Finite Group Databasebeta

← C2×C3×D4×D13 #11929274

Subgroups — C2×C3×D4×D13 #11929274

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×C3×D13C212yesmaximal, complemented
2C2×C3×D4×C13C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D13C212yesmaximal, complemented
4C3×D4×D13C218yesmaximal, direct product factor
5C2×C3×D52C211yesmaximal, characteristic, complemented
6C2×C3×C4×D13C211yesmaximal, characteristic, complemented
7C2×D4×D13C311yesmaximal, characteristic, direct product factor, Hall
8C23×C3×C13C2212yescomplemented
9C22×C3×D13—28no—
10C22×C3×D13C2211yescharacteristic
11C22×C3×D13C2218yescomplemented
12C22×C3×D13C2212yescomplemented
13C3×D4×C13C2214yescomplemented
14C2×C3×C4×C13C2211yescharacteristic, complemented
15C3×C22⋊D13C2218yescomplemented
16C2×C3×Dic13C2211yescharacteristic, complemented
17C3×D52C2214yescomplemented
18C3×C4×D13C2214yescomplemented
19C23×D13C2×C312yescomplemented
20C2×D4×C13C2×C311yescharacteristic, complemented
21C2×C22⋊D13C2×C312yescomplemented
22D4×D13C2×C318yesdirect product factor
23C2×D52C2×C311yescharacteristic, complemented
24C2×C4×D13C2×C311yescharacteristic, complemented
25C22×C3×C13—24no—
26C22×C3×C13C2311yescharacteristic
27C22×C3×C13C2314yescomplemented
28C2×C3×D13—24no—
29C2×C3×D13—216no—
30C2×C3×D13D414yesdirect product factor
31C2×C3×D13C2312yes—
32C2×C3×D13C2314yescomplemented
33C3×C4×C13C2312yescomplemented
34C3×Dic13C2312yescomplemented
35C23×C13C22×C312yescomplemented
36C22×D13—28no—
37C22×D13C22×C311yescharacteristic
38C22×D13C22×C318yescomplemented
39C22×D13C22×C312yescomplemented
40D4×C13C22×C314yescomplemented
41C2×C4×C13C22×C311yescharacteristic, complemented
42C22⋊D13C22×C318yescomplemented
43C2×Dic13C22×C311yescharacteristic, complemented
44D52C22×C314yescomplemented
45C4×D13C22×C314yescomplemented
46C22×C3×D4—131nomaximal, Hall
47C2×C3×C13—24no—
48C2×C3×C13C2×D412yescomplemented
49C2×C3×C13C2411yescharacteristic
50C3×D13—24no—
51C3×D13C2×D414yesdirect product factor
52C22×C13—24no—
53C22×C13C23×C311yescharacteristic
54C22×C13C23×C314yescomplemented
55C2×D13—24no—
56C2×D13—216no—
57C2×D13C3×D414yesdirect product factor
58C2×D13C23×C312yes—
59C2×D13C23×C314yescomplemented
60C4×C13C23×C312yescomplemented
61Dic13C23×C312yescomplemented
62C24×C3—132no—
63C2×C3×D4—132no—
64C2×C3×D4—138no—
65C2×C3×D4—131no—
66C2×C3×D4D1311yescharacteristic, direct product factor
67C22×C3×C4—131no—
68C3×C13C22×D411yescharacteristic, complemented, Hall
69C22×D4—131noSylow
70C2×C13—24no—
71C2×C13C2×C3×D412yescomplemented
72C2×C13C24×C311yescharacteristic
73D13—24no—
74D13C2×C3×D414yesdirect product factor
75C23×C3—131no—
76C23×C3—132no—
77C23×C3—138no—
78C23×C3—268no—
79C23×C3C2×D1312yescomplemented
80C3×D4—138no—
81C3×D4—134no—
82C3×D4C2×D1314yesdirect product factor
83C2×C3×C4—131no—
84C2×C3×C4—134no—
85C2×C3×C4C2×D1311yescharacteristic, complemented
86C24—132no—
87C2×D4—132no—
88C2×D4—138no—
89C2×D4—131no—
90C2×D4C3×D1311yescharacteristic, direct product factor
91C22×C4—131no—
92C13C22×C3×D411yescharacteristic, complemented, Sylow
93C22×C3—24no—
94C22×C3—134no—
95C22×C3—132no—
96C22×C3—134no—
97C22×C3—2616no—
98C22×C3—264no—
99C22×C3C22×D1311yescharacteristic
100C22×C3C22×D1314yescomplemented
101C3×C4—132no—
102C3×C4C22×D1312yescomplemented
103C23—131no—
104C23—132no—
105C23—138no—
106C23—268no—
107C23C2×C3×D1312yescomplemented
108D4—138no—
109D4—134no—
110D4C2×C3×D1314yesdirect product factor
111C2×C4—131no—
112C2×C4—134no—
113C2×C4C2×C3×D1311yescharacteristic, complemented
114C2×C3—24no—
115C2×C3—134no—
116C2×C3—264no—
117C2×C3D4×D1312yesdirect product factor
118C2×C3C23×D1311yescharacteristic
119C22—24no—
120C22—134no—
121C22—132no—
122C22—134no—
123C22—2616no—
124C22—264no—
125C22C22×C3×D1311yescharacteristic
126C22C22×C3×D1314yescomplemented
127C4—132no—
128C4C22×C3×D1312yescomplemented
129C3C2×D4×D1311yescharacteristic, direct product factor, Sylow
130C2—24no—
131C2—134no—
132C2—264no—
133C2C3×D4×D1312yesdirect product factor
134C2C23×C3×D1311yescharacteristic
subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC2×C13C24×C3
FrattiniC2C23×C3×D13
FittingC2×C3×D4×C13C2
socleC22×C3×C13C23
hypercenterC2×C3×D4D13
hypocenterC13C22×C3×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D13C2semidirect
2. C2×C3×D4×C13C2semidirect
3. C2×C3×C22⋊D13C2semidirect
4. C3×D4×D13C2direct (N × H)
5. C2×C3×D52C2semidirect
6. C2×C3×C4×D13C2semidirect
7. C2×D4×D13C3direct (N × H)
8. C23×C3×C13C22semidirect
11. C22×C3×D13C22semidirect
12. C22×C3×D13C22semidirect
13. C3×D4×C13C22semidirect
14. C2×C3×C4×C13C22semidirect
15. C3×C22⋊D13C22semidirect
16. C2×C3×Dic13C22semidirect
17. C3×D52C22semidirect
18. C3×C4×D13C22semidirect
19. C23×D13C2×C3semidirect
20. C2×D4×C13C2×C3semidirect
21. C2×C22⋊D13C2×C3semidirect
22. D4×D13C2×C3direct (N × H)
23. C2×D52C2×C3semidirect
24. C2×C4×D13C2×C3semidirect
27. C22×C3×C13C23semidirect
30. C2×C3×D13D4direct (N × H)
32. C2×C3×D13C23semidirect
33. C3×C4×C13C23semidirect
34. C3×Dic13C23semidirect
35. C23×C13C22×C3semidirect
38. C22×D13C22×C3semidirect
39. C22×D13C22×C3semidirect
40. D4×C13C22×C3semidirect
41. C2×C4×C13C22×C3semidirect
42. C22⋊D13C22×C3semidirect
43. C2×Dic13C22×C3semidirect
44. D52C22×C3semidirect
45. C4×D13C22×C3semidirect
48. C2×C3×C13C2×D4semidirect
51. C3×D13C2×D4direct (N × H)
54. C22×C13C23×C3semidirect
57. C2×D13C3×D4direct (N × H)
59. C2×D13C23×C3semidirect
60. C4×C13C23×C3semidirect
61. Dic13C23×C3semidirect
66. C2×C3×D4D13direct (N × H)
68. C3×C13C22×D4semidirect
71. C2×C13C2×C3×D4semidirect
74. D13C2×C3×D4direct (N × H)
79. C23×C3C2×D13semidirect
82. C3×D4C2×D13direct (N × H)
85. C2×C3×C4C2×D13semidirect
90. C2×D4C3×D13direct (N × H)
92. C13C22×C3×D4semidirect
100. C22×C3C22×D13semidirect
102. C3×C4C22×D13semidirect
107. C23C2×C3×D13semidirect
110. D4C2×C3×D13direct (N × H)
113. C2×C4C2×C3×D13semidirect
117. C2×C3D4×D13direct (N × H)
126. C22C22×C3×D13semidirect
128. C4C22×C3×D13semidirect
129. C3C2×D4×D13direct (N × H)
133. C2C3×D4×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D132
C2×C3×D4×C132
C2×C3×C22⋊D132
C3×D4×D132
C2×C3×D522
C2×C3×C4×D132
C2×D4×D133
C22×C3×D413