Finite Group Databasebeta

← #14739211

Subgroups — #14739211

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079551C211yesmaximal, characteristic, complemented
2#13078767C211yesmaximal, characteristic, complemented
3#13078676C211yesmaximal, characteristic, complemented
4#13068074C211yesmaximal, characteristic, complemented
5#13068067C211yesmaximal, characteristic, complemented
6#13068032C211yesmaximal, characteristic, complemented
7#13068025C211yesmaximal, characteristic, complemented
8#13067976C211yesmaximal, characteristic, complemented
9#13067971C211yesmaximal, characteristic, complemented
10#13067964C211yesmaximal, characteristic, complemented
11#13067957C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067309C211yesmaximal, characteristic, complemented
14#13067266C211yesmaximal, characteristic, complemented
15C11×#2988C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623008C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C8×D4×C11—21no—
22C8×D4×C11—21no—
23C8×D4×C11C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25C11×#431—21no—
26C11×#431C2211yescharacteristic
27C2×C11×C4⋊C8—21no—
28C2×C11×C4⋊C8C2211yescharacteristic
29#10622851—21no—
30#10622851—21no—
31#10622640C2211yescharacteristic
32#10622640C2211yescharacteristic
33#10622639—21no—
34C4×#4325—21no—
35#10622634C2211yescharacteristic
36#10622633C2211yescharacteristic
37#10622628C2211yescharacteristic
38#10622628C2211yescharacteristic
39#10622627—21no—
40C4×#4323—21no—
41#10622621C2211yescharacteristic
42#10622620C2211yescharacteristic
43#10622616—21no—
44#10622616—21no—
45#10622539C2211yescharacteristic
46#10622538C2211yescharacteristic
47#10622457—21no—
48#10622457—21no—
49#10622347—21no—
50#10622347—21no—
51#10622308C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622306C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622123C2211yescharacteristic
56#10622123C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×#4339—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325—21no—
84C2×#4325—21no—
85C2×#4323—21no—
86C2×#4323—21no—
87#66983—21no—
88#66983—21no—
89#66983—21no—
90#66983—21no—
91C2×D88—21no—
92C2×D88—21no—
93C2×#4314—21no—
94C2×#4314—21no—
95#66928—21no—
96#66928—21no—
97#66927C2311yescharacteristic
98#66927C2311yescharacteristic
99C4×D44—21no—
100C4×D44—21no—
101C4×D44—21no—
102C4×D44—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8D411yescharacteristic
109C11×C4⋊C8D411yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8D411yescharacteristic
115C11×C22⋊C8D411yescharacteristic
116C4×C8×C11—21no—
117C4×C8×C11—21no—
118C4×C8×C11C2311yescharacteristic
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66899—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66885—21no—
127#66885—21no—
128#66880—21no—
129#66880—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19412—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—41no—
157C2×C22⋊D11—41no—
158#4339—81no—
159#4339—81no—
160#4339—82no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×C4×D11—41no—
168C2×C4×D11—41no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—81no—
174C2×C8×C11—81no—
175C2×C8×C11—81no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194#4325—42no—
195#4325—42no—
196#4323—42no—
197#4323—42no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210D88—81no—
211D88—81no—
212#4314—81no—
213#4314—81no—
214#3207—111no—
215#3115—111no—
216#3106—111no—
217#2988D1111yescharacteristic, complemented
218#1684—111no—
219#1683—111no—
220#1678—111no—
221#1677—111no—
222#1668—111no—
223#1667—111no—
224#1666—111no—
225#1665—111no—
226#1572—111no—
227#1551—111no—
228#1540—111no—
229C23×C11—21no—
230C23×C11#12111yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233Q8×C11—21no—
234Q8×C11#13512yes—
235D4×C11—24no—
236D4×C11—21no—
237D4×C11#13512yes—
238C2×C4×C11—24no—
239C2×C4×C11—21no—
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—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—81no—
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—82no—
257C22⋊D11—82no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—81no—
269D44—81no—
270C4×D11—82no—
271C4×D11—82no—
272Dic22—41no—
273Dic22—41no—
274Dic22—81no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#532—111no—
286#532—111no—
287C4×#41C2×D1111yescharacteristic
288#493—111no—
289#492—111no—
290#487—111no—
291#486—111no—
292#482—221no—
293#482—221no—
294#477—111no—
295#476—111no—
296#475—111no—
297#474—111no—
298#463—221no—
299#463—221no—
300#460—111no—
301#460—111no—
302#459—111no—
303#459—111no—
304#449—221no—
305#449—221no—
306#449—221no—
307#449—221no—
308C8×Q8C2×D1111yescharacteristic
309C8×Q8C2×D1111yescharacteristic
310#442—221no—
311#440—221no—
312C4×SD16—221no—
313C4×D8—221no—
314C8×D4—21no—
315C8×D4—21no—
316C8×D4C2×D1111yescharacteristic
317C8×D4C2×D1111yescharacteristic
318#432—111no—
319#431—21no—
320#431—111no—
321#431C2×D1111yescharacteristic
322C2×C4⋊C8—21no—
323C2×C4⋊C8C2×D1111yescharacteristic
324#335—111no—
325#335—111no—
326#334—111no—
327#334—111no—
328#333—111no—
329#333—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334#331—111no—
335#331—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×#12111yescharacteristic
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13511yescharacteristic
357C4×C11C2×#13511yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—81no—
361Dic11—81no—
362C2×#41—221no—
363C2×#41—221no—
364C2×#41D4411yescharacteristic
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×D8—221no—
370C2×D8—221no—
371C2×D8—221no—
372C2×D8—221no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8—111no—
377C4⋊Q8—111no—
378#127—111no—
379#127—111no—
380#124—221no—
381#124—221no—
382#121—221no—
383#121—221no—
384#121—221no—
385#121—221no—
386C4×Q8D4411yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—221no—
391C4×D4—221no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4D4411yescharacteristic
395C4×D4C22×D1111yescharacteristic
396#117—21no—
397#117D4411yescharacteristic
398C2×C42—21no—
399C2×C42C22×D1111yescharacteristic
400#107—221no—
401#107—221no—
402#106—221no—
403#106—221no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8C22⋊D1111yescharacteristic
412C4⋊C8C22⋊D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414C4⋊C8C22×D1111yescharacteristic
415#103—221no—
416#103—221no—
417#103—221no—
418#103—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8C22⋊D1111yescharacteristic
432C22⋊C8C22⋊D1111yescharacteristic
433#97—221no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—41no—
440C2×C11—42no—
441C2×C11#304511yescharacteristic
442C2×C11#305011yescharacteristic
443C2×C11#306811yescharacteristic
444D11—161no—
445D11—161no—
446#41—22no—
447#41—22no—
448#41—881no—
449#41—881no—
450#41—882no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8C2×D4411yescharacteristic
454C2×D4—21no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4C2×D4411yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—441no—
468C22×C4—441no—
469C22×C4C2×D4411yescharacteristic
470C22×C4#433911yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472SD16—442no—
473SD16—442no—
474SD16—881no—
475SD16—881no—
476D8—442no—
477D8—442no—
478D8—881no—
479D8—881no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—81no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C2×C8C2×C22⋊D1111yescharacteristic
492C2×C8C2×C22⋊D1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4C2×D4411yescharacteristic
500C4⋊C4C2×D4411yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42C2×D4411yescharacteristic
512C42#433911yescharacteristic
513C42C2×C22⋊D1111yescharacteristic
514C42C23×D1111yescharacteristic
515C11#1941211yescharacteristic, complemented, Sylow
516C23—21no—
517C23—441no—
518C23—441no—
519C23#6698311yescharacteristic
520Q8—21no—
521Q8—441no—
522Q8—441no—
523Q8—881no—
524Q8#6695712yes—
525D4—24no—
526D4—21no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—441no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—881no—
536D4—881no—
537D4—882no—
538D4—882no—
539D4#6695712yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—81no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—882no—
555C2×C4—882no—
556C2×C4#6698311yescharacteristic
557C2×C4#6698311yescharacteristic
558C2×C4#6698311yescharacteristic
559C2×C4C22×D4411yescharacteristic
560C2×C4C2×#433911yescharacteristic
561C2×C4C22×C22⋊D1111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—441no—
569C8—441no—
570C8—441no—
571C8—441no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22C2×#6698311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—881no—
593C4—881no—
594C4C2×#6695711yescharacteristic
595C4C2×#6695711yescharacteristic
596C4#1062336611yescharacteristic
597C4#1062336811yescharacteristic
598C2—41no—
599C2—42no—
600C2—1761no—
601C2—1761no—
602C2#1307815511yescharacteristic
603C2#1307819711yescharacteristic
604C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
hypercenter#2988D11
hypocenterC11#19412
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079551C2semidirect
2. #13078767C2semidirect
3. #13078676C2semidirect
4. #13068074C2semidirect
5. #13068067C2semidirect
6. #13068032C2semidirect
7. #13068025C2semidirect
8. #13067976C2semidirect
9. #13067971C2semidirect
10. #13067964C2semidirect
11. #13067957C2semidirect
12. #13067396C2semidirect
13. #13067309C2semidirect
14. #13067266C2semidirect
15. C11×#2988C2semidirect
217. #2988D11semidirect
515. C11#19412semidirect

Maximal subgroups

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

subgroupindex
#130795512
#130787672
#130786762
#130680742
#130680672
#130680322
#130680252
#130679762
#130679712
#130679642
#130679572
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