Finite Group Databasebeta

← #13124976

Subgroups — #13124976

Order 1664.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#11719184C211yesmaximal, characteristic, complemented
2C2×C4×D52C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4#11718508C212yesmaximal, complemented
5#11718505C212yesmaximal, complemented
6#11718397C211yesmaximal, characteristic, complemented
7#11718393C211yesmaximal, characteristic
8#11718392C211yesmaximal, characteristic, complemented
9#11718382C211yesmaximal, characteristic, complemented
10#11718372C212yesmaximal, complemented
11#11718371C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13—21no—
14C2×C42×C13C2211yescharacteristic
15#88184C2211yescharacteristic
16#88183—21no—
17C4×C22⋊D13—21no—
18C2×#6103—21no—
19C2×C4⋊Dic13C2211yescharacteristic
20#88178C2211yescharacteristic
21C2×D104C2212yes—
22C2×#6095C2212yes—
23#88130—21no—
24#88129C2211yescharacteristic, complemented
25C4×D52—21no—
26C4×D52—21no—
27C4×D52C2212yes—
28C4×D52C2212yes—
29C4×D52C2211yescharacteristic, complemented
30#88126—21no—
31#88124C2211yescharacteristic, complemented
32C4×Dic26C2211yescharacteristic, complemented
33C13×C4⋊C8C2212yescomplemented
34C13×C22⋊C8C2211yescharacteristic
35C13×C22⋊C8C2211yescharacteristic
36C13×#97C2212yescomplemented
37#88061C2212yes—
38#88061C2212yes—
39#88061C2212yescomplemented
40#88058C2212yescomplemented
41#88057C2212yescomplemented
42#88056C2212yescomplemented
43C23×D13—21no—
44C22×C4×C13D411yescharacteristic
45C22×C4×C13D411yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C22×Dic13—21no—
49C2×D52—21no—
50C2×D52—24no—
51C2×D52C2311yescharacteristic
52C2×D52C2312yes—
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—44no—
57C2×Dic26C2311yescharacteristic
58C2×C8×C13C2312yes—
59C2×C8×C13C2312yes—
60C42×C13D411yescharacteristic
61C42×C13D411yescharacteristic
62C42×C13C2311yescharacteristic
63C42×C13C2311yescharacteristic
64C22⋊Dic13—21no—
65#6103—21no—
66#6103—21no—
67#6103—22no—
68#6103—22no—
69#6103—21no—
70#6103—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74C4⋊Dic13C2312yes—
75#6101—21no—
76#6101—21no—
77#6101—21no—
78#6101—21no—
79C4×Dic13—21no—
80D104—24no—
81#6095—24no—
82#3114—131nomaximal, Sylow
83C23×C13C2×D411yescharacteristic
84C22×D13—24no—
85C22×D13—22no—
86C22×D13—21no—
87C22×D13—42no—
88C22×D13—42no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—41no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—42no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—42no—
104D52—24no—
105D52—22no—
106D52—22no—
107D52#4114yes—
108C4×D13—42no—
109C4×D13—44no—
110C4×D13—44no—
111Dic26—22no—
112C8×C13—22no—
113C8×C13—22no—
114#529—131no—
115C2×C4×D4—131no—
116#483—131no—
117#480—131no—
118#478—132no—
119#463—132no—
120#450—131no—
121#447—131no—
122#442—132no—
123#440—132no—
124#432D1311yescharacteristic, complemented
125C22×C13—21no—
126C22×C13—21no—
127C22×C13AGL(1,ℤ/8)12yes—
128C22×C13C22×D411yescharacteristic
129C2×D13—24no—
130C2×D13—48no—
131C2×D13—42no—
132C2×D13—42no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—41no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13C2×#4112yes—
142Dic13—41no—
143Dic13—42no—
144Dic13—41no—
145Dic13—41no—
146C22×D4—131no—
147C23×C4—261no—
148C2×SD16—132no—
149C2×D8—132no—
150#126—261no—
151#125—131no—
152#124—131no—
153#123—261no—
154C22⋊Q8—131no—
155#121—131no—
156C4×Q8—131no—
157C4×D4—132no—
158C4×D4—132no—
159C4×D4—131no—
160C4×D4—261no—
161C4×D4—261no—
162C4×D4—261no—
163#117—261no—
164C2×C4⋊C4—131no—
165C2×C22⋊C4—261no—
166C2×C42C2×D1311yescharacteristic
167#107—132no—
168#106—132no—
169C4⋊C8C2×D1312yescomplemented
170#103—132no—
171#102—132no—
172#102—132no—
173#102—132no—
174C22⋊C8C2×D1311yescharacteristic
175C22⋊C8C2×D1311yescharacteristic
176#97C2×D1312yescomplemented
177C2×C13—22no—
178C2×C13#52511yescharacteristic
179C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C13#57511yescharacteristic
181D13—44no—
182D13—81no—
183C24—261no—
184C2×Q8—131no—
185C2×D4—132no—
186C2×D4—131no—
187C2×D4—264no—
188C2×D4—261no—
189C2×D4—261no—
190C22×C4—261no—
191C22×C4—261no—
192C22×C4—262no—
193C22×C4—262no—
194C22×C4—524no—
195C22×C4D5211yescharacteristic
196C22×C4D5211yescharacteristic
197C22×C4C22×D1311yescharacteristic
198SD16—264no—
199D8—264no—
200C2×C8C22×D1312yes—
201C2×C8C22×D1312yes—
202C4⋊C4—131no—
203C4⋊C4—131no—
204C4⋊C4—132no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4—261no—
209C4⋊C4—261no—
210C22⋊C4—261no—
211C22⋊C4—262no—
212C22⋊C4—262no—
213C22⋊C4—261no—
214C22⋊C4—261no—
215C22⋊C4—261no—
216C22⋊C4—261no—
217C42—261no—
218C42D5211yescharacteristic
219C42D5211yescharacteristic
220C42C22×D1311yescharacteristic
221C42C22×D1311yescharacteristic
222C13#311411yescharacteristic, complemented, Sylow
223C23—264no—
224C23—262no—
225C23—261no—
226C23—522no—
227C23—522no—
228C23C2×D5211yescharacteristic
229Q8—262no—
230D4—134no—
231D4—264no—
232D4—262no—
233D4—262no—
234D4—522no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—262no—
242C2×C4—522no—
243C2×C4—524no—
244C2×C4—524no—
245C2×C4—522no—
246C2×C4C2×D5211yescharacteristic
247C2×C4C2×D5211yescharacteristic
248C2×C4C2×D5211yescharacteristic
249C2×C4C2×D5211yescharacteristic
250C2×C4C2×D5211yescharacteristic
251C2×C4C23×D1311yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—264no—
257C22—528no—
258C22—522no—
259C22—522no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22#8816212yes—
264C22C22×D5211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—522no—
271C4—521no—
272C4—521no—
273C4—521no—
274C4#41×D1312yes—
275C2—22no—
276C2—524no—
277C2—1041no—
278C2#1171922911yescharacteristic
279C2C2×#8816211yescharacteristic
280C2#1171945311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#432C2
socleC22×C13C22×D4
prime radical#11718393C2
hypercenter#432D13
hypocenterC13#3114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #11719184C2semidirect
2. C2×C4×D52C2semidirect
3. C13×#432C2semidirect
4. #11718508C2semidirect
5. #11718505C2semidirect
6. #11718397C2semidirect
8. #11718392C2semidirect
9. #11718382C2semidirect
10. #11718372C2semidirect
11. #11718371C2semidirect
24. #88129C22semidirect
29. C4×D52C22semidirect
31. #88124C22semidirect
32. C4×Dic26C22semidirect
33. C13×C4⋊C8C22semidirect
36. C13×#97C22semidirect
39. #88061C22semidirect
40. #88058C22semidirect
41. #88057C22semidirect
42. #88056C22semidirect
124. #432D13semidirect
169. C4⋊C8C2×D13semidirect
176. #97C2×D13semidirect
222. C13#3114semidirect

Maximal subgroups

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

subgroupindex
#117191842
C2×C4×D522
C13×#4322
#117185082
#117185052
#117183972
#117183932
#117183922
#117183822
#117183722
#117183712
#311413