplemented
57#41C23×C431480yescomplemented
58C2×Q8C23×C43120yes—
59C2×Q8C23×C431120yescomplemented
60C2×D4C23×C43160yes—
61C2×D4C23×C431360yescomplemented
62C22×C4C23×C43115yes—
63C22×C4C23×C43145yes—
64C22×C4C23×C431120yescomplemented
65C23—430no—
66C23C24×C43115yes—
67C23C24×C43160yes—
68Q8C24×C43180yes—
69D4C24×C431240yes—
70C2×C4C24×C4311yescharacteristic
71C2×C4C24×C43115yes—
72C2×C4C24×C43160yes—
73C2×C4C24×C431180yes—
74C22—230no—
75C22—460no—
76C22C25×C43130yes—
77C22C25×C4311yescharacteristic
78C4C25×C4312yes—
79C4C25×C43130yes—
80C2—230no—
81C2C43×#58512yesdirect product factor
82C2C26×C4311yescharacteristic
subgroupG/H
centerC2×C4×C43C24
commutator, Frattini, cosocleC2C26×C43
socleC22×C43C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#585C2direct (N × H)
2. C2×2−1+4×C43C2semidirect
3. C2×H(5,𝔽2)×C43C2semidirect
4. C22×#41×C43C2semidirect
5. 2−1+4×C43C22semidirect
6. H(5,𝔽2)×C43C22semidirect
7. C2×#41×C43C22semidirect
8. C2×#41×C43C22semidirect
9. C2×#41×C43C22semidirect
10. C22×Q8×C43C22semidirect
11. C22×D4×C43C22semidirect
12. C23×C4×C43C22semidirect
14. #41×C43C23semidirect
15. #41×C43C23semidirect
17. C2×Q8×C43C23semidirect
19. C2×D4×C43C23semidirect
22. C22×C4×C43C23semidirect
38. C2×#585C43direct (N × H)
40. C2×C43#585direct (N × H)
42. #585C2×C43direct (N × H)
43. C2×2−1+4C2×C43semidirect
44. C2×H(5,𝔽2)C2×C43semidirect
45. C22×#41C2×C43semidirect
46. C43C2×#585direct (N × H)
47. 2−1+4C22×C43semidirect
48. H(5,𝔽2)C22×C43semidirect
49. C2×#41C22×C43semidirect
50. C2×#41C22×C43semidirect
51. C2×#41C22×C43semidirect
52. C22×Q8C22×C43semidirect
53. C22×D4C22×C43semidirect
54. C23×C4C22×C43semidirect
56. #41C23×C43semidirect
57. #41C23×C43semidirect
59. C2×Q8C23×C43semidirect
61. C2×D4C23×C43semidirect
64. C22×C4C23×C43semidirect
81. C2C43×#585direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#5852
C2×2−1+4×C432
C2×H(5,𝔽2)×C432
C22×#41×C432
C2×#58543