Finite Group Databasebeta

← C2×#10597743 #11929209

Subgroups — C2×#10597743 #11929209

Order 1248.

472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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×C4×D39C211yesmaximal, characteristic, complemented
3C2×C13×D12C211yesmaximal, characteristic, complemented
4C2×C3×D52C211yesmaximal, characteristic, complemented
5C2×#64602C212yesmaximal, complemented
6#10597743C218yesmaximal, direct product factor
7C2×D4×D13—31nomaximal, Hall
8C22×D39C2211yescharacteristic
9C22×D3×C13C2212yescomplemented
10C22×C3×D13C2212yescomplemented
11C2×D3×D13—28no—
12C2×D3×D13C2218yescomplemented
13C2×C3×C4×C13C2211yescharacteristic, complemented
14C2×Dic39C2211yescharacteristic, complemented
15C4×D39C2214yescomplemented
16C13×D12C2214yescomplemented
17C3×D52C2214yescomplemented
18#64602C2218yescomplemented
19C23×D13—32no—
20C2×D4×C13—31no—
21C2×C22⋊D13—32no—
22D4×D13—38no—
23C2×D52D311yescharacteristic, complemented
24C2×C4×D13—31no—
25C22×C3×C13C2311yescharacteristic
26C2×D39D414yescomplemented
27C2×D39C2312yes—
28C2×D3×C13—24no—
29C2×D3×C13C2314yescomplemented
30C2×C3×D13—24no—
31C2×C3×D13C2314yescomplemented
32D3×D13—216no—
33C3×C4×C13C2312yescomplemented
34Dic39C2312yescomplemented
35C23×C13—32no—
36C22×D13—31no—
37C22×D13—38no—
38C22×D13—68no—
39C22×D13C2×D312yescomplemented
40D4×C13—34no—
41C2×C4×C13C2×D311yescharacteristic, complemented
42C22⋊D13—38no—
43C2×Dic13—31no—
44D52C2×D314yescomplemented
45C4×D13—34no—
46C2×D3×D4—131nomaximal, Hall
47C2×C3×C13C2×D412yescomplemented
48C2×C3×C13C2411yescharacteristic
49D39C2×D414yescomplemented
50C3×D13—24no—
51D3×C13—24no—
52C22×C13—34no—
53C22×C13—64no—
54C22×C13C22×D311yescharacteristic
55C2×D13—24no—
56C2×D13—34no—
57C2×D13—32no—
58C2×D13—616no—
59C2×D13C22×D314yescomplemented
60C4×C13C22×D312yescomplemented
61Dic13—32no—
62C23×D3—132no—
63C2×C3×D4—131no—
64C2×#67—132no—
65D3×D4—138no—
66C2×D12D1311yescharacteristic, complemented
67C2×C4×D3—131no—
68C3×C13C22×D411yescharacteristic, complemented, Hall
69C22×D4—391noSylow
70C2×C13—64no—
71C2×C13D3×D412yescomplemented
72C2×C13C23×D311yescharacteristic
73D13—24no—
74D13—34no—
75C23×C3—132no—
76C22×D3—131no—
77C22×D3—138no—
78C22×D3—268no—
79C22×D3C2×D1312yescomplemented
80C3×D4—134no—
81C2×C3×C4C2×D1311yescharacteristic, complemented
82#67—138no—
83C2×Dic3—131no—
84D12C2×D1314yescomplemented
85C4×D3—134no—
86C24—392no—
87C2×D4—31no—
88C2×D4—131no—
89C2×D4—398no—
90C2×D4—392no—
91C22×C4—391no—
92C13C2×D3×D411yescharacteristic, complemented, Sylow
93C22×C3—134no—
94C22×C3—264no—
95C22×C3C22×D1311yescharacteristic
96C2×D3—24no—
97C2×D3—134no—
98C2×D3—132no—
99C2×D3—2616no—
100C2×D3C22×D1314yescomplemented
101C3×C4C22×D1312yescomplemented
102Dic3—132no—
103C23—32no—
104C23—132no—
105C23—398no—
106C23—391no—
107C23—788no—
108D4—34no—
109D4—134no—
110D4—398no—
111C2×C4—391no—
112C2×C4—394no—
113C2×C4D3×D1311yescharacteristic, complemented
114C2×C3—264no—
115C2×C3D4×D1312yescomplemented
116C2×C3C23×D1311yescharacteristic
117D3—24no—
118D3—134no—
119C22—34no—
120C22—64no—
121C22—134no—
122C22—264no—
123C22—394no—
124C22—392no—
125C22—7816no—
126C22C2×D3×D1311yescharacteristic
127C4—392no—
128C4C2×D3×D1312yescomplemented
129C3C2×D4×D1311yescharacteristic, complemented, Sylow
130C2—64no—
131C2—264no—
132C2—394no—
133C2#1059774312yesdirect 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×C4×D39C2semidirect
3. C2×C13×D12C2semidirect
4. C2×C3×D52C2semidirect
5. C2×#64602C2semidirect
6. #10597743C2direct (N × H)
9. C22×D3×C13C22semidirect
10. C22×C3×D13C22semidirect
12. C2×D3×D13C22semidirect
13. C2×C3×C4×C13C22semidirect
14. C2×Dic39C22semidirect
15. C4×D39C22semidirect
16. C13×D12C22semidirect
17. C3×D52C22semidirect
18. #64602C22semidirect
23. C2×D52D3semidirect
26. C2×D39D4semidirect
29. C2×D3×C13C23semidirect
31. C2×C3×D13C23semidirect
33. C3×C4×C13C23semidirect
34. Dic39C23semidirect
39. C22×D13C2×D3semidirect
41. C2×C4×C13C2×D3semidirect
44. D52C2×D3semidirect
47. C2×C3×C13C2×D4semidirect
49. D39C2×D4semidirect
59. C2×D13C22×D3semidirect
60. C4×C13C22×D3semidirect
66. C2×D12D13semidirect
68. C3×C13C22×D4semidirect
71. C2×C13D3×D4semidirect
79. C22×D3C2×D13semidirect
81. C2×C3×C4C2×D13semidirect
84. D12C2×D13semidirect
92. C13C2×D3×D4semidirect
100. C2×D3C22×D13semidirect
101. C3×C4C22×D13semidirect
113. C2×C4D3×D13semidirect
115. C2×C3D4×D13semidirect
128. C4C2×D3×D13semidirect
129. C3C2×D4×D13semidirect
133. C2#10597743direct (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×C4×D392
C2×C13×D122
C2×C3×D522
C2×#646022
#105977432
C2×D4×D133
C2×D3×D413