Finite Group Databasebeta

← #13124077

Subgroups — #13124077

Order 1664.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#6131C211yesmaximal, characteristic, complemented
2C2×C13×#137C211yesmaximal, characteristic, complemented
3#11719533C211yesmaximal, characteristic, complemented
4C2×#88203C211yesmaximal, characteristic, complemented
5#11718886C211yesmaximal, characteristic, complemented
6#11718848C214yesmaximal, complemented
7#11718833C214yesmaximal, complemented
8#11718792C211yesmaximal, characteristic, complemented
9#11718787C211yesmaximal, characteristic, complemented
10C2×C13×#41C2211yescharacteristic
11C22×Q8×C13C2211yescharacteristic
12C2×#6131—24no—
13C2×#6131—24no—
14C2×#6131—22no—
15C2×#6131C2214yes—
16C22×D52—21no—
17C22×D52C2211yescharacteristic
18C22×C4×D13—21no—
19C22×C4×D13C2211yescharacteristic
20C13×#137—24no—
21C2×C13×Q16C2212yescomplemented
22C2×C13×SD16C2212yescomplemented
23C2×C13×M16C2211yescharacteristic
24#88203—24no—
25#88200C2212yescomplemented
26C2×#6106C2212yescomplemented
27#88192C2212yescomplemented
28#88191—21no—
29#88189—21no—
30C2×#6104C2212yescomplemented
31C4×C22⋊D13—22no—
32#88180C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34#88075C2214yescomplemented
35#88061C2214yescomplemented
36#88060C2214yescomplemented
37C23×D13—21no—
38C23×D13D411yescharacteristic
39C13×#41—22no—
40C13×#41—22no—
41C2×Q8×C13—22no—
42C2×Q8×C13—21no—
43C2×Q8×C13D414yescomplemented
44C2×Q8×C13C2311yescharacteristic
45C2×Q8×C13C2312yes—
46C2×D4×C13—21no—
47C2×D4×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—22no—
52C22×Dic13D411yescharacteristic
53#6131—216no—
54#6131—28no—
55#6131—28no—
56C2×D52—28no—
57C2×D52—24no—
58C2×D52—21no—
59C2×D52—22no—
60C2×D52D414yescomplemented
61C2×D52C2312yes—
62C2×C4×D13—28no—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13—24no—
66C2×C4×D13D412yes—
67C2×C4×D13C2312yes—
68C13×Q16—24no—
69C13×SD16—24no—
70C13×M16—22no—
71C2×C8×C13C2312yes—
72C22⋊Dic13—21no—
73C22⋊Dic13—22no—
74#6106—24no—
75#6104—24no—
76#6103—22no—
77C4⋊Dic13C2312yes—
78#6101—22no—
79C4×Dic13—21no—
80#6099—22no—
81C2×#1055C2312yes—
82#3005—131nomaximal, Sylow
83C23×C13—21no—
84C23×C13C2×D411yescharacteristic
85C22×D13—22no—
86C22×D13—24no—
87C22×D13—22no—
88C22×D13—42no—
89C22×D13—44no—
90C22×D13C2×D412yes—
91Q8×C13—24no—
92Q8×C13—22no—
93Q8×C13—21no—
94Q8×C13—21no—
95Q8×C13C2×D414yes—
96D4×C13—21no—
97D4×C13—21no—
98D4×C13—42no—
99C2×C4×C13—24no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2411yescharacteristic
107C22⋊D13—44no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13C2×D412yes—
111D52—216no—
112D52—24no—
113D52—22no—
114D52C2×D414yes—
115C4×D13—216no—
116C4×D13—24no—
117C4×D13—22no—
118C4×D13—22no—
119C8×C13—22no—
120#1055—22no—
121C22×#41—131no—
122C2×#137D1311yescharacteristic, complemented
123C2×AGL(1,ℤ/8)—131no—
124#525—131no—
125#452—134no—
126#449—134no—
127#419—131no—
128#418—131no—
129#407—131no—
130C22×C13—22no—
131C22×C13—41no—
132C22×C13—42no—
133C22×C13#12012yes—
134C22×C13C22×D411yescharacteristic
135C2×D13—22no—
136C2×D13—24no—
137C2×D13—22no—
138C2×D13—22no—
139C2×D13—44no—
140C2×D13—48no—
141C2×D13—44no—
142C4×C13—24no—
143C4×C13—41no—
144C4×C13#12012yes—
145C4×C13C22×D411yescharacteristic
146C4×C13C22×D411yescharacteristic
147Dic13—22no—
148Dic13—42no—
149C2×#41—134no—
150C2×#41—262no—
151C2×#41—264no—
152C2×#41—264no—
153C2×#41C2×D1311yescharacteristic
154C22×Q8C2×D1311yescharacteristic
155C22×D4—131no—
156C22×D4—261no—
157C23×C4—131no—
158C23×C4—261no—
159#137—24no—
160AGL(1,ℤ/8)—264no—
161C2×Q16C2×D1312yescomplemented
162C2×SD16—132no—
163C2×SD16C2×D1312yescomplemented
164C2×D8—132no—
165C2×M16—131no—
166C2×M16C2×D1311yescharacteristic
167#123—261no—
168C22⋊Q8—132no—
169#121—132no—
170#120—261no—
171C4×D4—262no—
172#117—131no—
173#103—134no—
174#102—134no—
175C22⋊C8—134no—
176C2×C13—22no—
177C2×C13—81no—
178C2×C13C2×#12011yescharacteristic
179C2×C13#57512yes—
180D13—42no—
181D13—44no—
182C24—131no—
183C24—261no—
184#41—22no—
185#41—22no—
186#41—268no—
187#41—2616no—
188#41—268no—
189C2×Q8—22no—
190C2×Q8—21no—
191C2×Q8C22⋊D1314yescomplemented
192C2×Q8C22×D1311yescharacteristic
193C2×Q8C22×D1312yes—
194C2×D4—21no—
195C2×D4—134no—
196C2×D4—132no—
197C2×D4—264no—
198C2×D4—268no—
199C2×D4—262no—
200C2×D4—261no—
201C2×D4—262no—
202C2×D4C22×D1311yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—131no—
206C22×C4—132no—
207C22×C4—132no—
208C22×C4—264no—
209C22×C4—268no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4C22×D1311yescharacteristic
213Q16—24no—
214SD16—24no—
215SD16—264no—
216D8—264no—
217M16—22no—
218M16—262no—
219C2×C8—132no—
220C2×C8C22×D1312yes—
221C4⋊C4—132no—
222C4⋊C4—262no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—261no—
226C42—261no—
227C13#300511yescharacteristic, complemented, Sylow
228C23—21no—
229C23—132no—
230C23—264no—
231C23—262no—
232C23—262no—
233C23—522no—
234C23—524no—
235C23D4×D1311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—21no—
239Q8—21no—
240Q8C2×C22⋊D1314yes—
241D4—21no—
242D4—21no—
243D4—42no—
244D4—134no—
245D4—2616no—
246D4—264no—
247D4—262no—
248D4—524no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—132no—
254C2×C4—2616no—
255C2×C4—262no—
256C2×C4—264no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4D4×D1311yescharacteristic
261C2×C4D4×D1312yes—
262C2×C4C2×C22⋊D1312yes—
263C2×C4C23×D1311yescharacteristic
264C8—22no—
265C8—262no—
266C22—22no—
267C22—42no—
268C22—41no—
269C22—262no—
270C22—262no—
271C22—264no—
272C22—262no—
273C22—524no—
274C22—528no—
275C22—524no—
276C22#8819112yes—
277C22C2×D4×D1311yescharacteristic
278C4—24no—
279C4—41no—
280C4—262no—
281C4—522no—
282C4#8819112yes—
283C4C2×D4×D1311yescharacteristic
284C4C22×C22⋊D1311yescharacteristic
285C2—22no—
286C2—81no—
287C2—522no—
288C2—524no—
289C2#1171948212yes—
290C2C2×#8819111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#137C2
socleC22×C13C22×D4
hypercenterC2×#137D13
hypocenterC13#3005
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#6131C2semidirect
2. C2×C13×#137C2semidirect
3. #11719533C2semidirect
4. C2×#88203C2semidirect
5. #11718886C2semidirect
6. #11718848C2semidirect
7. #11718833C2semidirect
8. #11718792C2semidirect
9. #11718787C2semidirect
21. C2×C13×Q16C22semidirect
22. C2×C13×SD16C22semidirect
25. #88200C22semidirect
26. C2×#6106C22semidirect
27. #88192C22semidirect
30. C2×#6104C22semidirect
34. #88075C22semidirect
35. #88061C22semidirect
36. #88060C22semidirect
43. C2×Q8×C13D4semidirect
60. C2×D52D4semidirect
122. C2×#137D13semidirect
161. C2×Q16C2×D13semidirect
163. C2×SD16C2×D13semidirect
191. C2×Q8C22⋊D13semidirect
227. C13#3005semidirect

Maximal subgroups

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

subgroupindex
C22×#61312
C2×C13×#1372
#117195332
C2×#882032
#117188862
#117188482
#117188332
#117187922
#117187872
#300513