Finite Group Databasebeta

← #15848331

Subgroups — #15848331

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125751C211yesmaximal, characteristic, complemented
2#13124316C211yesmaximal, characteristic, complemented
3#13123947C211yesmaximal, characteristic, complemented
4#13114282C212yesmaximal, complemented
5#13114275C212yesmaximal, complemented
6#13114194C212yesmaximal, complemented
7#13114189C212yesmaximal, complemented
8#13113610C211yesmaximal, characteristic, complemented
9#13113513C211yesmaximal, characteristic, complemented
10C2×#11718077C211yesmaximal, characteristic, complemented
11C13×#3035C211yesmaximal, characteristic, complemented
12C2×C13×#135—21no—
13C13×#532C2211yescharacteristic
14C4×C13×#41C2211yescharacteristic
15C2×#88203—21no—
16C2×#88128C2211yescharacteristic
17C13×#464—21no—
18C13×#463—21no—
19C13×#462C2211yescharacteristic, complemented
20C13×#461C2211yescharacteristic, complemented
21C13×#460C2211yescharacteristic, complemented
22C13×#459C2211yescharacteristic, complemented
23C2×C13×C4⋊C8C2211yescharacteristic
24C13×#416—21no—
25#11718749C2212yes—
26#11718734C2212yes—
27#11718697—22no—
28#11718688—21no—
29#11718688C2212yes—
30Q8×#1055C2212yescomplemented
31#11718676—21no—
32#11718676—21no—
33#11718676—21no—
34#11718676C2212yes—
35D4×#1055—22no—
36D4×#1055C2212yescomplemented
37#11718662—21no—
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718585C2211yescharacteristic
41C2×C4⋊#1055—21no—
42C2×C4⋊#1055C2211yescharacteristic
43#11718139C2212yescomplemented
44#11718136C2212yescomplemented
45#11718077C2212yes—
46#11718077C2212yes—
47#11718071C2212yescomplemented
48#11718071C2212yescomplemented
49C2×C13×#41—21no—
50C2×C13×#41D411yescharacteristic
51C22×D52—21no—
52C22×D52—21no—
53C22×D52—21no—
54C13×#135—44no—
55C2×C13×Q16—21no—
56C2×C13×SD16—21no—
57C2×C13×SD16—21no—
58C2×C13×D8—21no—
59C22×C8×C13—21no—
60C13×C4⋊Q8C2311yescharacteristic
61C13×#127C2311yescharacteristic
62C13×#124—21no—
63C13×#121—21no—
64C13×#121—21no—
65C4×Q8×C13D411yescharacteristic
66C4×Q8×C13C2311yescharacteristic
67C4×D4×C13—21no—
68C4×D4×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13D411yescharacteristic
72C4×D4×C13C2311yescharacteristic
73C13×#117—21no—
74C13×#117D411yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77#88203—44no—
78C2×#6106—22no—
79C2×#6104—22no—
80C2×#6104—22no—
81C2×#6104—22no—
82C2×#6099—21no—
83C22×#1055—21no—
84C22×#1055—22no—
85#88128—21no—
86#88128—21no—
87#88128—21no—
88#88128C2312yes—
89C13×C4⋊C8—21no—
90C13×C4⋊C8C2311yescharacteristic
91C13×C4⋊C8C2311yescharacteristic
92C13×#103—21no—
93C13×#103—21no—
94C13×#102—21no—
95C13×#102—21no—
96C22⋊#1055—22no—
97C22⋊#1055D412yes—
98#88049—22no—
99#88049—22no—
100#88049—22no—
101#88049—22no—
102C4⋊#1055—21no—
103C4⋊#1055—21no—
104C4⋊#1055—22no—
105C4⋊#1055D411yescharacteristic
106C4⋊#1055D411yescharacteristic
107C4⋊#1055C2312yes—
108C4⋊#1055C2312yes—
109C4×#1055—22no—
110C4×#1055C2312yes—
111#19410—131nomaximal, Sylow
112C23×D13—41no—
113C13×#41—22no—
114C13×#41—42no—
115C13×#41—42no—
116C13×#41D814yescomplemented
117C2×Q8×C13—21no—
118C2×Q8×C13C2×D411yescharacteristic
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—41no—
124C2×D4×C13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—41no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13#4111yescharacteristic
132C2×D52—22no—
133C2×D52—22no—
134C2×D52—22no—
135C2×D52—42no—
136C2×D52—42no—
137C2×D52—41no—
138C2×D52—41no—
139C2×D52—41no—
140C2×D52—81no—
141C2×D52—81no—
142C2×D52—82no—
143C13×Q16—42no—
144C13×SD16—42no—
145C13×SD16—42no—
146C13×D8—42no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—42no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4C2×D411yescharacteristic
155C13×C4⋊C4C2×D411yescharacteristic
156C13×C22⋊C4—21no—
157C13×C22⋊C4—21no—
158C13×C22⋊C4—21no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13C2×D411yescharacteristic
165C42×C13C2×D411yescharacteristic
166C42×C13#4111yescharacteristic
167C42×C13C2411yescharacteristic
168#6106—44no—
169#6104—44no—
170#6104—82no—
171#6104—82no—
172#6099—42no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—82no—
176C2×#1055—81no—
177C2×#1055C2×D412yes—
178C2×#1055C2×D412yes—
179#3205—131no—
180#3038—131no—
181#3035D1311yescharacteristic, complemented
182#2988—131no—
183#1682—132no—
184#1681—132no—
185#1668—132no—
186#1667—132no—
187#1571—131no—
188#1547—131no—
189C2×#331—131no—
190C23×C13—21no—
191C23×C13—41no—
192C23×C13#12111yescharacteristic
193C22×D13—42no—
194C22×D13—82no—
195C22×D13—82no—
196C22×D13—82no—
197Q8×C13—21no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13C2×D812yes—
201D4×C13—24no—
202D4×C13—21no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—81no—
208D4×C13—82no—
209D4×C13C2×D812yes—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—24no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—81no—
221C2×C4×C13—82no—
222C2×C4×C13#12111yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13C2×D812yes—
226C2×C4×C13#13512yes—
227C2×C4×C13C22×D411yescharacteristic
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230D52—42no—
231D52—42no—
232D52—42no—
233D52—42no—
234D52—82no—
235D52—82no—
236D52—82no—
237D52—82no—
238C8×C13—41no—
239C8×C13—41no—
240#1055—22no—
241#1055—22no—
242#1055—42no—
243#1055—42no—
244C2×AGL(1,ℤ/8)—261no—
245C2×#135—21no—
246#532C2×D1311yescharacteristic
247C2×#127—131no—
248C4×#41C2×D1311yescharacteristic
249#493—132no—
250#486—132no—
251#464—21no—
252#463—21no—
253#462C2×D1311yescharacteristic, complemented
254#461C2×D1311yescharacteristic, complemented
255#460—132no—
256#460—261no—
257#460C2×D1311yescharacteristic, complemented
258#459—132no—
259#459—261no—
260#459—261no—
261#459—261no—
262#459C2×D1311yescharacteristic, complemented
263#447—262no—
264C8×Q8—132no—
265C8×D4—132no—
266C8×D4—262no—
267#431—131no—
268#431—261no—
269#423—131no—
270C2×C4⋊C8—131no—
271C2×C4⋊C8—261no—
272C2×C4⋊C8C2×D1311yescharacteristic
273#418—261no—
274#416—21no—
275#335—132no—
276#335—132no—
277#332—132no—
278#331—132no—
279#331—132no—
280#331—132no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—22no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13#46612yes—
290C22×C13C2×#12111yescharacteristic
291C2×D13—82no—
292C2×D13—82no—
293C2×D13—82no—
294C2×D13—164no—
295C4×C13—21no—
296C4×C13—22no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—41no—
300C4×C13—41no—
301C4×C13—81no—
302C4×C13#46612yes—
303C4×C13C22×D811yescharacteristic
304C4×C13C2×#13511yescharacteristic
305C4×C13#57611yescharacteristic
306C4×C13#57711yescharacteristic
307C2×#41—21no—
308C2×#41C22⋊D1311yescharacteristic
309C22×D4—261no—
310C22×D4—261no—
311C22×D4—261no—
312AGL(1,ℤ/8)—524no—
313#135—44no—
314C2×Q16—21no—
315C2×SD16—21no—
316C2×SD16—21no—
317C2×SD16—262no—
318C2×D8—21no—
319C2×D8—262no—
320C2×D8—262no—
321C2×D8—262no—
322C2×M16—261no—
323C22×C8—21no—
324C22×C8—262no—
325C22×C8—261no—
326C4⋊Q8C22×D1311yescharacteristic
327#127—132no—
328#127—261no—
329#127—261no—
330#127—261no—
331#127C22×D1311yescharacteristic
332#124—21no—
333#121—21no—
334#121—21no—
335C4×Q8C22⋊D1311yescharacteristic
336C4×Q8C22×D1311yescharacteristic
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4C22⋊D1311yescharacteristic
342C4×D4C22×D1311yescharacteristic
343#117—21no—
344#117C22⋊D1311yescharacteristic
345C2×C42—21no—
346C2×C42C22×D1311yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—131no—
349C4⋊C8—131no—
350C4⋊C8—132no—
351C4⋊C8—132no—
352C4⋊C8—262no—
353C4⋊C8—261no—
354C4⋊C8—261no—
355C4⋊C8C22×D1311yescharacteristic
356C4⋊C8C22×D1311yescharacteristic
357#103—21no—
358#103—21no—
359#102—21no—
360#102—21no—
361#102—262no—
362#102—262no—
363#102—262no—
364#102—262no—
365C22⋊C8—132no—
366C22⋊C8—262no—
367C4×C8—132no—
368C4×C8—262no—
369C2×C13—22no—
370C2×C13—42no—
371C2×C13—161no—
372C2×C13#304511yescharacteristic
373C2×C13C2×#46611yescharacteristic
374C2×C13#306811yescharacteristic
375D13—162no—
376C24—521no—
377#41—22no—
378#41—42no—
379#41—42no—
380#41#610414yescomplemented
381C2×Q8—21no—
382C2×Q8C2×C22⋊D1311yescharacteristic
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—262no—
389C2×D4—262no—
390C2×D4—262no—
391C2×D4—522no—
392C2×D4—521no—
393C2×D4—521no—
394C2×D4—521no—
395C2×D4—522no—
396C2×D4—1041no—
397C2×D4—1041no—
398C2×D4—1042no—
399C2×D4C2×C22⋊D1311yescharacteristic
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—41no—
404C22×C4D4×D1311yescharacteristic
405C22×C4#612911yescharacteristic
406C22×C4C2×C22⋊D1311yescharacteristic
407Q16—42no—
408SD16—42no—
409SD16—42no—
410SD16—524no—
411D8—42no—
412D8—524no—
413D8—1042no—
414D8—1042no—
415M16—522no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—42no—
419C2×C8—132no—
420C2×C8—132no—
421C2×C8—262no—
422C2×C8—262no—
423C2×C8—1042no—
424C2×C8—1041no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4C2×C22⋊D1311yescharacteristic
430C4⋊C4C2×C22⋊D1311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42D4×D1311yescharacteristic
440C42#612911yescharacteristic
441C42C2×C22⋊D1311yescharacteristic
442C42C23×D1311yescharacteristic
443C13#1941011yescharacteristic, complemented, Sylow
444C23—21no—
445C23—41no—
446C23—522no—
447C23—1042no—
448C23—1042no—
449C23—1042no—
450C23#8819311yescharacteristic
451Q8—21no—
452Q8—41no—
453Q8—41no—
454Q8C2×#610412yes—
455D4—24no—
456D4—21no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—81no—
462D4—82no—
463D4—522no—
464D4—522no—
465D4—522no—
466D4—522no—
467D4—1042no—
468D4—1042no—
469D4—1042no—
470D4—1042no—
471D4C2×#610412yes—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—81no—
483C2×C4—82no—
484C2×C4C2×#610412yes—
485C2×C4#8819311yescharacteristic
486C2×C4#8819311yescharacteristic
487C2×C4#8819311yescharacteristic
488C2×C4#8820412yes—
489C2×C4C2×D4×D1311yescharacteristic
490C2×C4C2×#612911yescharacteristic
491C2×C4C22×C22⋊D1311yescharacteristic
492C8—41no—
493C8—41no—
494C8—262no—
495C8—262no—
496C8—522no—
497C8—522no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—1042no—
507C22—1042no—
508C22—1042no—
509C22—2084no—
510C22#1171869912yes—
511C22C2×#8819311yescharacteristic
512C4—21no—
513C4—22no—
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—81no—
519C4#1171869912yes—
520C4#1171947411yescharacteristic
521C4#1171947511yescharacteristic
522C4C22×#610411yescharacteristic
523C4C2×#8820411yescharacteristic
524C2—22no—
525C2—42no—
526C2—161no—
527C2—2082no—
528C2#1312437311yescharacteristic
529C2C2×#1171869911yescharacteristic
530C2#1312456611yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3035C2
socleC22×C13C2×#121
hypercenter#3035D13
hypocenterC13#19410
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13125751C2semidirect
2. #13124316C2semidirect
3. #13123947C2semidirect
4. #13114282C2semidirect
5. #13114275C2semidirect
6. #13114194C2semidirect
7. #13114189C2semidirect
8. #13113610C2semidirect
9. #13113513C2semidirect
10. C2×#11718077C2semidirect
11. C13×#3035C2semidirect
19. C13×#462C22semidirect
20. C13×#461C22semidirect
21. C13×#460C22semidirect
22. C13×#459C22semidirect
30. Q8×#1055C22semidirect
36. D4×#1055C22semidirect
43. #11718139C22semidirect
44. #11718136C22semidirect
47. #11718071C22semidirect
48. #11718071C22semidirect
116. C13×#41D8semidirect
181. #3035D13semidirect
253. #462C2×D13semidirect
254. #461C2×D13semidirect
257. #460C2×D13semidirect
262. #459C2×D13semidirect
380. #41#6104semidirect
443. C13#19410semidirect

Maximal subgroups

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

subgroupindex
#131257512
#131243162
#131239472
#131142822
#131142752
#131141942
#131141892
#131136102
#131135132
C2×#117180772
C13×#30352
#1941013