Finite Group Databasebeta

← C2×#585×C89 #26018067

Subgroups — C2×#585×C89 #26018067

Order 11392.

5956 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#585×C89C2132yesmaximal, direct product factor
2C2×2−1+4×C89C216yesmaximal, complemented
3C2×H(5,𝔽2)×C89C2110yesmaximal, complemented
4C22×#41×C89C2115yesmaximal, complemented
52−1+4×C89C22196yescomplemented
6H(5,𝔽2)×C89C221160yescomplemented
7C2×#41×C89C22120yescomplemented
8C2×#41×C89C22160yescomplemented
9C2×#41×C89C221240yescomplemented
10C22×Q8×C89C22115yescomplemented
11C22×D4×C89C22145yescomplemented
12C23×C4×C89C22115yescomplemented
13C24×C89C23115yes—
14#41×C89C231160yescomplemented
15#41×C89C231480yescomplemented
16C2×Q8×C89C23120yes—
17C2×Q8×C89C231120yescomplemented
18C2×D4×C89C23160yes—
19C2×D4×C89C231360yescomplemented
20C22×C4×C89C23145yes—
21C22×C4×C89C23115yes—
22C22×C4×C89C231120yescomplemented
23C23×C89—430no—
24C23×C89C24115yes—
25C23×C89C24160yes—
26Q8×C89C24180yes—
27D4×C89C241240yes—
28C2×C4×C89C24115yes—
29C2×C4×C89C24160yes—
30C2×C4×C89C241180yes—
31C2×C4×C89C2411yescharacteristic
32C22×C89—230no—
33C22×C89—460no—
34C22×C89C25130yes—
35C22×C89C2511yescharacteristic
36C4×C89C2512yes—
37C4×C89C25130yes—
38C2×C89—230no—
39C2×C89#58512yesdirect product factor
40C2×C89C2611yescharacteristic
41C2×#585C8911yesmaximal, characteristic, direct product factor, Sylow
42C89C2×#58511yescharacteristic, direct product factor, Sylow
43#585C2×C89132yesdirect product factor
44C2×2−1+4C2×C8916yescomplemented
45C2×H(5,𝔽2)C2×C89110yescomplemented
46C22×#41C2×C89115yescomplemented
472−1+4C22×C89196yescomplemented
48H(5,𝔽2)C22×C891160yescomplemented
49C2×#41C22×C89120yescomplemented
50C2×#41C22×C89160yescomplemented
51C2×#41C22×C891240yescomplemented
52C22×Q8C22×C89115yescomplemented
53C22×D4C22×C89145yescomplemented
54C23×C4C22×C89115yescomplemented
55C24C23×C89115yes—
56#41C23×C891160yescomplemented
57#41C23×C891480yescomplemented
58C2×Q8C23×C89120yes—
59C2×Q8C23×C891120yescomplemented
60C2×D4C23×C89160yes—
61C2×D4C23×C891360yescomplemented
62C22×C4C23×C89115yes—
63C22×C4C23×C89145yes—
64C22×C4C23×C891120yescomplemented
65C23—430no—
66C23C24×C89115yes—
67C23C24×C89160yes—
68Q8C24×C89180yes—
69D4C24×C891240yes—
70C2×C4C24×C89115yes—
71C2×C4C24×C89160yes—
72C2×C4C24×C891180yes—
73C2×C4C24×C8911yescharacteristic
74C22—230no—
75C22—460no—
76C22C25×C89130yes—
77C22C25×C8911yescharacteristic
78C4C25×C8912yes—
79C4C25×C89130yes—
80C2—230no—
81C2#585×C8912yesdirect product factor
82C2C26×C8911yescharacteristic
subgroupG/H
centerC2×C4×C89C24
commutator, Frattini, cosocleC2C26×C89
socleC22×C89C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. #585×C89C2direct (N × H)
2. C2×2−1+4×C89C2semidirect
3. C2×H(5,𝔽2)×C89C2semidirect
4. C22×#41×C89C2semidirect
5. 2−1+4×C89C22semidirect
6. H(5,𝔽2)×C89C22semidirect
7. C2×#41×C89C22semidirect
8. C2×#41×C89C22semidirect
9. C2×#41×C89C22semidirect
10. C22×Q8×C89C22semidirect
11. C22×D4×C89C22semidirect
12. C23×C4×C89C22semidirect
14. #41×C89C23semidirect
15. #41×C89C23semidirect
17. C2×Q8×C89C23semidirect
19. C2×D4×C89C23semidirect
22. C22×C4×C89C23semidirect
39. C2×C89#585direct (N × H)
41. C2×#585C89direct (N × H)
42. C89C2×#585direct (N × H)
43. #585C2×C89direct (N × H)
44. C2×2−1+4C2×C89semidirect
45. C2×H(5,𝔽2)C2×C89semidirect
46. C22×#41C2×C89semidirect
47. 2−1+4C22×C89semidirect
48. H(5,𝔽2)C22×C89semidirect
49. C2×#41C22×C89semidirect
50. C2×#41C22×C89semidirect
51. C2×#41C22×C89semidirect
52. C22×Q8C22×C89semidirect
53. C22×D4C22×C89semidirect
54. C23×C4C22×C89semidirect
56. #41C23×C89semidirect
57. #41C23×C89semidirect
59. C2×Q8C23×C89semidirect
61. C2×D4C23×C89semidirect
64. C22×C4C23×C89semidirect
81. C2#585×C89direct (N × H)

Maximal subgroups

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

subgroupindex
#585×C892
C2×2−1+4×C892
C2×H(5,𝔽2)×C892
C22×#41×C892
C2×#58589