Finite Group Databasebeta

← C2×#26015038 #36378618

Subgroups — C2×#26015038 #36378618

Order 22592.

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#26015038C2116yesmaximal, direct product factor
2C2×#19150738C212yesmaximal, complemented
3C2×#19150737C213yesmaximal, complemented
4C22×D1412C213yesmaximal, complemented
5C2×D4×D353C216yesmaximal, complemented
6C2×#41×C353C211yesmaximal, characteristic, complemented
7C23×D353C2216yescomplemented
8#19150738C22116yescomplemented
9#19150737C22124yescomplemented
10C2×Dic706C2211yescharacteristic, complemented
11C2×D1412C2216yescomplemented
12C2×D1412C2213yescomplemented
13C2×D1412C22124yescomplemented
14C2×C22⋊D353C2216yescomplemented
15D4×D353C22148yescomplemented
16C2×C4×D353C2216yescomplemented
17#41×C353C2218yescomplemented
18C2×Q8×C353C2211yescharacteristic, complemented
19C2×D4×C353C2213yescomplemented
20C22×C4×C353C2213yescomplemented
21C22×D353—412no—
22C22×D353C2316yes—
23C22×D353C23124yescomplemented
24Dic706C2314yescomplemented
25D1412C23124yescomplemented
26D1412C23112yescomplemented
27C22⋊D353C23124yescomplemented
28C2×Dic353C2312yes—
29C4×D353C23124yescomplemented
30C23×C353C2313yes—
31Q8×C353C2314yescomplemented
32D4×C353C23112yescomplemented
33C2×C4×C353C2311yescharacteristic
34C2×C4×C353C2313yes—
35C2×C4×C353C23112yescomplemented
36C22×C353—26no—
37C22×C353C2416yes—
38C22×C353C2411yescharacteristic
39C2×D353—212no—
40C2×D353—424no—
41C2×D353C24112yes—
42C4×C353C2412yes—
43C4×C353C2416yes—
44Dic353C2414yes—
45C2×C353—26no—
46C2×C353H(5,𝔽2)12yescomplemented
47C2×C353C2511yescharacteristic
48D353—212no—
49C353C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—3531nomaximal, Sylow
51H(5,𝔽2)—35316no—
52C2×#41—3532no—
53C2×#41—3533no—
54C2×#41D35311yescharacteristic, complemented
55C22×D4—3536no—
56C22×D4—3533no—
57C24—3536no—
58#41—35316no—
59#41—35324no—
60#41C2×D35318yescomplemented
61C2×Q8—3531no—
62C2×Q8C2×D35311yescharacteristic, complemented
63C2×D4—3536no—
64C2×D4—35348no—
65C2×D4—3536no—
66C2×D4—3533no—
67C2×D4—35324no—
68C2×D4C2×D35313yescomplemented
69C22×C4—3536no—
70C22×C4C2×D35313yescomplemented
71C23—35324no—
72C23—3536no—
73C23—141212no—
74C23C22×D35313yes—
75Q8—3534no—
76Q8C22×D35314yescomplemented
77D4—35324no—
78D4—35324no—
79D4—35312no—
80D4C22×D353112yescomplemented
81C2×C4—3532no—
82C2×C4—35324no—
83C2×C4C22×D35313yes—
84C2×C4C22×D35311yescharacteristic
85C2×C4C22×D353112yescomplemented
86C22—26no—
87C22—35312no—
88C22—141224no—
89C22—70612no—
90C22C23×D35316yes—
91C22C23×D35311yescharacteristic
92C4—3534no—
93C4C23×D35316yes—
94C4C23×D35312yes—
95C2—26no—
96C2—70612no—
97C2#2601503812yesdirect product factor
98C2C24×D35311yescharacteristic
subgroupG/H
centerC22C23×D353
commutator, cosocleC2×C353C25
FrattiniC2C24×D353
FittingC2×#41×C353C2
socleC22×C353C24
hypercenterC2×#41D353
hypocenterC353C2×H(5,𝔽2)
LCSG ▷ C2×C353 ▷ C353
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26015038C2direct (N × H)
2. C2×#19150738C2semidirect
3. C2×#19150737C2semidirect
4. C22×D1412C2semidirect
5. C2×D4×D353C2semidirect
6. C2×#41×C353C2semidirect
7. C23×D353C22semidirect
8. #19150738C22semidirect
9. #19150737C22semidirect
10. C2×Dic706C22semidirect
11. C2×D1412C22semidirect
12. C2×D1412C22semidirect
13. C2×D1412C22semidirect
14. C2×C22⋊D353C22semidirect
15. D4×D353C22semidirect
16. C2×C4×D353C22semidirect
17. #41×C353C22semidirect
18. C2×Q8×C353C22semidirect
19. C2×D4×C353C22semidirect
20. C22×C4×C353C22semidirect
23. C22×D353C23semidirect
24. Dic706C23semidirect
25. D1412C23semidirect
26. D1412C23semidirect
27. C22⋊D353C23semidirect
29. C4×D353C23semidirect
31. Q8×C353C23semidirect
32. D4×C353C23semidirect
35. C2×C4×C353C23semidirect
46. C2×C353H(5,𝔽2)semidirect
49. C353C2×H(5,𝔽2)semidirect
54. C2×#41D353semidirect
60. #41C2×D353semidirect
62. C2×Q8C2×D353semidirect
68. C2×D4C2×D353semidirect
70. C22×C4C2×D353semidirect
76. Q8C22×D353semidirect
80. D4C22×D353semidirect
85. C2×C4C22×D353semidirect
97. C2#26015038direct (N × H)

Maximal subgroups

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

subgroupindex
#260150382
C2×#191507382
C2×#191507372
C22×D14122
C2×D4×D3532
C2×#41×C3532
C2×H(5,𝔽2)353