Finite Group Databasebeta

← D13⋊#327 #13130202

Subgroups — D13⋊#327 #13130202

Order 1664.

388 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D13×#121C211yesmaximal, characteristic
2C2×(C2×#261)⋊C4C211yesmaximal, characteristic, complemented
3D13⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal, complemented
5#11718240C212yesmaximal, complemented
6C23×#261—21no—
7C2×D4×D13—21no—
8C2×D4×D13C411yescharacteristic, complemented
9C22×C4×D13C2211yescharacteristic
10C2×D13⋊C8—21no—
11C13×#121C411yescharacteristic, complemented
12#88193—21no—
13#88192C2211yescharacteristic
14#88184C411yescharacteristic, complemented
15#88149C2211yescharacteristic
16C4⋊C4×D13C411yescharacteristic, complemented
17#88138—21no—
18C22⋊C4×D13—21no—
19C22⋊#1057—21no—
20(C2×#261)⋊C4—21no—
21(C2×#261)⋊C4C2212yescomplemented
22#88111C2212yescomplemented
23C23×D13—21no—
24C23×D13D411yescharacteristic
25C22×#261—24no—
26C22×#261—22no—
27C22×#261—42no—
28C22×#261—42no—
29C2×D4×C13—21no—
30C2×D4×C13C2×C411yescharacteristic, complemented
31C22×C4×C13C2×C411yescharacteristic
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C2×C22⋊D13—21no—
35C22×Dic13D411yescharacteristic
36D4×D13—42no—
37D4×D13—42no—
38D4×D13—42no—
39C2×D52—21no—
40C2×D52C2×C411yescharacteristic, complemented
41C2×C4×D13—21no—
42C2×C4×D13—42no—
43C2×C4×D13C2×C411yescharacteristic
44C2×C4×D13D411yescharacteristic
45C2×C4×D13D411yescharacteristic
46C2×C4×D13C2311yescharacteristic
47C2×#1057—22no—
48D13⋊C8—42no—
49C13×C4⋊C4C2×C411yescharacteristic, complemented
50C13×C22⋊C4—21no—
51C22⋊Dic13—21no—
52#6103—21no—
53#6103—21no—
54C4⋊Dic13C2×C411yescharacteristic, complemented
55#6101—21no—
56C2×#327—131nomaximal, Sylow
57C23×C13—21no—
58C23×C13C22⋊C411yescharacteristic
59C22×D13—22no—
60C22×D13—22no—
61C22×D13—21no—
62C22×D13—42no—
63C22×D13—42no—
64C22×D13—42no—
65C22×D13C22⋊C411yescharacteristic
66C22×D13D812yes—
67C22×D13SD1612yes—
68C22×D13C2×D411yescharacteristic
69C2×#261—24no—
70C2×#261—42no—
71C2×#261—48no—
72C2×#261—42no—
73D4×C13—41no—
74D4×C13—42no—
75C2×C4×C13—21no—
76C2×C4×C13—41no—
77C2×C4×C13C22⋊C411yescharacteristic
78C2×C4×C13C22×C411yescharacteristic
79C22⋊D13—42no—
80C22⋊D13—42no—
81C22⋊D13—41no—
82C22⋊D13—41no—
83C2×Dic13—21no—
84C2×Dic13—41no—
85C2×Dic13C22⋊C411yescharacteristic
86C2×Dic13C2×D411yescharacteristic
87D52—41no—
88D52—41no—
89D52—41no—
90C4×D13—22no—
91C4×D13—22no—
92C4×D13—41no—
93C4×D13—41no—
94C4×D13—42no—
95#1057—42no—
96C2×#121—131no—
97C2×C22⋊C8—131no—
98C2×#95—131no—
99#327—132no—
100#327—132no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—41no—
104C22×C13—41no—
105C22×C13—41no—
106C22×C13#10212yes—
107C22×C13C2×C22⋊C411yescharacteristic
108C2×D13—21no—
109C2×D13—21no—
110C2×D13—24no—
111C2×D13—24no—
112C2×D13—41no—
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—84no—
116C2×D13#9912yes—
117C2×D13#10212yes—
118C2×D13#10412yes—
119C2×D13C2×D811yescharacteristic
120C2×D13C2×SD1611yescharacteristic
121#261—44no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—41no—
125Dic13—21no—
126Dic13—21no—
127Dic13—41no—
128C22×D4—131no—
129C22×D4—261no—
130C23×C4—131no—
131C23×C4—261no—
132C22×C8—261no—
133#121—131no—
134#121—131no—
135#121—131no—
136#121—261no—
137#121—261no—
138#121#26111yescharacteristic, complemented
139C2×C4⋊C4—131no—
140C2×C22⋊C4—261no—
141C22⋊C8—132no—
142C22⋊C8—261no—
143#95—132no—
144#95—261no—
145C2×C13—22no—
146C2×C13—81no—
147C2×C13C2×#9911yescharacteristic
148C2×C13C2×#10211yescharacteristic
149C2×C13C2×#10411yescharacteristic
150D13—21no—
151D13—21no—
152D13—81no—
153D13#32714yescomplemented
154C24—131no—
155C24—261no—
156C2×D4—21no—
157C2×D4—131no—
158C2×D4—261no—
159C2×D4—261no—
160C2×D4—261no—
161C2×D4—261no—
162C2×D4—522no—
163C2×D4—522no—
164C2×D4—522no—
165C2×D4C2×#26111yescharacteristic, complemented
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—131no—
171C22×C4—261no—
172C22×C4—262no—
173C22×C4—264no—
174C22×C4—522no—
175C22×C4—522no—
176C22×C4—522no—
177C22×C4C2×#26111yescharacteristic
178C2×C8—262no—
179C2×C8—522no—
180C4⋊C4—131no—
181C4⋊C4—261no—
182C4⋊C4C2×#26111yescharacteristic, complemented
183C22⋊C4—21no—
184C22⋊C4—261no—
185C22⋊C4—261no—
186C22⋊C4—261no—
187C13C2×#32711yescharacteristic, complemented, Sylow
188C23—21no—
189C23—131no—
190C23—132no—
191C23—132no—
192C23—131no—
193C23—262no—
194C23—262no—
195C23—261no—
196C23—522no—
197C23—522no—
198C23—522no—
199C23C22⋊#26111yescharacteristic
200D4—41no—
201D4—42no—
202D4—521no—
203D4—521no—
204D4—521no—
205D4—522no—
206D4—521no—
207D4—521no—
208D4—522no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—131no—
212C2×C4—131no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—264no—
216C2×C4—261no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4—522no—
220C2×C4—521no—
221C2×C4—522no—
222C2×C4—528no—
223C2×C4—522no—
224C2×C4C22⋊#26111yescharacteristic
225C2×C4C22×#26111yescharacteristic
226C8—522no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—132no—
233C22—132no—
234C22—132no—
235C22—131no—
236C22—131no—
237C22—264no—
238C22—264no—
239C22—261no—
240C22—261no—
241C22—521no—
242C22—521no—
243C22—521no—
244C22—1044no—
245C22#8811512yes—
246C22C2×C22⋊#26111yescharacteristic
247C4—21no—
248C4—21no—
249C4—41no—
250C4—261no—
251C4—261no—
252C4—524no—
253C4—521no—
254C2—22no—
255C2—81no—
256C2—134no—
257C2—261no—
258C2—261no—
259C2—1041no—
260C2C2×#8811511yescharacteristic
261C2D13⋊#9911yescharacteristic
262C2D13⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radicalD13×#121C2
cosocleC2×C4×D13C23
hypercenter#121#261
hypocenterC13C2×#327
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×(C2×#261)⋊C4C2semidirect
3. D13⋊(C22⋊C8)C2semidirect
4. #11718292C2semidirect
5. #11718240C2semidirect
8. C2×D4×D13C4semidirect
11. C13×#121C4semidirect
14. #88184C4semidirect
16. C4⋊C4×D13C4semidirect
21. (C2×#261)⋊C4C22semidirect
22. #88111C22semidirect
30. C2×D4×C13C2×C4semidirect
40. C2×D52C2×C4semidirect
49. C13×C4⋊C4C2×C4semidirect
54. C4⋊Dic13C2×C4semidirect
138. #121#261semidirect
153. D13#327semidirect
165. C2×D4C2×#261semidirect
182. C4⋊C4C2×#261semidirect
187. C13C2×#327semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
C2×(C2×#261)⋊C42
D13⋊(C22⋊C8)2
#117182922
#117182402
C2×#32713