Finite Group Databasebeta

← C2×D3×D52 #11929208

Subgroups — C2×D3×D52 #11929208

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×C4×D3×C13C211yesmaximal, characteristic, complemented
4C2×C3×D52C211yesmaximal, characteristic, complemented
5C2×#64603C212yesmaximal, complemented
6D3×D52C218yesmaximal, direct product factor
7C22×D52—31nomaximal, Hall
8C22×D39C2212yescomplemented
9C22×D3×C13C2211yescharacteristic
10C22×C3×D13C2212yescomplemented
11C2×D3×D13—28no—
12C2×D3×D13C2218yescomplemented
13C2×C3×C4×C13C2211yescharacteristic, complemented
14D156C2214yescomplemented
15C2×Dic3×C13C2211yescharacteristic, complemented
16C4×D3×C13C2214yescomplemented
17C3×D52C2214yescomplemented
18#64603C2218yescomplemented
19C23×D13—32no—
20C22×C4×C13—31no—
21C2×D52—32no—
22C2×D52—31no—
23C2×D52—38no—
24C2×D52D311yescharacteristic, direct product factor
25C22×C3×C13C2311yescharacteristic
26C2×D39—24no—
27C2×D39C2314yescomplemented
28C2×D3×C13D414yescomplemented
29C2×D3×C13C2312yes—
30C2×C3×D13—24no—
31C2×C3×D13C2314yescomplemented
32D3×D13—216no—
33C3×C4×C13C2312yescomplemented
34Dic3×C13C2312yescomplemented
35C23×C13—31no—
36C22×D13—32no—
37C22×D13—38no—
38C22×D13—68no—
39C22×D13C2×D312yescomplemented
40C2×C4×C13—31no—
41C2×C4×C13—34no—
42C2×C4×C13C2×D311yescharacteristic, complemented
43D52—38no—
44D52—34no—
45D52C2×D314yesdirect product factor
46C2×D3×D4—131nomaximal, Hall
47C2×C3×C13C2×D412yescomplemented
48C2×C3×C13C2411yescharacteristic
49D39—24no—
50C3×D13—24no—
51D3×C13C2×D414yescomplemented
52C22×C13—34no—
53C22×C13—32no—
54C22×C13C22×D311yescharacteristic
55C2×D13—24no—
56C2×D13—34no—
57C2×D13—616no—
58C2×D13—64no—
59C2×D13C22×D314yescomplemented
60C4×C13—32no—
61C4×C13C22×D312yescomplemented
62C23×D3—132no—
63C2×C3×D4—131no—
64C2×#67—132no—
65D3×D4—138no—
66C2×D12—131no—
67C2×C4×D3D1311yescharacteristic, complemented
68C3×C13C22×D411yescharacteristic, complemented, Hall
69C22×D4—391noSylow
70C2×C13—34no—
71C2×C13D3×D412yescomplemented
72C2×C13C23×D311yescharacteristic
73D13—24no—
74D13—64no—
75C23×C3—132no—
76C22×D3—132no—
77C22×D3—138no—
78C22×D3—268no—
79C22×D3C2×D1311yescharacteristic
80C3×D4—134no—
81C2×C3×C4C2×D1311yescharacteristic, complemented
82#67—138no—
83C2×Dic3C2×D1311yescharacteristic, complemented
84D12—134no—
85C4×D3C2×D1314yescomplemented
86C24—392no—
87C2×D4—131no—
88C2×D4—398no—
89C2×D4—392no—
90C2×D4—391no—
91C22×C4—31no—
92C13C2×D3×D411yescharacteristic, complemented, Sylow
93C22×C3—134no—
94C22×C3—264no—
95C22×C3C22×D1311yescharacteristic
96C2×D3—134no—
97C2×D3—264no—
98C2×D3—2616no—
99C2×D3D5214yesdirect product factor
100C2×D3C22×D1312yes—
101C3×C4C22×D1312yescomplemented
102Dic3C22×D1312yescomplemented
103C23—31no—
104C23—132no—
105C23—398no—
106C23—392no—
107C23—788no—
108D4—134no—
109D4—398no—
110D4—394no—
111C2×C4—31no—
112C2×C4—34no—
113C2×C4D3×D1311yescharacteristic, complemented
114C2×C3—264no—
115C2×C3C2×D5212yescomplemented
116C2×C3C23×D1311yescharacteristic
117D3—264no—
118D3C2×D5214yesdirect product factor
119C22—34no—
120C22—32no—
121C22—134no—
122C22—264no—
123C22—394no—
124C22—7816no—
125C22—784no—
126C22C2×D3×D1311yescharacteristic
127C4—32no—
128C4C2×D3×D1312yescomplemented
129C3C22×D5211yescharacteristic, complemented, Sylow
130C2—34no—
131C2—264no—
132C2—784no—
133C2D3×D5212yesdirect 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×C4×D3×C13C2semidirect
4. C2×C3×D52C2semidirect
5. C2×#64603C2semidirect
6. D3×D52C2direct (N × H)
8. C22×D39C22semidirect
10. C22×C3×D13C22semidirect
12. C2×D3×D13C22semidirect
13. C2×C3×C4×C13C22semidirect
14. D156C22semidirect
15. C2×Dic3×C13C22semidirect
16. C4×D3×C13C22semidirect
17. C3×D52C22semidirect
18. #64603C22semidirect
24. C2×D52D3direct (N × H)
27. C2×D39C23semidirect
28. C2×D3×C13D4semidirect
31. C2×C3×D13C23semidirect
33. C3×C4×C13C23semidirect
34. Dic3×C13C23semidirect
39. C22×D13C2×D3semidirect
42. C2×C4×C13C2×D3semidirect
45. D52C2×D3direct (N × H)
47. C2×C3×C13C2×D4semidirect
51. D3×C13C2×D4semidirect
59. C2×D13C22×D3semidirect
61. C4×C13C22×D3semidirect
67. C2×C4×D3D13semidirect
68. C3×C13C22×D4semidirect
71. C2×C13D3×D4semidirect
81. C2×C3×C4C2×D13semidirect
83. C2×Dic3C2×D13semidirect
85. C4×D3C2×D13semidirect
92. C13C2×D3×D4semidirect
99. C2×D3D52direct (N × H)
101. C3×C4C22×D13semidirect
102. Dic3C22×D13semidirect
113. C2×C4D3×D13semidirect
115. C2×C3C2×D52semidirect
118. D3C2×D52direct (N × H)
128. C4C2×D3×D13semidirect
129. C3C22×D52semidirect
133. C2D3×D52direct (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×C4×D3×C132
C2×C3×D522
C2×#646032
D3×D522
C22×D523
C2×D3×D413