Finite Group Databasebeta

← C26×C4×C89 #36440942

Subgroups — C26×C4×C89 #36440942

Order 22784.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C89C211yesmaximal, characteristic
2C25×C4×C89C21126yesmaximal, direct product factor
3C26×C89C4164yesdirect product factor
4C26×C89C22163yes—
5C24×C4×C89C2212604yesdirect product factor
6C25×C89C2×C412016yesdirect product factor
7C25×C89C231651yes—
8C23×C4×C89C23111160yesdirect product factor
9C24×C89C22×C4110416yesdirect product factor
10C24×C89C2411395yes—
11C22×C4×C89C24110416yesdirect product factor
12C23×C89C23×C4111160yesdirect product factor
13C23×C89C251651yes—
14C2×C4×C89C2512016yesdirect product factor
15C22×C89C24×C412604yesdirect product factor
16C22×C89C26163yes—
17C4×C89C26164yesdirect product factor
18C26×C4C8911yesmaximal, characteristic, direct product factor, Sylow
19C2×C89C25×C41126yesdirect product factor
20C2×C89C2711yescharacteristic
21C27C2×C8911yescharacteristic
22C25×C4C2×C891126yesdirect product factor
23C89C26×C411yescharacteristic, direct product factor, Sylow
24C26C4×C89164yesdirect product factor
25C26C22×C89163yes—
26C24×C4C22×C8912604yesdirect product factor
27C25C2×C4×C8912016yesdirect product factor
28C25C23×C891651yes—
29C23×C4C23×C89111160yesdirect product factor
30C24C22×C4×C89110416yesdirect product factor
31C24C24×C8911395yes—
32C22×C4C24×C89110416yesdirect product factor
33C23C23×C4×C89111160yesdirect product factor
34C23C25×C891651yes—
35C2×C4C25×C8912016yesdirect product factor
36C22C24×C4×C8912604yesdirect product factor
37C22C26×C89163yes—
38C4C26×C89164yesdirect product factor
39C2C25×C4×C891126yesdirect product factor
40C2C27×C8911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C27×C89
socle, prime radicalC27×C89C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C89C2direct (N × H)
3. C26×C89C4direct (N × H)
5. C24×C4×C89C22direct (N × H)
6. C25×C89C2×C4direct (N × H)
8. C23×C4×C89C23direct (N × H)
9. C24×C89C22×C4direct (N × H)
11. C22×C4×C89C24direct (N × H)
12. C23×C89C23×C4direct (N × H)
14. C2×C4×C89C25direct (N × H)
15. C22×C89C24×C4direct (N × H)
17. C4×C89C26direct (N × H)
18. C26×C4C89direct (N × H)
19. C2×C89C25×C4direct (N × H)
22. C25×C4C2×C89direct (N × H)
23. C89C26×C4direct (N × H)
24. C26C4×C89direct (N × H)
26. C24×C4C22×C89direct (N × H)
27. C25C2×C4×C89direct (N × H)
29. C23×C4C23×C89direct (N × H)
30. C24C22×C4×C89direct (N × H)
32. C22×C4C24×C89direct (N × H)
33. C23C23×C4×C89direct (N × H)
35. C2×C4C25×C89direct (N × H)
36. C22C24×C4×C89direct (N × H)
38. C4C26×C89direct (N × H)
39. C2C25×C4×C89direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C892
C25×C4×C892
C26×C489