Finite Group Databasebeta

← #14736310

Subgroups — #14736310

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079125C211yesmaximal, characteristic, complemented
2#13078626C211yesmaximal, characteristic
3#13078623C211yesmaximal, characteristic
4D11×#436C211yesmaximal, characteristic
5#13068138C211yesmaximal, characteristic, complemented
6#13068137C211yesmaximal, characteristic, complemented
7#13068128C211yesmaximal, characteristic, complemented
8#13068127C211yesmaximal, characteristic, complemented
9#13068116C211yesmaximal, characteristic, complemented
10#13068115C211yesmaximal, characteristic, complemented
11#13068112C211yesmaximal, characteristic, complemented
12#13067363C211yesmaximal, characteristic, complemented
13#13067272C211yesmaximal, characteristic, complemented
14#13067270C211yesmaximal, characteristic, complemented
15C11×#1691C211yesmaximal, characteristic, complemented
16C2×M16×D11—21no—
17#10623259C2211yescharacteristic
18#10623259C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C11×#498C2211yescharacteristic, complemented
21C11×#476C2211yescharacteristic
22C11×#461C2211yescharacteristic
23C11×#436C2211yescharacteristic
24#10622782—21no—
25SD16×Dic11—21no—
26#10622741—21no—
27#10622697C2211yescharacteristic
28#10622696C2211yescharacteristic
29#10622691C2211yescharacteristic, complemented
30#10622691C2211yescharacteristic, complemented
31#10622632C2211yescharacteristic
32#10622625C2211yescharacteristic
33#10622621C2211yescharacteristic
34#10622475—21no—
35#10622473—21no—
36#10622473—21no—
37#10622471—21no—
38#10622471—21no—
39#10622465—21no—
40#10622455C2211yescharacteristic
41#10622454C2211yescharacteristic
42#10622451C2211yescharacteristic
43#10622446C2211yescharacteristic
44#10622446C2211yescharacteristic
45D11×C4⋊C8C2211yescharacteristic
46#10622418—21no—
47#10622401—21no—
48#10622389—21no—
49#10622371—21no—
50#10622342—21no—
51D11×C22⋊C8—21no—
52#10622301C2211yescharacteristic
53C4×C8×D11C2211yescharacteristic
54#10622293C2211yescharacteristic, complemented
55C11×#335C2211yescharacteristic, complemented
56C11×#333C2211yescharacteristic, complemented
57C11×#332C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622184C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622120C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622118C2211yescharacteristic, complemented
66#10622096C2211yescharacteristic, complemented
67C2×D4×D11D411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16—21no—
70C2×C11×M16—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66999—21no—
75#66999—21no—
76Q8×Dic11—21no—
77Q8×Dic11—21no—
78C2×#4325—21no—
79D4×Dic11D411yescharacteristic
80C2×#4324—21no—
81C4×C22⋊D11—21no—
82C2×#4318—21no—
83M16×D11—44no—
84C2×#4314—21no—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88C2×C8×D11D411yescharacteristic
89C2×C8×D11D411yescharacteristic
90#66950—21no—
91#66950—21no—
92#66946D411yescharacteristic
93#66945—21no—
94#66945—21no—
95C4⋊C4×D11D411yescharacteristic
96#66943—21no—
97#66943—21no—
98#66940—21no—
99#66940—21no—
100(C22⋊D11)⋊C4—21no—
101C22⋊C4×D11—21no—
102C4×D44C2311yescharacteristic
103C42×D11C2311yescharacteristic
104#66922C2311yescharacteristic
105#66922C2311yescharacteristic
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#102—21no—
114C11×C22⋊C8—21no—
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119#66885—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66881—21no—
125#66881—21no—
126#66881—21no—
127#66880—21no—
128Dic11⋊C8—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11D411yescharacteristic
132C8×Dic11D411yescharacteristic
133#66874—21no—
134#66873—21no—
135#66872—21no—
136#66872—21no—
137#66871—21no—
138#66871—21no—
139#66871—21no—
140#66871—21no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19137—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153D4×D11—41no—
154D4×D11—41no—
155C2×D44C2×D411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11#4111yescharacteristic
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×SD16—42no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4325—42no—
182#4324—42no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192C4⋊Dic11—41no—
193C4⋊Dic11C2×D411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198C4×Dic11—41no—
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11#4111yescharacteristic
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4314—42no—
209#4313—42no—
210#4313—42no—
211C8×D11—22no—
212C8×D11—42no—
213C8×D11SD1614yescomplemented
214#3160—111no—
215#3101—111no—
216#3101—111no—
217C2×#436—111no—
218#1695—111no—
219#1695—111no—
220#1693—111no—
221#1693—111no—
222#1691—111no—
223#1691—111no—
224#1691—111no—
225#1691D1111yescharacteristic, complemented
226#1564—111no—
227#1542—111no—
228#1542—111no—
229C23×C11—21no—
230C22×D11—21no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11#12111yescharacteristic
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—81no—
238D4×C11—21no—
239D4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—42no—
249C2×Dic11—21no—
250C2×Dic11—42no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11#12111yescharacteristic
254C2×Dic11#12111yescharacteristic
255C2×Dic11#12111yescharacteristic
256D44—21no—
257D44—21no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—41no—
261C4×D11—42no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—42no—
265C4×D11C2×SD1612yes—
266C4×D11#13712yes—
267Dic22—41no—
268Dic22—41no—
269Dic22—81no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11C2×SD1612yes—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8C2×SD1612yes—
280C22×M16—221no—
281#533—111no—
282#533—111no—
283C2×C4×D4—111no—
284#500—111no—
285#500—111no—
286#499—221no—
287#499—221no—
288#498—111no—
289#498C2×D1111yescharacteristic, complemented
290#483—221no—
291#483—221no—
292#476—111no—
293#476—111no—
294#476—111no—
295#476C2×D1111yescharacteristic
296#461—111no—
297#461—111no—
298#461—111no—
299#461C2×D1111yescharacteristic
300#450—221no—
301#450—221no—
302C4×SD16—221no—
303C4×SD16—221no—
304C4×SD16—221no—
305C4×SD16—221no—
306#436—111no—
307#436—111no—
308#436—111no—
309#436—221no—
310#436—221no—
311#436C2×D1111yescharacteristic
312#431—111no—
313#431—111no—
314#427—221no—
315#427—221no—
316C2×C4⋊C8—111no—
317C2×C22⋊C8—221no—
318C2×C4×C8—111no—
319#335—111no—
320#335C2×D1111yescharacteristic, complemented
321#334—111no—
322#334—111no—
323#333—111no—
324#333—111no—
325#333—111no—
326#333C2×D1111yescharacteristic, complemented
327#332—111no—
328#332—111no—
329#332—111no—
330#332C2×D1111yescharacteristic, complemented
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×#12111yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—84no—
341C2×D11#46112yes—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C22×SD1611yescharacteristic
347C4×C11C2×#13711yescharacteristic
348C4×C11#57511yescharacteristic
349C4×C11#57511yescharacteristic
350Dic11—21no—
351Dic11—21no—
352Dic11—41no—
353Dic11—81no—
354Dic11—81no—
355Dic11#46112yes—
356C22×D4—111no—
357C23×C4—221no—
358C2×SD16—21no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×M16—21no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—444no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—221no—
370C4⋊Q8—111no—
371C4⋊Q8—111no—
372C4⋊Q8C22×D1111yescharacteristic
373C4⋊Q8C22×D1111yescharacteristic
374#125—221no—
375#125—221no—
376C22⋊Q8—221no—
377C22⋊Q8—221no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C4×Q8—221no—
381C4×Q8—221no—
382C4×Q8—221no—
383C4×Q8—221no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—221no—
391#117—221no—
392C2×C4⋊C4—111no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395#107—221no—
396#107—221no—
397#107—221no—
398#107—221no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—221no—
403#106—221no—
404#106—221no—
405#106—221no—
406#106—221no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414#103—21no—
415#103—221no—
416#103—221no—
417#103—221no—
418#102—21no—
419#102—221no—
420#102—221no—
421#102—221no—
422C22⋊C8—21no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—221no—
432C4×C8—221no—
433C4×C8C22×D1111yescharacteristic
434C2×C11—81no—
435C2×C11C2×#46111yescharacteristic
436C2×C11#305411yescharacteristic
437C2×C11#306711yescharacteristic
438D11—22no—
439D11—81no—
440C24—221no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×D4—111no—
446C2×D4—221no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4D4×D1111yescharacteristic
450C22×C4—21no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—442no—
459C22×C4—442no—
460SD16—42no—
461SD16—442no—
462SD16—442no—
463SD16—442no—
464M16—42no—
465M16—442no—
466M16—442no—
467M16—442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—111no—
472C2×C8—114no—
473C2×C8—111no—
474C2×C8—222no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—442no—
479C2×C8D4×D1111yescharacteristic
480C2×C8D4×D1111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—111no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—441no—
492C4⋊C4—441no—
493C4⋊C4—441no—
494C4⋊C4—441no—
495C4⋊C4D4×D1111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C42—111no—
503C42—111no—
504C42—111no—
505C42—441no—
506C42—441no—
507C42C23×D1111yescharacteristic
508C11#1913711yescharacteristic, complemented, Sylow
509C23—21no—
510C23—111no—
511C23—221no—
512C23—442no—
513C23—442no—
514C23—442no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—441no—
519Q8—441no—
520Q8—881no—
521D4—21no—
522D4—21no—
523D4—221no—
524D4—221no—
525D4—442no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—111no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—111no—
535C2×C4—111no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—441no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4C2×D4×D1111yescharacteristic
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—112no—
555C8—221no—
556C8—441no—
557C8—441no—
558C8—441no—
559C8SD16×D1112yes—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—112no—
564C22—221no—
565C22—221no—
566C22—441no—
567C22—441no—
568C22—441no—
569C22—884no—
570C22D11×#12111yescharacteristic
571C4—21no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—112no—
576C4—221no—
577C4—221no—
578C4—441no—
579C4—881no—
580C4—881no—
581C4C2×SD16×D1111yescharacteristic
582C4#1062330411yescharacteristic
583C4D11×#13711yescharacteristic
584C4#1062330811yescharacteristic
585C2—81no—
586C2—222no—
587C2—881no—
588C2D11×#46111yescharacteristic
589C2#1307822011yescharacteristic
590C2#1307833111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1691C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1691D11
hypocenterC11#19137
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1691

Complements

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

NH ≅ G/Ntype
1. #13079125C2semidirect
5. #13068138C2semidirect
6. #13068137C2semidirect
7. #13068128C2semidirect
8. #13068127C2semidirect
9. #13068116C2semidirect
10. #13068115C2semidirect
11. #13068112C2semidirect
12. #13067363C2semidirect
13. #13067272C2semidirect
14. #13067270C2semidirect
15. C11×#1691C2semidirect
20. C11×#498C22semidirect
29. #10622691C22semidirect
30. #10622691C22semidirect
54. #10622293C22semidirect
55. C11×#335C22semidirect
56. C11×#333C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622184C22semidirect
60. #10622124C22semidirect
61. #10622120C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622118C22semidirect
66. #10622096C22semidirect
213. C8×D11SD16semidirect
225. #1691D11semidirect
289. #498C2×D11semidirect
320. #335C2×D11semidirect
326. #333C2×D11semidirect
330. #332C2×D11semidirect
508. C11#19137semidirect

Maximal subgroups

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

subgroupindex
#130791252
#130786262
#130786232
D11×#4362
#130681382
#130681372
#130681282
#130681272
#130681162
#130681152
#130681122
#130673632
#130672722
#130672702
C11×#16912
#1913711