Finite Group Databasebeta

← D3×D4×D13 #11929217

Subgroups — D3×D4×D13 #11929217

Order 1248.

472 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 122 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
2D4×D39C211yesmaximal, characteristic, complemented
3D3×D4×C13C211yesmaximal, characteristic, complemented
4C3×D4×D13C211yesmaximal, characteristic, complemented
5#10597756C212yesmaximal, complemented
6D3×C22⋊D13C212yesmaximal, complemented
7#67×D13C212yesmaximal, complemented
8#10597743C211yesmaximal, characteristic, complemented
9D3×D52C211yesmaximal, characteristic, complemented
10D12×D13C211yesmaximal, characteristic, complemented
11C4×D3×D13C211yesmaximal, characteristic, complemented
12C2×D4×D13—31nomaximal, Hall
13C22×D39C2212yescomplemented
14C22×D3×C13C2212yescomplemented
15C22×C3×D13C2212yescomplemented
16C2×D3×D13—28no—
17C2×D3×D13C2211yescharacteristic
18C2×D3×D13C2212yescomplemented
19C2×D3×D13C2212yescomplemented
20C2×D3×D13C2212yescomplemented
21C3×D4×C13C2211yescharacteristic, complemented
22#64625C2212yescomplemented
23D156C2211yescharacteristic, complemented
24C4×D39C2211yescharacteristic, complemented
25C13×#67C2212yescomplemented
26C13×D12C2211yescharacteristic, complemented
27C4×D3×C13C2211yescharacteristic, complemented
28C3×C22⋊D13C2212yescomplemented
29C3×D52C2211yescharacteristic, complemented
30C3×C4×D13C2211yescharacteristic, complemented
31#64604C2212yescomplemented
32#64603C2212yescomplemented
33#64602C2212yescomplemented
34#64601C2211yescharacteristic, complemented
35D3×Dic13C2211yescharacteristic, complemented
36Dic3×D13C2211yescharacteristic, complemented
37C23×D13—32no—
38C2×D4×C13—31no—
39C2×C22⋊D13—32no—
40D4×D13—32no—
41D4×D13—31no—
42D4×D13—32no—
43D4×D13—31no—
44D4×D13—31no—
45D4×D13D311yescharacteristic, direct product factor
46C2×D52—31no—
47C2×C4×D13—31no—
48C22×C3×C13C2312yescomplemented
49C2×D39—24no—
50C2×D39C2311yescharacteristic
51C2×D39C2312yescomplemented
52C2×D3×C13—24no—
53C2×D3×C13C2311yescharacteristic
54C2×D3×C13C2312yescomplemented
55C2×C3×D13—24no—
56C2×C3×D13C2311yescharacteristic
57C2×C3×D13C2312yescomplemented
58D3×D13—24no—
59D3×D13—24no—
60D3×D13—24no—
61D3×D13D414yesdirect product factor
62C3×C4×C13C2311yescharacteristic, complemented
63Dic39C2311yescharacteristic, complemented
64C3×Dic13C2311yescharacteristic, complemented
65Dic3×C13C2311yescharacteristic, complemented
66C23×C13—32no—
67C22×D13—31no—
68C22×D13—32no—
69C22×D13—32no—
70C22×D13—32no—
71C22×D13—32no—
72C22×D13—68no—
73C22×D13C2×D312yescomplemented
74D4×C13—32no—
75D4×C13—31no—
76D4×C13C2×D311yescharacteristic, complemented
77C2×C4×C13—31no—
78C22⋊D13—32no—
79C22⋊D13—32no—
80C22⋊D13—32no—
81C22⋊D13C2×D312yescomplemented
82C2×Dic13—31no—
83D52—32no—
84D52—31no—
85D52C2×D311yescharacteristic, complemented
86C4×D13—31no—
87C4×D13—31no—
88C4×D13—31no—
89C4×D13C2×D311yescharacteristic, complemented
90C2×D3×D4—131nomaximal, Hall
91C2×C3×C13—22no—
92C2×C3×C13C2411yescharacteristic
93D39—22no—
94D39C2×D412yescomplemented
95C3×D13—22no—
96C3×D13C2×D412yescomplemented
97D3×C13—22no—
98D3×C13C2×D412yescomplemented
99C22×C13—31no—
100C22×C13—32no—
101C22×C13—64no—
102C22×C13C22×D312yescomplemented
103C2×D13—24no—
104C2×D13—31no—
105C2×D13—34no—
106C2×D13—32no—
107C2×D13—64no—
108C2×D13—64no—
109C2×D13—64no—
110C2×D13—64no—
111C2×D13C22×D311yescharacteristic
112C2×D13C22×D312yescomplemented
113C4×C13—31no—
114C4×C13C22×D311yescharacteristic, complemented
115Dic13—31no—
116Dic13C22×D311yescharacteristic, complemented
117C23×D3—132no—
118C2×C3×D4—131no—
119C2×#67—132no—
120D3×D4—132no—
121D3×D4—131no—
122D3×D4—132no—
123D3×D4—131no—
124D3×D4—131no—
125D3×D4D1311yescharacteristic, direct product factor
126C2×D12—131no—
127C2×C4×D3—131no—
128C3×C13C22×D411yescharacteristic, complemented, Hall
129C22×D4—391noSylow
130C2×C13—22no—
131C2×C13—32no—
132C2×C13—62no—
133C2×C13C23×D311yescharacteristic
134D13—22no—
135D13—32no—
136D13—62no—
137D13D3×D412yesdirect product factor
138C23×C3—132no—
139C22×D3—131no—
140C22×D3—132no—
141C22×D3—132no—
142C22×D3—132no—
143C22×D3—132no—
144C22×D3—268no—
145C22×D3C2×D1312yescomplemented
146C3×D4—132no—
147C3×D4—131no—
148C3×D4C2×D1311yescharacteristic, complemented
149C2×C3×C4—131no—
150#67—132no—
151#67—132no—
152#67—132no—
153#67C2×D1312yescomplemented
154C2×Dic3—131no—
155D12—132no—
156D12—131no—
157D12C2×D1311yescharacteristic, complemented
158C4×D3—131no—
159C4×D3—131no—
160C4×D3—131no—
161C4×D3C2×D1311yescharacteristic, complemented
162C24—392no—
163C2×D4—31no—
164C2×D4—131no—
165C2×D4—391no—
166C2×D4—391no—
167C2×D4—392no—
168C2×D4—391no—
169C2×D4—392no—
170C2×D4—392no—
171C2×D4—391no—
172C22×C4—391no—
173C13C2×D3×D411yescharacteristic, complemented, Sylow
174C22×C3—131no—
175C22×C3—132no—
176C22×C3—264no—
177C22×C3C22×D1312yescomplemented
178C2×D3—24no—
179C2×D3—131no—
180C2×D3—134no—
181C2×D3—132no—
182C2×D3—264no—
183C2×D3—264no—
184C2×D3—264no—
185C2×D3—264no—
186C2×D3C22×D1311yescharacteristic
187C2×D3C22×D1312yescomplemented
188C3×C4—131no—
189C3×C4C22×D1311yescharacteristic, complemented
190Dic3—131no—
191Dic3C22×D1311yescharacteristic, complemented
192C23—32no—
193C23—132no—
194C23—391no—
195C23—392no—
196C23—392no—
197C23—392no—
198C23—392no—
199C23—788no—
200D4—32no—
201D4—31no—
202D4—132no—
203D4—131no—
204D4—392no—
205D4—392no—
206D4—392no—
207D4—392no—
208D4—391no—
209D4D3×D1311yescharacteristic, direct product factor
210C2×C4—31no—
211C2×C4—131no—
212C2×C4—391no—
213C2×C4—391no—
214C2×C4—391no—
215C2×C4—391no—
216C2×C3—22no—
217C2×C3—132no—
218C2×C3—262no—
219C2×C3C23×D1311yescharacteristic
220D3—22no—
221D3—132no—
222D3—262no—
223D3D4×D1312yesdirect product factor
224C22—31no—
225C22—32no—
226C22—64no—
227C22—131no—
228C22—132no—
229C22—264no—
230C22—394no—
231C22—391no—
232C22—392no—
233C22—784no—
234C22—784no—
235C22—784no—
236C22—784no—
237C22C2×D3×D1312yescomplemented
238C4—31no—
239C4—131no—
240C4—391no—
241C4C2×D3×D1311yescharacteristic, complemented
242C3C2×D4×D1311yescharacteristic, complemented, Sylow
243C2—22no—
244C2—32no—
245C2—62no—
246C2—132no—
247C2—262no—
248C2—392no—
249C2—782no—
250C2C22×D3×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FittingC3×D4×C13C22
hypercenterD4D3×D13
hypocenterC3×C13C22×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D13C2semidirect
2. D4×D39C2semidirect
3. D3×D4×C13C2semidirect
4. C3×D4×D13C2semidirect
5. #10597756C2semidirect
6. D3×C22⋊D13C2semidirect
7. #67×D13C2semidirect
8. #10597743C2semidirect
9. D3×D52C2semidirect
10. D12×D13C2semidirect
11. C4×D3×D13C2semidirect
13. C22×D39C22semidirect
14. C22×D3×C13C22semidirect
15. C22×C3×D13C22semidirect
18. C2×D3×D13C22semidirect
19. C2×D3×D13C22semidirect
20. C2×D3×D13C22semidirect
21. C3×D4×C13C22semidirect
22. #64625C22semidirect
23. D156C22semidirect
24. C4×D39C22semidirect
25. C13×#67C22semidirect
26. C13×D12C22semidirect
27. C4×D3×C13C22semidirect
28. C3×C22⋊D13C22semidirect
29. C3×D52C22semidirect
30. C3×C4×D13C22semidirect
31. #64604C22semidirect
32. #64603C22semidirect
33. #64602C22semidirect
34. #64601C22semidirect
35. D3×Dic13C22semidirect
36. Dic3×D13C22semidirect
45. D4×D13D3direct (N × H)
48. C22×C3×C13C23semidirect
51. C2×D39C23semidirect
54. C2×D3×C13C23semidirect
57. C2×C3×D13C23semidirect
61. D3×D13D4direct (N × H)
62. C3×C4×C13C23semidirect
63. Dic39C23semidirect
64. C3×Dic13C23semidirect
65. Dic3×C13C23semidirect
73. C22×D13C2×D3semidirect
76. D4×C13C2×D3semidirect
81. C22⋊D13C2×D3semidirect
85. D52C2×D3semidirect
89. C4×D13C2×D3semidirect
94. D39C2×D4semidirect
96. C3×D13C2×D4semidirect
98. D3×C13C2×D4semidirect
102. C22×C13C22×D3semidirect
112. C2×D13C22×D3semidirect
114. C4×C13C22×D3semidirect
116. Dic13C22×D3semidirect
125. D3×D4D13direct (N × H)
128. C3×C13C22×D4semidirect
137. D13D3×D4direct (N × H)
145. C22×D3C2×D13semidirect
148. C3×D4C2×D13semidirect
153. #67C2×D13semidirect
157. D12C2×D13semidirect
161. C4×D3C2×D13semidirect
173. C13C2×D3×D4semidirect
177. C22×C3C22×D13semidirect
187. C2×D3C22×D13semidirect
189. C3×C4C22×D13semidirect
191. Dic3C22×D13semidirect
209. D4D3×D13direct (N × H)
223. D3D4×D13direct (N × H)
237. C22C2×D3×D13semidirect
241. C4C2×D3×D13semidirect
242. C3C2×D4×D13semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D132
D4×D392
D3×D4×C132
C3×D4×D132
#105977562
D3×C22⋊D132
#67×D132
#105977432
D3×D522
D12×D132
C4×D3×D132
C2×D4×D133
C2×D3×D413