Finite Group Databasebeta

← #13126319

Subgroups — #13126319

Order 1664.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719534C211yesmaximal, characteristic, complemented
2C2×#88203C211yesmaximal, characteristic, complemented
3C2×D8×D13C211yesmaximal, characteristic, complemented
4#11719314C211yesmaximal, characteristic, complemented
5C13×#449C211yesmaximal, characteristic, complemented
6#11718837C211yesmaximal, characteristic, complemented
7#11718830C211yesmaximal, characteristic, complemented
8#11718811C211yesmaximal, characteristic, complemented
9#11718700C211yesmaximal, characteristic, complemented
10#11718480C211yesmaximal, characteristic, complemented
11#11718468C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718434C211yesmaximal, characteristic, complemented
14#11718393C211yesmaximal, characteristic, complemented
15#11718389C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic, complemented
17C2×D4×D13—21no—
18C2×D4×D13C2211yescharacteristic
19C2×D4×D13C2211yescharacteristic, complemented
20C22×D52C2211yescharacteristic, complemented
21C2×C13×SD16C2211yescharacteristic, complemented
22C2×C13×D8C2211yescharacteristic, complemented
23C13×#121C2211yescharacteristic, complemented
24#88203—24no—
25#88201C2211yescharacteristic, complemented
26#88200C2211yescharacteristic, complemented
27C2×#6106C2211yescharacteristic, complemented
28C2×#6106C2211yescharacteristic, complemented
29#88194C2211yescharacteristic, complemented
30#88193—21no—
31#88191—21no—
32#88191—21no—
33D4×Dic13C2211yescharacteristic, complemented
34C2×#6104C2211yescharacteristic
35C2×#6104C2211yescharacteristic, complemented
36C2×#6104C2211yescharacteristic, complemented
37#88184C2211yescharacteristic, complemented
38#88183—21no—
39C4×C22⋊D13C2211yescharacteristic
40C2×#6103—21no—
41C2×#6099C2211yescharacteristic, complemented
42D8×D13—24no—
43C2×D104C2211yescharacteristic
44C2×D104C2211yescharacteristic, complemented
45C2×C8×D13C2211yescharacteristic, complemented
46#88149C2211yescharacteristic
47#88147C2211yescharacteristic, complemented
48#88138—21no—
49#88136—21no—
50C13×#103C2211yescharacteristic, complemented
51C13×#102C2211yescharacteristic, complemented
52C13×C22⋊C8C2211yescharacteristic, complemented
53#88072C2211yescharacteristic, complemented
54#88061C2211yescharacteristic, complemented
55#88061C2211yescharacteristic, complemented
56#88060C2211yescharacteristic, complemented
57#88055C2211yescharacteristic, complemented
58#88054C2211yescharacteristic, complemented
59#88049C2211yescharacteristic, complemented
60#88048C2211yescharacteristic, complemented
61C23×D13—21no—
62C23×D13—21no—
63C23×D13—21no—
64C13×#41—22no—
65C13×#41—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13C2311yescharacteristic
70C2×D4×C13C2311yescharacteristic
71C22×C4×C13—21no—
72C22×C4×C13C2311yescharacteristic
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13D411yescharacteristic
79C22×Dic13—21no—
80D4×D13—22no—
81D4×D13—22no—
82D4×D13—41no—
83D4×D13—41no—
84D4×D13—44no—
85C2×D52—22no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—41no—
89C2×D52C2311yescharacteristic
90C2×D52C2311yescharacteristic
91C2×D52C2311yescharacteristic
92C2×C4×D13—21no—
93C2×C4×D13C2311yescharacteristic
94C13×SD16—41no—
95C13×D8—22no—
96C2×C8×C13C2311yescharacteristic
97C2×C8×C13C2311yescharacteristic
98C13×C4⋊C4C2311yescharacteristic
99C13×C22⋊C4—21no—
100C22⋊Dic13—21no—
101C22⋊Dic13D411yescharacteristic
102#6106—22no—
103#6106—22no—
104#6104—22no—
105#6104—22no—
106#6104D414yescomplemented
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103—21no—
111#6103—21no—
112#6103—21no—
113#6103D411yescharacteristic
114C4⋊Dic13C2311yescharacteristic
115#6101—21no—
116#6101D411yescharacteristic
117C4×Dic13C2311yescharacteristic
118#6099—22no—
119C2×#1055C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121D104—22no—
122D104—41no—
123C8×D13—22no—
124#3264—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13—21no—
127C23×C13C2×D411yescharacteristic
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—42no—
132C22×D13—42no—
133C22×D13—42no—
134C22×D13—42no—
135C22×D13—42no—
136C22×D13—42no—
137C22×D13—81no—
138C22×D13—81no—
139C22×D13—81no—
140C22×D13C2×D411yescharacteristic
141Q8×C13—21no—
142Q8×C13—21no—
143D4×C13—21no—
144D4×C13—21no—
145D4×C13—21no—
146D4×C13—42no—
147D4×C13—42no—
148D4×C13C2×D412yescomplemented
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—42no—
154C2×C4×C13C2×D411yescharacteristic
155C2×C4×C13C2411yescharacteristic
156C22⋊D13—22no—
157C22⋊D13—42no—
158C22⋊D13—42no—
159C22⋊D13—42no—
160C22⋊D13—81no—
161C22⋊D13—81no—
162C2×Dic13—21no—
163C2×Dic13—81no—
164C2×Dic13C2×D411yescharacteristic
165C2×Dic13C2×D411yescharacteristic
166C2×Dic13C2×D411yescharacteristic
167D52—21no—
168D52—21no—
169D52—21no—
170D52—21no—
171D52—21no—
172D52—42no—
173D52—42no—
174D52C2×D412yes—
175C4×D13—21no—
176C4×D13—21no—
177C4×D13—42no—
178C8×C13—21no—
179C8×C13—21no—
180#1055—21no—
181#1055C2×D412yescomplemented
182C2×AGL(1,ℤ/8)—131no—
183C22×D8—131no—
184#546—131no—
185D42—131no—
186#496—131no—
187#469—131no—
188#465—131no—
189#463—131no—
190#459—131no—
191#450—131no—
192#449D1311yescharacteristic, complemented
193#447—131no—
194#447—131no—
195#442—131no—
196#435—131no—
197C22×C13—22no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13C22×D411yescharacteristic
207C2×D13—21no—
208C2×D13—21no—
209C2×D13—22no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C2×D13—41no—
214C2×D13—41no—
215C2×D13—41no—
216C2×D13—41no—
217C2×D13—41no—
218C2×D13—84no—
219C2×D13—84no—
220C2×D13—84no—
221C2×D13AGL(1,ℤ/8)12yescomplemented
222C4×C13—21no—
223C4×C13—41no—
224C4×C13—41no—
225C4×C13C22×D411yescharacteristic
226C4×C13H(5,𝔽2)11yescharacteristic
227Dic13—21no—
228Dic13—21no—
229Dic13—21no—
230Dic13—41no—
231C2×#41C2×D1311yescharacteristic, complemented
232C22×D4—131no—
233C22×D4—131no—
234C22×D4—131no—
235C22×D4—261no—
236AGL(1,ℤ/8)—264no—
237C2×SD16—131no—
238C2×SD16—131no—
239C2×SD16C2×D1311yescharacteristic, complemented
240C2×D8—131no—
241C2×D8—131no—
242C2×D8—131no—
243C2×D8—131no—
244C2×D8—131no—
245C2×D8—264no—
246C2×D8C2×D1311yescharacteristic, complemented
247C2×M16—131no—
248C22×C8—131no—
249#127—131no—
250#124—131no—
251#123—261no—
252C22⋊Q8—131no—
253#121—131no—
254#121—131no—
255#121—261no—
256#121—261no—
257#121C2×D1311yescharacteristic, complemented
258#120—261no—
259#120—261no—
260#120—261no—
261C4×D4—131no—
262C4×D4—131no—
263C4×D4—131no—
264C2×C22⋊C4—261no—
265#106—131no—
266C4⋊C8—131no—
267#103C2×D1311yescharacteristic, complemented
268#102—131no—
269#102—131no—
270#102—131no—
271#102—131no—
272#102C2×D1311yescharacteristic, complemented
273C22⋊C8—131no—
274C22⋊C8C2×D1311yescharacteristic, complemented
275#97—131no—
276C2×C13—41no—
277C2×C13—42no—
278C2×C13—81no—
279C2×C13D4211yescharacteristic
280C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
281C2×C13#57611yescharacteristic
282D13—22no—
283D13—42no—
284D13—81no—
285D13—81no—
286C24—261no—
287C24—261no—
288C24—261no—
289#41—22no—
290#41—41no—
291C2×Q8C22×D1311yescharacteristic
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—131no—
295C2×D4—131no—
296C2×D4—131no—
297C2×D4—131no—
298C2×D4—262no—
299C2×D4—261no—
300C2×D4—261no—
301C2×D4—261no—
302C2×D4—261no—
303C2×D4—261no—
304C2×D4—262no—
305C2×D4—262no—
306C2×D4—261no—
307C2×D4—261no—
308C2×D4—521no—
309C2×D4—521no—
310C2×D4—521no—
311C2×D4—524no—
312C2×D4C22×D1311yescharacteristic
313C2×D4C22×D1311yescharacteristic
314C22×C4—21no—
315C22×C4—131no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4C22×D1311yescharacteristic
319SD16—41no—
320SD16—262no—
321SD16—262no—
322D8—22no—
323D8—134no—
324D8—262no—
325D8—262no—
326D8—262no—
327D8—521no—
328M16—262no—
329C2×C8—131no—
330C2×C8—131no—
331C2×C8—262no—
332C2×C8C22×D1311yescharacteristic
333C2×C8C22×D1311yescharacteristic
334C4⋊C4—131no—
335C4⋊C4—131no—
336C4⋊C4—261no—
337C4⋊C4C22×D1311yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—131no—
340C22⋊C4—131no—
341C22⋊C4—261no—
342C22⋊C4—261no—
343C22⋊C4—261no—
344C22⋊C4—261no—
345C22⋊C4—261no—
346C22⋊C4—261no—
347C22⋊C4—261no—
348C42—131no—
349C13#326411yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—131no—
353C23—261no—
354C23—261no—
355C23—261no—
356C23—522no—
357C23—522no—
358C23—522no—
359C23—522no—
360C23—522no—
361C23—522no—
362C23—1041no—
363C23—1041no—
364C23—1041no—
365C23D4×D1311yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—42no—
372D4—42no—
373D4—132no—
374D4—262no—
375D4—261no—
376D4—261no—
377D4—261no—
378D4—261no—
379D4—261no—
380D4—522no—
381D4—522no—
382D4—522no—
383D4—522no—
384D4—522no—
385D4—1041no—
386D4—1041no—
387D4D4×D1312yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—42no—
393C2×C4—131no—
394C2×C4—131no—
395C2×C4—131no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—261no—
399C2×C4—522no—
400C2×C4—1041no—
401C2×C4D4×D1311yescharacteristic
402C2×C4C23×D1311yescharacteristic
403C8—21no—
404C8—21no—
405C8—132no—
406C8—261no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—132no—
417C22—261no—
418C22—261no—
419C22—262no—
420C22—521no—
421C22—521no—
422C22—521no—
423C22—521no—
424C22—521no—
425C22—521no—
426C22—521no—
427C22—521no—
428C22—1044no—
429C22—1044no—
430C22—1044no—
431C22C2×D4×D1311yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—261no—
436C4—261no—
437C4—261no—
438C4—521no—
439C4C2×D4×D1311yescharacteristic
440C4#8825111yescharacteristic
441C2—41no—
442C2—42no—
443C2—81no—
444C2—262no—
445C2—522no—
446C2—1041no—
447C2—1041no—
448C2#1171929511yescharacteristic
449C2#1171947411yescharacteristic
450C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3264
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. #11719534C2semidirect
2. C2×#88203C2semidirect
3. C2×D8×D13C2semidirect
4. #11719314C2semidirect
5. C13×#449C2semidirect
6. #11718837C2semidirect
7. #11718830C2semidirect
8. #11718811C2semidirect
9. #11718700C2semidirect
10. #11718480C2semidirect
11. #11718468C2semidirect
12. #11718446C2semidirect
13. #11718434C2semidirect
14. #11718393C2semidirect
15. #11718389C2semidirect
16. C2×C13×#41C22semidirect
19. C2×D4×D13C22semidirect
20. C22×D52C22semidirect
21. C2×C13×SD16C22semidirect
22. C2×C13×D8C22semidirect
23. C13×#121C22semidirect
25. #88201C22semidirect
26. #88200C22semidirect
27. C2×#6106C22semidirect
28. C2×#6106C22semidirect
29. #88194C22semidirect
33. D4×Dic13C22semidirect
35. C2×#6104C22semidirect
36. C2×#6104C22semidirect
37. #88184C22semidirect
41. C2×#6099C22semidirect
44. C2×D104C22semidirect
45. C2×C8×D13C22semidirect
47. #88147C22semidirect
50. C13×#103C22semidirect
51. C13×#102C22semidirect
52. C13×C22⋊C8C22semidirect
53. #88072C22semidirect
54. #88061C22semidirect
55. #88061C22semidirect
56. #88060C22semidirect
57. #88055C22semidirect
58. #88054C22semidirect
59. #88049C22semidirect
60. #88048C22semidirect
106. #6104D4semidirect
148. D4×C13C2×D4semidirect
181. #1055C2×D4semidirect
192. #449D13semidirect
221. C2×D13AGL(1,ℤ/8)semidirect
231. C2×#41C2×D13semidirect
239. C2×SD16C2×D13semidirect
246. C2×D8C2×D13semidirect
257. #121C2×D13semidirect
267. #103C2×D13semidirect
272. #102C2×D13semidirect
274. C22⋊C8C2×D13semidirect
349. C13#3264semidirect
387. D4D4×D13semidirect

Maximal subgroups

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

subgroupindex
#117195342
C2×#882032
C2×D8×D132
#117193142
C13×#4492
#117188372
#117188302
#117188112
#117187002
#117184802
#117184682
#117184462
#117184342
#117183932
#117183892
#326413