Finite Group Databasebeta

← C2×#23756543 #34094983

Subgroups — C2×#23756543 #34094983

Order 20032.

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#23756543C2116yesmaximal, direct product factor
2C2×#19097562C212yesmaximal, complemented
3C2×#19097561C213yesmaximal, complemented
4C22×D1252C213yesmaximal, complemented
5C2×D4×D313C216yesmaximal, complemented
6C2×#41×C313C211yesmaximal, characteristic, complemented
7C23×D313C2216yescomplemented
8#19097562C22116yescomplemented
9#19097561C22124yescomplemented
10C2×Dic626C2211yescharacteristic, complemented
11C2×D1252C2216yescomplemented
12C2×D1252C2213yescomplemented
13C2×D1252C22124yescomplemented
14C2×C22⋊D313C2216yescomplemented
15D4×D313C22148yescomplemented
16C2×C4×D313C2216yescomplemented
17#41×C313C2218yescomplemented
18C2×Q8×C313C2211yescharacteristic, complemented
19C2×D4×C313C2213yescomplemented
20C22×C4×C313C2213yescomplemented
21C22×D313—412no—
22C22×D313C2316yes—
23C22×D313C23124yescomplemented
24Dic626C2314yescomplemented
25D1252C23124yescomplemented
26D1252C23112yescomplemented
27C22⋊D313C23124yescomplemented
28C2×Dic313C2312yes—
29C4×D313C23124yescomplemented
30C23×C313C2313yes—
31Q8×C313C2314yescomplemented
32D4×C313C23112yescomplemented
33C2×C4×C313C2311yescharacteristic
34C2×C4×C313C2313yes—
35C2×C4×C313C23112yescomplemented
36C22×C313—26no—
37C22×C313C2416yes—
38C22×C313C2411yescharacteristic
39C2×D313—212no—
40C2×D313—424no—
41C2×D313C24112yes—
42C4×C313C2412yes—
43C4×C313C2416yes—
44Dic313C2414yes—
45C2×C313—26no—
46C2×C313H(5,𝔽2)12yescomplemented
47C2×C313C2511yescharacteristic
48D313—212no—
49C313C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—3131nomaximal, Sylow
51H(5,𝔽2)—31316no—
52C2×#41—3132no—
53C2×#41—3133no—
54C2×#41D31311yescharacteristic, complemented
55C22×D4—3136no—
56C22×D4—3133no—
57C24—3136no—
58#41—31316no—
59#41—31324no—
60#41C2×D31318yescomplemented
61C2×Q8—3131no—
62C2×Q8C2×D31311yescharacteristic, complemented
63C2×D4—3136no—
64C2×D4—31348no—
65C2×D4—3136no—
66C2×D4—3133no—
67C2×D4—31324no—
68C2×D4C2×D31313yescomplemented
69C22×C4—3136no—
70C22×C4C2×D31313yescomplemented
71C23—3136no—
72C23—31324no—
73C23—125212no—
74C23C22×D31313yes—
75Q8—3134no—
76Q8C22×D31314yescomplemented
77D4—31324no—
78D4—31324no—
79D4—31312no—
80D4C22×D313112yescomplemented
81C2×C4—3132no—
82C2×C4—31324no—
83C2×C4C22×D31313yes—
84C2×C4C22×D31311yescharacteristic
85C2×C4C22×D313112yescomplemented
86C22—26no—
87C22—31312no—
88C22—62612no—
89C22—125224no—
90C22C23×D31316yes—
91C22C23×D31311yescharacteristic
92C4—3134no—
93C4C23×D31316yes—
94C4C23×D31312yes—
95C2—26no—
96C2—62612no—
97C2#2375654312yesdirect product factor
98C2C24×D31311yescharacteristic
subgroupG/H
centerC22C23×D313
commutator, cosocleC2×C313C25
FrattiniC2C24×D313
FittingC2×#41×C313C2
socleC22×C313C24
hypercenterC2×#41D313
hypocenterC313C2×H(5,𝔽2)
LCSG ▷ C2×C313 ▷ C313
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23756543C2direct (N × H)
2. C2×#19097562C2semidirect
3. C2×#19097561C2semidirect
4. C22×D1252C2semidirect
5. C2×D4×D313C2semidirect
6. C2×#41×C313C2semidirect
7. C23×D313C22semidirect
8. #19097562C22semidirect
9. #19097561C22semidirect
10. C2×Dic626C22semidirect
11. C2×D1252C22semidirect
12. C2×D1252C22semidirect
13. C2×D1252C22semidirect
14. C2×C22⋊D313C22semidirect
15. D4×D313C22semidirect
16. C2×C4×D313C22semidirect
17. #41×C313C22semidirect
18. C2×Q8×C313C22semidirect
19. C2×D4×C313C22semidirect
20. C22×C4×C313C22semidirect
23. C22×D313C23semidirect
24. Dic626C23semidirect
25. D1252C23semidirect
26. D1252C23semidirect
27. C22⋊D313C23semidirect
29. C4×D313C23semidirect
31. Q8×C313C23semidirect
32. D4×C313C23semidirect
35. C2×C4×C313C23semidirect
46. C2×C313H(5,𝔽2)semidirect
49. C313C2×H(5,𝔽2)semidirect
54. C2×#41D313semidirect
60. #41C2×D313semidirect
62. C2×Q8C2×D313semidirect
68. C2×D4C2×D313semidirect
70. C22×C4C2×D313semidirect
76. Q8C22×D313semidirect
80. D4C22×D313semidirect
85. C2×C4C22×D313semidirect
97. C2#23756543direct (N × H)

Maximal subgroups

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

subgroupindex
#237565432
C2×#190975622
C2×#190975612
C22×D12522
C2×D4×D3132
C2×#41×C3132
C2×H(5,𝔽2)313