Finite Group Databasebeta

← C2×C23×#585 #15671212

Subgroups — C2×C23×#585 #15671212

Order 2944.

5956 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#585C2132yesmaximal, direct product factor
2C2×C23×2−1+4C216yesmaximal, complemented
3C2×C23×H(5,𝔽2)C2110yesmaximal, complemented
4C22×#41×C23C2115yesmaximal, complemented
5C23×2−1+4C22196yescomplemented
6C23×H(5,𝔽2)C221160yescomplemented
7C2×#41×C23C22120yescomplemented
8C2×#41×C23C22160yescomplemented
9C2×#41×C23C221240yescomplemented
10C22×Q8×C23C22115yescomplemented
11C22×D4×C23C22145yescomplemented
12C23×C4×C23C22115yescomplemented
13C24×C23C23115yes—
14#41×C23C231160yescomplemented
15#41×C23C231480yescomplemented
16C2×Q8×C23C23120yes—
17C2×Q8×C23C231120yescomplemented
18C2×D4×C23C23160yes—
19C2×D4×C23C231360yescomplemented
20C22×C4×C23C23145yes—
21C22×C4×C23C23115yes—
22C22×C4×C23C231120yescomplemented
23C23×C23—430no—
24C23×C23C24115yes—
25C23×C23C24160yes—
26Q8×C23C24180yes—
27D4×C23C241240yes—
28C2×C4×C23C24115yes—
29C2×C4×C23C24160yes—
30C2×C4×C23C241180yes—
31C2×C4×C23C2411yescharacteristic
32C2×#585C2311yesmaximal, characteristic, direct product factor, Sylow
33C22×C23—230no—
34C22×C23—460no—
35C22×C23C25130yes—
36C22×C23C2511yescharacteristic
37C4×C23C2512yes—
38C4×C23C25130yes—
39#585C2×C23132yesdirect product factor
40C2×2−1+4C2×C2316yescomplemented
41C2×H(5,𝔽2)C2×C23110yescomplemented
42C22×#41C2×C23115yescomplemented
43C2×C23—230no—
44C2×C23#58512yesdirect product factor
45C2×C23C2611yescharacteristic
462−1+4C22×C23196yescomplemented
47H(5,𝔽2)C22×C231160yescomplemented
48C2×#41C22×C23120yescomplemented
49C2×#41C22×C23160yescomplemented
50C2×#41C22×C231240yescomplemented
51C22×Q8C22×C23115yescomplemented
52C22×D4C22×C23145yescomplemented
53C23×C4C22×C23115yescomplemented
54C23C2×#58511yescharacteristic, direct product factor, Sylow
55C24C23×C23115yes—
56#41C23×C231160yescomplemented
57#41C23×C231480yescomplemented
58C2×Q8C23×C23120yes—
59C2×Q8C23×C231120yescomplemented
60C2×D4C23×C23160yes—
61C2×D4C23×C231360yescomplemented
62C22×C4C23×C23115yes—
63C22×C4C23×C23145yes—
64C22×C4C23×C231120yescomplemented
65C23—430no—
66C23C24×C23115yes—
67C23C24×C23160yes—
68Q8C24×C23180yes—
69D4C24×C231240yes—
70C2×C4C24×C2311yescharacteristic
71C2×C4C24×C23115yes—
72C2×C4C24×C23160yes—
73C2×C4C24×C231180yes—
74C22—230no—
75C22—460no—
76C22C25×C23130yes—
77C22C25×C2311yescharacteristic
78C4C25×C2312yes—
79C4C25×C23130yes—
80C2—230no—
81C2C23×#58512yesdirect product factor
82C2C26×C2311yescharacteristic
subgroupG/H
centerC2×C4×C23C24
commutator, Frattini, cosocleC2C26×C23
socleC22×C23C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#585C2direct (N × H)
2. C2×C23×2−1+4C2semidirect
3. C2×C23×H(5,𝔽2)C2semidirect
4. C22×#41×C23C2semidirect
5. C23×2−1+4C22semidirect
6. C23×H(5,𝔽2)C22semidirect
7. C2×#41×C23C22semidirect
8. C2×#41×C23C22semidirect
9. C2×#41×C23C22semidirect
10. C22×Q8×C23C22semidirect
11. C22×D4×C23C22semidirect
12. C23×C4×C23C22semidirect
14. #41×C23C23semidirect
15. #41×C23C23semidirect
17. C2×Q8×C23C23semidirect
19. C2×D4×C23C23semidirect
22. C22×C4×C23C23semidirect
32. C2×#585C23direct (N × H)
39. #585C2×C23direct (N × H)
40. C2×2−1+4C2×C23semidirect
41. C2×H(5,𝔽2)C2×C23semidirect
42. C22×#41C2×C23semidirect
44. C2×C23#585direct (N × H)
46. 2−1+4C22×C23semidirect
47. H(5,𝔽2)C22×C23semidirect
48. C2×#41C22×C23semidirect
49. C2×#41C22×C23semidirect
50. C2×#41C22×C23semidirect
51. C22×Q8C22×C23semidirect
52. C22×D4C22×C23semidirect
53. C23×C4C22×C23semidirect
54. C23C2×#585direct (N × H)
56. #41C23×C23semidirect
57. #41C23×C23semidirect
59. C2×Q8C23×C23semidirect
61. C2×D4C23×C23semidirect
64. C22×C4C23×C23semidirect
81. C2C23×#585direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5852
C2×C23×2−1+42
C2×C23×H(5,𝔽2)2
C22×#41×C232
C2×#58523