Finite Group Databasebeta

← C2×#22582925 #31824294

Subgroups — C2×#22582925 #31824294

Order 17984.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22582925C2116yesmaximal, direct product factor
2C2×#17985139C212yesmaximal, complemented
3C2×#17985138C213yesmaximal, complemented
4C22×D1124C213yesmaximal, complemented
5C2×D4×D281C216yesmaximal, complemented
6C2×#41×C281C211yesmaximal, characteristic, complemented
7C23×D281C2216yescomplemented
8#17985139C22116yescomplemented
9#17985138C22124yescomplemented
10C2×Dic562C2211yescharacteristic, complemented
11C2×D1124C2216yescomplemented
12C2×D1124C2213yescomplemented
13C2×D1124C22124yescomplemented
14C2×C22⋊D281C2216yescomplemented
15D4×D281C22148yescomplemented
16C2×C4×D281C2216yescomplemented
17#41×C281C2218yescomplemented
18C2×Q8×C281C2211yescharacteristic, complemented
19C2×D4×C281C2213yescomplemented
20C22×C4×C281C2213yescomplemented
21C22×D281—412no—
22C22×D281C2316yes—
23C22×D281C23124yescomplemented
24Dic562C2314yescomplemented
25D1124C23124yescomplemented
26D1124C23112yescomplemented
27C22⋊D281C23124yescomplemented
28C2×Dic281C2312yes—
29C4×D281C23124yescomplemented
30C23×C281C2313yes—
31Q8×C281C2314yescomplemented
32D4×C281C23112yescomplemented
33C2×C4×C281C2311yescharacteristic
34C2×C4×C281C2313yes—
35C2×C4×C281C23112yescomplemented
36C22×C281—26no—
37C22×C281C2416yes—
38C22×C281C2411yescharacteristic
39C2×D281—212no—
40C2×D281—424no—
41C2×D281C24112yes—
42C4×C281C2412yes—
43C4×C281C2416yes—
44Dic281C2414yes—
45C2×C281—26no—
46C2×C281H(5,𝔽2)12yescomplemented
47C2×C281C2511yescharacteristic
48D281—212no—
49C281C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—2811nomaximal, Sylow
51H(5,𝔽2)—28116no—
52C2×#41—2812no—
53C2×#41—2813no—
54C2×#41D28111yescharacteristic, complemented
55C22×D4—2816no—
56C22×D4—2813no—
57C24—2816no—
58#41—28116no—
59#41—28124no—
60#41C2×D28118yescomplemented
61C2×Q8—2811no—
62C2×Q8C2×D28111yescharacteristic, complemented
63C2×D4—2816no—
64C2×D4—28148no—
65C2×D4—2816no—
66C2×D4—2813no—
67C2×D4—28124no—
68C2×D4C2×D28113yescomplemented
69C22×C4—2816no—
70C22×C4C2×D28113yescomplemented
71C23—2816no—
72C23—28124no—
73C23—112412no—
74C23C22×D28113yes—
75Q8—2814no—
76Q8C22×D28114yescomplemented
77D4—28124no—
78D4—28124no—
79D4—28112no—
80D4C22×D281112yescomplemented
81C2×C4—2812no—
82C2×C4—28124no—
83C2×C4C22×D28113yes—
84C2×C4C22×D28111yescharacteristic
85C2×C4C22×D281112yescomplemented
86C22—26no—
87C22—28112no—
88C22—56212no—
89C22—112424no—
90C22C23×D28116yes—
91C22C23×D28111yescharacteristic
92C4—2814no—
93C4C23×D28116yes—
94C4C23×D28112yes—
95C2—26no—
96C2—56212no—
97C2#2258292512yesdirect product factor
98C2C24×D28111yescharacteristic
subgroupG/H
centerC22C23×D281
commutator, cosocleC2×C281C25
FrattiniC2C24×D281
FittingC2×#41×C281C2
socleC22×C281C24
hypercenterC2×#41D281
hypocenterC281C2×H(5,𝔽2)
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #22582925C2direct (N × H)
2. C2×#17985139C2semidirect
3. C2×#17985138C2semidirect
4. C22×D1124C2semidirect
5. C2×D4×D281C2semidirect
6. C2×#41×C281C2semidirect
7. C23×D281C22semidirect
8. #17985139C22semidirect
9. #17985138C22semidirect
10. C2×Dic562C22semidirect
11. C2×D1124C22semidirect
12. C2×D1124C22semidirect
13. C2×D1124C22semidirect
14. C2×C22⋊D281C22semidirect
15. D4×D281C22semidirect
16. C2×C4×D281C22semidirect
17. #41×C281C22semidirect
18. C2×Q8×C281C22semidirect
19. C2×D4×C281C22semidirect
20. C22×C4×C281C22semidirect
23. C22×D281C23semidirect
24. Dic562C23semidirect
25. D1124C23semidirect
26. D1124C23semidirect
27. C22⋊D281C23semidirect
29. C4×D281C23semidirect
31. Q8×C281C23semidirect
32. D4×C281C23semidirect
35. C2×C4×C281C23semidirect
46. C2×C281H(5,𝔽2)semidirect
49. C281C2×H(5,𝔽2)semidirect
54. C2×#41D281semidirect
60. #41C2×D281semidirect
62. C2×Q8C2×D281semidirect
68. C2×D4C2×D281semidirect
70. C22×C4C2×D281semidirect
76. Q8C22×D281semidirect
80. D4C22×D281semidirect
85. C2×C4C22×D281semidirect
97. C2#22582925direct (N × H)

Maximal subgroups

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

subgroupindex
#225829252
C2×#179851392
C2×#179851382
C22×D11242
C2×D4×D2812
C2×#41×C2812
C2×H(5,𝔽2)281