Finite Group Databasebeta

← C2×#20259867 #27135744

Subgroups — C2×#20259867 #27135744

Order 12352.

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×D193C211yesmaximal, characteristic, complemented
2C22×C22⋊D193C212yesmaximal, complemented
3#20259867C218yesmaximal, direct product factor
4C2×C22⋊Dic193C211yesmaximal, characteristic, complemented
5C2×#15690532C212yesmaximal, complemented
6C22×D4×C193C211yesmaximal, characteristic, complemented
7C23×D193—28no—
8C23×D193—24no—
9C23×D193C2212yes—
10C23×D193C2214yescomplemented
11C2×C22⋊D193—28no—
12C2×C22⋊D193C2218yescomplemented
13C22×Dic193C2212yescomplemented
14C22⋊Dic193C2214yescomplemented
15#15690532C2218yescomplemented
16C24×C193C2211yescharacteristic
17C24×C193C2211yescharacteristic, complemented
18C2×D4×C193—24no—
19C2×D4×C193C2214yescomplemented
20C22×C4×C193C2211yescharacteristic, complemented
21C22×D193—232no—
22C22×D193—24no—
23C22×D193—24no—
24C22×D193—28no—
25C22×D193—216no—
26C22×D193D418yescomplemented
27C22×D193C2314yes—
28C22⋊D193—216no—
29C2×Dic193—24no—
30C2×Dic193C2314yescomplemented
31C23×C193—24no—
32C23×C193—22no—
33C23×C193—24no—
34C23×C193D414yescomplemented
35C23×C193C2312yes—
36C23×C193C2311yescharacteristic
37C23×C193C2312yescomplemented
38D4×C193—28no—
39C2×C4×C193—22no—
40C2×C4×C193C2312yescomplemented
41C22×C193—28no—
42C22×C193—24no—
43C22×C193—22no—
44C22×C193—24no—
45C22×C193—44no—
46C22×C193C2×D414yes—
47C22×C193C2×D412yes—
48C22×C193C2×D414yescomplemented
49C22×C193C2411yescharacteristic
50C2×D193—232no—
51C2×D193—216no—
52C2×D193—24no—
53C2×D193—24no—
54C2×D193C2×D418yescomplemented
55C4×C193—22no—
56Dic193—24no—
57C2×C193—24no—
58C2×C193—42no—
59C2×C193#12014yescomplemented
60C2×C193C22×D412yes—
61C2×C193C22×D411yescharacteristic
62D193—28no—
63C193C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—1931nomaximal, Sylow
65C25—1931no—
66C22×D4—1932no—
67C22×D4D19311yescharacteristic, complemented
68#120—1938no—
69C2×C22⋊C4—1931no—
70C2×C22⋊C4—1932no—
71C24—3868no—
72C24—3864no—
73C24—1934no—
74C24—1932no—
75C24C2×D19311yescharacteristic
76C24C2×D19311yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—3868no—
79C2×D4—1938no—
80C2×D4C2×D19314yescomplemented
81C22×C4—1932no—
82C22×C4C2×D19311yescharacteristic, complemented
83C22⋊C4—1934no—
84C22⋊C4—1938no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—38632no—
89C23—38616no—
90C23—3864no—
91C23—3864no—
92C23—3868no—
93C23—1938no—
94C23—1934no—
95C23C22⋊D19314yescomplemented
96C23C22×D19312yes—
97C23C22×D19311yescharacteristic
98C23C22×D19312yescomplemented
99D4—28no—
100D4—38616no—
101C2×C4—22no—
102C2×C4—3864no—
103C2×C4—1934no—
104C2×C4C22×D19312yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—38632no—
111C22—38616no—
112C22—3864no—
113C22—3864no—
114C22—1938no—
115C22D4×D19314yes—
116C22C2×C22⋊D19312yes—
117C22C2×C22⋊D19314yescomplemented
118C22C23×D19311yescharacteristic
119C4—22no—
120C4—3864no—
121C2—24no—
122C2—42no—
123C2—3868no—
124C2#2025986714yesdirect product factor
125C2C2×D4×D19312yes—
126C2C22×C22⋊D19311yescharacteristic
subgroupG/H
centerC23C22×D193
commutator, cosocleC22×C193C24
FrattiniC22C23×D193
FittingC22×D4×C193C2
socleC23×C193C23
hypercenterC22×D4D193
hypocenterC193C2×#120
LCSG ▷ C22×C193 ▷ C193
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D193C2semidirect
2. C22×C22⋊D193C2semidirect
3. #20259867C2direct (N × H)
4. C2×C22⋊Dic193C2semidirect
5. C2×#15690532C2semidirect
6. C22×D4×C193C2semidirect
10. C23×D193C22semidirect
12. C2×C22⋊D193C22semidirect
13. C22×Dic193C22semidirect
14. C22⋊Dic193C22semidirect
15. #15690532C22semidirect
17. C24×C193C22semidirect
19. C2×D4×C193C22semidirect
20. C22×C4×C193C22semidirect
26. C22×D193D4semidirect
30. C2×Dic193C23semidirect
34. C23×C193D4semidirect
37. C23×C193C23semidirect
40. C2×C4×C193C23semidirect
48. C22×C193C2×D4semidirect
54. C2×D193C2×D4semidirect
59. C2×C193#120semidirect
63. C193C2×#120semidirect
67. C22×D4D193semidirect
76. C24C2×D193semidirect
80. C2×D4C2×D193semidirect
82. C22×C4C2×D193semidirect
95. C23C22⋊D193semidirect
98. C23C22×D193semidirect
104. C2×C4C22×D193semidirect
117. C22C2×C22⋊D193semidirect
124. C2#20259867direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D1932
C22×C22⋊D1932
#202598672
C2×C22⋊Dic1932
C2×#156905322
C22×D4×C1932
C2×#120193