Finite Group Databasebeta

← C2×D12×D13 #11929207

Subgroups — C2×D12×D13 #11929207

Order 1248.

472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C22×D3×D13C212yesmaximal, complemented
2C2×D156C211yesmaximal, characteristic, complemented
3C2×C13×D12C211yesmaximal, characteristic, complemented
4C2×C3×C4×D13C211yesmaximal, characteristic, complemented
5C2×#64604C212yesmaximal, complemented
6D12×D13C218yesmaximal, direct product factor
7C2×D4×D13—31nomaximal, Hall
8C22×D39C2212yescomplemented
9C22×D3×C13C2212yescomplemented
10C22×C3×D13C2211yescharacteristic
11C2×D3×D13—28no—
12C2×D3×D13C2218yescomplemented
13C2×C3×C4×C13C2211yescharacteristic, complemented
14D156C2214yescomplemented
15C13×D12C2214yescomplemented
16C2×C3×Dic13C2211yescharacteristic, complemented
17C3×C4×D13C2214yescomplemented
18#64604C2218yescomplemented
19C23×D13—32no—
20C2×D4×C13—31no—
21C2×C22⋊D13—32no—
22D4×D13—38no—
23C2×D52—31no—
24C2×C4×D13D311yescharacteristic, complemented
25C22×C3×C13C2311yescharacteristic
26C2×D39—24no—
27C2×D39C2314yescomplemented
28C2×D3×C13—24no—
29C2×D3×C13C2314yescomplemented
30C2×C3×D13D414yescomplemented
31C2×C3×D13C2312yes—
32D3×D13—216no—
33C3×C4×C13C2312yescomplemented
34C3×Dic13C2312yescomplemented
35C23×C13—32no—
36C22×D13—32no—
37C22×D13—38no—
38C22×D13—68no—
39C22×D13C2×D311yescharacteristic
40D4×C13—34no—
41C2×C4×C13C2×D311yescharacteristic, complemented
42C22⋊D13—38no—
43C2×Dic13C2×D311yescharacteristic, complemented
44D52—34no—
45C4×D13C2×D314yescomplemented
46C22×D12—131nomaximal, Hall
47C2×C3×C13C2×D412yescomplemented
48C2×C3×C13C2411yescharacteristic
49D39—24no—
50C3×D13C2×D414yescomplemented
51D3×C13—24no—
52C22×C13—34no—
53C22×C13—64no—
54C22×C13C22×D311yescharacteristic
55C2×D13—34no—
56C2×D13—64no—
57C2×D13—616no—
58C2×D13D1214yesdirect product factor
59C2×D13C22×D312yes—
60C4×C13C22×D312yescomplemented
61Dic13C22×D312yescomplemented
62C23×D3—132no—
63C22×C3×C4—131no—
64C2×D12—132no—
65C2×D12—131no—
66C2×D12—138no—
67C2×D12D1311yescharacteristic, direct product factor
68C3×C13C22×D411yescharacteristic, complemented, Hall
69C22×D4—391noSylow
70C2×C13—64no—
71C2×C13C2×D1212yescomplemented
72C2×C13C23×D311yescharacteristic
73D13—64no—
74D13C2×D1214yesdirect product factor
75C23×C3—131no—
76C22×D3—132no—
77C22×D3—138no—
78C22×D3—268no—
79C22×D3C2×D1312yescomplemented
80C2×C3×C4—131no—
81C2×C3×C4—134no—
82C2×C3×C4C2×D1311yescharacteristic, complemented
83D12—138no—
84D12—134no—
85D12C2×D1314yesdirect product factor
86C24—392no—
87C2×D4—31no—
88C2×D4—398no—
89C2×D4—392no—
90C2×D4—391no—
91C22×C4—131no—
92C13C22×D1211yescharacteristic, complemented, Sylow
93C22×C3—134no—
94C22×C3—132no—
95C22×C3C22×D1311yescharacteristic
96C2×D3—24no—
97C2×D3—134no—
98C2×D3—2616no—
99C2×D3—264no—
100C2×D3C22×D1314yescomplemented
101C3×C4—132no—
102C3×C4C22×D1312yescomplemented
103C23—32no—
104C23—131no—
105C23—398no—
106C23—392no—
107C23—788no—
108D4—34no—
109D4—398no—
110D4—394no—
111C2×C4—131no—
112C2×C4—134no—
113C2×C4D3×D1311yescharacteristic, complemented
114C2×C3—134no—
115C2×C3D4×D1312yescomplemented
116C2×C3C23×D1311yescharacteristic
117D3—24no—
118D3—264no—
119C22—34no—
120C22—64no—
121C22—134no—
122C22—132no—
123C22—394no—
124C22—7816no—
125C22—784no—
126C22C2×D3×D1311yescharacteristic
127C4—132no—
128C4C2×D3×D1312yescomplemented
129C3C2×D4×D1311yescharacteristic, complemented, Sylow
130C2—64no—
131C2—134no—
132C2—784no—
133C2D12×D1312yesdirect product factor
134C2C22×D3×D1311yescharacteristic
subgroupG/H
centerC22C2×D3×D13
commutator, cosocleC2×C3×C13C24
FrattiniC2C22×D3×D13
FittingC2×C3×C4×C13C22
socleC22×C3×C13C23
hypercenterC2×C4D3×D13
hypocenterC3×C13C22×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D13C2semidirect
2. C2×D156C2semidirect
3. C2×C13×D12C2semidirect
4. C2×C3×C4×D13C2semidirect
5. C2×#64604C2semidirect
6. D12×D13C2direct (N × H)
8. C22×D39C22semidirect
9. C22×D3×C13C22semidirect
12. C2×D3×D13C22semidirect
13. C2×C3×C4×C13C22semidirect
14. D156C22semidirect
15. C13×D12C22semidirect
16. C2×C3×Dic13C22semidirect
17. C3×C4×D13C22semidirect
18. #64604C22semidirect
24. C2×C4×D13D3semidirect
27. C2×D39C23semidirect
29. C2×D3×C13C23semidirect
30. C2×C3×D13D4semidirect
33. C3×C4×C13C23semidirect
34. C3×Dic13C23semidirect
41. C2×C4×C13C2×D3semidirect
43. C2×Dic13C2×D3semidirect
45. C4×D13C2×D3semidirect
47. C2×C3×C13C2×D4semidirect
50. C3×D13C2×D4semidirect
58. C2×D13D12direct (N × H)
60. C4×C13C22×D3semidirect
61. Dic13C22×D3semidirect
67. C2×D12D13direct (N × H)
68. C3×C13C22×D4semidirect
71. C2×C13C2×D12semidirect
74. D13C2×D12direct (N × H)
79. C22×D3C2×D13semidirect
82. C2×C3×C4C2×D13semidirect
85. D12C2×D13direct (N × H)
92. C13C22×D12semidirect
100. C2×D3C22×D13semidirect
102. C3×C4C22×D13semidirect
113. C2×C4D3×D13semidirect
115. C2×C3D4×D13semidirect
128. C4C2×D3×D13semidirect
129. C3C2×D4×D13semidirect
133. C2D12×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D132
C2×D1562
C2×C13×D122
C2×C3×C4×D132
C2×#646042
D12×D132
C2×D4×D133
C22×D1213