Finite Group Databasebeta

← C89×#63103 #36440951

Subgroups — C89×#63103 #36440951

Order 22784.

59452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×2−1+6C2128yesmaximal, complemented
2C89×H(7,𝔽2)C2136yesmaximal, complemented
3C2×#585×C89C2163yesmaximal, complemented
4#585×C89C221336yescomplemented
5#585×C89C2211008yescomplemented
6C2×2−1+4×C89C221378yescomplemented
7C2×H(5,𝔽2)×C89C221630yescomplemented
8C22×#41×C89C221315yescomplemented
92−1+4×C89C2312016yescomplemented
10H(5,𝔽2)×C89C2313360yescomplemented
11C2×#41×C89C2311260yescomplemented
12C2×#41×C89C2313780yescomplemented
13C22×Q8×C89C231315yescomplemented
14C22×D4×C89C231945yescomplemented
15C23×C4×C89C231135yescomplemented
16C24×C89C241135yes—
17#41×C89C241336yes—
18#41×C89C2415040yes—
19C2×Q8×C89C2411260yes—
20C2×D4×C89C2413780yes—
21C22×C4×C89C241315yes—
22C22×C4×C89C241945yes—
23C23×C89—8135no—
24C23×C89C251315yes—
25Q8×C89C251336yes—
26D4×C89C2511008yes—
27C2×C4×C89C251945yes—
28C2×C4×C89C25163yes—
29C22×C89—4315no—
30C22×C89C26163yes—
31C4×C89C26163yes—
32C4×C89C2611yescharacteristic
33#63103C8911yesmaximal, characteristic, direct product factor, Sylow
34C2×C89—263no—
35C2×C89C2711yescharacteristic
362−1+6C2×C89128yescomplemented
37H(7,𝔽2)C2×C89136yescomplemented
38C2×#585C2×C89163yescomplemented
39C89#6310311yescharacteristic, direct product factor, Sylow
40#585C22×C891336yescomplemented
41#585C22×C8911008yescomplemented
42C2×2−1+4C22×C891378yescomplemented
43C2×H(5,𝔽2)C22×C891630yescomplemented
44C22×#41C22×C891315yescomplemented
452−1+4C23×C8912016yescomplemented
46H(5,𝔽2)C23×C8913360yescomplemented
47C2×#41C23×C8911260yescomplemented
48C2×#41C23×C8913780yescomplemented
49C22×Q8C23×C891315yescomplemented
50C22×D4C23×C891945yescomplemented
51C23×C4C23×C891135yescomplemented
52C24C24×C891135yes—
53#41C24×C891336yes—
54#41C24×C8915040yes—
55C2×Q8C24×C8911260yes—
56C2×D4C24×C8913780yes—
57C22×C4C24×C891315yes—
58C22×C4C24×C891945yes—
59C23—8135no—
60C23C25×C891315yes—
61Q8C25×C891336yes—
62D4C25×C8911008yes—
63C2×C4C25×C89163yes—
64C2×C4C25×C891945yes—
65C22—4315no—
66C22C26×C89163yes—
67C4C26×C8911yescharacteristic
68C4C26×C89163yes—
69C2—263no—
70C2C27×C8911yescharacteristic
subgroupG/H
centerC4×C89C26
commutator, Frattini, cosocleC2C27×C89
socleC2×C89C27
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×2−1+6C2semidirect
2. C89×H(7,𝔽2)C2semidirect
3. C2×#585×C89C2semidirect
4. #585×C89C22semidirect
5. #585×C89C22semidirect
6. C2×2−1+4×C89C22semidirect
7. C2×H(5,𝔽2)×C89C22semidirect
8. C22×#41×C89C22semidirect
9. 2−1+4×C89C23semidirect
10. H(5,𝔽2)×C89C23semidirect
11. C2×#41×C89C23semidirect
12. C2×#41×C89C23semidirect
13. C22×Q8×C89C23semidirect
14. C22×D4×C89C23semidirect
15. C23×C4×C89C23semidirect
33. #63103C89direct (N × H)
36. 2−1+6C2×C89semidirect
37. H(7,𝔽2)C2×C89semidirect
38. C2×#585C2×C89semidirect
39. C89#63103direct (N × H)
40. #585C22×C89semidirect
41. #585C22×C89semidirect
42. C2×2−1+4C22×C89semidirect
43. C2×H(5,𝔽2)C22×C89semidirect
44. C22×#41C22×C89semidirect
45. 2−1+4C23×C89semidirect
46. H(5,𝔽2)C23×C89semidirect
47. C2×#41C23×C89semidirect
48. C2×#41C23×C89semidirect
49. C22×Q8C23×C89semidirect
50. C22×D4C23×C89semidirect
51. C23×C4C23×C89semidirect

Maximal subgroups

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

subgroupindex
C89×2−1+62
C89×H(7,𝔽2)2
C2×#585×C892
#6310389