Finite Group Databasebeta

← C2×D3×D4×C13 #11929289

Subgroups — C2×D3×D4×C13 #11929289

Order 1248.

472 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 194 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
1C23×D3×C13C212yesmaximal, complemented
2C2×C3×D4×C13C211yesmaximal, characteristic, complemented
3C2×C13×#67C212yesmaximal, complemented
4D3×D4×C13C218yesmaximal, direct product factor
5C2×C13×D12C211yesmaximal, characteristic, complemented
6C2×C4×D3×C13C211yesmaximal, characteristic, complemented
7C22×D4×C13—31nomaximal, Hall
8C23×C3×C13C2212yescomplemented
9C22×D3×C13—28no—
10C22×D3×C13C2211yescharacteristic
11C22×D3×C13C2218yescomplemented
12C22×D3×C13C2212yescomplemented
13C3×D4×C13C2214yescomplemented
14C2×C3×C4×C13C2211yescharacteristic, complemented
15C13×#67C2218yescomplemented
16C2×Dic3×C13C2211yescharacteristic, complemented
17C13×D12C2214yescomplemented
18C4×D3×C13C2214yescomplemented
19C24×C13—32no—
20C2×D4×C13—32no—
21C2×D4×C13—38no—
22C2×D4×C13—31no—
23C2×D4×C13D311yescharacteristic, direct product factor
24C22×C4×C13—31no—
25C22×C3×C13—24no—
26C22×C3×C13C2311yescharacteristic
27C22×C3×C13C2314yescomplemented
28C2×D3×C13—24no—
29C2×D3×C13—216no—
30C2×D3×C13D414yesdirect product factor
31C2×D3×C13C2312yes—
32C2×D3×C13C2314yescomplemented
33C3×C4×C13C2312yescomplemented
34Dic3×C13C2312yescomplemented
35C23×C13—31no—
36C23×C13—32no—
37C23×C13—38no—
38C23×C13—68no—
39C23×C13C2×D312yescomplemented
40D4×C13—38no—
41D4×C13—34no—
42D4×C13C2×D314yesdirect product factor
43C2×C4×C13—31no—
44C2×C4×C13—34no—
45C2×C4×C13C2×D311yescharacteristic, complemented
46C2×D3×D4C1311yesmaximal, characteristic, direct product factor, Hall
47C2×C3×C13—24no—
48C2×C3×C13C2×D412yescomplemented
49C2×C3×C13C2411yescharacteristic
50D3×C13—24no—
51D3×C13C2×D414yesdirect product factor
52C22×C13—24no—
53C22×C13—34no—
54C22×C13—32no—
55C22×C13—34no—
56C22×C13—616no—
57C22×C13—64no—
58C22×C13C22×D311yescharacteristic
59C22×C13C22×D314yescomplemented
60C4×C13—32no—
61C4×C13C22×D312yescomplemented
62C23×D3C2×C1312yescomplemented
63C2×C3×D4C2×C1311yescharacteristic, complemented
64C2×#67C2×C1312yescomplemented
65D3×D4C2×C1318yesdirect product factor
66C2×D12C2×C1311yescharacteristic, complemented
67C2×C4×D3C2×C1311yescharacteristic, complemented
68C3×C13C22×D411yescharacteristic, complemented, Hall
69C22×D4—31noSylow
70C2×C13—24no—
71C2×C13—34no—
72C2×C13—64no—
73C2×C13D3×D412yesdirect product factor
74C2×C13C23×D311yescharacteristic
75C23×C3C22×C1312yescomplemented
76C22×D3—28no—
77C22×D3C22×C1311yescharacteristic
78C22×D3C22×C1318yescomplemented
79C22×D3C22×C1312yescomplemented
80C3×D4C22×C1314yescomplemented
81C2×C3×C4C22×C1311yescharacteristic, complemented
82#67C22×C1318yescomplemented
83C2×Dic3C22×C1311yescharacteristic, complemented
84D12C22×C1314yescomplemented
85C4×D3C22×C1314yescomplemented
86C24—32no—
87C2×D4—32no—
88C2×D4—38no—
89C2×D4—31no—
90C2×D4D3×C1311yescharacteristic, direct product factor
91C22×C4—31no—
92C13C2×D3×D411yescharacteristic, direct product factor, Sylow
93C22×C3—24no—
94C22×C3C23×C1311yescharacteristic
95C22×C3C23×C1314yescomplemented
96C2×D3—24no—
97C2×D3—216no—
98C2×D3D4×C1314yesdirect product factor
99C2×D3C23×C1312yes—
100C2×D3C23×C1314yescomplemented
101C3×C4C23×C1312yescomplemented
102Dic3C23×C1312yescomplemented
103C23—31no—
104C23—32no—
105C23—38no—
106C23—68no—
107C23C2×D3×C1312yescomplemented
108D4—38no—
109D4—34no—
110D4C2×D3×C1314yesdirect product factor
111C2×C4—31no—
112C2×C4—34no—
113C2×C4C2×D3×C1311yescharacteristic, complemented
114C2×C3—24no—
115C2×C3C2×D4×C1312yescomplemented
116C2×C3C24×C1311yescharacteristic
117D3—24no—
118D3C2×D4×C1314yesdirect product factor
119C22—24no—
120C22—34no—
121C22—32no—
122C22—34no—
123C22—616no—
124C22—64no—
125C22C22×D3×C1311yescharacteristic
126C22C22×D3×C1314yescomplemented
127C4—32no—
128C4C22×D3×C1312yescomplemented
129C3C22×D4×C1311yescharacteristic, complemented, Sylow
130C2—24no—
131C2—34no—
132C2—64no—
133C2D3×D4×C1312yesdirect product factor
134C2C23×D3×C1311yescharacteristic
subgroupG/H
centerC22×C13C22×D3
commutator, cosocleC2×C3C24×C13
FrattiniC2C23×D3×C13
FittingC2×C3×D4×C13C2
socleC22×C3×C13C23
hypercenterC2×D4×C13D3
hypocenterC3C22×D4×C13
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C13 ◁ C2×D4×C13

Complements

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

NH ≅ G/Ntype
1. C23×D3×C13C2semidirect
2. C2×C3×D4×C13C2semidirect
3. C2×C13×#67C2semidirect
4. D3×D4×C13C2direct (N × H)
5. C2×C13×D12C2semidirect
6. C2×C4×D3×C13C2semidirect
8. C23×C3×C13C22semidirect
11. C22×D3×C13C22semidirect
12. C22×D3×C13C22semidirect
13. C3×D4×C13C22semidirect
14. C2×C3×C4×C13C22semidirect
15. C13×#67C22semidirect
16. C2×Dic3×C13C22semidirect
17. C13×D12C22semidirect
18. C4×D3×C13C22semidirect
23. C2×D4×C13D3direct (N × H)
27. C22×C3×C13C23semidirect
30. C2×D3×C13D4direct (N × H)
32. C2×D3×C13C23semidirect
33. C3×C4×C13C23semidirect
34. Dic3×C13C23semidirect
39. C23×C13C2×D3semidirect
42. D4×C13C2×D3direct (N × H)
45. C2×C4×C13C2×D3semidirect
46. C2×D3×D4C13direct (N × H)
48. C2×C3×C13C2×D4semidirect
51. D3×C13C2×D4direct (N × H)
59. C22×C13C22×D3semidirect
61. C4×C13C22×D3semidirect
62. C23×D3C2×C13semidirect
63. C2×C3×D4C2×C13semidirect
64. C2×#67C2×C13semidirect
65. D3×D4C2×C13direct (N × H)
66. C2×D12C2×C13semidirect
67. C2×C4×D3C2×C13semidirect
68. C3×C13C22×D4semidirect
73. C2×C13D3×D4direct (N × H)
75. C23×C3C22×C13semidirect
78. C22×D3C22×C13semidirect
79. C22×D3C22×C13semidirect
80. C3×D4C22×C13semidirect
81. C2×C3×C4C22×C13semidirect
82. #67C22×C13semidirect
83. C2×Dic3C22×C13semidirect
84. D12C22×C13semidirect
85. C4×D3C22×C13semidirect
90. C2×D4D3×C13direct (N × H)
92. C13C2×D3×D4direct (N × H)
95. C22×C3C23×C13semidirect
98. C2×D3D4×C13direct (N × H)
100. C2×D3C23×C13semidirect
101. C3×C4C23×C13semidirect
102. Dic3C23×C13semidirect
107. C23C2×D3×C13semidirect
110. D4C2×D3×C13direct (N × H)
113. C2×C4C2×D3×C13semidirect
115. C2×C3C2×D4×C13semidirect
118. D3C2×D4×C13direct (N × H)
126. C22C22×D3×C13semidirect
128. C4C22×D3×C13semidirect
129. C3C22×D4×C13semidirect
133. C2D3×D4×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×C132
C2×C3×D4×C132
C2×C13×#672
D3×D4×C132
C2×C13×D122
C2×C4×D3×C132
C22×D4×C133
C2×D3×D413