Finite Group Databasebeta

← #13125603

Subgroups — #13125603

Order 1664.

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

normal subgroups only

This group has 472 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#11719496C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic, complemented
3C2×C13×C22⋊C8C211yesmaximal, characteristic, complemented
4#11718776C212yesmaximal, complemented
5#11718775C212yesmaximal, complemented
6#11718398C212yesmaximal, complemented
7#11718396C211yesmaximal, characteristic, complemented
8#11718395C212yesmaximal, complemented
9#11718393C211yesmaximal, characteristic, complemented
10#11718392C211yesmaximal, characteristic, complemented
11#11718383C211yesmaximal, characteristic, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C2×#6127C2211yescharacteristic, complemented
15C22×D52C2211yescharacteristic
16C22×C8×C13C2212yescomplemented
17#88207—21no—
18#88184—21no—
19#88184—21no—
20#88184C2212yes—
21#88184C2212yes—
22#88184C2211yescharacteristic
23#88184C2211yescharacteristic, complemented
24#88183—21no—
25C4×C22⋊D13—21no—
26C4×C22⋊D13—21no—
27C2×#6103—21no—
28#88180C2211yescharacteristic, complemented
29C2×C4⋊Dic13C2211yescharacteristic
30#88178C2211yescharacteristic
31#88178C2211yescharacteristic, complemented
32C2×D104C2212yescomplemented
33C2×#6095C2212yescomplemented
34C13×C22⋊C8C2211yescharacteristic
35C13×C22⋊C8C2211yescharacteristic
36C13×C22⋊C8C2212yescomplemented
37#88061C2212yescomplemented
38#88061C2212yescomplemented
39#88061C2212yescomplemented
40#88058C2212yescomplemented
41#88057C2212yescomplemented
42#88056C2212yescomplemented
43C24×C13D411yescharacteristic
44C23×D13—21no—
45C22×C4×C13—42no—
46C22×C4×C13D411yescharacteristic
47C22×C4×C13D411yescharacteristic
48C22×C4×C13D411yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C2×C22⋊D13—21no—
55C2×C22⋊D13—22no—
56C2×C22⋊D13—22no—
57C2×C22⋊D13—44no—
58C22×Dic13—21no—
59#6127—42no—
60C2×D52—21no—
61C2×D52—42no—
62C2×D52C2312yes—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×Dic26C2311yescharacteristic
66C2×C8×C13—42no—
67C2×C8×C13C2312yes—
68C2×C8×C13C2312yes—
69C22⋊Dic13—21no—
70C22⋊Dic13—21no—
71C22⋊Dic13—21no—
72#6103—22no—
73#6103—22no—
74#6103—21no—
75#6103—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13C2311yescharacteristic
78C4⋊Dic13C2311yescharacteristic
79C4⋊Dic13C2312yes—
80#6101—21no—
81#6101—21no—
82C4×Dic13—21no—
83D104—42no—
84#6095—42no—
85#3188—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—22no—
88C23×C13—41no—
89C23×C13C2×D411yescharacteristic
90C23×C13C2×D411yescharacteristic
91C23×C13C2×D411yescharacteristic
92C22×D13—21no—
93C22×D13—22no—
94C22×D13—42no—
95C22×D13—42no—
96C22×D13—42no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2411yescharacteristic
107C22⋊D13—42no—
108C22⋊D13—44no—
109C22⋊D13—42no—
110C22⋊D13—42no—
111C22⋊D13—44no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—22no—
116C2×Dic13—42no—
117D52—22no—
118D52—22no—
119D52—22no—
120D52—42no—
121C4×D13—42no—
122Dic26—22no—
123C8×C13—22no—
124C8×C13—22no—
125#525—131no—
126C2×#121—131no—
127#484—131no—
128#482—132no—
129#481—131no—
130#466—132no—
131#465—132no—
132#450—131no—
133#449—132no—
134#447—131no—
135C2×C22⋊C8D1311yescharacteristic, complemented
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—44no—
144C22×C13#13512yes—
145C22×C13AGL(1,ℤ/8)12yes—
146C22×C13C22×D411yescharacteristic
147C2×D13—41no—
148C2×D13—42no—
149C2×D13—41no—
150C2×D13—42no—
151C2×D13—42no—
152C2×D13—41no—
153C2×D13—84no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13H(5,𝔽2)12yes—
158Dic13—41no—
159Dic13—41no—
160Dic13—42no—
161Dic13—41no—
162C2×#41—131no—
163C22×D4—131no—
164C22×D4—261no—
165C23×C4C2×D1311yescharacteristic
166C2×SD16—132no—
167C2×D8—132no—
168C22×C8C2×D1312yescomplemented
169#123—261no—
170C22⋊Q8—131no—
171C22⋊Q8—131no—
172#121—132no—
173#121—132no—
174#121—131no—
175#121—131no—
176#121—261no—
177#121—261no—
178#120—261no—
179C4×D4—261no—
180C4×D4—261no—
181#117—131no—
182C2×C4⋊C4—131no—
183C2×C22⋊C4—261no—
184#107—132no—
185#106—132no—
186#103—132no—
187#102—132no—
188#102—132no—
189#102—132no—
190C22⋊C8C2×D1311yescharacteristic
191C22⋊C8C2×D1311yescharacteristic
192C22⋊C8C2×D1312yescomplemented
193C2×C13—22no—
194C2×C13—22no—
195C2×C13—41no—
196C2×C13#53411yescharacteristic
197C2×C13C2×#13511yescharacteristic
198C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
199D13—81no—
200D13—82no—
201C24—261no—
202C24D5211yescharacteristic
203#41—522no—
204C2×Q8—131no—
205C2×D4—131no—
206C2×D4—132no—
207C2×D4—261no—
208C2×D4—261no—
209C2×D4—261no—
210C2×D4—262no—
211C2×D4—262no—
212C2×D4—261no—
213C2×D4—522no—
214C2×D4—524no—
215C22×C4—42no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4D5211yescharacteristic
219C22×C4D5211yescharacteristic
220C22×C4D5211yescharacteristic
221C22×C4C22×D1311yescharacteristic
222C22×C4C22×D1311yescharacteristic
223C22×C4C22×D1311yescharacteristic
224SD16—522no—
225D8—522no—
226C2×C8—42no—
227C2×C8C22×D1312yes—
228C2×C8C22×D1312yes—
229C4⋊C4—131no—
230C4⋊C4—131no—
231C4⋊C4—132no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4—261no—
235C22⋊C4—261no—
236C22⋊C4—261no—
237C22⋊C4—261no—
238C22⋊C4—262no—
239C22⋊C4—262no—
240C22⋊C4—261no—
241C22⋊C4—261no—
242C42—261no—
243C13#318811yescharacteristic, complemented, Sylow
244C23—22no—
245C23—22no—
246C23—41no—
247C23—261no—
248C23—262no—
249C23—522no—
250C23—522no—
251C23—522no—
252C23C2×D5211yescharacteristic
253C23C2×D5211yescharacteristic
254C23C2×D5211yescharacteristic
255Q8—262no—
256D4—262no—
257D4—262no—
258D4—262no—
259D4—522no—
260D4—524no—
261D4—522no—
262D4—522no—
263D4—522no—
264D4—524no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—262no—
274C2×C4—261no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4C2×D5211yescharacteristic
278C2×C4C2×D5211yescharacteristic
279C2×C4C2×D5211yescharacteristic
280C2×C4C23×D1311yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—521no—
292C22—522no—
293C22—522no—
294C22—521no—
295C22—521no—
296C22—522no—
297C22—1044no—
298C22#8815812yes—
299C22#8816212yes—
300C22C22×D5211yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—521no—
305C4—522no—
306C4—521no—
307C4—521no—
308C4#8825112yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—1042no—
313C2—1041no—
314C2#1171919811yescharacteristic
315C2C2×#8815811yescharacteristic
316C2C2×#8816211yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C22⋊C8C2
socleC22×C13C22×D4
hypercenterC2×C22⋊C8D13
hypocenterC13#3188
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #11719496C2semidirect
2. C2×#88184C2semidirect
3. C2×C13×C22⋊C8C2semidirect
4. #11718776C2semidirect
5. #11718775C2semidirect
6. #11718398C2semidirect
7. #11718396C2semidirect
8. #11718395C2semidirect
9. #11718393C2semidirect
10. #11718392C2semidirect
11. #11718383C2semidirect
14. C2×#6127C22semidirect
16. C22×C8×C13C22semidirect
23. #88184C22semidirect
28. #88180C22semidirect
31. #88178C22semidirect
32. C2×D104C22semidirect
33. C2×#6095C22semidirect
36. C13×C22⋊C8C22semidirect
37. #88061C22semidirect
38. #88061C22semidirect
39. #88061C22semidirect
40. #88058C22semidirect
41. #88057C22semidirect
42. #88056C22semidirect
135. C2×C22⋊C8D13semidirect
168. C22×C8C2×D13semidirect
192. C22⋊C8C2×D13semidirect
243. C13#3188semidirect

Maximal subgroups

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

subgroupindex
#117194962
C2×#881842
C2×C13×C22⋊C82
#117187762
#117187752
#117183982
#117183962
#117183952
#117183932
#117183922
#117183832
#318813