Finite Group Databasebeta

← H(13,𝔽2) #72274298

Subgroups — H(13,𝔽2) #72274298

Order 8192.

488205468839 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×H(11,𝔽2)C212079yesmaximal, complemented
2#72274291C212016yesmaximal, complemented
3C2×#72258201C2211031184yescomplemented
4C22×H(9,𝔽2)C221365211yescomplemented
5C22×#63103C23143825320yescomplemented
62−1+10C221333312yescomplemented
7H(11,𝔽2)C2211064448yescomplemented
8#72258201C231175988736yescomplemented
9C2×2−1+8C23141247360yescomplemented
10C2×H(9,𝔽2)C231140241024yescomplemented
11C23×H(7,𝔽2)C2317043355yescomplemented
122−1+8C2412111864832yescomplemented
13H(9,𝔽2)C2413989078016yescomplemented
14C2×#63103C2415609640960yescomplemented
15C22×2−1+6C241409036320yescomplemented
16C22×H(7,𝔽2)C2411577711520yescomplemented
17C23×#585C241197213940yescomplemented
18C24×H(5,𝔽2)C24116434495yescomplemented
19#63103C25147868936192yescomplemented
20C2×2−1+6C25115706994688yescomplemented
21C2×H(7,𝔽2)C25133657845760yescomplemented
22C22×#585C25114725307520yescomplemented
23C23×2−1+4C251394427880yescomplemented
24C23×H(5,𝔽2)C2511972139400yescomplemented
25C24×#41C25198606970yescomplemented
26C25×D4C2514771305yescomplemented
27C27C261151470yescomplemented
282−1+6C26137231394816yescomplemented
29H(7,𝔽2)C26161545775104yescomplemented
30C2×#585C26194241968128yescomplemented
31C22×2−1+4C2618835184512yescomplemented
32C22×H(5,𝔽2)C26124542179200yescomplemented
33C23×#41C2613944278800yescomplemented
34C24×Q8C26132868990yescomplemented
35C24×D4C261295820910yescomplemented
36C25×C4C2614771305yescomplemented
37C26—64151470no—
38C26C2714771305yes—
39#585C27147868936192yes—
40C2×2−1+4C27115706994688yes—
41C2×H(5,𝔽2)C27133657845760yes—
42C22×#41C27114725307520yes—
43C23×Q8C271394427880yes—
44C23×D4C2711972139400yes—
45C24×C4C27198606970yes—
46C25—324771305no—
47C25C28116434495yes—
482−1+4C2812111864832yes—
49H(5,𝔽2)C2813989078016yes—
50C2×#41C2815609640960yes—
51C22×Q8C281409036320yes—
52C22×D4C2811577711520yes—
53C23×C4C281197213940yes—
54C24—1616434495no—
55C24C2917043355yes—
56#41C291175988736yes—
57C2×Q8C29141247360yes—
58C2×D4C291140241024yes—
59C22×C4C29143825320yes—
60C23—87043355no—
61C23C2101365211yes—
62Q8C2101333312yes—
63D4C21011064448yes—
64C2×C4C21011031184yes—
65C22—4365211no—
66C22C21112079yes—
67C4C21112016yes—
68C2—22079no—
69C2C21211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC2C212
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ G
LECSG ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×H(11,𝔽2)C2semidirect
2. #72274291C2semidirect
3. C2×#72258201C22semidirect
4. C22×H(9,𝔽2)C22semidirect
5. C22×#63103C23semidirect
6. 2−1+10C22semidirect
7. H(11,𝔽2)C22semidirect
8. #72258201C23semidirect
9. C2×2−1+8C23semidirect
10. C2×H(9,𝔽2)C23semidirect
11. C23×H(7,𝔽2)C23semidirect
12. 2−1+8C24semidirect
13. H(9,𝔽2)C24semidirect
14. C2×#63103C24semidirect
15. C22×2−1+6C24semidirect
16. C22×H(7,𝔽2)C24semidirect
17. C23×#585C24semidirect
18. C24×H(5,𝔽2)C24semidirect
19. #63103C25semidirect
20. C2×2−1+6C25semidirect
21. C2×H(7,𝔽2)C25semidirect
22. C22×#585C25semidirect
23. C23×2−1+4C25semidirect
24. C23×H(5,𝔽2)C25semidirect
25. C24×#41C25semidirect
26. C25×D4C25semidirect
27. C27C26semidirect
28. 2−1+6C26semidirect
29. H(7,𝔽2)C26semidirect
30. C2×#585C26semidirect
31. C22×2−1+4C26semidirect
32. C22×H(5,𝔽2)C26semidirect
33. C23×#41C26semidirect
34. C24×Q8C26semidirect
35. C24×D4C26semidirect
36. C25×C4C26semidirect

Maximal subgroups

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

subgroupindex
C2×H(11,𝔽2)2
#722742912