Finite Group Databasebeta

← #13126331

Subgroups — #13126331

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
1C22×C13×SD16C211yesmaximal, characteristic, complemented
2#11719522C211yesmaximal, characteristic, complemented
3D4×C22⋊D13C211yesmaximal, characteristic, complemented
4C2×#88168C211yesmaximal, characteristic, complemented
5#11718888C211yesmaximal, characteristic, complemented
6#11718878C211yesmaximal, characteristic, complemented
7#11718837C211yesmaximal, characteristic, complemented
8#11718835C211yesmaximal, characteristic, complemented
9#11718833C211yesmaximal, characteristic, complemented
10#11718830C211yesmaximal, characteristic, complemented
11#11718826C211yesmaximal, characteristic, complemented
12#11718825C211yesmaximal, characteristic, complemented
13#11718824C211yesmaximal, characteristic, complemented
14#11718776C211yesmaximal, characteristic, complemented
15#11718772C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic, complemented
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13—21no—
19C2×#6131C2211yescharacteristic, complemented
20C2×D4×D13C2211yescharacteristic
21C2×C13×SD16—24no—
22C2×C13×SD16C2211yescharacteristic
23C2×C13×SD16C2211yescharacteristic
24C2×C13×SD16C2211yescharacteristic, complemented
25C2×C13×SD16C2211yescharacteristic, complemented
26C22×C8×C13C2211yescharacteristic, complemented
27#88207—21no—
28#88201—21no—
29#88201C2211yescharacteristic, complemented
30#88200—21no—
31#88200C2211yescharacteristic, complemented
32Q8×Dic13C2211yescharacteristic, complemented
33C2×#6106C2211yescharacteristic, complemented
34C2×#6106C2211yescharacteristic, complemented
35#88194C2211yescharacteristic
36#88193—21no—
37#88192C2211yescharacteristic
38#88191—21no—
39D4×Dic13C2211yescharacteristic
40C2×#6104C2211yescharacteristic
41C2×#6104C2211yescharacteristic, complemented
42#88184—21no—
43#88184C2211yescharacteristic
44#88184C2211yescharacteristic, complemented
45C4×C22⋊D13—21no—
46C4×C22⋊D13C2211yescharacteristic
47#88168—24no—
48C2×D104C2211yescharacteristic, complemented
49C2×#6094C2211yescharacteristic, complemented
50#88075C2211yescharacteristic, complemented
51#88075C2211yescharacteristic, complemented
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic, complemented
55#88061C2211yescharacteristic, complemented
56#88061C2211yescharacteristic, complemented
57#88060C2211yescharacteristic, complemented
58#88058C2211yescharacteristic, complemented
59#88055C2211yescharacteristic, complemented
60#88054C2211yescharacteristic, complemented
61C24×C13—21no—
62C23×D13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13—22no—
69C2×D4×C13—21no—
70C2×D4×C13—41no—
71C2×D4×C13C2311yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C22×C4×C13—21no—
74C22×C4×C13C2311yescharacteristic
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—21no—
80C2×C22⋊D13—21no—
81C2×C22⋊D13—44no—
82C2×C22⋊D13D411yescharacteristic
83C22×Dic13—21no—
84#6131—22no—
85#6131—41no—
86D4×D13—22no—
87D4×D13—41no—
88C2×D52—21no—
89C2×D52C2311yescharacteristic
90C2×D52C2311yescharacteristic
91C2×C4×D13—21no—
92C2×C4×D13C2311yescharacteristic
93C13×SD16—22no—
94C13×SD16—22no—
95C13×SD16—22no—
96C13×SD16D414yescomplemented
97C2×C8×C13—22no—
98C2×C8×C13C2311yescharacteristic
99C2×C8×C13C2311yescharacteristic
100C22⋊Dic13—21no—
101C22⋊Dic13—21no—
102C22⋊Dic13D411yescharacteristic
103#6106—22no—
104#6106—41no—
105#6104—22no—
106#6104—41no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103—21no—
111#6103—21no—
112#6103D411yescharacteristic
113C4⋊Dic13—21no—
114C4⋊Dic13C2311yescharacteristic
115C4⋊Dic13C2311yescharacteristic
116#6101—21no—
117#6101D411yescharacteristic
118C4×Dic13—21no—
119C4×Dic13C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122D104—22no—
123#6094—22no—
124#3265—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—81no—
130C23×C13C2×D411yescharacteristic
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—42no—
134C22×D13—42no—
135C22×D13—81no—
136C22×D13C2×D411yescharacteristic
137Q8×C13—21no—
138Q8×C13—21no—
139Q8×C13—21no—
140Q8×C13—42no—
141Q8×C13C2×D412yescomplemented
142D4×C13—21no—
143D4×C13—21no—
144D4×C13—21no—
145D4×C13—42no—
146D4×C13C2×D412yes—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—42no—
152C2×C4×C13C2×D411yescharacteristic
153C2×C4×C13C2411yescharacteristic
154C22⋊D13—22no—
155C22⋊D13—42no—
156C22⋊D13—42no—
157C22⋊D13—42no—
158C22⋊D13—42no—
159C22⋊D13—42no—
160C22⋊D13—81no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—42no—
164C2×Dic13C2×D411yescharacteristic
165C2×Dic13C2×D411yescharacteristic
166C2×Dic13C2×D411yescharacteristic
167D52—21no—
168D52—21no—
169D52—21no—
170D52—21no—
171D52—42no—
172C4×D13—21no—
173C4×D13—21no—
174C4×D13—42no—
175C8×C13—21no—
176C8×C13C2×D412yescomplemented
177#1055—21no—
178#1055—21no—
179C2×AGL(1,ℤ/8)—131no—
180C22×SD16D1311yescharacteristic, complemented
181#548—131no—
182D42—131no—
183#496—131no—
184#468—131no—
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—22no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—84no—
203C22×C13AGL(1,ℤ/8)12yescomplemented
204C22×C13C22×D411yescharacteristic
205C2×D13—21no—
206C2×D13—21no—
207C2×D13—21no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C2×D13—41no—
214C2×D13—84no—
215C4×C13—22no—
216C4×C13—21no—
217C4×C13—41no—
218C4×C13C22×D411yescharacteristic
219C4×C13H(5,𝔽2)11yescharacteristic
220Dic13—21no—
221Dic13—21no—
222Dic13—21no—
223Dic13—41no—
224Dic13—41no—
225C2×#41—131no—
226C22×Q8C2×D1311yescharacteristic, complemented
227C22×D4—131no—
228C22×D4—261no—
229C22×D4C2×D1311yescharacteristic
230AGL(1,ℤ/8)—264no—
231C2×SD16—24no—
232C2×SD16—131no—
233C2×SD16—131no—
234C2×SD16C2×D1311yescharacteristic
235C2×SD16C2×D1311yescharacteristic
236C2×SD16C2×D1311yescharacteristic, complemented
237C2×SD16C2×D1311yescharacteristic, complemented
238C2×D8—131no—
239C2×D8—131no—
240C2×D8—131no—
241C2×M16—131no—
242C22×C8C2×D1311yescharacteristic, complemented
243#127—131no—
244#124—131no—
245#124—261no—
246C22⋊Q8—131no—
247C22⋊Q8—261no—
248#121—131no—
249#121—131no—
250#121—131no—
251#121—261no—
252#121—261no—
253#120—261no—
254#120—261no—
255C4×Q8—131no—
256C4×D4—131no—
257C4×D4—131no—
258C4×D4—261no—
259#107—131no—
260C4⋊C8—131no—
261#103—131no—
262#103—131no—
263#102—131no—
264#102—131no—
265#102—131no—
266#102—131no—
267C22⋊C8—131no—
268C22⋊C8—131no—
269#97—131no—
270C2×C13—22no—
271C2×C13—42no—
272C2×C13—81no—
273C2×C13D4211yescharacteristic
274C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
275C2×C13#57711yescharacteristic
276D13—41no—
277D13—81no—
278D13—81no—
279C24—21no—
280C24—261no—
281#41—262no—
282#41—521no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8C22×D1311yescharacteristic
287C2×Q8C22×D1311yescharacteristic
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—131no—
292C2×D4—131no—
293C2×D4—131no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4—261no—
298C2×D4—262no—
299C2×D4—261no—
300C2×D4—261no—
301C2×D4—261no—
302C2×D4—521no—
303C2×D4—524no—
304C2×D4C22×D1311yescharacteristic
305C2×D4C22×D1311yescharacteristic
306C22×C4—21no—
307C22×C4—131no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4C22×D1311yescharacteristic
311SD16—22no—
312SD16—22no—
313SD16—22no—
314SD16—262no—
315SD16—521no—
316SD16C22⋊D1314yescomplemented
317D8—262no—
318D8—262no—
319D8—521no—
320M16—262no—
321C2×C8—22no—
322C2×C8—131no—
323C2×C8—131no—
324C2×C8C22×D1311yescharacteristic
325C2×C8C22×D1311yescharacteristic
326C4⋊C4—131no—
327C4⋊C4—131no—
328C4⋊C4—131no—
329C4⋊C4—261no—
330C4⋊C4—261no—
331C22⋊C4—131no—
332C22⋊C4—131no—
333C22⋊C4—261no—
334C22⋊C4—261no—
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—21no—
345C23—42no—
346C23—42no—
347C23—81no—
348C23—131no—
349C23—261no—
350C23—261no—
351C23—522no—
352C23—522no—
353C23—1041no—
354C23D4×D1311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8C2×C22⋊D1312yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—262no—
365D4—261no—
366D4—261no—
367D4—261no—
368D4—261no—
369D4—522no—
370D4—522no—
371D4—522no—
372D4—522no—
373D4—522no—
374D4—522no—
375D4—1041no—
376D4C2×C22⋊D1312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—131no—
383C2×C4—131no—
384C2×C4—131no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4D4×D1311yescharacteristic
392C2×C4C23×D1311yescharacteristic
393C8—21no—
394C8—261no—
395C8—261no—
396C8C2×C22⋊D1312yescomplemented
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—84no—
406C22—261no—
407C22—261no—
408C22—261no—
409C22—521no—
410C22—521no—
411C22—521no—
412C22—521no—
413C22—521no—
414C22—521no—
415C22—1044no—
416C22#8816812yescomplemented
417C22C2×D4×D1311yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—261no—
422C4—261no—
423C4—261no—
424C4—521no—
425C4—521no—
426C4#8825111yescharacteristic
427C4C22×C22⋊D1311yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—521no—
432C2—1041no—
433C2—1041no—
434C2C2×#8816811yescharacteristic
435C2#1171946711yescharacteristic
436C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×SD16C2
socleC22×C13C22×D4
hypercenterC22×SD16D13
hypocenterC13#3265
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C13×SD16C2semidirect
2. #11719522C2semidirect
3. D4×C22⋊D13C2semidirect
4. C2×#88168C2semidirect
5. #11718888C2semidirect
6. #11718878C2semidirect
7. #11718837C2semidirect
8. #11718835C2semidirect
9. #11718833C2semidirect
10. #11718830C2semidirect
11. #11718826C2semidirect
12. #11718825C2semidirect
13. #11718824C2semidirect
14. #11718776C2semidirect
15. #11718772C2semidirect
16. C22×Q8×C13C22semidirect
19. C2×#6131C22semidirect
24. C2×C13×SD16C22semidirect
25. C2×C13×SD16C22semidirect
26. C22×C8×C13C22semidirect
29. #88201C22semidirect
31. #88200C22semidirect
32. Q8×Dic13C22semidirect
33. C2×#6106C22semidirect
34. C2×#6106C22semidirect
41. C2×#6104C22semidirect
44. #88184C22semidirect
48. C2×D104C22semidirect
49. C2×#6094C22semidirect
50. #88075C22semidirect
51. #88075C22semidirect
53. #88072C22semidirect
54. C22⋊#1055C22semidirect
55. #88061C22semidirect
56. #88061C22semidirect
57. #88060C22semidirect
58. #88058C22semidirect
59. #88055C22semidirect
60. #88054C22semidirect
96. C13×SD16D4semidirect
141. Q8×C13C2×D4semidirect
176. C8×C13C2×D4semidirect
180. C22×SD16D13semidirect
203. C22×C13AGL(1,ℤ/8)semidirect
226. C22×Q8C2×D13semidirect
236. C2×SD16C2×D13semidirect
237. C2×SD16C2×D13semidirect
242. C22×C8C2×D13semidirect
316. SD16C22⋊D13semidirect
342. C13#3265semidirect
359. Q8C2×C22⋊D13semidirect
396. C8C2×C22⋊D13semidirect
416. C22#88168semidirect

Maximal subgroups

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

subgroupindex
C22×C13×SD162
#117195222
D4×C22⋊D132
C2×#881682
#117188882
#117188782
#117188372
#117188352
#117188332
#117188302
#117188262
#117188252
#117188242
#117187762
#117187722
#326513