Finite Group Databasebeta

← #14908083

Subgroups — #14908083

Order 2816.

748 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic, complemented
3#13079096C211yesmaximal, characteristic, complemented
4#13077463C211yesmaximal, characteristic, complemented
5#13070672C211yesmaximal, characteristic, complemented
6#13070671C211yesmaximal, characteristic, complemented
7#13070670C211yesmaximal, characteristic, complemented
8#13070669C211yesmaximal, characteristic, complemented
9#13070650C211yesmaximal, characteristic, complemented
10#13070649C211yesmaximal, characteristic, complemented
11#13070648C211yesmaximal, characteristic, complemented
12#13070373C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14#13070320C211yesmaximal, characteristic, complemented
15C11×#2206C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×#66964—21no—
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623246—21no—
21#10623076—21no—
22C2×C11×D16C2211yescharacteristic
23C2×C11×D16C2211yescharacteristic, complemented
24C11×#493C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic, complemented
26#10622768C2211yescharacteristic, complemented
27#10622767—21no—
28#10622764C2211yescharacteristic, complemented
29D8×Dic11C2211yescharacteristic, complemented
30C2×#66891C2211yescharacteristic, complemented
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33C2×#66890C2211yescharacteristic, complemented
34#10622687—21no—
35#10622627—21no—
36#10622524—24no—
37D11×D16—24no—
38C2×#66864C2211yescharacteristic, complemented
39C2×D176C2211yescharacteristic
40C2×#66862C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42#10622493C2211yescharacteristic
43#10622485C2211yescharacteristic, complemented
44#10622398—21no—
45#10622383—21no—
46#10622309C2211yescharacteristic, complemented
47C4×D88C2211yescharacteristic, complemented
48#10622302C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#357C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4341—21no—
62C2×D4×D11—21no—
63C2×D4×D11—21no—
64C2×C11×D8—21no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C11×#127—21no—
69C4×D4×C11—21no—
70#66993—21no—
71#66992—41no—
72#66992—41no—
73#66990—41no—
74#66990—41no—
75#66989—21no—
76D4×Dic11—21no—
77C2×#4324—21no—
78C2×#4324—21no—
79C2×#4323—21no—
80C2×#4323—21no—
81C2×#4323—21no—
82C4×C22⋊D11—41no—
83C2×(C2×D11)⋊C4—41no—
84#66965—22no—
85#66965—22no—
86#66964—44no—
87D8×D11—22no—
88D8×D11—22no—
89D8×D11—22no—
90D8×D11D414yescomplemented
91C2×Dic44C2311yescharacteristic
92C2×D88C2311yescharacteristic
93C2×D88C2311yescharacteristic
94C2×#4314—21no—
95C2×#4313D411yescharacteristic
96C2×C8×D11C2311yescharacteristic
97#66946—21no—
98#66945—21no—
99(C22⋊D11)⋊C4—41no—
100C22⋊C4×D11—41no—
101#66928—21no—
102C4×D44—21no—
103#66925D411yescharacteristic
104C11×D16—22no—
105C11×D16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66896—21no—
112#66891—22no—
113#66890—22no—
114#66890—22no—
115#66890—22no—
116#66885—21no—
117#66882C2311yescharacteristic
118#66879D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66873—21no—
123#66872—21no—
124#66867D411yescharacteristic
125#66864—22no—
126D176—22no—
127#66862—22no—
128C16×D11—22no—
129#33585—111nomaximal, Sylow
130C23×D11—41no—
131C23×D11—41no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C22×C4×C11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C22×Dic11—41no—
144C22×Dic11—41no—
145#4341—42no—
146#4341—42no—
147D4×D11—24no—
148D4×D11—42no—
149D4×D11—42no—
150D4×D11—42no—
151C2×D44—21no—
152C2×D44—21no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11C2×D411yescharacteristic
156C2×Dic22—21no—
157C11×D8—21no—
158C11×D8—21no—
159C11×D8—21no—
160C11×D8—21no—
161C11×D8—21no—
162C11×D8—42no—
163C11×D8C2×D412yes—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C22⋊C4—41no—
168C42×C11C2×D411yescharacteristic
169C22⋊Dic11—41no—
170C22⋊Dic11—41no—
171C22⋊Dic11—41no—
172#4324—42no—
173#4324—42no—
174#4323—24no—
175#4323—42no—
176#4323—42no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4D811yescharacteristic
183(C2×D11)⋊C4D811yescharacteristic
184C4⋊Dic11—21no—
185Dic11⋊C4D811yescharacteristic
186Dic11⋊C4D811yescharacteristic
187C4×Dic11—41no—
188C4×Dic11C2×D411yescharacteristic
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191Dic44—21no—
192Dic44—21no—
193D88—21no—
194D88—21no—
195D88—21no—
196D88C2×D412yes—
197#4314—42no—
198#4313—22no—
199C8×D11C2×D412yes—
200C8×D11#4112yes—
201C11×C16—21no—
202C11×C16—21no—
203C11⋊C16—21no—
204C11⋊C16—21no—
205C2×#509—111no—
206C22×D16—111no—
207#3155—111no—
208#2948—111no—
209#2210—111no—
210#2210—111no—
211#2210—111no—
212#2210—111no—
213#2206—111no—
214#2206—111no—
215#2206—111no—
216#2206D1111yescharacteristic, complemented
217#2151—111no—
218#2140—111no—
219#2138—111no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C22×D11—41no—
224C22×D11—44no—
225C22×D11—41no—
226C22×D11—82no—
227C22×D11—161no—
228C22×D11—161no—
229C22×D11—161no—
230C22×D11—161no—
231C22×D11C2×D811yescharacteristic
232D4×C11—22no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—161no—
239D4×C11—161no—
240C2×C4×C11—41no—
241C2×C4×C11—161no—
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C2×D811yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C22⋊D11—44no—
246C22⋊D11—82no—
247C22⋊D11—82no—
248C22⋊D11—161no—
249C22⋊D11—161no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—82no—
253C2×Dic11—161no—
254C2×Dic11C2×D811yescharacteristic
255C2×Dic11C2×D811yescharacteristic
256C2×Dic11C2×D811yescharacteristic
257D44—22no—
258D44—41no—
259D44—41no—
260D44—41no—
261C4×D11—161no—
262C4×D11—161no—
263C4×D11#12112yes—
264C4×D11AGL(1,ℤ/8)12yes—
265Dic22—41no—
266Dic22—41no—
267C8×C11—21no—
268C8×C11C22×D411yescharacteristic
269C8×C11C2×#4111yescharacteristic
270C11⋊C8—21no—
271C11⋊C8#12112yes—
272C2×AGL(1,ℤ/8)—221no—
273C2×#135—111no—
274C22×D8—111no—
275C22×D8—111no—
276#535—221no—
277#518—221no—
278#509—224no—
279C2×SD32—111no—
280C2×SD32—111no—
281C2×D16—111no—
282C2×D16—111no—
283C2×D16—111no—
284C2×D16—111no—
285C2×D16—224no—
286C2×D16C2×D1111yescharacteristic
287C2×D16C2×D1111yescharacteristic, complemented
288C2×M32—111no—
289C22×C16—111no—
290#496—221no—
291#496—221no—
292#495—111no—
293#495—111no—
294#493—111no—
295#493C2×D1111yescharacteristic, complemented
296#442—221no—
297#442—221no—
298C4×D8—111no—
299C4×D8—111no—
300C4×D8—111no—
301C4×D8C2×D1111yescharacteristic, complemented
302#427—111no—
303#418—221no—
304#405—111no—
305C4⋊C16—111no—
306C4⋊C16—111no—
307C4⋊C16—111no—
308C4⋊C16C2×D1111yescharacteristic, complemented
309#358—111no—
310#358—111no—
311#357—111no—
312#357—111no—
313#357—111no—
314#357—111no—
315#357C2×D1111yescharacteristic, complemented
316#357C2×D1111yescharacteristic, complemented
317C22×C11—42no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11C22×D811yescharacteristic
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—164no—
336C2×D11—164no—
337C2×D11#45912yes—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—81no—
341C4×C11C2×#12111yescharacteristic
342C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
343Dic11—21no—
344Dic11—21no—
345Dic11—81no—
346Dic11—81no—
347Dic11#45912yes—
348C2×#41—221no—
349C22×D4—221no—
350C22×D4—221no—
351AGL(1,ℤ/8)—444no—
352#135—222no—
353#135—222no—
354C2×Q16—111no—
355C2×SD16—221no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×D8—21no—
359C2×D8—114no—
360C2×D8—111no—
361C2×D8—111no—
362C2×D8—222no—
363C2×D8—222no—
364C2×D8—222no—
365C2×D8—221no—
366C2×D8—221no—
367C2×D8—221no—
368C2×D8C22×D1111yescharacteristic
369C2×D8C22×D1111yescharacteristic
370C2×D8C22×D1111yescharacteristic
371C2×M16—111no—
372C22×C8—111no—
373#127—21no—
374#127—221no—
375#124—221no—
376#124—221no—
377#121—441no—
378#121—441no—
379#120—441no—
380#120—441no—
381C4×D4—21no—
382C4×D4—221no—
383C4×D4—221no—
384C4×D4—221no—
385C4×D4—441no—
386C4×D4—441no—
387#117—111no—
388#117—221no—
389C2×C22⋊C4—441no—
390C2×C22⋊C4—441no—
391SD32—222no—
392SD32—222no—
393D16—22no—
394D16—22no—
395D16—222no—
396D16—222no—
397D16—222no—
398D16—222no—
399M32—222no—
400C2×C16—111no—
401C2×C16—111no—
402C2×C16—222no—
403C2×C16C22×D1111yescharacteristic
404C2×C16C22×D1111yescharacteristic
405#107—111no—
406#107C22×D1111yescharacteristic
407#106—221no—
408#102—21no—
409#102—221no—
410#102—221no—
411#102—221no—
412#97—111no—
413#97—111no—
414C4×C8—111no—
415C4×C8C22×D1111yescharacteristic
416C2×C11—82no—
417C2×C11—161no—
418C2×C11—161no—
419C2×C11C2×#45911yescharacteristic
420C2×C11#341511yescharacteristic
421C2×C11#341511yescharacteristic
422D11—22no—
423D11—82no—
424D11—161no—
425C24—441no—
426C24—441no—
427#41—442no—
428#41—442no—
429C2×Q8—221no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—224no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—442no—
439C2×D4—442no—
440C2×D4—442no—
441C2×D4—441no—
442C2×D4—441no—
443C2×D4—441no—
444C2×D4—441no—
445C2×D4—441no—
446C22×C4—41no—
447C22×C4—111no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452Q16—221no—
453Q16—221no—
454SD16—442no—
455SD16—442no—
456SD16—442no—
457D8—21no—
458D8—21no—
459D8—21no—
460D8—21no—
461D8—21no—
462D8—42no—
463D8—112no—
464D8—224no—
465D8—221no—
466D8—221no—
467D8—221no—
468D8—442no—
469D8—442no—
470D8D4×D1112yes—
471M16—222no—
472C2×C8—111no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—111no—
476C2×C8D4×D1111yescharacteristic
477C2×C8C23×D1111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—111no—
480C4⋊C4—111no—
481C4⋊C4—221no—
482C22⋊C4—41no—
483C22⋊C4—111no—
484C22⋊C4—111no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C42—111no—
494C42—441no—
495C42D4×D1111yescharacteristic
496C16—21no—
497C16—21no—
498C16—221no—
499C16—221no—
500C11#3358511yescharacteristic, complemented, Sylow
501C23—41no—
502C23—41no—
503C23—41no—
504C23—111no—
505C23—444no—
506C23—441no—
507C23—441no—
508C23—882no—
509C23—1761no—
510C23—1761no—
511C23—1761no—
512C23—1761no—
513Q8—441no—
514Q8—441no—
515D4—22no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—161no—
522D4—161no—
523D4—222no—
524D4—444no—
525D4—441no—
526D4—441no—
527D4—441no—
528D4—882no—
529D4—882no—
530D4—1761no—
531D4—1761no—
532C2×C4—41no—
533C2×C4—111no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—161no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—882no—
542C2×C4—1761no—
543C2×C4—1761no—
544C2×C4—1761no—
545C2×C4D8×D1111yescharacteristic
546C2×C4D8×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C8—21no—
549C8—112no—
550C8—221no—
551C8C2×D4×D1111yescharacteristic
552C8#41×D1111yescharacteristic
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—112no—
563C22—221no—
564C22—221no—
565C22—442no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22—881no—
570C22—881no—
571C22—1764no—
572C22—1764no—
573C22C2×D8×D1111yescharacteristic
574C4—21no—
575C4—21no—
576C4—81no—
577C4—112no—
578C4—221no—
579C4—221no—
580C4—881no—
581C4—881no—
582C4D11×#12111yescharacteristic
583C4D11×AGL(1,ℤ/8)11yescharacteristic
584C2—82no—
585C2—161no—
586C2—161no—
587C2—222no—
588C2—882no—
589C2—1761no—
590C2D11×#45911yescharacteristic
591C2#1308175311yescharacteristic
592C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2206C2
socleC22×C11C22×D8
hypercenter#2206D11
hypocenterC11#33585
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×D11×D16C2semidirect
3. #13079096C2semidirect
4. #13077463C2semidirect
5. #13070672C2semidirect
6. #13070671C2semidirect
7. #13070670C2semidirect
8. #13070669C2semidirect
9. #13070650C2semidirect
10. #13070649C2semidirect
11. #13070648C2semidirect
12. #13070373C2semidirect
13. #13070330C2semidirect
14. #13070320C2semidirect
15. C11×#2206C2semidirect
23. C2×C11×D16C22semidirect
24. C11×#493C22semidirect
25. C4×C11×D8C22semidirect
26. #10622768C22semidirect
28. #10622764C22semidirect
29. D8×Dic11C22semidirect
30. C2×#66891C22semidirect
33. C2×#66890C22semidirect
38. C2×#66864C22semidirect
43. #10622485C22semidirect
46. #10622309C22semidirect
47. C4×D88C22semidirect
49. C11×C4⋊C16C22semidirect
50. C11×#357C22semidirect
51. C11×#357C22semidirect
52. #10622200C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622130C22semidirect
59. #10622129C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
90. D8×D11D4semidirect
216. #2206D11semidirect
287. C2×D16C2×D11semidirect
295. #493C2×D11semidirect
301. C4×D8C2×D11semidirect
308. C4⋊C16C2×D11semidirect
315. #357C2×D11semidirect
316. #357C2×D11semidirect
500. C11#33585semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C2×D11×D162
#130790962
#130774632
#130706722
#130706712
#130706702
#130706692
#130706502
#130706492
#130706482
#130703732
#130703302
#130703202
C11×#22062
#3358511