Finite Group Databasebeta

← #13125884

Subgroups — #13125884

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719535C211yesmaximal, characteristic, complemented
2#11719324C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718837C211yesmaximal, characteristic, complemented
6#11718826C211yesmaximal, characteristic, complemented
7#11718812C211yesmaximal, characteristic, complemented
8#11718811C211yesmaximal, characteristic, complemented
9#11718697C211yesmaximal, characteristic, complemented
10#11718480C211yesmaximal, characteristic, complemented
11#11718461C211yesmaximal, characteristic, complemented
12#11718447C211yesmaximal, characteristic, complemented
13#11718425C211yesmaximal, characteristic, complemented
14#11718393C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic, complemented
19C2×C13×D8C2211yescharacteristic, complemented
20C13×#121C2211yescharacteristic
21#88201C2211yescharacteristic
22#88201C2211yescharacteristic
23C2×#6106C2211yescharacteristic, complemented
24#88194C2211yescharacteristic
25#88194C2211yescharacteristic
26#88194C2211yescharacteristic, complemented
27#88193—21no—
28#88192—21no—
29#88191—21no—
30#88191—21no—
31D4×Dic13C2211yescharacteristic, complemented
32C2×#6104C2211yescharacteristic
33C2×#6104C2211yescharacteristic
34C2×#6104C2211yescharacteristic, complemented
35#88184—21no—
36#88184—21no—
37#88184C2211yescharacteristic
38#88180C2211yescharacteristic
39C2×D104C2211yescharacteristic
40C2×D104C2211yescharacteristic
41#88147C2211yescharacteristic, complemented
42#88144C2211yescharacteristic, complemented
43#88140—21no—
44#88137—21no—
45C13×#103C2211yescharacteristic, complemented
46C13×#102C2211yescharacteristic, complemented
47C13×C22⋊C8C2211yescharacteristic
48#88075C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic
51#88061C2211yescharacteristic
52#88061C2211yescharacteristic
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88054C2211yescharacteristic, complemented
56C8×Dic13C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58#88049C2211yescharacteristic
59C23×D13—21no—
60C13×#41—41no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C22×Dic13—21no—
77C2×D52—21no—
78C2×D52—41no—
79C2×D52—41no—
80C2×D52C2311yescharacteristic
81C2×D52C2311yescharacteristic
82C2×D52C2311yescharacteristic
83C2×C4×D13—21no—
84C13×SD16—41no—
85C13×D8—41no—
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13D411yescharacteristic
92C22⋊Dic13D411yescharacteristic
93#6106—41no—
94#6104—41no—
95#6104—41no—
96#6104—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13D411yescharacteristic
105C4⋊Dic13D411yescharacteristic
106C4⋊Dic13C2311yescharacteristic
107#6101—21no—
108C4×Dic13C2311yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112D104—41no—
113D104—41no—
114#3220—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×D411yescharacteristic
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—42no—
122C22×D13—81no—
123C22×D13—81no—
124Q8×C13—21no—
125Q8×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—21no—
130D4×C13—42no—
131D4×C13—81no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—42no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2411yescharacteristic
139C22⋊D13—81no—
140C22⋊D13—81no—
141C22⋊D13—81no—
142C22⋊D13—81no—
143C22⋊D13—81no—
144C22⋊D13—81no—
145C22⋊D13—81no—
146C2×Dic13—21no—
147C2×Dic13—81no—
148C2×Dic13C2×D411yescharacteristic
149C2×Dic13C2×D411yescharacteristic
150C2×Dic13C2×D411yescharacteristic
151C2×Dic13C2×D411yescharacteristic
152D52—21no—
153D52—21no—
154D52—21no—
155D52—21no—
156D52—21no—
157D52—21no—
158D52—42no—
159C4×D13—81no—
160C8×C13—21no—
161C8×C13—21no—
162#1055—21no—
163#1055—21no—
164#540—131no—
165#535—131no—
166#496—131no—
167#493—131no—
168#490—131no—
169#488—131no—
170#463—131no—
171#463—131no—
172#459—131no—
173#459—131no—
174#449—131no—
175#449D1311yescharacteristic, complemented
176#447—131no—
177#447—131no—
178#433—131no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13C22×D411yescharacteristic
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—84no—
199C4×C13—21no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13H(5,𝔽2)11yescharacteristic
203C4×C13H(5,𝔽2)11yescharacteristic
204Dic13—21no—
205Dic13—21no—
206Dic13—21no—
207Dic13—21no—
208Dic13—41no—
209C2×#41C2×D1311yescharacteristic
210C22×D4—131no—
211C2×SD16—131no—
212C2×SD16C2×D1311yescharacteristic, complemented
213C2×D8—131no—
214C2×D8—131no—
215C2×D8—131no—
216C2×D8—131no—
217C2×D8—131no—
218C2×D8C2×D1311yescharacteristic, complemented
219#127—131no—
220#127—131no—
221#127—131no—
222#125—131no—
223#124—131no—
224#124—131no—
225#123—261no—
226#123—261no—
227#121—131no—
228#121—261no—
229#121—261no—
230#121—261no—
231#121—261no—
232#121C2×D1311yescharacteristic
233#120—261no—
234#120—261no—
235C4×D4—131no—
236C4×D4—131no—
237#117—131no—
238C4⋊C8—131no—
239C4⋊C8—131no—
240#103—131no—
241#103C2×D1311yescharacteristic, complemented
242#102—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102—131no—
247#102C2×D1311yescharacteristic, complemented
248C22⋊C8—131no—
249C22⋊C8C2×D1311yescharacteristic
250#97—131no—
251C4×C8—131no—
252C2×C13—41no—
253C2×C13—81no—
254C2×C13—81no—
255C2×C13#53511yescharacteristic
256C2×C13#57611yescharacteristic
257C2×C13#57611yescharacteristic
258D13—81no—
259D13—81no—
260D13—81no—
261C24—261no—
262#41—41no—
263#41—41no—
264C2×Q8C22×D1311yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—131no—
268C2×D4—131no—
269C2×D4—131no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C2×D4—261no—
278C2×D4—521no—
279C2×D4—521no—
280C2×D4C22×D1311yescharacteristic
281C2×D4C22×D1311yescharacteristic
282C22×C4—21no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4C22×D1311yescharacteristic
286SD16—41no—
287SD16—521no—
288D8—41no—
289D8—521no—
290D8—521no—
291D8—521no—
292D8—521no—
293D8—521no—
294C2×C8—131no—
295C2×C8—131no—
296C2×C8C22×D1311yescharacteristic
297C2×C8C22×D1311yescharacteristic
298C4⋊C4—131no—
299C4⋊C4—131no—
300C4⋊C4—131no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4C22×D1311yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—131no—
306C22⋊C4—131no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C22⋊C4—261no—
313C22⋊C4—261no—
314C42—131no—
315C42—131no—
316C13#322011yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23—522no—
323C23—1041no—
324C23—1041no—
325C23D4×D1311yescharacteristic
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—261no—
335D4—261no—
336D4—261no—
337D4—261no—
338D4—261no—
339D4—261no—
340D4—522no—
341D4—1041no—
342D4—1041no—
343D4—1041no—
344D4—1041no—
345D4—1041no—
346D4—1041no—
347D4—1041no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—131no—
354C2×C4—131no—
355C2×C4—131no—
356C2×C4—131no—
357C2×C4—261no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4D4×D1311yescharacteristic
361C2×C4C23×D1311yescharacteristic
362C8—21no—
363C8—21no—
364C8—261no—
365C8—261no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—521no—
376C22—521no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—521no—
382C22—521no—
383C22—521no—
384C22—1044no—
385C22C2×D4×D1311yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—261no—
390C4—261no—
391C4—261no—
392C4—261no—
393C4—521no—
394C4#8825111yescharacteristic
395C4#8825111yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—1041no—
400C2—1041no—
401C2—1041no—
402C2#1171929711yescharacteristic
403C2#1171947411yescharacteristic
404C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3220
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719535C2semidirect
2. #11719324C2semidirect
3. C13×#449C2semidirect
4. #11718899C2semidirect
5. #11718837C2semidirect
6. #11718826C2semidirect
7. #11718812C2semidirect
8. #11718811C2semidirect
9. #11718697C2semidirect
10. #11718480C2semidirect
11. #11718461C2semidirect
12. #11718447C2semidirect
13. #11718425C2semidirect
14. #11718393C2semidirect
15. #11718381C2semidirect
18. C2×C13×SD16C22semidirect
19. C2×C13×D8C22semidirect
23. C2×#6106C22semidirect
26. #88194C22semidirect
31. D4×Dic13C22semidirect
34. C2×#6104C22semidirect
41. #88147C22semidirect
42. #88144C22semidirect
45. C13×#103C22semidirect
46. C13×#102C22semidirect
48. #88075C22semidirect
49. #88072C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
55. #88054C22semidirect
56. C8×Dic13C22semidirect
175. #449D13semidirect
212. C2×SD16C2×D13semidirect
218. C2×D8C2×D13semidirect
241. #103C2×D13semidirect
247. #102C2×D13semidirect
316. C13#3220semidirect

Maximal subgroups

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

subgroupindex
#117195352
#117193242
C13×#4492
#117188992
#117188372
#117188262
#117188122
#117188112
#117186972
#117184802
#117184612
#117184472
#117184252
#117183932
#117183812
#322013