Finite Group Databasebeta

← #13125606

Subgroups — #13125606

Order 1664.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719332C211yesmaximal, characteristic, complemented
2C2×#88149C211yesmaximal, characteristic, complemented
3C13×#484C211yesmaximal, characteristic, complemented
4#11718707C211yesmaximal, characteristic, complemented
5#11718629C211yesmaximal, characteristic, complemented
6#11718546C212yesmaximal, complemented
7#11718544C212yesmaximal, complemented
8#11718472C212yesmaximal, complemented
9#11718468C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic, complemented
11D13×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic, complemented
13C22×D52—21no—
14C22×D52C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C13×C22⋊Q8C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88200C2211yescharacteristic, complemented
19C2×#6106C2212yescomplemented
20#88184C2211yescharacteristic
21C2×#6103—21no—
22C2×D104C2212yescomplemented
23C2×C8×D13C2212yescomplemented
24#88149—21no—
25#88149—21no—
26#88149C2212yes—
27#88149C2212yes—
28#88149C2211yescharacteristic, complemented
29#88148—21no—
30#88147—21no—
31#88146C2211yescharacteristic, complemented
32#88136—21no—
33#88135—21no—
34C13×#107C2212yescomplemented
35C13×#103C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38#88061C2212yescomplemented
39#88060C2212yescomplemented
40#88049C2212yescomplemented
41#88049C2212yescomplemented
42#88048C2212yescomplemented
43C23×D13—21no—
44C23×D13D411yescharacteristic
45C2×Q8×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—21no—
49C22×Dic13D411yescharacteristic
50#6131—42no—
51C2×D52—21no—
52C2×D52—21no—
53C2×D52—22no—
54C2×D52—22no—
55C2×D52—21no—
56C2×D52—42no—
57C2×D52—44no—
58C2×D52C2312yes—
59C2×D52C2311yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13—42no—
62C2×C4×D13D411yescharacteristic
63C2×C4×D13D411yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×C4×D13C2311yescharacteristic
66C2×C8×C13C2312yes—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2312yes—
70C13×C4⋊C4C2311yescharacteristic
71C13×C22⋊C4—21no—
72#6106—42no—
73#6103—21no—
74#6103—21no—
75#6103—21no—
76#6103—21no—
77#6103—22no—
78#6103—22no—
79C4⋊Dic13C2311yescharacteristic
80#6101—21no—
81C4×Dic13—21no—
82C2×#1055C2312yes—
83D104—42no—
84C8×D13—42no—
85#3188—131nomaximal, Sylow
86C23×C13C2×D411yescharacteristic
87C22×D13—22no—
88C22×D13—22no—
89C22×D13—21no—
90C22×D13—22no—
91C22×D13—41no—
92C22×D13—42no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13C2×D411yescharacteristic
96C22×D13C2×D411yescharacteristic
97Q8×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—42no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2411yescharacteristic
105C22⋊D13—42no—
106C2×Dic13—21no—
107C2×Dic13—41no—
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110D52—22no—
111D52—22no—
112D52—22no—
113D52—42no—
114D52—44no—
115D52—42no—
116D52—42no—
117D52—44no—
118C4×D13—22no—
119C4×D13—22no—
120C4×D13—41no—
121C4×D13—41no—
122C4×D13—42no—
123C8×C13—22no—
124#1055—22no—
125#525—131no—
126C2×#121—131no—
127#484D1311yescharacteristic, complemented
128#482—132no—
129#481—131no—
130#466—132no—
131#465—132no—
132#450—131no—
133#449—132no—
134#447—131no—
135C2×C22⋊C8—131no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13#13512yes—
139C22×C13C22×D411yescharacteristic
140C2×D13—21no—
141C2×D13—21no—
142C2×D13—21no—
143C2×D13—21no—
144C2×D13—21no—
145C2×D13—44no—
146C2×D13—41no—
147C2×D13—42no—
148C2×D13—41no—
149C2×D13—42no—
150C2×D13—42no—
151C2×D13—41no—
152C2×D13—84no—
153C2×D13AGL(1,ℤ/8)12yes—
154C4×C13—21no—
155C4×C13—41no—
156C4×C13—42no—
157C4×C13—41no—
158C4×C13H(5,𝔽2)12yes—
159Dic13—21no—
160Dic13—21no—
161Dic13—41no—
162C2×#41—131no—
163C22×D4—131no—
164C22×D4—261no—
165C23×C4—131no—
166C2×SD16—132no—
167C2×D8—132no—
168C22×C8—132no—
169#123—261no—
170C22⋊Q8—131no—
171C22⋊Q8C2×D1311yescharacteristic
172#121—131no—
173#121—132no—
174#121—132no—
175#121—131no—
176#121—261no—
177#121—261no—
178#120—261no—
179C4×D4—261no—
180C4×D4—261no—
181#117—131no—
182C2×C4⋊C4C2×D1311yescharacteristic
183C2×C22⋊C4—261no—
184#107C2×D1312yescomplemented
185#106—132no—
186#103C2×D1312yescomplemented
187#102—132no—
188#102—132no—
189#102—132no—
190C22⋊C8—131no—
191C22⋊C8—132no—
192C22⋊C8C2×D1311yescharacteristic
193C2×C13—22no—
194C2×C13#53411yescharacteristic
195C2×C13C2×#13511yescharacteristic
196C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
197D13—22no—
198D13—41no—
199D13—81no—
200D13—82no—
201C24—131no—
202C24—261no—
203#41—522no—
204C2×Q8C22×D1311yescharacteristic
205C2×D4—131no—
206C2×D4—132no—
207C2×D4—261no—
208C2×D4—261no—
209C2×D4—262no—
210C2×D4—262no—
211C2×D4—261no—
212C2×D4—261no—
213C2×D4—522no—
214C2×D4—524no—
215C22×C4—21no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—261no—
222C22×C4—522no—
223C22×C4C22×D1311yescharacteristic
224SD16—522no—
225D8—522no—
226C2×C8—132no—
227C2×C8—522no—
228C2×C8C22×D1312yes—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—131no—
232C4⋊C4—261no—
233C4⋊C4C22×D1311yescharacteristic
234C4⋊C4C22×D1312yes—
235C22⋊C4—21no—
236C22⋊C4—262no—
237C22⋊C4—262no—
238C22⋊C4—261no—
239C22⋊C4—261no—
240C22⋊C4—261no—
241C22⋊C4—261no—
242C42—261no—
243C13#318811yescharacteristic, complemented, Sylow
244C23—131no—
245C23—131no—
246C23—262no—
247C23—262no—
248C23—261no—
249C23—262no—
250C23—521no—
251C23—522no—
252C23—522no—
253C23—522no—
254C23D4×D1311yescharacteristic
255Q8—22no—
256D4—262no—
257D4—262no—
258D4—262no—
259D4—522no—
260D4—522no—
261D4—524no—
262D4—524no—
263D4—522no—
264D4—522no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—261no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—522no—
278C2×C4—521no—
279C2×C4D4×D1311yescharacteristic
280C2×C4C23×D1311yescharacteristic
281C8—22no—
282C8—262no—
283C22—21no—
284C22—21no—
285C22—132no—
286C22—261no—
287C22—261no—
288C22—261no—
289C22—261no—
290C22—261no—
291C22—524no—
292C22—521no—
293C22—522no—
294C22—522no—
295C22—521no—
296C22—521no—
297C22—522no—
298C22—1044no—
299C22#8817312yes—
300C22C2×D4×D1311yescharacteristic
301C4—21no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—261no—
306C4—261no—
307C4—521no—
308C4#8825612yes—
309C2—22no—
310C2—262no—
311C2—521no—
312C2—1042no—
313C2—1041no—
314C2#1171935811yescharacteristic
315C2C2×#8817311yescharacteristic
316C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
hypercenter#484D13
hypocenterC13#3188
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #11719332C2semidirect
2. C2×#88149C2semidirect
3. C13×#484C2semidirect
4. #11718707C2semidirect
5. #11718629C2semidirect
6. #11718546C2semidirect
7. #11718544C2semidirect
8. #11718472C2semidirect
9. #11718468C2semidirect
10. #11718393C2semidirect
11. D13×C22⋊C8C2semidirect
12. C2×#6131C22semidirect
18. #88200C22semidirect
19. C2×#6106C22semidirect
22. C2×D104C22semidirect
23. C2×C8×D13C22semidirect
28. #88149C22semidirect
31. #88146C22semidirect
34. C13×#107C22semidirect
35. C13×#103C22semidirect
38. #88061C22semidirect
39. #88060C22semidirect
40. #88049C22semidirect
41. #88049C22semidirect
42. #88048C22semidirect
127. #484D13semidirect
184. #107C2×D13semidirect
186. #103C2×D13semidirect
243. C13#3188semidirect

Maximal subgroups

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

subgroupindex
#117193322
C2×#881492
C13×#4842
#117187072
#117186292
#117185462
#117185442
#117184722
#117184682
#117183932
D13×C22⋊C82
#318813