Finite Group Databasebeta

← C2×D13×SD64 #16021036

Subgroups — C2×D13×SD64 #16021036

Order 3328.

502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×D13×Q32C211yesmaximal, characteristic, complemented
2C2×D13×D16C211yesmaximal, characteristic
3C2×#11718041C211yesmaximal, characteristic, complemented
4C2×#11718112C211yesmaximal, characteristic, complemented
5C2×#11718113C211yesmaximal, characteristic, complemented
6D13×SD64C218yesmaximal, direct product factor
7C2×D13×C32C211yesmaximal, characteristic, complemented
8C2×C13×SD64C211yesmaximal, characteristic, complemented
9C2×Q16×D13—21no—
10C2×D8×D13—21no—
11C2×C13×Q32C2211yescharacteristic, complemented
12C2×C13×D16C2211yescharacteristic
13C2×#88069—21no—
14C2×#88066—21no—
15D13×Q32—22no—
16D13×Q32C2214yescomplemented
17D13×D16—22no—
18D13×D16C2214yes—
19C2×Dic104C2211yescharacteristic, complemented
20C2×D208C2211yescharacteristic
21C2×C16×D13C2211yescharacteristic
22C13×SD64C2214yescomplemented
23C2×C13×C32C2211yescharacteristic, complemented
24#11718113C2214yescomplemented
25#11718112C2214yescomplemented
26C2×#88034C2211yescharacteristic, complemented
27#11718041C2214yescomplemented
28D13×C32C2214yescomplemented
29C2×Q8×D13—41no—
30C2×D4×D13—41no—
31C2×C13×Q16—21no—
32C2×C13×D8—21no—
33C2×#6107—41no—
34C2×#6104—41no—
35Q16×D13—24no—
36Q16×D13—42no—
37D8×D13—24no—
38D8×D13—42no—
39C2×Dic52—21no—
40C2×D104—21no—
41C2×C8×D13D411yescharacteristic
42C13×Q32—21no—
43C13×Q32C2312yescomplemented
44C13×D16—21no—
45C13×D16C2312yes—
46C2×C13×C16C2311yescharacteristic
47#88069—24no—
48#88066—24no—
49C2×#6090D411yescharacteristic
50Dic104—21no—
51Dic104C2312yescomplemented
52D208—21no—
53D208C2312yes—
54C16×D13D412yes—
55C16×D13C2312yes—
56C13×C32C2312yescomplemented
57#88034C2312yescomplemented
58C22×SD64—131nomaximal, Sylow
59C23×D13—81no—
60C2×Q8×C13—41no—
61C2×D4×C13—41no—
62C2×C22⋊D13—81no—
63Q8×D13—44no—
64Q8×D13—82no—
65D4×D13—44no—
66D4×D13—82no—
67C2×D52—41no—
68C2×C4×D13—81no—
69C2×C4×D13D811yescharacteristic
70C2×Dic26—41no—
71C2×Dic26—81no—
72C13×Q16—22no—
73C13×Q16—41no—
74C13×D8—22no—
75C13×D8—41no—
76C2×C8×C13C2×D411yescharacteristic
77#6107—44no—
78#6104—44no—
79C2×#1055D811yescharacteristic
80Dic52—22no—
81Dic52—41no—
82D104—22no—
83D104—41no—
84C8×D13D812yes—
85C8×D13C2×D412yes—
86C13×C16C2×D411yescharacteristic
87C13×C16C2411yescharacteristic
88#6090C2×D412yes—
89C22×Q32—131no—
90C22×D16—131no—
91C2×SD64—131no—
92C2×SD64—131no—
93C2×SD64—138no—
94C2×SD64—131no—
95C2×SD64D1311yescharacteristic, direct product factor
96C22×C32—131no—
97C23×C13—81no—
98C22×D13—81no—
99C22×D13—84no—
100C22×D13—164no—
101C22×D13D1611yescharacteristic
102Q8×C13—42no—
103Q8×C13—81no—
104D4×C13—42no—
105D4×C13—81no—
106C2×C4×C13—81no—
107C2×C4×C13C2×D811yescharacteristic
108C22⋊D13—84no—
109C2×Dic13—81no—
110C2×Dic13D1611yescharacteristic
111D52—42no—
112D52—81no—
113C4×D13—84no—
114C4×D13D1612yes—
115C4×D13C2×D812yes—
116Dic26—42no—
117Dic26—81no—
118Dic26—84no—
119C8×C13C2×D811yescharacteristic
120C8×C13C22×D411yescharacteristic
121#1055C2×D812yes—
122C22×Q16—261no—
123C22×D8—261no—
124C2×Q32—134no—
125C2×Q32—131no—
126C2×Q32—262no—
127C2×Q32—261no—
128C2×Q32C2×D1311yescharacteristic, complemented
129C2×D16—134no—
130C2×D16—131no—
131C2×D16—262no—
132C2×D16—261no—
133C2×D16C2×D1311yescharacteristic
134C22×C16—131no—
135SD64—134no—
136SD64—134no—
137SD64—134no—
138SD64C2×D1314yesdirect product factor
139C2×C32—131no—
140C2×C32—134no—
141C2×C32C2×D1311yescharacteristic, complemented
142C22×C13—82no—
143C22×C13—162no—
144C22×C13C2×D1611yescharacteristic
145C2×D13—82no—
146C2×D13—162no—
147C2×D13—168no—
148C2×D13SD6414yesdirect product factor
149C2×D13C2×D1612yes—
150C4×C13—82no—
151C4×C13C2×D1611yescharacteristic
152C4×C13C22×D811yescharacteristic
153Dic13—82no—
154Dic13C2×D1612yes—
155C22×Q8—521no—
156C22×D4—521no—
157C2×Q16—21no—
158C2×Q16—264no—
159C2×Q16—261no—
160C2×Q16—522no—
161C2×Q16—521no—
162C2×D8—21no—
163C2×D8—264no—
164C2×D8—261no—
165C2×D8—522no—
166C2×D8—521no—
167C22×C8—131no—
168Q32—21no—
169Q32—132no—
170Q32—264no—
171Q32—261no—
172Q32C22×D1312yescomplemented
173D16—21no—
174D16—132no—
175D16—264no—
176D16—261no—
177D16C22×D1312yes—
178C2×C16—131no—
179C2×C16—132no—
180C2×C16—132no—
181C2×C16C22×D1311yescharacteristic
182C32—132no—
183C32C22×D1312yescomplemented
184C2×C13—162no—
185C2×C13C2×SD6412yescomplemented
186C2×C13C22×D1611yescharacteristic
187D13—162no—
188D13C2×SD6414yesdirect product factor
189C24—1041no—
190C2×Q8—41no—
191C2×Q8—524no—
192C2×Q8—521no—
193C2×Q8—1041no—
194C2×Q8—1042no—
195C2×D4—41no—
196C2×D4—524no—
197C2×D4—521no—
198C2×D4—1042no—
199C2×D4—1041no—
200C22×C4—131no—
201C22×C4—1041no—
202Q16—22no—
203Q16—41no—
204Q16—262no—
205Q16—524no—
206Q16—521no—
207D8—22no—
208D8—41no—
209D8—262no—
210D8—524no—
211D8—521no—
212C2×C8—131no—
213C2×C8—132no—
214C2×C8—132no—
215C2×C8D4×D1311yescharacteristic
216C16—132no—
217C16D4×D1311yescharacteristic
218C16C23×D1311yescharacteristic
219C13C22×SD6411yescharacteristic, complemented, Sylow
220C23—81no—
221C23—131no—
222C23—1044no—
223C23—1041no—
224C23—2084no—
225Q8—42no—
226Q8—81no—
227Q8—522no—
228Q8—1044no—
229Q8—1041no—
230D4—42no—
231D4—81no—
232D4—522no—
233D4—1044no—
234D4—1041no—
235C2×C4—81no—
236C2×C4—131no—
237C2×C4—132no—
238C2×C4—132no—
239C2×C4—1044no—
240C2×C4—1041no—
241C2×C4D8×D1311yescharacteristic
242C8—132no—
243C8D8×D1311yescharacteristic
244C8C2×D4×D1311yescharacteristic
245C22—82no—
246C22—132no—
247C22—134no—
248C22—162no—
249C22—1042no—
250C22—2088no—
251C22—2082no—
252C22D13×D1611yescharacteristic
253C4—82no—
254C4—132no—
255C4—1042no—
256C4D13×D1611yescharacteristic
257C4C2×D8×D1311yescharacteristic
258C2—134no—
259C2—162no—
260C2—2082no—
261C2D13×SD6412yesdirect product factor
262C2C2×D13×D1611yescharacteristic
subgroupG/H
centerC22D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC2×C13×SD64C2
socleC22×C13C2×D16
prime radicalC2×D13×D16C2
hypercenterC2×SD64D13
hypocenterC13C22×SD64
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×D13×Q32C2semidirect
3. C2×#11718041C2semidirect
4. C2×#11718112C2semidirect
5. C2×#11718113C2semidirect
6. D13×SD64C2direct (N × H)
7. C2×D13×C32C2semidirect
8. C2×C13×SD64C2semidirect
11. C2×C13×Q32C22semidirect
16. D13×Q32C22semidirect
19. C2×Dic104C22semidirect
22. C13×SD64C22semidirect
23. C2×C13×C32C22semidirect
24. #11718113C22semidirect
25. #11718112C22semidirect
26. C2×#88034C22semidirect
27. #11718041C22semidirect
28. D13×C32C22semidirect
43. C13×Q32C23semidirect
51. Dic104C23semidirect
56. C13×C32C23semidirect
57. #88034C23semidirect
95. C2×SD64D13direct (N × H)
128. C2×Q32C2×D13semidirect
138. SD64C2×D13direct (N × H)
141. C2×C32C2×D13semidirect
148. C2×D13SD64direct (N × H)
172. Q32C22×D13semidirect
183. C32C22×D13semidirect
185. C2×C13C2×SD64semidirect
188. D13C2×SD64direct (N × H)
219. C13C22×SD64semidirect
261. C2D13×SD64direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×Q322
C2×D13×D162
C2×#117180412
C2×#117181122
C2×#117181132
D13×SD642
C2×D13×C322
C2×C13×SD642
C22×SD6413