Finite Group Databasebeta

← C2×D4×D39 #11929304

Subgroups — C2×D4×D39 #11929304

Order 1248.

472 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 135 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×D39C212yesmaximal, complemented
2C2×C3×D4×C13C211yesmaximal, characteristic, complemented
3C2×#64625C212yesmaximal, complemented
4D4×D39C218yesmaximal, direct product factor
5C2×D156C211yesmaximal, characteristic, complemented
6C2×C4×D39C211yesmaximal, characteristic, complemented
7C2×D4×D13—31nomaximal, Hall
8C23×C3×C13C2212yescomplemented
9C22×D39—28no—
10C22×D39C2211yescharacteristic
11C22×D39C2218yescomplemented
12C22×D39C2212yescomplemented
13C3×D4×C13C2214yescomplemented
14C2×C3×C4×C13C2211yescharacteristic, complemented
15#64625C2218yescomplemented
16C2×Dic39C2211yescharacteristic, complemented
17D156C2214yescomplemented
18C4×D39C2214yescomplemented
19C23×D13—32no—
20C2×D4×C13D311yescharacteristic, complemented
21C2×C22⋊D13—32no—
22D4×D13—38no—
23C2×D52—31no—
24C2×C4×D13—31no—
25C22×C3×C13—24no—
26C22×C3×C13C2311yescharacteristic
27C22×C3×C13C2314yescomplemented
28C2×D39—24no—
29C2×D39—216no—
30C2×D39D414yesdirect product factor
31C2×D39C2312yes—
32C2×D39C2314yescomplemented
33C3×C4×C13C2312yescomplemented
34Dic39C2312yescomplemented
35C23×C13C2×D312yescomplemented
36C22×D13—31no—
37C22×D13—32no—
38C22×D13—38no—
39C22×D13—68no—
40D4×C13C2×D314yescomplemented
41C2×C4×C13C2×D311yescharacteristic, complemented
42C22⋊D13—38no—
43C2×Dic13—31no—
44D52—34no—
45C4×D13—34no—
46C2×D3×D4—131nomaximal, Hall
47C2×C3×C13—24no—
48C2×C3×C13C2×D412yescomplemented
49C2×C3×C13C2411yescharacteristic
50D39—24no—
51D39C2×D414yesdirect product factor
52C22×C13—24no—
53C22×C13C22×D311yescharacteristic
54C22×C13C22×D314yescomplemented
55C2×D13—34no—
56C2×D13—32no—
57C2×D13—34no—
58C2×D13—616no—
59C2×D13—64no—
60C4×C13C22×D312yescomplemented
61Dic13—32no—
62C23×D3—132no—
63C2×C3×D4D1311yescharacteristic, complemented
64C2×#67—132no—
65D3×D4—138no—
66C2×D12—131no—
67C2×C4×D3—131no—
68C3×C13C22×D411yescharacteristic, complemented, Hall
69C22×D4—391noSylow
70C2×C13—24no—
71C2×C13D3×D412yescomplemented
72C2×C13C23×D311yescharacteristic
73D13—34no—
74D13—64no—
75C23×C3C2×D1312yescomplemented
76C22×D3—131no—
77C22×D3—132no—
78C22×D3—138no—
79C22×D3—268no—
80C3×D4C2×D1314yescomplemented
81C2×C3×C4C2×D1311yescharacteristic, complemented
82#67—138no—
83C2×Dic3—131no—
84D12—134no—
85C4×D3—134no—
86C24—392no—
87C2×D4—392no—
88C2×D4—398no—
89C2×D4—391no—
90C2×D4D3911yescharacteristic, direct product factor
91C22×C4—391no—
92C13C2×D3×D411yescharacteristic, complemented, Sylow
93C22×C3—24no—
94C22×C3C22×D1311yescharacteristic
95C22×C3C22×D1314yescomplemented
96C2×D3—134no—
97C2×D3—132no—
98C2×D3—134no—
99C2×D3—2616no—
100C2×D3—264no—
101C3×C4C22×D1312yescomplemented
102Dic3—132no—
103C23—391no—
104C23—392no—
105C23—398no—
106C23—788no—
107C23C2×D3912yescomplemented
108D4—398no—
109D4—394no—
110D4C2×D3914yesdirect product factor
111C2×C4—391no—
112C2×C4—394no—
113C2×C4C2×D3911yescharacteristic, complemented
114C2×C3—24no—
115C2×C3D4×D1312yescomplemented
116C2×C3C23×D1311yescharacteristic
117D3—134no—
118D3—264no—
119C22—24no—
120C22—394no—
121C22—392no—
122C22—394no—
123C22—7816no—
124C22—784no—
125C22C22×D3911yescharacteristic
126C22C22×D3914yescomplemented
127C4—392no—
128C4C22×D3912yescomplemented
129C3C2×D4×D1311yescharacteristic, complemented, Sylow
130C2—24no—
131C2—394no—
132C2—784no—
133C2D4×D3912yesdirect product factor
134C2C23×D3911yescharacteristic
subgroupG/H
centerC22C22×D39
commutator, cosocleC2×C3×C13C24
FrattiniC2C23×D39
FittingC2×C3×D4×C13C2
socleC22×C3×C13C23
hypercenterC2×D4D39
hypocenterC3×C13C22×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×D39C2semidirect
2. C2×C3×D4×C13C2semidirect
3. C2×#64625C2semidirect
4. D4×D39C2direct (N × H)
5. C2×D156C2semidirect
6. C2×C4×D39C2semidirect
8. C23×C3×C13C22semidirect
11. C22×D39C22semidirect
12. C22×D39C22semidirect
13. C3×D4×C13C22semidirect
14. C2×C3×C4×C13C22semidirect
15. #64625C22semidirect
16. C2×Dic39C22semidirect
17. D156C22semidirect
18. C4×D39C22semidirect
20. C2×D4×C13D3semidirect
27. C22×C3×C13C23semidirect
30. C2×D39D4direct (N × H)
32. C2×D39C23semidirect
33. C3×C4×C13C23semidirect
34. Dic39C23semidirect
35. C23×C13C2×D3semidirect
40. D4×C13C2×D3semidirect
41. C2×C4×C13C2×D3semidirect
48. C2×C3×C13C2×D4semidirect
51. D39C2×D4direct (N × H)
54. C22×C13C22×D3semidirect
60. C4×C13C22×D3semidirect
63. C2×C3×D4D13semidirect
68. C3×C13C22×D4semidirect
71. C2×C13D3×D4semidirect
75. C23×C3C2×D13semidirect
80. C3×D4C2×D13semidirect
81. C2×C3×C4C2×D13semidirect
90. C2×D4D39direct (N × H)
92. C13C2×D3×D4semidirect
95. C22×C3C22×D13semidirect
101. C3×C4C22×D13semidirect
107. C23C2×D39semidirect
110. D4C2×D39direct (N × H)
113. C2×C4C2×D39semidirect
115. C2×C3D4×D13semidirect
126. C22C22×D39semidirect
128. C4C22×D39semidirect
129. C3C2×D4×D13semidirect
133. C2D4×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D392
C2×C3×D4×C132
C2×#646252
D4×D392
C2×D1562
C2×C4×D392
C2×D4×D133
C2×D3×D413