Finite Group Databasebeta

← #13124081

Subgroups — #13124081

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
2#11719496C211yesmaximal, characteristic, complemented
3C2×#88163C211yesmaximal, characteristic, complemented
4C2×#88162C211yesmaximal, characteristic, complemented
5C13×#407C211yesmaximal, characteristic, complemented
6#11718792C211yesmaximal, characteristic, complemented
7#11718781C211yesmaximal, characteristic, complemented
8#11718395C214yesmaximal, complemented
9#11718394C214yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13—21no—
12C2×#6127—22no—
13C2×#6127—24no—
14C2×#6127—24no—
15C2×#6127C2211yescharacteristic
16C2×#6127C2214yes—
17C22×D52C2211yescharacteristic
18C22×C4×D13—21no—
19C22×Dic26C2211yescharacteristic
20C2×C13×M16C2211yescharacteristic
21C2×C13×M16C2211yescharacteristic
22#88207—21no—
23#88184C2212yescomplemented
24#88183—21no—
25C4×C22⋊D13—22no—
26#88180C2211yescharacteristic
27#88178C2212yescomplemented
28#88163—24no—
29#88162—24no—
30C2×Dic52C2212yescomplemented
31C2×D104C2212yescomplemented
32C2×#6095C2212yescomplemented
33C2×#6095C2212yescomplemented
34C13×C22⋊C8C2214yescomplemented
35#88061C2214yescomplemented
36#88056C2214yescomplemented
37C24×C13D411yescharacteristic
38C23×D13—21no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13D412yes—
42C22×C4×C13D411yescharacteristic
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—28no—
46C2×C22⋊D13—24no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—21no—
49C22×Dic13—21no—
50#6127—216no—
51#6127—28no—
52#6127—22no—
53#6127—22no—
54#6127—28no—
55C2×D52—21no—
56C2×D52—22no—
57C2×D52D414yescomplemented
58C2×D52C2311yescharacteristic
59C2×D52C2312yes—
60C2×C4×D13—28no—
61C2×C4×D13—24no—
62C2×C4×D13—21no—
63C2×Dic26—21no—
64C2×Dic26—22no—
65C2×Dic26D414yescomplemented
66C2×Dic26C2311yescharacteristic
67C2×Dic26C2312yes—
68C13×M16—22no—
69C13×M16—22no—
70C2×C8×C13C2312yes—
71C2×C8×C13C2312yes—
72C22⋊Dic13—22no—
73C22⋊Dic13—21no—
74#6103—22no—
75C4⋊Dic13C2312yes—
76#6101—22no—
77C4×Dic13—21no—
78Dic52—24no—
79D104—24no—
80#6095—24no—
81#6095—24no—
82#3005—131nomaximal, Sylow
83C23×C13—22no—
84C23×C13—42no—
85C23×C13C2×D412yes—
86C23×C13C2×D411yescharacteristic
87C22×D13—24no—
88C22×D13—22no—
89C22×D13—21no—
90C22×D13—44no—
91C2×C4×C13—22no—
92C2×C4×C13—24no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13C2×D412yes—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D412yes—
99C2×C4×C13C2411yescharacteristic
100C22⋊D13—216no—
101C22⋊D13—44no—
102C22⋊D13—42no—
103C2×Dic13—24no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107D52—24no—
108D52—22no—
109D52—21no—
110D52—21no—
111D52C2×D414yes—
112C4×D13—216no—
113C4×D13—42no—
114Dic26—24no—
115Dic26—22no—
116Dic26—21no—
117Dic26—21no—
118Dic26C2×D414yes—
119C8×C13—22no—
120C8×C13—22no—
121C22×#41—131no—
122C2×#137—131no—
123C2×AGL(1,ℤ/8)—131no—
124#525—131no—
125#452—134no—
126#449—134no—
127#419—131no—
128#418—131no—
129#407D1311yescharacteristic, complemented
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—44no—
135C22×C13#12012yes—
136C22×C13C22×D411yescharacteristic
137C2×D13—24no—
138C2×D13—48no—
139C2×D13—44no—
140C2×D13—41no—
141C2×D13—42no—
142C4×C13—22no—
143C4×C13#12012yes—
144C4×C13C22×D411yescharacteristic
145C4×C13C22×D411yescharacteristic
146Dic13—24no—
147Dic13—41no—
148Dic13—42no—
149C2×#41—131no—
150C2×#41—134no—
151C2×#41—264no—
152C2×#41—264no—
153C2×#41—262no—
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×M16C2×D1311yescharacteristic
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⋊C8C2×D1314yescomplemented
176C2×C13—22no—
177C2×C13—42no—
178C2×C13C2×#12011yescharacteristic
179C2×C13#57512yes—
180D13—44no—
181D13—81no—
182C24—261no—
183C24D5211yescharacteristic
184#41—268no—
185#41—268no—
186#41—2616no—
187#41—262no—
188#41—262no—
189C2×Q8—134no—
190C2×Q8—132no—
191C2×Q8—131no—
192C2×Q8—261no—
193C2×Q8—262no—
194C2×D4—134no—
195C2×D4—132no—
196C2×D4—131no—
197C2×D4—268no—
198C2×D4—264no—
199C2×D4—262no—
200C2×D4—261no—
201C2×D4—261no—
202C2×D4—262no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—268no—
206C22×C4—261no—
207C22×C4—264no—
208C22×C4—261no—
209C22×C4D5212yes—
210C22×C4D5211yescharacteristic
211C22×C4C22×D1312yes—
212C22×C4C22×D1311yescharacteristic
213Q16—264no—
214SD16—264no—
215SD16—264no—
216D8—264no—
217M16—22no—
218M16—22no—
219C2×C8C22×D1312yes—
220C2×C8C22×D1312yes—
221C4⋊C4—132no—
222C4⋊C4—262no—
223C22⋊C4—261no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C42—261no—
227C13#300511yescharacteristic, complemented, Sylow
228C23—22no—
229C23—42no—
230C23—264no—
231C23—262no—
232C23—261no—
233C23—524no—
234C23C2×D5212yes—
235C23C2×D5211yescharacteristic
236Q8—134no—
237Q8—264no—
238Q8—262no—
239Q8—261no—
240Q8—261no—
241D4—134no—
242D4—2616no—
243D4—264no—
244D4—262no—
245D4—261no—
246D4—261no—
247D4—524no—
248D4—522no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—2616no—
254C2×C4—264no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—261no—
258C2×C4—522no—
259C2×C4C2×D5212yes—
260C2×C4C2×D5211yescharacteristic
261C2×C4D4×D1312yes—
262C2×C4D4×D1312yes—
263C2×C4C23×D1311yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—264no—
272C22—528no—
273C22—524no—
274C22—521no—
275C22—522no—
276C22#8813612yes—
277C22C22×D5211yescharacteristic
278C4—22no—
279C4—264no—
280C4—521no—
281C4—522no—
282C4#8813612yes—
283C4C2×D4×D1311yescharacteristic
284C4C2×D4×D1311yescharacteristic
285C2—22no—
286C2—42no—
287C2—524no—
288C2—1041no—
289C2C2×#8813611yescharacteristic
290C2#1171945312yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#407C2
socleC22×C13C22×D4
hypercenter#407D13
hypocenterC13#3005
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#6127C2semidirect
2. #11719496C2semidirect
3. C2×#88163C2semidirect
4. C2×#88162C2semidirect
5. C13×#407C2semidirect
6. #11718792C2semidirect
7. #11718781C2semidirect
8. #11718395C2semidirect
9. #11718394C2semidirect
23. #88184C22semidirect
27. #88178C22semidirect
30. C2×Dic52C22semidirect
31. C2×D104C22semidirect
32. C2×#6095C22semidirect
33. C2×#6095C22semidirect
34. C13×C22⋊C8C22semidirect
35. #88061C22semidirect
36. #88056C22semidirect
57. C2×D52D4semidirect
65. C2×Dic26D4semidirect
129. #407D13semidirect
175. C22⋊C8C2×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
#117194962
C2×#881632
C2×#881622
C13×#4072
#117187922
#117187812
#117183952
#117183942
#300513