Finite Group Databasebeta

← C2×#28381931 #43248547

Subgroups — C2×#28381931 #43248547

Order 28352.

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#28381931C2116yesmaximal, direct product factor
2C2×#20296787C212yesmaximal, complemented
3C2×#20296786C214yesmaximal, complemented
4C22×C22⋊D443C214yesmaximal, complemented
5C2×D4×D443C214yesmaximal, complemented
6C22×D4×C443C211yesmaximal, characteristic, complemented
7C23×D443C2214yescomplemented
8#20296787C22116yescomplemented
9#20296786C22132yescomplemented
10C2×Dic886C2212yescomplemented
11C2×D1772C2212yescomplemented
12C2×C22⋊D443C2218yescomplemented
13C2×C22⋊D443C2214yescomplemented
14C2×C22⋊D443C22132yescomplemented
15D4×D443C22132yescomplemented
16C22×Dic443C2214yescomplemented
17C2×C4×D443C2214yescomplemented
18C24×C443C2212yescomplemented
19C2×D4×C443C2214yescomplemented
20C2×D4×C443C2218yescomplemented
21C22×C4×C443C2211yescharacteristic, complemented
22C22×D443—48no—
23C22×D443C2314yes—
24C22×D443C23116yescomplemented
25Dic886C2318yescomplemented
26D1772C2318yescomplemented
27C22⋊D443C23132yescomplemented
28C22⋊D443C23116yescomplemented
29C2×Dic443C2314yes—
30C2×Dic443C23116yescomplemented
31C4×D443C23116yescomplemented
32C23×C443—44no—
33C23×C443C2311yescharacteristic
34C23×C443C2314yes—
35C23×C443C2318yescomplemented
36D4×C443C23116yescomplemented
37C2×C4×C443C2312yes—
38C2×C4×C443C2314yescomplemented
39C22×C443—22no—
40C22×C443—28no—
41C22×C443—48no—
42C22×C443C2412yes—
43C22×C443C2418yes—
44C22×C443C2411yescharacteristic
45C2×D443—28no—
46C2×D443—416no—
47C2×D443C2418yes—
48C4×C443C2414yes—
49Dic443C2418yes—
50C2×C443—28no—
51C2×C443—22no—
52C2×C443H(5,𝔽2)12yescomplemented
53C2×C443C2511yescharacteristic
54D443—28no—
55C443C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—4431nomaximal, Sylow
57H(5,𝔽2)—44316no—
58C2×#41—4434no—
59C2×#41—4432no—
60C22×D4—4434no—
61C22×D4—4434no—
62C22×D4D44311yescharacteristic, complemented
63C24—4434no—
64C24C2×D44312yescomplemented
65#41—44332no—
66#41—44316no—
67C2×Q8—4432no—
68C2×D4—4438no—
69C2×D4—4434no—
70C2×D4—44332no—
71C2×D4—44332no—
72C2×D4—4432no—
73C2×D4C2×D44314yescomplemented
74C2×D4C2×D44318yescomplemented
75C22×C4—4434no—
76C22×C4—4434no—
77C22×C4C2×D44311yescharacteristic, complemented
78C23—44no—
79C23—4434no—
80C23—44316no—
81C23—17728no—
82C23C22×D44314yes—
83C23C22×D44311yescharacteristic
84C23C22×D44318yescomplemented
85Q8—4438no—
86D4—44332no—
87D4—44316no—
88D4—4438no—
89D4C22×D443116yescomplemented
90C2×C4—44316no—
91C2×C4—4434no—
92C2×C4—44316no—
93C2×C4C22×D44312yes—
94C2×C4C22×D44314yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—8868no—
99C22—4438no—
100C22—177216no—
101C22C23×D44318yes—
102C22C23×D44312yes—
103C22C23×D44311yescharacteristic
104C4—4438no—
105C4C23×D44314yes—
106C2—22no—
107C2—28no—
108C2—8868no—
109C2#2838193112yesdirect product factor
110C2C24×D44311yescharacteristic
subgroupG/H
centerC22C23×D443
commutator, cosocleC2×C443C25
FrattiniC2C24×D443
FittingC22×D4×C443C2
socleC22×C443C24
hypercenterC22×D4D443
hypocenterC443C2×H(5,𝔽2)
LCSG ▷ C2×C443 ▷ C443
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #28381931C2direct (N × H)
2. C2×#20296787C2semidirect
3. C2×#20296786C2semidirect
4. C22×C22⋊D443C2semidirect
5. C2×D4×D443C2semidirect
6. C22×D4×C443C2semidirect
7. C23×D443C22semidirect
8. #20296787C22semidirect
9. #20296786C22semidirect
10. C2×Dic886C22semidirect
11. C2×D1772C22semidirect
12. C2×C22⋊D443C22semidirect
13. C2×C22⋊D443C22semidirect
14. C2×C22⋊D443C22semidirect
15. D4×D443C22semidirect
16. C22×Dic443C22semidirect
17. C2×C4×D443C22semidirect
18. C24×C443C22semidirect
19. C2×D4×C443C22semidirect
20. C2×D4×C443C22semidirect
21. C22×C4×C443C22semidirect
24. C22×D443C23semidirect
25. Dic886C23semidirect
26. D1772C23semidirect
27. C22⋊D443C23semidirect
28. C22⋊D443C23semidirect
30. C2×Dic443C23semidirect
31. C4×D443C23semidirect
35. C23×C443C23semidirect
36. D4×C443C23semidirect
38. C2×C4×C443C23semidirect
52. C2×C443H(5,𝔽2)semidirect
55. C443C2×H(5,𝔽2)semidirect
62. C22×D4D443semidirect
64. C24C2×D443semidirect
73. C2×D4C2×D443semidirect
74. C2×D4C2×D443semidirect
77. C22×C4C2×D443semidirect
84. C23C22×D443semidirect
89. D4C22×D443semidirect
94. C2×C4C22×D443semidirect
109. C2#28381931direct (N × H)

Maximal subgroups

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

subgroupindex
#283819312
C2×#202967872
C2×#202967862
C22×C22⋊D4432
C2×D4×D4432
C22×D4×C4432
C2×H(5,𝔽2)443