Finite Group Databasebeta

← C2×#26045760 #37559907

Subgroups — C2×#26045760 #37559907

Order 23872.

662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C24×D373C211yesmaximal, characteristic, complemented
2C22×C22⋊D373C212yesmaximal, complemented
3#26045760C218yesmaximal, direct product factor
4C2×C22⋊Dic373C211yesmaximal, characteristic, complemented
5C2×#20238587C212yesmaximal, complemented
6C22×D4×C373C211yesmaximal, characteristic, complemented
7C23×D373—28no—
8C23×D373—24no—
9C23×D373C2212yes—
10C23×D373C2214yescomplemented
11C2×C22⋊D373—28no—
12C2×C22⋊D373C2218yescomplemented
13C22×Dic373C2212yescomplemented
14C22⋊Dic373C2214yescomplemented
15#20238587C2218yescomplemented
16C24×C373C2211yescharacteristic
17C24×C373C2211yescharacteristic, complemented
18C2×D4×C373—24no—
19C2×D4×C373C2214yescomplemented
20C22×C4×C373C2211yescharacteristic, complemented
21C22×D373—232no—
22C22×D373—24no—
23C22×D373—24no—
24C22×D373—28no—
25C22×D373—216no—
26C22×D373D418yescomplemented
27C22×D373C2314yes—
28C22⋊D373—216no—
29C2×Dic373—24no—
30C2×Dic373C2314yescomplemented
31C23×C373—24no—
32C23×C373—24no—
33C23×C373—22no—
34C23×C373D414yescomplemented
35C23×C373C2312yes—
36C23×C373C2311yescharacteristic
37C23×C373C2312yescomplemented
38D4×C373—28no—
39C2×C4×C373—22no—
40C2×C4×C373C2312yescomplemented
41C22×C373—28no—
42C22×C373—24no—
43C22×C373—22no—
44C22×C373—24no—
45C22×C373—44no—
46C22×C373C2×D414yes—
47C22×C373C2×D412yes—
48C22×C373C2×D414yescomplemented
49C22×C373C2411yescharacteristic
50C2×D373—232no—
51C2×D373—216no—
52C2×D373—24no—
53C2×D373—24no—
54C2×D373C2×D418yescomplemented
55C4×C373—22no—
56Dic373—24no—
57C2×C373—24no—
58C2×C373—42no—
59C2×C373#12014yescomplemented
60C2×C373C22×D412yes—
61C2×C373C22×D411yescharacteristic
62D373—28no—
63C373C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—3731nomaximal, Sylow
65C25—3731no—
66C22×D4—3732no—
67C22×D4D37311yescharacteristic, complemented
68#120—3738no—
69C2×C22⋊C4—3731no—
70C2×C22⋊C4—3732no—
71C24—3732no—
72C24—3734no—
73C24—7468no—
74C24—7464no—
75C24C2×D37311yescharacteristic
76C24C2×D37311yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—3738no—
79C2×D4—7468no—
80C2×D4C2×D37314yescomplemented
81C22×C4—3732no—
82C22×C4C2×D37311yescharacteristic, complemented
83C22⋊C4—3734no—
84C22⋊C4—3738no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—3738no—
89C23—3734no—
90C23—74616no—
91C23—74632no—
92C23—7464no—
93C23—7464no—
94C23—7468no—
95C23C22⋊D37314yescomplemented
96C23C22×D37312yes—
97C23C22×D37311yescharacteristic
98C23C22×D37312yescomplemented
99D4—28no—
100D4—74616no—
101C2×C4—22no—
102C2×C4—3734no—
103C2×C4—7464no—
104C2×C4C22×D37312yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—3738no—
111C22—74632no—
112C22—74616no—
113C22—7464no—
114C22—7464no—
115C22D4×D37314yes—
116C22C2×C22⋊D37312yes—
117C22C2×C22⋊D37314yescomplemented
118C22C23×D37311yescharacteristic
119C4—22no—
120C4—7464no—
121C2—24no—
122C2—42no—
123C2—7468no—
124C2#2604576014yesdirect product factor
125C2C2×D4×D37312yes—
126C2C22×C22⋊D37311yescharacteristic
subgroupG/H
centerC23C22×D373
commutator, cosocleC22×C373C24
FrattiniC22C23×D373
FittingC22×D4×C373C2
socleC23×C373C23
hypercenterC22×D4D373
hypocenterC373C2×#120
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D373C2semidirect
2. C22×C22⋊D373C2semidirect
3. #26045760C2direct (N × H)
4. C2×C22⋊Dic373C2semidirect
5. C2×#20238587C2semidirect
6. C22×D4×C373C2semidirect
10. C23×D373C22semidirect
12. C2×C22⋊D373C22semidirect
13. C22×Dic373C22semidirect
14. C22⋊Dic373C22semidirect
15. #20238587C22semidirect
17. C24×C373C22semidirect
19. C2×D4×C373C22semidirect
20. C22×C4×C373C22semidirect
26. C22×D373D4semidirect
30. C2×Dic373C23semidirect
34. C23×C373D4semidirect
37. C23×C373C23semidirect
40. C2×C4×C373C23semidirect
48. C22×C373C2×D4semidirect
54. C2×D373C2×D4semidirect
59. C2×C373#120semidirect
63. C373C2×#120semidirect
67. C22×D4D373semidirect
76. C24C2×D373semidirect
80. C2×D4C2×D373semidirect
82. C22×C4C2×D373semidirect
95. C23C22⋊D373semidirect
98. C23C22×D373semidirect
104. C2×C4C22×D373semidirect
117. C22C2×C22⋊D373semidirect
124. C2#26045760direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3732
C22×C22⋊D3732
#260457602
C2×C22⋊Dic3732
C2×#202385872
C22×D4×C3732
C2×#120373