Finite Group Databasebeta

← C2×#23756465 #34094637

Subgroups — C2×#23756465 #34094637

Order 20032.

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×D313C211yesmaximal, characteristic, complemented
2C22×C22⋊D313C212yesmaximal, complemented
3#23756465C218yesmaximal, direct product factor
4C2×C22⋊Dic313C211yesmaximal, characteristic, complemented
5C2×#19097538C212yesmaximal, complemented
6C22×D4×C313C211yesmaximal, characteristic, complemented
7C23×D313—28no—
8C23×D313—24no—
9C23×D313C2212yes—
10C23×D313C2214yescomplemented
11C2×C22⋊D313—28no—
12C2×C22⋊D313C2218yescomplemented
13C22×Dic313C2212yescomplemented
14C22⋊Dic313C2214yescomplemented
15#19097538C2218yescomplemented
16C24×C313C2211yescharacteristic
17C24×C313C2211yescharacteristic, complemented
18C2×D4×C313—24no—
19C2×D4×C313C2214yescomplemented
20C22×C4×C313C2211yescharacteristic, complemented
21C22×D313—232no—
22C22×D313—24no—
23C22×D313—24no—
24C22×D313—28no—
25C22×D313—216no—
26C22×D313D418yescomplemented
27C22×D313C2314yes—
28C22⋊D313—216no—
29C2×Dic313—24no—
30C2×Dic313C2314yescomplemented
31C23×C313—24no—
32C23×C313—22no—
33C23×C313—24no—
34C23×C313D414yescomplemented
35C23×C313C2312yes—
36C23×C313C2311yescharacteristic
37C23×C313C2312yescomplemented
38D4×C313—28no—
39C2×C4×C313—22no—
40C2×C4×C313C2312yescomplemented
41C22×C313—28no—
42C22×C313—24no—
43C22×C313—22no—
44C22×C313—24no—
45C22×C313—44no—
46C22×C313C2×D414yes—
47C22×C313C2×D412yes—
48C22×C313C2×D414yescomplemented
49C22×C313C2411yescharacteristic
50C2×D313—232no—
51C2×D313—216no—
52C2×D313—24no—
53C2×D313—24no—
54C2×D313C2×D418yescomplemented
55C4×C313—22no—
56Dic313—24no—
57C2×C313—24no—
58C2×C313—42no—
59C2×C313#12014yescomplemented
60C2×C313C22×D412yes—
61C2×C313C22×D411yescharacteristic
62D313—28no—
63C313C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—3131nomaximal, Sylow
65C25—3131no—
66C22×D4—3132no—
67C22×D4D31311yescharacteristic, complemented
68#120—3138no—
69C2×C22⋊C4—3131no—
70C2×C22⋊C4—3132no—
71C24—3132no—
72C24—3134no—
73C24—6268no—
74C24—6264no—
75C24C2×D31311yescharacteristic
76C24C2×D31311yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—3138no—
79C2×D4—6268no—
80C2×D4C2×D31314yescomplemented
81C22×C4—3132no—
82C22×C4C2×D31311yescharacteristic, complemented
83C22⋊C4—3134no—
84C22⋊C4—3138no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—3138no—
89C23—3134no—
90C23—62616no—
91C23—62632no—
92C23—6264no—
93C23—6264no—
94C23—6268no—
95C23C22⋊D31314yescomplemented
96C23C22×D31312yes—
97C23C22×D31311yescharacteristic
98C23C22×D31312yescomplemented
99D4—28no—
100D4—62616no—
101C2×C4—22no—
102C2×C4—3134no—
103C2×C4—6264no—
104C2×C4C22×D31312yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—3138no—
111C22—62632no—
112C22—62616no—
113C22—6264no—
114C22—6264no—
115C22D4×D31314yes—
116C22C2×C22⋊D31312yes—
117C22C2×C22⋊D31314yescomplemented
118C22C23×D31311yescharacteristic
119C4—22no—
120C4—6264no—
121C2—24no—
122C2—42no—
123C2—6268no—
124C2#2375646514yesdirect product factor
125C2C2×D4×D31312yes—
126C2C22×C22⋊D31311yescharacteristic
subgroupG/H
centerC23C22×D313
commutator, cosocleC22×C313C24
FrattiniC22C23×D313
FittingC22×D4×C313C2
socleC23×C313C23
hypercenterC22×D4D313
hypocenterC313C2×#120
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D313C2semidirect
2. C22×C22⋊D313C2semidirect
3. #23756465C2direct (N × H)
4. C2×C22⋊Dic313C2semidirect
5. C2×#19097538C2semidirect
6. C22×D4×C313C2semidirect
10. C23×D313C22semidirect
12. C2×C22⋊D313C22semidirect
13. C22×Dic313C22semidirect
14. C22⋊Dic313C22semidirect
15. #19097538C22semidirect
17. C24×C313C22semidirect
19. C2×D4×C313C22semidirect
20. C22×C4×C313C22semidirect
26. C22×D313D4semidirect
30. C2×Dic313C23semidirect
34. C23×C313D4semidirect
37. C23×C313C23semidirect
40. C2×C4×C313C23semidirect
48. C22×C313C2×D4semidirect
54. C2×D313C2×D4semidirect
59. C2×C313#120semidirect
63. C313C2×#120semidirect
67. C22×D4D313semidirect
76. C24C2×D313semidirect
80. C2×D4C2×D313semidirect
82. C22×C4C2×D313semidirect
95. C23C22⋊D313semidirect
98. C23C22×D313semidirect
104. C2×C4C22×D313semidirect
117. C22C2×C22⋊D313semidirect
124. C2#23756465direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3132
C22×C22⋊D3132
#237564652
C2×C22⋊Dic3132
C2×#190975382
C22×D4×C3132
C2×#120313