Finite Group Databasebeta

← #13125318

Subgroups — #13125318

Order 1664.

596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88173C211yesmaximal, characteristic, complemented
2C2×#88168C212yesmaximal, complemented
3C2×D8×D13C211yesmaximal, characteristic, complemented
4#11719379C212yesmaximal, complemented
5C13×#495C211yesmaximal, characteristic, complemented
6#11718852C211yesmaximal, characteristic, complemented
7#11718837C212yesmaximal, complemented
8#11718812C211yesmaximal, characteristic, complemented
9#11718719C212yesmaximal, complemented
10#11718356C211yesmaximal, characteristic, complemented
11#11718350C211yesmaximal, characteristic, complemented
12C2×#6131C2212yes—
13C2×D4×D13C2212yes—
14C2×C13×Q16C2211yescharacteristic, complemented
15C2×C13×SD16C2212yescomplemented
16C2×C13×D8C2211yescharacteristic
17C13×#124C2212yescomplemented
18#88201C2212yescomplemented
19C2×#6106C2212yescomplemented
20C2×#6106C2212yescomplemented
21#88194C2212yescomplemented
22C2×#6104C2212yes—
23C2×#6104C2212yescomplemented
24#88173—24no—
25#88168—28no—
26D8×D13—24no—
27C2×D104C2211yescharacteristic
28C2×D104C2212yescomplemented
29C2×D104C2211yescharacteristic, complemented
30C2×#6094C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32#88138—24no—
33#88136—24no—
34#88128C2212yescomplemented
35#88126C2211yescharacteristic
36C4×C8×C13C2211yescharacteristic, complemented
37#88055C2211yescharacteristic, complemented
38C8×Dic13C2211yescharacteristic, complemented
39#88043C2211yescharacteristic, complemented
40C23×D13—22no—
41C2×Q8×C13C2312yes—
42C2×D4×C13C2312yes—
43C2×C22⋊D13—22no—
44C2×C22⋊D13—24no—
45#6131—24no—
46#6131—24no—
47D4×D13—24no—
48D4×D13—24no—
49C2×D52—22no—
50C2×D52—24no—
51C2×D52C2312yes—
52C2×D52C2312yes—
53C2×C4×D13—22no—
54C2×C4×D13C2311yescharacteristic
55C13×Q16—22no—
56C13×SD16—24no—
57C13×D8—22no—
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2311yescharacteristic
60C13×C22⋊C4—24no—
61C42×C13C2311yescharacteristic
62#6106—24no—
63#6106—24no—
64#6104—24no—
65#6104—24no—
66#6103—24no—
67#6103D412yes—
68#6101D412yes—
69C4×Dic13C2311yescharacteristic
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72D104—22no—
73D104—24no—
74D104—22no—
75#6094D414yescomplemented
76C8×D13D414yescomplemented
77#3155—131nomaximal, Sylow
78C23×C13—22no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—44no—
82C22×D13—84no—
83C22×D13C2×D411yescharacteristic
84Q8×C13—22no—
85Q8×C13—22no—
86D4×C13—22no—
87D4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13C2×D412yes—
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—44no—
92C22⋊D13—84no—
93C2×Dic13C2×D412yes—
94C2×Dic13C2×D411yescharacteristic
95D52—22no—
96D52—22no—
97D52—22no—
98D52—22no—
99D52—44no—
100D52—84no—
101C4×D13—44no—
102C4×D13C2×D412yes—
103C4×D13C2×D412yes—
104C8×C13C2×D412yes—
105C8×C13C2×D412yes—
106#1055C2×D412yes—
107#1055C2×D412yes—
108C2×AGL(1,ℤ/8)—132no—
109C2×#135—131no—
110C22×D8—131no—
111#535—132no—
112#496—132no—
113#496—132no—
114#495—131no—
115#495D1311yescharacteristic, complemented
116#493—131no—
117#493—131no—
118#405—131no—
119C22×C13—42no—
120C22×C13—44no—
121C22×C13C22×D411yescharacteristic
122C2×D13—22no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—44no—
126C2×D13—44no—
127C2×D13—88no—
128C2×D13#12712yes—
129C4×C13—22no—
130C4×C13—42no—
131C4×C13C22×D411yescharacteristic
132C4×C13C22×D411yescharacteristic
133Dic13—22no—
134Dic13#12712yes—
135C2×#41—132no—
136C22×D4—132no—
137AGL(1,ℤ/8)—268no—
138#135—264no—
139C2×Q16C2×D1311yescharacteristic, complemented
140C2×SD16—132no—
141C2×SD16—132no—
142C2×SD16C2×D1312yescomplemented
143C2×D8—132no—
144C2×D8—132no—
145C2×D8—131no—
146C2×D8—131no—
147C2×D8—132no—
148C2×D8—264no—
149C2×D8C2×D1311yescharacteristic
150C2×M16—131no—
151C22×C8—131no—
152#127—132no—
153#127—132no—
154#124—132no—
155#124C2×D1312yescomplemented
156#121—264no—
157#120—264no—
158#117—131no—
159#97—131no—
160#97—131no—
161C4×C8—131no—
162C4×C8C2×D1311yescharacteristic, complemented
163C2×C13—82no—
164C2×C13C2×#12711yescharacteristic
165C2×C13#57612yes—
166D13—22no—
167D13—82no—
168D13—82no—
169C24—262no—
170#41—264no—
171#41—264no—
172C2×Q8C22×D1312yes—
173C2×D4—132no—
174C2×D4—132no—
175C2×D4—262no—
176C2×D4—264no—
177C2×D4—264no—
178C2×D4—262no—
179C2×D4—264no—
180C2×D4—264no—
181C2×D4C22×D1312yes—
182C22×C4—131no—
183C22×C4—262no—
184Q16—22no—
185SD16—24no—
186SD16—264no—
187SD16—264no—
188D8—22no—
189D8—264no—
190D8—264no—
191D8—262no—
192D8—262no—
193D8—264no—
194M16—134no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8—134no—
198C2×C8C22×D1311yescharacteristic
199C2×C8C22×D1311yescharacteristic
200C4⋊C4—132no—
201C22⋊C4—24no—
202C22⋊C4—132no—
203C22⋊C4—264no—
204C42—131no—
205C42C22×D1311yescharacteristic
206C13#315511yescharacteristic, complemented, Sylow
207C23—22no—
208C23—131no—
209C23—262no—
210C23—262no—
211C23—524no—
212C23—1044no—
213Q8—22no—
214Q8—22no—
215D4—22no—
216D4—22no—
217D4—262no—
218D4—262no—
219D4—262no—
220D4—262no—
221D4—524no—
222D4—524no—
223D4—1044no—
224D4—1044no—
225C2×C4—22no—
226C2×C4—131no—
227C2×C4—132no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—524no—
231C2×C4D4×D1312yes—
232C2×C4C23×D1311yescharacteristic
233C8—132no—
234C8—132no—
235C8D4×D1312yes—
236C8D4×D1312yes—
237C22—44no—
238C22—42no—
239C22—132no—
240C22—262no—
241C22—524no—
242C22—524no—
243C22—522no—
244C22—522no—
245C22—1048no—
246C22C2×D4×D1311yescharacteristic
247C4—22no—
248C4—42no—
249C4—132no—
250C4—262no—
251C4C2×D4×D1311yescharacteristic
252C4C2×D4×D1311yescharacteristic
253C2—82no—
254C2—262no—
255C2—1042no—
256C2—1042no—
257C2D13×#12711yescharacteristic
258C2#1171947412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#495C2
socleC22×C13C22×D4
hypercenter#495D13
hypocenterC13#3155
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#88173C2semidirect
2. C2×#88168C2semidirect
3. C2×D8×D13C2semidirect
4. #11719379C2semidirect
5. C13×#495C2semidirect
6. #11718852C2semidirect
7. #11718837C2semidirect
8. #11718812C2semidirect
9. #11718719C2semidirect
10. #11718356C2semidirect
11. #11718350C2semidirect
14. C2×C13×Q16C22semidirect
15. C2×C13×SD16C22semidirect
17. C13×#124C22semidirect
18. #88201C22semidirect
19. C2×#6106C22semidirect
20. C2×#6106C22semidirect
21. #88194C22semidirect
23. C2×#6104C22semidirect
28. C2×D104C22semidirect
29. C2×D104C22semidirect
34. #88128C22semidirect
36. C4×C8×C13C22semidirect
37. #88055C22semidirect
38. C8×Dic13C22semidirect
39. #88043C22semidirect
75. #6094D4semidirect
76. C8×D13D4semidirect
115. #495D13semidirect
139. C2×Q16C2×D13semidirect
142. C2×SD16C2×D13semidirect
155. #124C2×D13semidirect
162. C4×C8C2×D13semidirect
206. C13#3155semidirect

Maximal subgroups

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

subgroupindex
C2×#881732
C2×#881682
C2×D8×D132
#117193792
C13×#4952
#117188522
#117188372
#117188122
#117187192
#117183562
#117183502
#315513