Finite Group Databasebeta

← #13126338

Subgroups — #13126338

Order 1664.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D13C211yesmaximal, characteristic, complemented
2C2×#88162C211yesmaximal, characteristic, complemented
3#11719338C211yesmaximal, characteristic, complemented
4#11719314C211yesmaximal, characteristic, complemented
5C13×#468C211yesmaximal, characteristic, complemented
6#11718837C211yesmaximal, characteristic, complemented
7#11718788C211yesmaximal, characteristic, complemented
8#11718707C211yesmaximal, characteristic, complemented
9#11718698C211yesmaximal, characteristic, complemented
10#11718550C211yesmaximal, characteristic, complemented
11#11718544C211yesmaximal, characteristic, complemented
12#11718480C211yesmaximal, characteristic, complemented
13#11718467C211yesmaximal, characteristic, complemented
14#11718434C211yesmaximal, characteristic, complemented
15#11718423C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic, complemented
17C2×D4×D13—21no—
18C2×D4×D13C2211yescharacteristic
19C2×#6127C2211yescharacteristic, complemented
20C22×D52C2211yescharacteristic
21C2×C13×SD16C2211yescharacteristic, complemented
22C2×C13×M16C2211yescharacteristic, complemented
23C13×C22⋊Q8C2211yescharacteristic, complemented
24C13×#121C2211yescharacteristic
25#88201C2211yescharacteristic, complemented
26C2×#6106C2211yescharacteristic
27C2×#6106C2211yescharacteristic, complemented
28#88194C2211yescharacteristic
29#88191—21no—
30C2×#6105C2211yescharacteristic, complemented
31C2×#6104C2211yescharacteristic, complemented
32C4×C22⋊D13C2211yescharacteristic
33SD16×D13—24no—
34#88162—24no—
35C2×D104C2211yescharacteristic
36C2×D104C2211yescharacteristic, complemented
37C2×#6095C2211yescharacteristic
38C2×#6095C2211yescharacteristic, complemented
39C2×C8×D13C2211yescharacteristic, complemented
40#88150—21no—
41#88149C2211yescharacteristic
42#88149C2211yescharacteristic, complemented
43#88147—21no—
44#88147C2211yescharacteristic
45#88141C2211yescharacteristic, complemented
46#88139—21no—
47#88138—21no—
48#88138—21no—
49#88136—21no—
50C13×#107C2211yescharacteristic, complemented
51C13×#103C2211yescharacteristic, complemented
52C13×#102C2211yescharacteristic, complemented
53C22⋊#1055C2211yescharacteristic, complemented
54#88060C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88049C2211yescharacteristic
59#88049C2211yescharacteristic, complemented
60#88049C2211yescharacteristic, complemented
61C23×D13—21no—
62C23×D13—21no—
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13D411yescharacteristic
72Q8×D13—22no—
73Q8×D13—41no—
74D4×D13—22no—
75D4×D13—41no—
76D4×D13—44no—
77#6127—22no—
78#6127—41no—
79C2×D52—22no—
80C2×D52—21no—
81C2×D52—21no—
82C2×D52—21no—
83C2×D52—41no—
84C2×D52C2311yescharacteristic
85C2×D52C2311yescharacteristic
86C2×D52C2311yescharacteristic
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×C4×D13C2311yescharacteristic
91C2×Dic26—21no—
92C2×Dic26C2311yescharacteristic
93C13×SD16—22no—
94C13×M16—22no—
95C2×C8×C13C2311yescharacteristic
96C2×C8×C13C2311yescharacteristic
97C13×C4⋊C4—21no—
98C13×C4⋊C4C2311yescharacteristic
99C13×C4⋊C4C2311yescharacteristic
100C13×C22⋊C4—21no—
101C13×C22⋊C4—21no—
102C22⋊Dic13D411yescharacteristic
103#6106—22no—
104#6106—41no—
105#6105—22no—
106#6104—41no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103—21no—
111#6103—21no—
112#6103D411yescharacteristic
113#6101—21no—
114#6101D411yescharacteristic
115C4×Dic13—21no—
116C4×Dic13C2311yescharacteristic
117C2×#1055C2311yescharacteristic
118C2×#1055C2311yescharacteristic
119D104—22no—
120D104—22no—
121#6095—22no—
122#6095D414yescomplemented
123C8×D13—22no—
124#3265—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13C2×D411yescharacteristic
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—42no—
131C22×D13—42no—
132C22×D13—42no—
133C22×D13—42no—
134C22×D13—81no—
135C22×D13—81no—
136C22×D13C2×D411yescharacteristic
137Q8×C13—21no—
138Q8×C13—21no—
139D4×C13—21no—
140D4×C13—21no—
141D4×C13—42no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13C2×D411yescharacteristic
148C2×C4×C13C2411yescharacteristic
149C22⋊D13—22no—
150C22⋊D13—42no—
151C22⋊D13—42no—
152C22⋊D13—42no—
153C22⋊D13—81no—
154C2×Dic13—21no—
155C2×Dic13C2×D411yescharacteristic
156C2×Dic13C2×D411yescharacteristic
157C2×Dic13C2×D411yescharacteristic
158D52—21no—
159D52—21no—
160D52—21no—
161D52—21no—
162D52—21no—
163D52—42no—
164D52—42no—
165D52—42no—
166D52C2×D412yes—
167C4×D13—21no—
168C4×D13—21no—
169C4×D13—42no—
170C4×D13—42no—
171C4×D13—42no—
172Dic26—21no—
173Dic26—42no—
174Dic26C2×D412yescomplemented
175C8×C13—21no—
176C8×C13C2×D412yescomplemented
177#1055—21no—
178#1055—21no—
179C2×AGL(1,ℤ/8)—131no—
180C22×SD16—131no—
181#548—131no—
182D42—131no—
183#496—131no—
184#468D1311yescharacteristic, complemented
185#466—131no—
186#463—131no—
187#460—131no—
188#450—131no—
189#449—131no—
190#448—131no—
191#447—131no—
192#440—131no—
193#435—131no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13C22×D411yescharacteristic
201C2×D13—21no—
202C2×D13—21no—
203C2×D13—22no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—84no—
213C2×D13—84no—
214C2×D13AGL(1,ℤ/8)12yescomplemented
215C4×C13—21no—
216C4×C13—41no—
217C4×C13—41no—
218C4×C13—41no—
219C4×C13C22×D411yescharacteristic
220C4×C13H(5,𝔽2)11yescharacteristic
221Dic13—22no—
222Dic13—21no—
223Dic13—21no—
224Dic13—21no—
225C2×#41—131no—
226C22×Q8—131no—
227C22×D4—131no—
228C22×D4—131no—
229C22×D4—261no—
230AGL(1,ℤ/8)—264no—
231C2×SD16—131no—
232C2×SD16—131no—
233C2×SD16—131no—
234C2×SD16—131no—
235C2×SD16—131no—
236C2×SD16—264no—
237C2×SD16C2×D1311yescharacteristic, complemented
238C2×D8—131no—
239C2×D8—131no—
240C2×D8—131no—
241C2×M16C2×D1311yescharacteristic, complemented
242C22×C8—131no—
243#127—131no—
244#124—131no—
245#124—261no—
246C22⋊Q8—261no—
247C22⋊Q8C2×D1311yescharacteristic, complemented
248#121—131no—
249#121—131no—
250#121—261no—
251#121—261no—
252#121C2×D1311yescharacteristic
253#120—261no—
254#120—261no—
255C4×Q8—131no—
256C4×D4—131no—
257C4×D4—131no—
258C4×D4—261no—
259#107C2×D1311yescharacteristic, complemented
260C4⋊C8—131no—
261#103—131no—
262#103C2×D1311yescharacteristic, complemented
263#102—131no—
264#102—131no—
265#102—131no—
266#102C2×D1311yescharacteristic, complemented
267C22⋊C8—131no—
268C22⋊C8—131no—
269#97—131no—
270C2×C13—41no—
271C2×C13—81no—
272C2×C13D4211yescharacteristic
273C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
274C2×C13#57711yescharacteristic
275D13—22no—
276D13—42no—
277D13—81no—
278D13—81no—
279C24—261no—
280C24—261no—
281#41—262no—
282#41—521no—
283C2×Q8—131no—
284C2×Q8—261no—
285C2×Q8—262no—
286C2×Q8—521no—
287C2×Q8C22×D1311yescharacteristic
288C2×D4—21no—
289C2×D4—131no—
290C2×D4—131no—
291C2×D4—131no—
292C2×D4—131no—
293C2×D4—262no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4—261no—
298C2×D4—261no—
299C2×D4—262no—
300C2×D4—261no—
301C2×D4—261no—
302C2×D4—521no—
303C2×D4—521no—
304C2×D4—524no—
305C2×D4C22×D1311yescharacteristic
306C22×C4—131no—
307C22×C4—261no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4C22×D1311yescharacteristic
311SD16—22no—
312SD16—134no—
313SD16—262no—
314SD16—262no—
315SD16—262no—
316SD16—521no—
317D8—262no—
318D8—262no—
319D8—521no—
320M16—22no—
321C2×C8—131no—
322C2×C8—131no—
323C2×C8—262no—
324C2×C8C22×D1311yescharacteristic
325C2×C8C22×D1311yescharacteristic
326C4⋊C4—21no—
327C4⋊C4—131no—
328C4⋊C4—261no—
329C4⋊C4C22×D1311yescharacteristic
330C4⋊C4C22×D1311yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—131no—
334C22⋊C4—131no—
335C22⋊C4—261no—
336C22⋊C4—261no—
337C22⋊C4—261no—
338C22⋊C4—261no—
339C22⋊C4—261no—
340C42—131no—
341C42—261no—
342C13#326511yescharacteristic, complemented, Sylow
343C23—21no—
344C23—131no—
345C23—261no—
346C23—261no—
347C23—261no—
348C23—522no—
349C23—522no—
350C23—522no—
351C23—522no—
352C23—1041no—
353C23—1041no—
354C23D4×D1311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—132no—
358Q8—261no—
359Q8—522no—
360D4—21no—
361D4—21no—
362D4—42no—
363D4—132no—
364D4—262no—
365D4—261no—
366D4—261no—
367D4—261no—
368D4—261no—
369D4—261no—
370D4—522no—
371D4—522no—
372D4—522no—
373D4—522no—
374D4—522no—
375D4—522no—
376D4—1041no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—131no—
383C2×C4—131no—
384C2×C4—131no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4D4×D1311yescharacteristic
392C2×C4C23×D1311yescharacteristic
393C8—21no—
394C8—261no—
395C8—261no—
396C8D4×D1312yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—132no—
404C22—261no—
405C22—261no—
406C22—262no—
407C22—521no—
408C22—521no—
409C22—521no—
410C22—521no—
411C22—521no—
412C22—521no—
413C22—521no—
414C22—521no—
415C22—1044no—
416C22—1044no—
417C22C2×D4×D1311yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—261no—
423C4—261no—
424C4—261no—
425C4—262no—
426C4C2×D4×D1311yescharacteristic
427C4#8825611yescharacteristic
428C2—41no—
429C2—81no—
430C2—262no—
431C2—522no—
432C2—1041no—
433C2—1041no—
434C2#1171931411yescharacteristic
435C2D13×AGL(1,ℤ/8)11yescharacteristic
436C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
hypercenter#468D13
hypocenterC13#3265
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D13C2semidirect
2. C2×#88162C2semidirect
3. #11719338C2semidirect
4. #11719314C2semidirect
5. C13×#468C2semidirect
6. #11718837C2semidirect
7. #11718788C2semidirect
8. #11718707C2semidirect
9. #11718698C2semidirect
10. #11718550C2semidirect
11. #11718544C2semidirect
12. #11718480C2semidirect
13. #11718467C2semidirect
14. #11718434C2semidirect
15. #11718423C2semidirect
16. C2×Q8×D13C22semidirect
19. C2×#6127C22semidirect
21. C2×C13×SD16C22semidirect
22. C2×C13×M16C22semidirect
23. C13×C22⋊Q8C22semidirect
25. #88201C22semidirect
27. C2×#6106C22semidirect
30. C2×#6105C22semidirect
31. C2×#6104C22semidirect
36. C2×D104C22semidirect
38. C2×#6095C22semidirect
39. C2×C8×D13C22semidirect
42. #88149C22semidirect
45. #88141C22semidirect
50. C13×#107C22semidirect
51. C13×#103C22semidirect
52. C13×#102C22semidirect
53. C22⋊#1055C22semidirect
54. #88060C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
57. #88050C22semidirect
59. #88049C22semidirect
60. #88049C22semidirect
122. #6095D4semidirect
174. Dic26C2×D4semidirect
176. C8×C13C2×D4semidirect
184. #468D13semidirect
214. C2×D13AGL(1,ℤ/8)semidirect
237. C2×SD16C2×D13semidirect
241. C2×M16C2×D13semidirect
247. C22⋊Q8C2×D13semidirect
259. #107C2×D13semidirect
262. #103C2×D13semidirect
266. #102C2×D13semidirect
342. C13#3265semidirect
396. C8D4×D13semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D132
C2×#881622
#117193382
#117193142
C13×#4682
#117188372
#117187882
#117187072
#117186982
#117185502
#117185442
#117184802
#117184672
#117184342
#117184232
#326513