Finite Group Databasebeta

← #13124076

Subgroups — #13124076

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×#6127C211yesmaximal, characteristic, complemented
2C13×#525C211yesmaximal, characteristic, complemented
3C2×#88205C211yesmaximal, characteristic, complemented
4C2×#88203C211yesmaximal, characteristic, complemented
5#11718868C211yesmaximal, characteristic, complemented
6#11718708C214yesmaximal, complemented
7#11718698C214yesmaximal, complemented
8#11718665C211yesmaximal, characteristic, complemented
9#11718662C211yesmaximal, characteristic, complemented
10C2×C13×#41C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13—21no—
13C2×#6127—22no—
14C2×#6127—24no—
15C2×#6127—24no—
16C2×#6127C2214yes—
17C22×D52C2211yescharacteristic
18C22×C4×D13—21no—
19C22×Dic26C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8C2212yescomplemented
22C13×#121C2212yescomplemented
23C13×#120—21no—
24C4×D4×C13—22no—
25C13×#117C2211yescharacteristic
26#88205—24no—
27#88203—24no—
28C2×#6107C2212yescomplemented
29C2×#6106C2212yescomplemented
30C2×#6105C2212yescomplemented
31C2×#6104C2212yescomplemented
32C2×#6099C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22⋊#1055C2214yescomplemented
35#88050C2214yescomplemented
36#88049C2214yescomplemented
37C24×C13D411yescharacteristic
38C23×D13—21no—
39C13×#41—22no—
40C13×#41—22no—
41C2×Q8×C13C2311yescharacteristic
42C2×D4×C13—22no—
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—21no—
48C22×C4×C13D412yes—
49C22×C4×C13D411yescharacteristic
50C22×C4×C13C2312yes—
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—28no—
53C2×C22⋊D13—24no—
54C22×Dic13—21no—
55#6127—216no—
56#6127—28no—
57#6127—28no—
58C2×D52—21no—
59C2×D52—22no—
60C2×D52D414yescomplemented
61C2×D52C2312yes—
62C2×C4×D13—28no—
63C2×C4×D13—24no—
64C2×Dic26—21no—
65C2×Dic26—22no—
66C2×Dic26D414yescomplemented
67C2×Dic26C2312yes—
68C13×C4⋊C4—22no—
69C13×C4⋊C4C2312yes—
70C13×C22⋊C4—21no—
71C13×C22⋊C4—22no—
72C13×C22⋊C4—22no—
73C42×C13—21no—
74#6107—24no—
75#6106—24no—
76#6105—24no—
77#6104—24no—
78#6099—22no—
79#6099—22no—
80C2×#1055C2312yes—
81C2×#1055C2312yes—
82#3005—131nomaximal, Sylow
83C23×C13—22no—
84C23×C13—21no—
85C23×C13—42no—
86C23×C13C2×D412yes—
87C23×C13C2×D411yescharacteristic
88C22×D13—24no—
89C22×D13—22no—
90C22×D13—44no—
91Q8×C13—21no—
92Q8×C13—21no—
93D4×C13—21no—
94D4×C13—21no—
95D4×C13—44no—
96D4×C13—42no—
97C2×C4×C13—22no—
98C2×C4×C13—24no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2×D412yes—
107C2×C4×C13C2×D412yes—
108C2×C4×C13C2411yescharacteristic
109C22⋊D13—216no—
110C2×Dic13—24no—
111C2×Dic13—22no—
112D52—24no—
113D52—22no—
114D52C2×D414yes—
115C4×D13—216no—
116Dic26—24no—
117Dic26—22no—
118Dic26C2×D414yes—
119#1055—22no—
120#1055—22no—
121C22×#41—131no—
122C2×#137—131no—
123C2×AGL(1,ℤ/8)—131no—
124#525D1311yescharacteristic, complemented
125#452—134no—
126#449—134no—
127#419—131no—
128#418—131no—
129#407—131no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—44no—
135C22×C13—41no—
136C22×C13—42no—
137C22×C13#12012yes—
138C22×C13C22×D411yescharacteristic
139C2×D13—24no—
140C2×D13—48no—
141C2×D13—44no—
142C4×C13—22no—
143C4×C13—41no—
144C4×C13—42no—
145C4×C13#12012yes—
146C4×C13C22×D411yescharacteristic
147C4×C13C22×D411yescharacteristic
148Dic13—24no—
149C2×#41—134no—
150C2×#41—264no—
151C2×#41—264no—
152C2×#41—262no—
153C2×#41C2×D1311yescharacteristic
154C22×Q8—131no—
155C22×D4—131no—
156C22×D4—261no—
157C23×C4—261no—
158C23×C4C2×D1311yescharacteristic
159#137—264no—
160AGL(1,ℤ/8)—264no—
161C2×Q16—132no—
162C2×SD16—132no—
163C2×SD16—132no—
164C2×D8—132no—
165C2×M16—131no—
166C2×M16—131no—
167#123—21no—
168C22⋊Q8C2×D1312yescomplemented
169#121C2×D1312yescomplemented
170#120—21no—
171C4×D4—22no—
172#117C2×D1311yescharacteristic
173#103—134no—
174#102—134no—
175C22⋊C8—134no—
176C2×C13—22no—
177C2×C13—42no—
178C2×C13—81no—
179C2×C13C2×#12011yescharacteristic
180C2×C13#57512yes—
181D13—44no—
182C24—261no—
183C24C22⋊D1311yescharacteristic
184#41—22no—
185#41—22no—
186#41—268no—
187#41—268no—
188#41—2616no—
189C2×Q8—134no—
190C2×Q8—132no—
191C2×Q8—262no—
192C2×Q8—261no—
193C2×Q8C22×D1311yescharacteristic
194C2×D4—22no—
195C2×D4—21no—
196C2×D4—134no—
197C2×D4—132no—
198C2×D4—268no—
199C2×D4—264no—
200C2×D4—262no—
201C2×D4—261no—
202C2×D4C22×D1311yescharacteristic
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—268no—
207C22×C4—261no—
208C22×C4—264no—
209C22×C4C22⋊D1312yes—
210C22×C4C22⋊D1311yescharacteristic
211C22×C4C22×D1312yes—
212C22×C4C22×D1311yescharacteristic
213Q16—264no—
214SD16—264no—
215SD16—264no—
216D8—264no—
217M16—262no—
218M16—262no—
219C2×C8—132no—
220C2×C8—132no—
221C4⋊C4—22no—
222C4⋊C4C22×D1312yes—
223C22⋊C4—21no—
224C22⋊C4—22no—
225C22⋊C4—22no—
226C42—21no—
227C13#300511yescharacteristic, complemented, Sylow
228C23—22no—
229C23—21no—
230C23—42no—
231C23—264no—
232C23—262no—
233C23—524no—
234C23C2×C22⋊D1312yes—
235C23C2×C22⋊D1311yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—134no—
239Q8—264no—
240Q8—262no—
241D4—21no—
242D4—21no—
243D4—44no—
244D4—42no—
245D4—134no—
246D4—2616no—
247D4—264no—
248D4—262no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—2616no—
257C2×C4—264no—
258C2×C4—262no—
259C2×C4D4×D1312yes—
260C2×C4D4×D1312yes—
261C2×C4C2×C22⋊D1312yes—
262C2×C4C2×C22⋊D1311yescharacteristic
263C2×C4C23×D1311yescharacteristic
264C8—262no—
265C8—262no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—41no—
272C22—42no—
273C22—264no—
274C22—528no—
275C22—524no—
276C22#8819112yes—
277C22C22×C22⋊D1311yescharacteristic
278C4—22no—
279C4—41no—
280C4—42no—
281C4—264no—
282C4#8819112yes—
283C4C2×D4×D1311yescharacteristic
284C4C2×D4×D1311yescharacteristic
285C2—22no—
286C2—42no—
287C2—81no—
288C2—524no—
289C2C2×#8819111yescharacteristic
290C2#1171952712yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#525C2
socleC22×C13C22×D4
hypercenter#525D13
hypocenterC13#3005
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#6127C2semidirect
2. C13×#525C2semidirect
3. C2×#88205C2semidirect
4. C2×#88203C2semidirect
5. #11718868C2semidirect
6. #11718708C2semidirect
7. #11718698C2semidirect
8. #11718665C2semidirect
9. #11718662C2semidirect
21. C13×C22⋊Q8C22semidirect
22. C13×#121C22semidirect
28. C2×#6107C22semidirect
29. C2×#6106C22semidirect
30. C2×#6105C22semidirect
31. C2×#6104C22semidirect
34. C22⋊#1055C22semidirect
35. #88050C22semidirect
36. #88049C22semidirect
60. C2×D52D4semidirect
66. C2×Dic26D4semidirect
124. #525D13semidirect
168. C22⋊Q8C2×D13semidirect
169. #121C2×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×#61272
C13×#5252
C2×#882052
C2×#882032
#117188682
#117187082
#117186982
#117186652
#117186622
#300513