Finite Group Databasebeta

← C2×#22554515 #30682768

Subgroups — C2×#22554515 #30682768

Order 16832.

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#22554515C2116yesmaximal, direct product factor
2C2×#16862376C212yesmaximal, complemented
3C2×#16862375C214yesmaximal, complemented
4C22×C22⋊D263C214yesmaximal, complemented
5C2×D4×D263C214yesmaximal, complemented
6C22×D4×C263C211yesmaximal, characteristic, complemented
7C23×D263C2214yescomplemented
8#16862376C22116yescomplemented
9#16862375C22132yescomplemented
10C2×Dic526C2212yescomplemented
11C2×D1052C2212yescomplemented
12C2×C22⋊D263C2218yescomplemented
13C2×C22⋊D263C2214yescomplemented
14C2×C22⋊D263C22132yescomplemented
15D4×D263C22132yescomplemented
16C22×Dic263C2214yescomplemented
17C2×C4×D263C2214yescomplemented
18C24×C263C2212yescomplemented
19C2×D4×C263C2214yescomplemented
20C2×D4×C263C2218yescomplemented
21C22×C4×C263C2211yescharacteristic, complemented
22C22×D263—48no—
23C22×D263C2314yes—
24C22×D263C23116yescomplemented
25Dic526C2318yescomplemented
26D1052C2318yescomplemented
27C22⋊D263C23132yescomplemented
28C22⋊D263C23116yescomplemented
29C2×Dic263C2314yes—
30C2×Dic263C23116yescomplemented
31C4×D263C23116yescomplemented
32C23×C263—44no—
33C23×C263C2311yescharacteristic
34C23×C263C2314yes—
35C23×C263C2318yescomplemented
36D4×C263C23116yescomplemented
37C2×C4×C263C2312yes—
38C2×C4×C263C2314yescomplemented
39C22×C263—22no—
40C22×C263—28no—
41C22×C263—48no—
42C22×C263C2412yes—
43C22×C263C2418yes—
44C22×C263C2411yescharacteristic
45C2×D263—28no—
46C2×D263—416no—
47C2×D263C2418yes—
48C4×C263C2414yes—
49Dic263C2418yes—
50C2×C263—28no—
51C2×C263—22no—
52C2×C263H(5,𝔽2)12yescomplemented
53C2×C263C2511yescharacteristic
54D263—28no—
55C263C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—2631nomaximal, Sylow
57H(5,𝔽2)—26316no—
58C2×#41—2634no—
59C2×#41—2632no—
60C22×D4—2634no—
61C22×D4—2634no—
62C22×D4D26311yescharacteristic, complemented
63C24—2634no—
64C24C2×D26312yescomplemented
65#41—26332no—
66#41—26316no—
67C2×Q8—2632no—
68C2×D4—2638no—
69C2×D4—2634no—
70C2×D4—26332no—
71C2×D4—26332no—
72C2×D4—2632no—
73C2×D4C2×D26314yescomplemented
74C2×D4C2×D26318yescomplemented
75C22×C4—2634no—
76C22×C4—2634no—
77C22×C4C2×D26311yescharacteristic, complemented
78C23—44no—
79C23—2634no—
80C23—26316no—
81C23—10528no—
82C23C22×D26314yes—
83C23C22×D26311yescharacteristic
84C23C22×D26318yescomplemented
85Q8—2638no—
86D4—26332no—
87D4—26316no—
88D4—2638no—
89D4C22×D263116yescomplemented
90C2×C4—26316no—
91C2×C4—2634no—
92C2×C4—26316no—
93C2×C4C22×D26312yes—
94C2×C4C22×D26314yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—2638no—
99C22—5268no—
100C22—105216no—
101C22C23×D26318yes—
102C22C23×D26312yes—
103C22C23×D26311yescharacteristic
104C4—2638no—
105C4C23×D26314yes—
106C2—22no—
107C2—28no—
108C2—5268no—
109C2#2255451512yesdirect product factor
110C2C24×D26311yescharacteristic
subgroupG/H
centerC22C23×D263
commutator, cosocleC2×C263C25
FrattiniC2C24×D263
FittingC22×D4×C263C2
socleC22×C263C24
hypercenterC22×D4D263
hypocenterC263C2×H(5,𝔽2)
LCSG ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #22554515C2direct (N × H)
2. C2×#16862376C2semidirect
3. C2×#16862375C2semidirect
4. C22×C22⋊D263C2semidirect
5. C2×D4×D263C2semidirect
6. C22×D4×C263C2semidirect
7. C23×D263C22semidirect
8. #16862376C22semidirect
9. #16862375C22semidirect
10. C2×Dic526C22semidirect
11. C2×D1052C22semidirect
12. C2×C22⋊D263C22semidirect
13. C2×C22⋊D263C22semidirect
14. C2×C22⋊D263C22semidirect
15. D4×D263C22semidirect
16. C22×Dic263C22semidirect
17. C2×C4×D263C22semidirect
18. C24×C263C22semidirect
19. C2×D4×C263C22semidirect
20. C2×D4×C263C22semidirect
21. C22×C4×C263C22semidirect
24. C22×D263C23semidirect
25. Dic526C23semidirect
26. D1052C23semidirect
27. C22⋊D263C23semidirect
28. C22⋊D263C23semidirect
30. C2×Dic263C23semidirect
31. C4×D263C23semidirect
35. C23×C263C23semidirect
36. D4×C263C23semidirect
38. C2×C4×C263C23semidirect
52. C2×C263H(5,𝔽2)semidirect
55. C263C2×H(5,𝔽2)semidirect
62. C22×D4D263semidirect
64. C24C2×D263semidirect
73. C2×D4C2×D263semidirect
74. C2×D4C2×D263semidirect
77. C22×C4C2×D263semidirect
84. C23C22×D263semidirect
89. D4C22×D263semidirect
94. C2×C4C22×D263semidirect
109. C2#22554515direct (N × H)

Maximal subgroups

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

subgroupindex
#225545152
C2×#168623762
C2×#168623752
C22×C22⋊D2632
C2×D4×D2632
C22×D4×C2632
C2×H(5,𝔽2)263