Finite Group Databasebeta

← #14744141

Subgroups — #14744141

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081261C211yesmaximal, characteristic, complemented
2#13080852C211yesmaximal, characteristic
3#13080442C211yesmaximal, characteristic, complemented
4#13068274C211yesmaximal, characteristic, complemented
5#13068189C211yesmaximal, characteristic, complemented
6#13068034C211yesmaximal, characteristic, complemented
7#13068025C211yesmaximal, characteristic, complemented
8#13067988C211yesmaximal, characteristic, complemented
9#13067794C211yesmaximal, characteristic, complemented
10#13067761C211yesmaximal, characteristic, complemented
11#13067749C211yesmaximal, characteristic, complemented
12#13067726C211yesmaximal, characteristic, complemented
13#13067460C211yesmaximal, characteristic, complemented
14#13067438C211yesmaximal, characteristic, complemented
15C11×#3340C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic, complemented
17C11×#555C2211yescharacteristic
18#10623110C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#498C2211yescharacteristic, complemented
21C11×#485—21no—
22C11×#482—21no—
23C11×#477C2211yescharacteristic, complemented
24C11×#474C2211yescharacteristic
25C11×#465—21no—
26C4×C11×SD16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic, complemented
28C11×#427—21no—
29#10622782—21no—
30#10622705C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622697C2211yescharacteristic
34#10622696C2211yescharacteristic
35#10622694C2211yescharacteristic, complemented
36#10622670—21no—
37#10622669—21no—
38#10622652—21no—
39#10622649—21no—
40#10622640C2211yescharacteristic
41C4×#4325—21no—
42Q8×C11⋊C8C2211yescharacteristic, complemented
43#10622635—21no—
44#10622628C2211yescharacteristic
45C4×#4323C2211yescharacteristic
46#10622625C2211yescharacteristic
47#10622621C2211yescharacteristic
48#10622621C2211yescharacteristic, complemented
49#10622616—21no—
50#10622614—21no—
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11—21no—
68C22×D44—21no—
69C2×C11×SD16D411yescharacteristic
70C22×C8×C11—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—41no—
74C11×#124—21no—
75C11×#124—41no—
76C11×C22⋊Q8—21no—
77C11×#121—21no—
78C11×#121—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C11×#117—21no—
86#66999—21no—
87C2×#4326—41no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4323—21no—
91C2×#4323D411yescharacteristic
92#66983—21no—
93C2×#4318—21no—
94C2×C8×D11—21no—
95#66949—41no—
96#66948—21no—
97C4⋊C4×D11—21no—
98#66935—41no—
99#66927C2311yescharacteristic
100C4×D44—21no—
101C4×D44C2311yescharacteristic
102#66923—21no—
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106D411yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103D411yescharacteristic
112C11×#102—21no—
113C11×#102D411yescharacteristic
114C11×C22⋊C8—21no—
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66896—21no—
120#66896—21no—
121#66896D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123#66885—21no—
124#66885—21no—
125(C2×D11)⋊C8—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—41no—
132#66873D411yescharacteristic
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66871D411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19823—111nomaximal, Sylow
145C23×D11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—41no—
150C2×D4×C11C2×D411yescharacteristic
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C2×C22⋊D11—41no—
155D4×D11—42no—
156D4×D11—81no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—41no—
161C2×D44—42no—
162C2×D44—81no—
163C2×D44C2×D411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—41no—
166C2×Dic22—21no—
167C11×SD16—41no—
168C2×C8×C11—21no—
169C2×C8×C11—42no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C42×C11—21no—
188C42×C11—41no—
189C42×C11—41no—
190C42×C11C2411yescharacteristic
191#4326—82no—
192#4325—42no—
193#4325—81no—
194#4323—22no—
195#4323—81no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—41no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2×D411yescharacteristic
202Dic11⋊C4—41no—
203Dic11⋊C4—41no—
204#4318—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C8×D11—81no—
212#3360—111no—
213#3340D1111yescharacteristic, complemented
214#3325—111no—
215#3295—111no—
216#1720—111no—
217#1703—111no—
218#1678—111no—
219#1677—111no—
220#1671—111no—
221#1639—111no—
222#1634—111no—
223#1632—111no—
224#1628—111no—
225#1583—111no—
226#1580—111no—
227C23×C11—21no—
228C23×C11—21no—
229C22×D11—21no—
230C22×D11—41no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—161no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—81no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—161no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C22⋊D11—82no—
258C2×Dic11—21no—
259C2×Dic11—41no—
260D44—21no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—81no—
266D44—82no—
267D44#13512yes—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—161no—
271Dic22—81no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281#556C2×D1111yescharacteristic, complemented
282#555C2×D1111yescharacteristic
283#554—111no—
284D42—111no—
285#498C2×D1111yescharacteristic, complemented
286#494—111no—
287#488—221no—
288#487—111no—
289#486—111no—
290#486—111no—
291#486—111no—
292#485—21no—
293#482—21no—
294#482—221no—
295#481—221no—
296#479—221no—
297#477C2×D1111yescharacteristic, complemented
298#476—111no—
299#476—111no—
300#476—111no—
301#474C2×D1111yescharacteristic
302#469—221no—
303#465—21no—
304#465—221no—
305#463—221no—
306#461—111no—
307#460—111no—
308#459—111no—
309#450—221no—
310#447—221no—
311C8×Q8—111no—
312C4×SD16—221no—
313C4×SD16C2×D1111yescharacteristic
314C4×D8—111no—
315#436—111no—
316C8×D4—111no—
317C8×D4C2×D1111yescharacteristic, complemented
318#427—21no—
319#418—221no—
320C2×#102—221no—
321#334—111no—
322#334—111no—
323#333—111no—
324#333—111no—
325#332—111no—
326#331—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331#322—111no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11D4211yescharacteristic
339C2×D11—22no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—164no—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11C2×#13511yescharacteristic
354C4×C11#57511yescharacteristic
355C4×C11#57711yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—41no—
358Dic11—81no—
359C22×D4—221no—
360C22×D4—221no—
361C2×Q16—441no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×SD16C22⋊D1111yescharacteristic
365C2×D8—111no—
366C2×D8—221no—
367C2×M16—221no—
368C22×C8—21no—
369C22×C8—221no—
370C4⋊Q8—111no—
371C4⋊Q8C22×D1111yescharacteristic
372C4⋊Q8C22×D1111yescharacteristic
373#127—111no—
374#126—41no—
375#125—221no—
376#124—21no—
377#124—41no—
378C22⋊Q8—21no—
379C22⋊Q8—221no—
380C22⋊Q8—441no—
381#121—21no—
382#121—21no—
383#121—221no—
384#121—221no—
385#120—441no—
386C4×Q8—21no—
387C4×Q8C22×D1111yescharacteristic
388C4×D4—111no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391C4×D4C22×D1111yescharacteristic
392#117—21no—
393#117—21no—
394#117—21no—
395C2×C4⋊C4—221no—
396#107—21no—
397#107—21no—
398#107—111no—
399#106—21no—
400#106—21no—
401#106—221no—
402#106—221no—
403#106—221no—
404#106C22⋊D1111yescharacteristic
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8C22×D1111yescharacteristic
410#103—21no—
411#103—221no—
412#103—221no—
413#103—221no—
414#103C22⋊D1111yescharacteristic
415#102—21no—
416#102—111no—
417#102—111no—
418#102—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—
427#102—441no—
428#102C22⋊D1111yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C2×C11—81no—
437C2×C11—81no—
438C2×C11#326711yescharacteristic
439C2×C11#328211yescharacteristic
440C2×C11#328811yescharacteristic
441D11—42no—
442D11—161no—
443C24—441no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—221no—
447C2×Q8C2×C22⋊D1111yescharacteristic
448C2×D4—41no—
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—441no—
454C2×D4—442no—
455C2×D4—441no—
456C2×D4—442no—
457C2×D4—881no—
458C2×D4—881no—
459C2×D4D4×D1111yescharacteristic
460C2×D4C2×C22⋊D1111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—221no—
464C22×C4—441no—
465Q16—882no—
466SD16—41no—
467SD16—442no—
468SD16—881no—
469D8—222no—
470D8—881no—
471M16—881no—
472C2×C8—21no—
473C2×C8—42no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—881no—
481C2×C8C2×C22⋊D1111yescharacteristic
482C2×C8C2×C22⋊D1111yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—111no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—441no—
493C4⋊C4—441no—
494C4⋊C4D4×D1111yescharacteristic
495C4⋊C4C2×C22⋊D1111yescharacteristic
496C4⋊C4C2×C22⋊D1111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—221no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42C23×D1111yescharacteristic
510C11#1982311yescharacteristic, complemented, Sylow
511C23—21no—
512C23—21no—
513C23—221no—
514C23—441no—
515C23—882no—
516C23—882no—
517C23—1761no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—881no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—112no—
529D4—161no—
530D4—221no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—881no—
536D4—882no—
537D4—882no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—221no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—1761no—
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—41no—
559C8—221no—
560C8—221no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8—441no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—222no—
572C22—441no—
573C22—441no—
574C22—881no—
575C22—881no—
576C22—881no—
577C22—1764no—
578C22D4×C22⋊D1111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—441no—
587C4—881no—
588C4D11×#13511yescharacteristic
589C4#1062330111yescharacteristic
590C4#1062335311yescharacteristic
591C4#1062336811yescharacteristic
592C2—81no—
593C2—81no—
594C2—442no—
595C2—1761no—
596C2#1308014211yescharacteristic
597C2#1308031711yescharacteristic
598C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3340C2
socleC22×C11D42
prime radical#13080852C2
hypercenter#3340D11
hypocenterC11#19823
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3340

Complements

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

NH ≅ G/Ntype
1. #13081261C2semidirect
3. #13080442C2semidirect
4. #13068274C2semidirect
5. #13068189C2semidirect
6. #13068034C2semidirect
7. #13068025C2semidirect
8. #13067988C2semidirect
9. #13067794C2semidirect
10. #13067761C2semidirect
11. #13067749C2semidirect
12. #13067726C2semidirect
13. #13067460C2semidirect
14. #13067438C2semidirect
15. C11×#3340C2semidirect
16. C11×#556C22semidirect
20. C11×#498C22semidirect
23. C11×#477C22semidirect
27. C8×D4×C11C22semidirect
30. #10622705C22semidirect
35. #10622694C22semidirect
42. Q8×C11⋊C8C22semidirect
48. #10622621C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. #10622092C22semidirect
213. #3340D11semidirect
281. #556C2×D11semidirect
285. #498C2×D11semidirect
297. #477C2×D11semidirect
317. C8×D4C2×D11semidirect
510. C11#19823semidirect

Maximal subgroups

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

subgroupindex
#130812612
#130808522
#130804422
#130682742
#130681892
#130680342
#130680252
#130679882
#130677942
#130677612
#130677492
#130677262
#130674602
#130674382
C11×#33402
#1982311