Finite Group Databasebeta

← #14737437

Subgroups — #14737437

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079588C211yesmaximal, characteristic
2#13079335C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068179C211yesmaximal, characteristic, complemented
5#13068161C211yesmaximal, characteristic, complemented
6#13068132C211yesmaximal, characteristic, complemented
7#13068090C211yesmaximal, characteristic, complemented
8#13068062C211yesmaximal, characteristic, complemented
9#13068044C211yesmaximal, characteristic, complemented
10#13068003C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067281C211yesmaximal, characteristic, complemented
14#13067266C211yesmaximal, characteristic, complemented
15C11×#3248C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#479—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#467—21no—
23C11×#465—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622698C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622681—21no—
33#10622672—21no—
34#10622662—21no—
35#10622662—21no—
36#10622660—21no—
37#10622650—21no—
38#10622644C2211yescharacteristic
39#10622640C2211yescharacteristic
40#10622639—21no—
41#10622639—21no—
42#10622637C2211yescharacteristic
43Q8×C11⋊C8C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622628C2211yescharacteristic
46#10622625—21no—
47#10622625C2211yescharacteristic
48#10622624—21no—
49D4×C11⋊C8C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53#10622538C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C22×C8×C11—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#124D411yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8D411yescharacteristic
81C11×#121D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4324—21no—
95C2×#4323—21no—
96#66983—21no—
97#66983—21no—
98C2×#4318—21no—
99C2×#4318D411yescharacteristic
100C2×#4318D411yescharacteristic
101C22×C11⋊C8—21no—
102#66928—21no—
103#66927C2311yescharacteristic
104C4×D44—21no—
105C4×D44—21no—
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#103—21no—
114C11×#103—21no—
115C11×#102—21no—
116#66899—21no—
117#66899—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19246—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×C22⋊D11—41no—
155#4339—81no—
156#4339—81no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×C4×D11—41no—
161C2×Dic22—21no—
162C11×Q16—81no—
163C11×SD16—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—81no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4326—81no—
192#4325—42no—
193#4325—42no—
194#4325—81no—
195#4324—81no—
196#4323—81no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—41no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201#4318—22no—
202#4318—41no—
203#4318—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3248D1111yescharacteristic, complemented
214#3212—111no—
215#3182—111no—
216#2969—111no—
217#1701—111no—
218#1699—111no—
219#1694—111no—
220#1686—111no—
221#1682—111no—
222#1680—111no—
223#1673—111no—
224#1665—111no—
225#1565—111no—
226#1544—111no—
227#1540—111no—
228C23×C11—21no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—81no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—82no—
259C2×Dic11—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—81no—
265C4×D11—82no—
266Dic22—41no—
267Dic22—41no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8#13512yes—
278#533C2×D1111yescharacteristic
279#532—111no—
280#529C2×D1111yescharacteristic
281#500—111no—
282#495—221no—
283#492—111no—
284#488—221no—
285#487—111no—
286#486—111no—
287#479—21no—
288#475C2×D1111yescharacteristic
289#474C2×D1111yescharacteristic
290#468—221no—
291#468—221no—
292#467—21no—
293#465—21no—
294#464—21no—
295#462—111no—
296#462C2×D1111yescharacteristic
297#461—111no—
298#461C2×D1111yescharacteristic
299#460—111no—
300#459—111no—
301#452—221no—
302#449—221no—
303#446—111no—
304C8×Q8—111no—
305#440—221no—
306#440—221no—
307#436—111no—
308#436—221no—
309#435—221no—
310C8×D4—111no—
311#433—221no—
312#431—111no—
313#431—111no—
314C2×C4⋊C8C2×D1111yescharacteristic
315#405—221no—
316C4×M16—111no—
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#331—111no—
328#331—111no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×#12111yescharacteristic
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11C2×#13511yescharacteristic
349C4×C11#57511yescharacteristic
350C4×C11#57611yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—81no—
353C2×#41—221no—
354C2×Q16—21no—
355C2×Q16—221no—
356C2×SD16—21no—
357C2×SD16—221no—
358C2×SD16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×D8—221no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—221no—
365C22×C8—21no—
366C22×C8—221no—
367C4⋊Q8—111no—
368C4⋊Q8C22×D1111yescharacteristic
369C4⋊Q8C22×D1111yescharacteristic
370#127—111no—
371#126—21no—
372#125—21no—
373#125C22⋊D1111yescharacteristic
374#124—221no—
375#124C22⋊D1111yescharacteristic
376#123—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8C22⋊D1111yescharacteristic
380#121—221no—
381#121—221no—
382#121C22⋊D1111yescharacteristic
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C22×D1111yescharacteristic
386C4×D4—21no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391#117—21no—
392C2×C42C22×D1111yescharacteristic
393#107—21no—
394#107—221no—
395#107—221no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405C4⋊C8C22×D1111yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#102—21no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422#97—111no—
423#97—111no—
424#97—221no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8—221no—
430C2×C11—41no—
431C2×C11—81no—
432C2×C11#303511yescharacteristic
433C2×C11#306211yescharacteristic
434C2×C11#306911yescharacteristic
435D11—161no—
436#41—881no—
437#41—881no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—221no—
441C2×Q8C2×C22⋊D1111yescharacteristic
442C2×D4—21no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4C2×C22⋊D1111yescharacteristic
448C22×C4—21no—
449C22×C4—441no—
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453Q16—81no—
454Q16—881no—
455SD16—81no—
456SD16—442no—
457SD16—442no—
458SD16—881no—
459SD16—881no—
460D8—881no—
461M16—222no—
462M16—441no—
463M16—442no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—442no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4C2×C22⋊D1111yescharacteristic
489C4⋊C4C2×C22⋊D1111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C42—21no—
499C42—41no—
500C42D4×D1111yescharacteristic
501C42#434111yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C23×D1111yescharacteristic
504C11#1924611yescharacteristic, complemented, Sylow
505C23—21no—
506C23—441no—
507C23#6699211yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—441no—
515Q8—441no—
516D4—21no—
517D4—21no—
518D4—81no—
519D4—441no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—881no—
524D4—882no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—441no—
538C2×C4—882no—
539C2×C4#6699211yescharacteristic
540C2×C4#6699211yescharacteristic
541C2×C4#6699211yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—41no—
546C8—41no—
547C8—112no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8—441no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22C2×#6699211yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—881no—
575C4D11×#13511yescharacteristic
576C4#1062329911yescharacteristic
577C4#1062336611yescharacteristic
578C4#1062336811yescharacteristic
579C2—41no—
580C2—81no—
581C2—1761no—
582C2#1307806711yescharacteristic
583C2#1307829811yescharacteristic
584C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3248C2
socleC22×C11C2×#121
prime radical#13079588C2
hypercenter#3248D11
hypocenterC11#19246
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #13079335C2semidirect
3. #13077621C2semidirect
4. #13068179C2semidirect
5. #13068161C2semidirect
6. #13068132C2semidirect
7. #13068090C2semidirect
8. #13068062C2semidirect
9. #13068044C2semidirect
10. #13068003C2semidirect
11. #13067959C2semidirect
12. #13067366C2semidirect
13. #13067281C2semidirect
14. #13067266C2semidirect
15. C11×#3248C2semidirect
213. #3248D11semidirect
504. C11#19246semidirect

Maximal subgroups

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

subgroupindex
#130795882
#130793352
#130776212
#130681792
#130681612
#130681322
#130680902
#130680622
#130680442
#130680032
#130679592
#130673662
#130672812
#130672662
C11×#32482
#1924611