Finite Group Databasebeta

← C2×C4×D3×D13 #11929206

Subgroups — C2×C4×D3×D13 #11929206

Order 1248.

472 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 180 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×D13C211yesmaximal, characteristic
2C2×C4×D39C211yesmaximal, characteristic, complemented
3C2×C4×D3×C13C211yesmaximal, characteristic, complemented
4C2×C3×C4×D13C211yesmaximal, characteristic, complemented
5C2×#64601C211yesmaximal, characteristic, complemented
6C2×D3×Dic13C211yesmaximal, characteristic, complemented
7C2×Dic3×D13C211yesmaximal, characteristic, complemented
8C4×D3×D13C218yesmaximal, direct product factor
9C22×C4×D13—31nomaximal, Hall
10C22×D39C2211yescharacteristic
11C22×D3×C13C2211yescharacteristic
12C22×C3×D13C2211yescharacteristic
13C2×D3×D13C418yesdirect product factor
14C2×D3×D13C2214yes—
15C2×C3×C4×C13C2211yescharacteristic, complemented
16C2×Dic39C2211yescharacteristic, complemented
17C4×D39C2214yescomplemented
18C2×Dic3×C13C2211yescharacteristic, complemented
19C4×D3×C13C2214yescomplemented
20C2×C3×Dic13C2211yescharacteristic, complemented
21C3×C4×D13C2214yescomplemented
22#64601C2214yescomplemented
23D3×Dic13C2214yescomplemented
24Dic3×D13C2214yescomplemented
25C23×D13—31no—
26C22×C4×C13—31no—
27C22×Dic13—31no—
28C2×C4×D13—31no—
29C2×C4×D13—31no—
30C2×C4×D13—31no—
31C2×C4×D13—38no—
32C2×C4×D13D311yescharacteristic, direct product factor
33C22×C3×C13C2311yescharacteristic
34C2×D39C2×C414yescomplemented
35C2×D39C2312yes—
36C2×D3×C13C2×C414yescomplemented
37C2×D3×C13C2312yes—
38C2×C3×D13C2×C414yescomplemented
39C2×C3×D13C2312yes—
40D3×D13C2×C4116yesdirect product factor
41C3×C4×C13C2312yescomplemented
42Dic39C2312yescomplemented
43C3×Dic13C2312yescomplemented
44Dic3×C13C2312yescomplemented
45C23×C13—31no—
46C22×D13—31no—
47C22×D13—38no—
48C22×D13—34no—
49C22×D13C2×D311yescharacteristic
50C2×C4×C13—31no—
51C2×C4×C13—34no—
52C2×C4×C13C2×D311yescharacteristic, complemented
53C2×Dic13—31no—
54C2×Dic13—34no—
55C2×Dic13C2×D311yescharacteristic, complemented
56C4×D13—34no—
57C4×D13—34no—
58C4×D13—34no—
59C4×D13C2×D314yesdirect product factor
60C22×C4×D3—131nomaximal, Hall
61C2×C3×C13C22×C412yescomplemented
62C2×C3×C13C2411yescharacteristic
63D39C22×C414yescomplemented
64C3×D13C22×C414yescomplemented
65D3×C13C22×C414yescomplemented
66C22×C13—34no—
67C22×C13—32no—
68C22×C13C22×D311yescharacteristic
69C2×D13—34no—
70C2×D13—32no—
71C2×D13—316no—
72C2×D13C4×D314yesdirect product factor
73C2×D13C22×D312yes—
74C4×C13—32no—
75C4×C13C22×D312yescomplemented
76Dic13—32no—
77Dic13C22×D312yescomplemented
78C23×D3—131no—
79C22×C3×C4—131no—
80C22×Dic3—131no—
81C2×C4×D3—131no—
82C2×C4×D3—131no—
83C2×C4×D3—131no—
84C2×C4×D3—138no—
85C2×C4×D3D1311yescharacteristic, direct product factor
86C3×C13C23×C411yescharacteristic, complemented, Hall
87C23×C4—391noSylow
88C2×C13—34no—
89C2×C13C2×C4×D312yescomplemented
90C2×C13C23×D311yescharacteristic
91D13—34no—
92D13C2×C4×D314yesdirect product factor
93C23×C3—131no—
94C22×D3—131no—
95C22×D3—138no—
96C22×D3—134no—
97C22×D3C2×D1311yescharacteristic
98C2×C3×C4—131no—
99C2×C3×C4—134no—
100C2×C3×C4C2×D1311yescharacteristic, complemented
101C2×Dic3—131no—
102C2×Dic3—134no—
103C2×Dic3C2×D1311yescharacteristic, complemented
104C4×D3—134no—
105C4×D3—134no—
106C4×D3—134no—
107C4×D3C2×D1314yesdirect product factor
108C24—391no—
109C22×C4—31no—
110C22×C4—131no—
111C22×C4—391no—
112C22×C4—398no—
113C22×C4—391no—
114C22×C4—391no—
115C22×C4—391no—
116C13C22×C4×D311yescharacteristic, complemented, Sylow
117C22×C3—134no—
118C22×C3—132no—
119C22×C3C22×D1311yescharacteristic
120C2×D3—134no—
121C2×D3—132no—
122C2×D3—1316no—
123C2×D3C4×D1314yesdirect product factor
124C2×D3C22×D1312yes—
125C3×C4—132no—
126C3×C4C22×D1312yescomplemented
127Dic3—132no—
128Dic3C22×D1312yescomplemented
129C23—31no—
130C23—131no—
131C23—394no—
132C23—398no—
133C23—391no—
134C2×C4—31no—
135C2×C4—34no—
136C2×C4—131no—
137C2×C4—134no—
138C2×C4—394no—
139C2×C4—394no—
140C2×C4—394no—
141C2×C4—391no—
142C2×C4—394no—
143C2×C4D3×D1311yescharacteristic, direct product factor
144C2×C3—134no—
145C2×C3C2×C4×D1312yescomplemented
146C2×C3C23×D1311yescharacteristic
147D3—134no—
148D3C2×C4×D1314yesdirect product factor
149C22—34no—
150C22—32no—
151C22—134no—
152C22—132no—
153C22—3916no—
154C22—394no—
155C22—392no—
156C22C2×D3×D1311yescharacteristic
157C4—32no—
158C4—132no—
159C4—392no—
160C4C2×D3×D1312yesdirect product factor
161C3C22×C4×D1311yescharacteristic, complemented, Sylow
162C2—34no—
163C2—134no—
164C2—394no—
165C2C4×D3×D1312yesdirect product factor
166C2C22×D3×D1311yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×D13
commutator, hypocenterC3×C13C23×C4
FrattiniC2C22×D3×D13
FittingC2×C3×C4×C13C22
socleC22×C3×C13C23
prime radicalC22×D3×D13C2
cosocleC2×C3×C13C24
LCSG ▷ C3×C13
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D39C2semidirect
3. C2×C4×D3×C13C2semidirect
4. C2×C3×C4×D13C2semidirect
5. C2×#64601C2semidirect
6. C2×D3×Dic13C2semidirect
7. C2×Dic3×D13C2semidirect
8. C4×D3×D13C2direct (N × H)
13. C2×D3×D13C4direct (N × H)
15. C2×C3×C4×C13C22semidirect
16. C2×Dic39C22semidirect
17. C4×D39C22semidirect
18. C2×Dic3×C13C22semidirect
19. C4×D3×C13C22semidirect
20. C2×C3×Dic13C22semidirect
21. C3×C4×D13C22semidirect
22. #64601C22semidirect
23. D3×Dic13C22semidirect
24. Dic3×D13C22semidirect
32. C2×C4×D13D3direct (N × H)
34. C2×D39C2×C4semidirect
36. C2×D3×C13C2×C4semidirect
38. C2×C3×D13C2×C4semidirect
40. D3×D13C2×C4direct (N × H)
41. C3×C4×C13C23semidirect
42. Dic39C23semidirect
43. C3×Dic13C23semidirect
44. Dic3×C13C23semidirect
52. C2×C4×C13C2×D3semidirect
55. C2×Dic13C2×D3semidirect
59. C4×D13C2×D3direct (N × H)
61. C2×C3×C13C22×C4semidirect
63. D39C22×C4semidirect
64. C3×D13C22×C4semidirect
65. D3×C13C22×C4semidirect
72. C2×D13C4×D3direct (N × H)
75. C4×C13C22×D3semidirect
77. Dic13C22×D3semidirect
85. C2×C4×D3D13direct (N × H)
86. C3×C13C23×C4semidirect
89. C2×C13C2×C4×D3semidirect
92. D13C2×C4×D3direct (N × H)
100. C2×C3×C4C2×D13semidirect
103. C2×Dic3C2×D13semidirect
107. C4×D3C2×D13direct (N × H)
116. C13C22×C4×D3semidirect
123. C2×D3C4×D13direct (N × H)
126. C3×C4C22×D13semidirect
128. Dic3C22×D13semidirect
143. C2×C4D3×D13direct (N × H)
145. C2×C3C2×C4×D13semidirect
148. D3C2×C4×D13direct (N × H)
160. C4C2×D3×D13direct (N × H)
161. C3C22×C4×D13semidirect
165. C2C4×D3×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×C4×D392
C2×C4×D3×C132
C2×C3×C4×D132
C2×#646012
C2×D3×Dic132
C2×Dic3×D132
C4×D3×D132
C22×C4×D133
C22×C4×D313