Finite Group Databasebeta

← #14908086

Subgroups — #14908086

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×#10622527C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic, complemented
3#13079098C211yesmaximal, characteristic, complemented
4#13077463C211yesmaximal, characteristic, complemented
5#13070674C211yesmaximal, characteristic, complemented
6#13070673C211yesmaximal, characteristic, complemented
7#13070668C211yesmaximal, characteristic, complemented
8#13070652C211yesmaximal, characteristic, complemented
9#13070651C211yesmaximal, characteristic, complemented
10#13070650C211yesmaximal, characteristic, complemented
11#13070649C211yesmaximal, characteristic, complemented
12#13070373C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14#13070322C211yesmaximal, characteristic, complemented
15C11×#2210C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66967—21no—
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623205—21no—
21#10623076—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic
24C11×#495C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic, complemented
26#10622804C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28#10622789—21no—
29#10622764C2211yescharacteristic, complemented
30D8×Dic11C2211yescharacteristic, complemented
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33C2×#66890C2211yescharacteristic, complemented
34#10622671—21no—
35#10622627—21no—
36#10622527—24no—
37D11×D16—24no—
38C2×D176C2211yescharacteristic
39C2×D176C2211yescharacteristic, complemented
40C2×#66862C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42#10622493C2211yescharacteristic
43#10622485C2211yescharacteristic, complemented
44#10622398—21no—
45#10622383—21no—
46#10622308C2211yescharacteristic, complemented
47C4×D88C2211yescharacteristic, complemented
48#10622302C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×D4×D11—21no—
63C2×D4×D11—21no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C11×#124—21no—
69C4×D4×C11—21no—
70#67000—21no—
71C2×#4325—21no—
72C2×#4325—21no—
73#66993—21no—
74D4×Dic11—21no—
75C2×#4323—21no—
76C2×#4323—21no—
77C2×#4323—21no—
78C4×C22⋊D11—41no—
79C2×(C2×D11)⋊C4—41no—
80#66972—22no—
81#66972—22no—
82#66967—44no—
83D8×D11—22no—
84D8×D11—22no—
85D8×D11—22no—
86D8×D11D414yescomplemented
87C2×D88—21no—
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×#4313D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66946—21no—
94#66945—21no—
95#66937—41no—
96#66937—41no—
97#66935—41no—
98#66935—41no—
99(C22⋊D11)⋊C4—41no—
100C22⋊C4×D11—41no—
101#66927—21no—
102C4×D44—21no—
103#66925D411yescharacteristic
104C11×SD32—22no—
105C11×D16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66896—21no—
112#66892—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
125D176—22no—
126D176—22no—
127#66862—22no—
128C16×D11—22no—
129#33585—111nomaximal, Sylow
130C23×D11—41no—
131C23×D11—41no—
132C2×Q8×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C22×C4×C11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C22×Dic11—41no—
141#4343—42no—
142#4343—42no—
143D4×D11—24no—
144D4×D11—42no—
145D4×D11—42no—
146D4×D11—42no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11—41no—
156C2×C4×D11C2×D411yescharacteristic
157C11×Q16—21no—
158C11×Q16—21no—
159C11×SD16—42no—
160C11×D8—21no—
161C11×D8—21no—
162C11×D8—21no—
163C11×D8C2×D412yes—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C42×C11C2×D411yescharacteristic
171C22⋊Dic11—41no—
172#4325—42no—
173#4325—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
191D88—21no—
192D88—21no—
193D88—21no—
194D88—21no—
195D88—21no—
196D88—42no—
197D88C2×D412yes—
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#2210D1111yescharacteristic, complemented
213#2206—111no—
214#2206—111no—
215#2206—111no—
216#2206—111no—
217#2151—111no—
218#2140—111no—
219#2138—111no—
220C23×C11—41no—
221C23×C11—41no—
222C22×D11—41no—
223C22×D11—44no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—82no—
227C22×D11—161no—
228C22×D11—161no—
229C22×D11—161no—
230C22×D11—161no—
231C22×D11C2×D811yescharacteristic
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—22no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—161no—
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C22⋊D11—44no—
245C22⋊D11—82no—
246C22⋊D11—161no—
247C22⋊D11—161no—
248C2×Dic11—41no—
249C2×Dic11—161no—
250C2×Dic11C2×D811yescharacteristic
251C2×Dic11C2×D811yescharacteristic
252C2×Dic11C2×D811yescharacteristic
253D44—22no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—82no—
260D44—161no—
261D44—161no—
262C4×D11—82no—
263C4×D11—161no—
264C4×D11—161no—
265C4×D11#12112yes—
266C4×D11AGL(1,ℤ/8)12yes—
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×SD32C2×D1111yescharacteristic, complemented
281C2×D16—111no—
282C2×D16—111no—
283C2×D16—111no—
284C2×D16—111no—
285C2×D16—111no—
286C2×D16—224no—
287C2×D16C2×D1111yescharacteristic
288C2×M32—111no—
289C22×C16—111no—
290#496—221no—
291#496—221no—
292#495—111no—
293#495C2×D1111yescharacteristic, complemented
294#493—111no—
295#493—111no—
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#358C2×D1111yescharacteristic, complemented
311#357—111no—
312#357—111no—
313#357—111no—
314#357—111no—
315#357—111no—
316#357C2×D1111yescharacteristic, complemented
317C22×C11—42no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11C22×D811yescharacteristic
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
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×C11—81no—
342C4×C11C2×#12111yescharacteristic
343C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
344Dic11—21no—
345Dic11—21no—
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×Q16C22×D1111yescharacteristic
355C2×SD16—21no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×D8—114no—
359C2×D8—111no—
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×D8—221no—
369C2×D8C22×D1111yescharacteristic
370C2×D8C22×D1111yescharacteristic
371C2×M16—111no—
372C22×C8—111no—
373#127—221no—
374#127—221no—
375#124—21no—
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—22no—
392SD32—222no—
393D16—22no—
394D16—222no—
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×C11C2×#45911yescharacteristic
419C2×C11#341511yescharacteristic
420C2×C11#341511yescharacteristic
421D11—22no—
422D11—82no—
423D11—161no—
424D11—161no—
425C24—441no—
426C24—441no—
427#41—442no—
428#41—442no—
429C2×Q8—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—224no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—441no—
437C2×D4—442no—
438C2×D4—442no—
439C2×D4—442no—
440C2×D4—441no—
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—21no—
453Q16—21no—
454SD16—42no—
455SD16—442no—
456SD16—442no—
457D8—21no—
458D8—21no—
459D8—21no—
460D8—112no—
461D8—224no—
462D8—221no—
463D8—221no—
464D8—221no—
465D8—221no—
466D8—221no—
467D8—442no—
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—41no—
484C22⋊C4—41no—
485C22⋊C4—111no—
486C22⋊C4—111no—
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—111no—
504C23—444no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—882no—
509C23—1761no—
510C23—1761no—
511C23—1761no—
512C23—1761no—
513Q8—41no—
514Q8—41no—
515D4—22no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—222no—
520D4—444no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—882no—
527D4—882no—
528D4—1761no—
529D4—1761no—
530D4—1761no—
531D4—1761no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—111no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—111no—
538C2×C4—111no—
539C2×C4—161no—
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—112no—
560C22—221no—
561C22—221no—
562C22—442no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22—881no—
570C22—881no—
571C22—1764no—
572C22—1764no—
573C22C2×D8×D1111yescharacteristic
574C4—21no—
575C4—21no—
576C4—81no—
577C4—81no—
578C4—112no—
579C4—221no—
580C4—221no—
581C4—881no—
582C4D11×#12111yescharacteristic
583C4D11×AGL(1,ℤ/8)11yescharacteristic
584C2—82no—
585C2—161no—
586C2—222no—
587C2—882no—
588C2—1761no—
589C2—1761no—
590C2D11×#45911yescharacteristic
591C2#1308175411yescharacteristic
592C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
hypercenter#2210D11
hypocenterC11#33585
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C2×D11×D16C2semidirect
3. #13079098C2semidirect
4. #13077463C2semidirect
5. #13070674C2semidirect
6. #13070673C2semidirect
7. #13070668C2semidirect
8. #13070652C2semidirect
9. #13070651C2semidirect
10. #13070650C2semidirect
11. #13070649C2semidirect
12. #13070373C2semidirect
13. #13070330C2semidirect
14. #13070322C2semidirect
15. C11×#2210C2semidirect
22. C2×C11×SD32C22semidirect
24. C11×#495C22semidirect
25. C4×C11×D8C22semidirect
26. #10622804C22semidirect
27. C2×#66892C22semidirect
29. #10622764C22semidirect
30. D8×Dic11C22semidirect
33. C2×#66890C22semidirect
39. C2×D176C22semidirect
43. #10622485C22semidirect
46. #10622308C22semidirect
47. C4×D88C22semidirect
49. C11×C4⋊C16C22semidirect
50. C11×#358C22semidirect
51. C11×#357C22semidirect
52. #10622202C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622147C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622129C22semidirect
59. #10622129C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
86. D8×D11D4semidirect
212. #2210D11semidirect
280. C2×SD32C2×D11semidirect
293. #495C2×D11semidirect
301. C4×D8C2×D11semidirect
308. C4⋊C16C2×D11semidirect
310. #358C2×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×#106225272
C2×D11×D162
#130790982
#130774632
#130706742
#130706732
#130706682
#130706522
#130706512
#130706502
#130706492
#130703732
#130703302
#130703222
C11×#22102
#3358511