Finite Group Databasebeta

← C2×#13117150 #16021053

Subgroups — C2×#13117150 #16021053

Order 3328.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11718580C211yesmaximal, characteristic, complemented
2C2×D13×D16C211yesmaximal, characteristic, complemented
3#13117150C218yesmaximal, direct product factor
4C2×#11718113C211yesmaximal, characteristic, complemented
5C2×D416C211yesmaximal, characteristic, complemented
6C2×#11718111C211yesmaximal, characteristic, complemented
7C2×#11718039C211yesmaximal, characteristic, complemented
8C2×C13×SD64C211yesmaximal, characteristic, complemented
9C2×#88173—21no—
10C2×D8×D13—21no—
11C2×C13×Q32C2211yescharacteristic, complemented
12C2×C13×D16C2211yescharacteristic
13C2×#88068—21no—
14C2×#88066—21no—
15#11718580—22no—
16#11718580C2214yescomplemented
17D13×D16—22no—
18D13×D16C2214yescomplemented
19C2×D208C2211yescharacteristic
20C2×D208C2211yescharacteristic, complemented
21C2×C16×D13C2211yescharacteristic
22C13×SD64C2214yescomplemented
23C2×C13×C32C2211yescharacteristic, complemented
24#11718113C2214yescomplemented
25#11718111C2214yescomplemented
26C2×#88034C2211yescharacteristic, complemented
27D416C2214yescomplemented
28#11718039C2214yescomplemented
29C2×#6131—41no—
30C2×D4×D13—41no—
31C2×C13×Q16—21no—
32C2×C13×D8—21no—
33C2×#6106—41no—
34C2×#6104—41no—
35#88173—24no—
36#88173—42no—
37D8×D13—24no—
38D8×D13—42no—
39C2×D104—21no—
40C2×D104—21no—
41C2×C8×D13D411yescharacteristic
42C13×Q32—21no—
43C13×Q32C2312yescomplemented
44C13×D16—21no—
45C13×D16C2312yes—
46C2×C13×C16C2311yescharacteristic
47#88068—24no—
48#88066—24no—
49C2×#6090D411yescharacteristic
50D208—21no—
51D208—21no—
52D208C2312yes—
53D208C2312yescomplemented
54C16×D13D412yes—
55C16×D13C2312yes—
56C13×C32C2312yescomplemented
57#88034C2312yescomplemented
58C2×#2263—131nomaximal, Sylow
59C23×D13—81no—
60C2×Q8×C13—41no—
61C2×D4×C13—41no—
62C2×C22⋊D13—81no—
63#6131—44no—
64#6131—82no—
65D4×D13—44no—
66D4×D13—82no—
67C2×D52—41no—
68C2×D52—41no—
69C2×D52—81no—
70C2×C4×D13—81no—
71C2×C4×D13D811yescharacteristic
72C13×Q16—22no—
73C13×Q16—41no—
74C13×D8—22no—
75C13×D8—41no—
76C2×C8×C13C2×D411yescharacteristic
77#6106—44no—
78#6104—44no—
79C2×#1055D811yescharacteristic
80D104—22no—
81D104—22no—
82D104—41no—
83D104—41no—
84C8×D13D812yes—
85C8×D13C2×D412yes—
86C13×C16C2×D411yescharacteristic
87C13×C16C2411yescharacteristic
88#6090C2×D412yes—
89C2×#508—131no—
90C22×D16—131no—
91#2263—138no—
92C2×SD64—131no—
93C2×SD64D1311yescharacteristic, complemented
94C2×D32—131no—
95C2×D32—131no—
96C2×M64—131no—
97C23×C13—81no—
98C22×D13—81no—
99C22×D13—81no—
100C22×D13—84no—
101C22×D13—164no—
102C22×D13D1611yescharacteristic
103Q8×C13—42no—
104Q8×C13—81no—
105D4×C13—42no—
106D4×C13—81no—
107C2×C4×C13—81no—
108C2×C4×C13C2×D811yescharacteristic
109C22⋊D13—84no—
110C2×Dic13D1611yescharacteristic
111D52—42no—
112D52—42no—
113D52—84no—
114D52—81no—
115D52—81no—
116C4×D13—84no—
117C4×D13D1612yes—
118C4×D13C2×D812yes—
119C8×C13C2×D811yescharacteristic
120C8×C13C22×D411yescharacteristic
121#1055C2×D812yes—
122C2×#135—261no—
123C22×D8—261no—
124#508—134no—
125#508—262no—
126C2×Q32C2×D1311yescharacteristic, complemented
127C2×SD32—261no—
128C2×D16—134no—
129C2×D16—131no—
130C2×D16—131no—
131C2×D16—262no—
132C2×D16—261no—
133C2×D16C2×D1311yescharacteristic
134C22×C16—131no—
135SD64—134no—
136SD64C2×D1314yescomplemented
137D32—134no—
138D32—134no—
139M64—134no—
140C2×C32—131no—
141C2×C32C2×D1311yescharacteristic, complemented
142C22×C13—82no—
143C22×C13—162no—
144C22×C13C2×D1611yescharacteristic
145C2×D13—22no—
146C2×D13—82no—
147C2×D13—82no—
148C2×D13—168no—
149C2×D13—162no—
150C2×D13—162no—
151C2×D13C2×D1612yes—
152C4×C13—82no—
153C4×C13C2×D1611yescharacteristic
154C4×C13C22×D811yescharacteristic
155Dic13C2×D1612yes—
156C2×#41—521no—
157C22×D4—521no—
158#135—264no—
159#135—522no—
160C2×Q16—21no—
161C2×SD16—521no—
162C2×D8—21no—
163C2×D8—264no—
164C2×D8—261no—
165C2×D8—261no—
166C2×D8—522no—
167C2×D8—521no—
168C22×C8—131no—
169Q32—21no—
170Q32C22×D1312yescomplemented
171SD32—264no—
172D16—21no—
173D16—132no—
174D16—132no—
175D16—264no—
176D16—261no—
177D16—261no—
178D16C22×D1312yes—
179C2×C16—131no—
180C2×C16—132no—
181C2×C16—132no—
182C2×C16C22×D1311yescharacteristic
183C32—132no—
184C32C22×D1312yescomplemented
185C2×C13—162no—
186C2×C13#226312yescomplemented
187C2×C13C22×D1611yescharacteristic
188D13—22no—
189D13—162no—
190D13—162no—
191C24—1041no—
192#41—524no—
193#41—1042no—
194C2×Q8—41no—
195C2×D4—41no—
196C2×D4—524no—
197C2×D4—521no—
198C2×D4—521no—
199C2×D4—1041no—
200C2×D4—1042no—
201C2×D4—1041no—
202C22×C4—131no—
203C22×C4—1041no—
204Q16—22no—
205Q16—41no—
206SD16—524no—
207D8—22no—
208D8—41no—
209D8—262no—
210D8—262no—
211D8—524no—
212D8—521no—
213D8—521no—
214C2×C8—131no—
215C2×C8—132no—
216C2×C8—132no—
217C2×C8D4×D1311yescharacteristic
218C16—132no—
219C16D4×D1311yescharacteristic
220C16C23×D1311yescharacteristic
221C13C2×#226311yescharacteristic, complemented, Sylow
222C23—81no—
223C23—131no—
224C23—1044no—
225C23—1041no—
226C23—1041no—
227C23—2084no—
228Q8—42no—
229Q8—81no—
230D4—42no—
231D4—81no—
232D4—522no—
233D4—522no—
234D4—1044no—
235D4—1044no—
236D4—1041no—
237D4—1041no—
238C2×C4—81no—
239C2×C4—131no—
240C2×C4—132no—
241C2×C4—132no—
242C2×C4—1044no—
243C2×C4D8×D1311yescharacteristic
244C8—132no—
245C8D8×D1311yescharacteristic
246C8C2×D4×D1311yescharacteristic
247C22—82no—
248C22—132no—
249C22—162no—
250C22—262no—
251C22—1042no—
252C22—1042no—
253C22—2088no—
254C22—2082no—
255C22—2082no—
256C22D13×D1611yescharacteristic
257C4—82no—
258C4—132no—
259C4D13×D1611yescharacteristic
260C4C2×D8×D1311yescharacteristic
261C2—162no—
262C2—262no—
263C2—2082no—
264C2—2082no—
265C2#1311715012yesdirect product factor
266C2C2×D13×D1611yescharacteristic
subgroupG/H
centerC22D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC2×C13×SD64C2
socleC22×C13C2×D16
hypercenterC2×SD64D13
hypocenterC13C2×#2263
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×#11718580C2semidirect
2. C2×D13×D16C2semidirect
3. #13117150C2direct (N × H)
4. C2×#11718113C2semidirect
5. C2×D416C2semidirect
6. C2×#11718111C2semidirect
7. C2×#11718039C2semidirect
8. C2×C13×SD64C2semidirect
11. C2×C13×Q32C22semidirect
16. #11718580C22semidirect
18. D13×D16C22semidirect
20. C2×D208C22semidirect
22. C13×SD64C22semidirect
23. C2×C13×C32C22semidirect
24. #11718113C22semidirect
25. #11718111C22semidirect
26. C2×#88034C22semidirect
27. D416C22semidirect
28. #11718039C22semidirect
43. C13×Q32C23semidirect
53. D208C23semidirect
56. C13×C32C23semidirect
57. #88034C23semidirect
93. C2×SD64D13semidirect
126. C2×Q32C2×D13semidirect
136. SD64C2×D13semidirect
141. C2×C32C2×D13semidirect
170. Q32C22×D13semidirect
184. C32C22×D13semidirect
186. C2×C13#2263semidirect
221. C13C2×#2263semidirect
265. C2#13117150direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117185802
C2×D13×D162
#131171502
C2×#117181132
C2×D4162
C2×#117181112
C2×#117180392
C2×C13×SD642
C2×#226313