Finite Group Databasebeta

← C2×#26045837 #37560252

Subgroups — C2×#26045837 #37560252

Order 23872.

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#26045837C2116yesmaximal, direct product factor
2C2×#20238610C212yesmaximal, complemented
3C2×#20238609C214yesmaximal, complemented
4C22×C22⋊D373C214yesmaximal, complemented
5C2×D4×D373C214yesmaximal, complemented
6C22×D4×C373C211yesmaximal, characteristic, complemented
7C23×D373C2214yescomplemented
8#20238610C22116yescomplemented
9#20238609C22132yescomplemented
10C2×Dic746C2212yescomplemented
11C2×D1492C2212yescomplemented
12C2×C22⋊D373C2218yescomplemented
13C2×C22⋊D373C2214yescomplemented
14C2×C22⋊D373C22132yescomplemented
15D4×D373C22132yescomplemented
16C22×Dic373C2214yescomplemented
17C2×C4×D373C2214yescomplemented
18C24×C373C2212yescomplemented
19C2×D4×C373C2214yescomplemented
20C2×D4×C373C2218yescomplemented
21C22×C4×C373C2211yescharacteristic, complemented
22C22×D373—48no—
23C22×D373C2314yes—
24C22×D373C23116yescomplemented
25Dic746C2318yescomplemented
26D1492C2318yescomplemented
27C22⋊D373C23132yescomplemented
28C22⋊D373C23116yescomplemented
29C2×Dic373C2314yes—
30C2×Dic373C23116yescomplemented
31C4×D373C23116yescomplemented
32C23×C373—44no—
33C23×C373C2314yes—
34C23×C373C2311yescharacteristic
35C23×C373C2318yescomplemented
36D4×C373C23116yescomplemented
37C2×C4×C373C2312yes—
38C2×C4×C373C2314yescomplemented
39C22×C373—22no—
40C22×C373—28no—
41C22×C373—48no—
42C22×C373C2412yes—
43C22×C373C2418yes—
44C22×C373C2411yescharacteristic
45C2×D373—28no—
46C2×D373—416no—
47C2×D373C2418yes—
48C4×C373C2414yes—
49Dic373C2418yes—
50C2×C373—28no—
51C2×C373—22no—
52C2×C373H(5,𝔽2)12yescomplemented
53C2×C373C2511yescharacteristic
54D373—28no—
55C373C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—3731nomaximal, Sylow
57H(5,𝔽2)—37316no—
58C2×#41—3734no—
59C2×#41—3732no—
60C22×D4—3734no—
61C22×D4—3734no—
62C22×D4D37311yescharacteristic, complemented
63C24—3734no—
64C24C2×D37312yescomplemented
65#41—37332no—
66#41—37316no—
67C2×Q8—3732no—
68C2×D4—3738no—
69C2×D4—3734no—
70C2×D4—37332no—
71C2×D4—37332no—
72C2×D4—3732no—
73C2×D4C2×D37314yescomplemented
74C2×D4C2×D37318yescomplemented
75C22×C4—3734no—
76C22×C4—3734no—
77C22×C4C2×D37311yescharacteristic, complemented
78C23—44no—
79C23—37316no—
80C23—3734no—
81C23—14928no—
82C23C22×D37314yes—
83C23C22×D37311yescharacteristic
84C23C22×D37318yescomplemented
85Q8—3738no—
86D4—37332no—
87D4—37316no—
88D4—3738no—
89D4C22×D373116yescomplemented
90C2×C4—37316no—
91C2×C4—3734no—
92C2×C4—37316no—
93C2×C4C22×D37312yes—
94C2×C4C22×D37314yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—3738no—
99C22—149216no—
100C22—7468no—
101C22C23×D37318yes—
102C22C23×D37312yes—
103C22C23×D37311yescharacteristic
104C4—3738no—
105C4C23×D37314yes—
106C2—22no—
107C2—28no—
108C2—7468no—
109C2#2604583712yesdirect product factor
110C2C24×D37311yescharacteristic
subgroupG/H
centerC22C23×D373
commutator, cosocleC2×C373C25
FrattiniC2C24×D373
FittingC22×D4×C373C2
socleC22×C373C24
hypercenterC22×D4D373
hypocenterC373C2×H(5,𝔽2)
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #26045837C2direct (N × H)
2. C2×#20238610C2semidirect
3. C2×#20238609C2semidirect
4. C22×C22⋊D373C2semidirect
5. C2×D4×D373C2semidirect
6. C22×D4×C373C2semidirect
7. C23×D373C22semidirect
8. #20238610C22semidirect
9. #20238609C22semidirect
10. C2×Dic746C22semidirect
11. C2×D1492C22semidirect
12. C2×C22⋊D373C22semidirect
13. C2×C22⋊D373C22semidirect
14. C2×C22⋊D373C22semidirect
15. D4×D373C22semidirect
16. C22×Dic373C22semidirect
17. C2×C4×D373C22semidirect
18. C24×C373C22semidirect
19. C2×D4×C373C22semidirect
20. C2×D4×C373C22semidirect
21. C22×C4×C373C22semidirect
24. C22×D373C23semidirect
25. Dic746C23semidirect
26. D1492C23semidirect
27. C22⋊D373C23semidirect
28. C22⋊D373C23semidirect
30. C2×Dic373C23semidirect
31. C4×D373C23semidirect
35. C23×C373C23semidirect
36. D4×C373C23semidirect
38. C2×C4×C373C23semidirect
52. C2×C373H(5,𝔽2)semidirect
55. C373C2×H(5,𝔽2)semidirect
62. C22×D4D373semidirect
64. C24C2×D373semidirect
73. C2×D4C2×D373semidirect
74. C2×D4C2×D373semidirect
77. C22×C4C2×D373semidirect
84. C23C22×D373semidirect
89. D4C22×D373semidirect
94. C2×C4C22×D373semidirect
109. C2#26045837direct (N × H)

Maximal subgroups

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

subgroupindex
#260458372
C2×#202386102
C2×#202386092
C22×C22⋊D3732
C2×D4×D3732
C22×D4×C3732
C2×H(5,𝔽2)373