Finite Group Databasebeta

← #15623466

Subgroups — #15623466

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082432C211yesmaximal, characteristic
2#13082428C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic, complemented
4#13079159C212yesmaximal, complemented
5#13079157C212yesmaximal, complemented
6#13079154C214yesmaximal, complemented
7#13079151C218yesmaximal, complemented
8#13079126C211yesmaximal, characteristic, complemented
9#13079125C212yesmaximal, complemented
10C2×#10622691C211yesmaximal, characteristic, complemented
11D11×#500C212yesmaximal, complemented
12#13077215C214yesmaximal
13C4×#66960C211yesmaximal, characteristic
14C11×#3165C211yesmaximal, characteristic, complemented
15C11×#533C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17Q8×C22⋊D11—22no—
18C2×#66960C2212yes—
19#10623261—21no—
20#10623260C2214yes—
21#10623259C2212yes—
22#10623259C2212yes—
23#10623258—21no—
24D11×C4⋊Q8C2212yes—
25D11×C4⋊Q8C2212yes—
26#10623253—21no—
27#10623252—21no—
28#10623220C2214yes—
29#10623166—22no—
30#10623163—22no—
31#10623110—21no—
32Q8×D44—21no—
33#10623098—21no—
34Q8×Dic22—21no—
35#10623054C2212yes—
36#10623050C2212yes—
37#10623042—22no—
38#10623035C2212yes—
39#10623031C2212yes—
40C4×#4339C2211yescharacteristic
41#10623001C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C11×#501C2214yes—
44C11×#500C2212yes—
45C11×#498C2212yes—
46C11×#428C2214yes—
47C4×C11×M16C2211yescharacteristic
48#10622735C2212yes—
49#10622734C2214yes—
50#10622692C2211yescharacteristic
51#10622692C2211yescharacteristic
52#10622691C2211yescharacteristic
53#10622691C2212yes—
54#10622691C2214yes—
55#10622691C2212yes—
56#10622691C2211yescharacteristic
57#10622677C2214yes—
58#10622611C2214yes—
59C2×#66871C2214yes—
60C2×C4×C11⋊C8C2211yescharacteristic
61#10622494C2218yes—
62D11×#107C2218yes—
63#10622489C2218yes—
64#10622487C2218yes—
65#10622474C2218yes—
66#10622473C2218yes—
67#10622471C2218yes—
68#10622469C2218yes—
69#10622321C2214yes—
70#10622315C2214yes—
71C4×#4313C2212yes—
72C4×C8×D11C2212yes—
73#10622295C2212yes—
74#10622293C2212yes—
75C22×Q8×C11—21no—
76C2×Q8×D11—22no—
77C2×Q8×D11—22no—
78C2×#4339C2311yescharacteristic
79C22×Dic22—21no—
80C2×C11×M16C2312yes—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2312yes—
85C11×C4⋊Q8C2311yescharacteristic
86C11×C4⋊Q8C2312yes—
87C11×#125C2312yes—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C11×#117C2312yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2312yes—
95C2×C42×C11C2311yescharacteristic
96#66999—22no—
97#66999—22no—
98#66999—24no—
99Q8×Dic11—22no—
100Q8×Dic11—22no—
101#66997—24no—
102#66997—22no—
103#66997—22no—
104C4×C22⋊D11—24no—
105C4×C22⋊D11D412yes—
106C4×C22⋊D11D412yes—
107#66979C2312yes—
108#66979C2311yescharacteristic
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2312yes—
111#66977—21no—
112#66977—21no—
113#66977—24no—
114C22×C11⋊C8C2312yes—
115#66960Q8116yescomplemented
116C2×#4313C2314yes—
117C2×C8×D11C2314yes—
118#66950—22no—
119#66950—22no—
120#66950—24no—
121#66949—24no—
122#66949—24no—
123#66946—22no—
124#66945C2314yes—
125#66945C2314yes—
126C4⋊C4×D11—22no—
127C4⋊C4×D11—22no—
128C4⋊C4×D11C2314yes—
129C4⋊C4×D11C2314yes—
130#66943—22no—
131#66943C2314yes—
132#66943C2314yes—
133#66942—24no—
134#66942—24no—
135#66941—22no—
136#66941—24no—
137#66941—22no—
138#66941—22no—
139#66941C2314yes—
140#66941C2314yes—
141#66940—22no—
142#66940—22no—
143#66940—22no—
144(C22⋊D11)⋊C4—24no—
145#66931—24no—
146C4×D44—22no—
147C4×D44D411yescharacteristic
148C4×D44D411yescharacteristic
149#66925C2312yes—
150C42×D11C2312yes—
151#66923—22no—
152#66923C2312yes—
153#66922—21no—
154#66922—21no—
155#66922—22no—
156#66922C2311yescharacteristic
157#66922C2312yes—
158#66922C2312yes—
159#66922C2311yescharacteristic
160C4×Dic22—22no—
161C4×Dic22—21no—
162C4×Dic22—21no—
163C4×Dic22D411yescharacteristic
164C4×Dic22D411yescharacteristic
165C11×#107C2318yes—
166C11×#106C2318yes—
167C11×#97C2312yes—
168C4×C8×C11C2312yes—
169#66882C2318yes—
170#66881C2318yes—
171#66879C2314yes—
172C8×Dic11C2314yes—
173#66872C2314yes—
174#66872C2314yes—
175#66871C2318yes—
176#66871C2314yes—
177#66871C2318yes—
178#66871C2314yes—
179C4×C11⋊C8C2311yescharacteristic
180C4×C11⋊C8C2311yescharacteristic
181C4×C11⋊C8C2312yes—
182#60667—111nomaximal, Sylow
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—21no—
186C2×Q8×C11—22no—
187C2×Q8×C11—82no—
188C22×C4×C11—22no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11C2×D412yes—
193C22×Dic11—22no—
194Q8×D11—84no—
195Q8×D11—84no—
196#4339C2×Q818yes—
197C2×D44C2×D411yescharacteristic
198C2×C4×D11—24no—
199C2×C4×D11—24no—
200C2×C4×D11C2×D412yes—
201C2×C4×D11C2×D412yes—
202C2×C4×D11C2412yes—
203C2×Dic22—24no—
204C2×Dic22—24no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—22no—
208C2×Dic22—22no—
209C2×Dic22—82no—
210C2×Dic22C2×D411yescharacteristic
211C11×M16C2×Q818yescomplemented
212C2×C8×C11C2414yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4C2414yes—
221C11×C4⋊C4C2412yes—
222C11×C4⋊C4C2412yes—
223C11×C22⋊C4—22no—
224C42×C11—22no—
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228C42×C11C2411yescharacteristic
229C22⋊Dic11—22no—
230C22⋊Dic11C2×D412yes—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4C2×D412yes—
234(C2×D11)⋊C4C2×D412yes—
235C4⋊Dic11—24no—
236C4⋊Dic11—24no—
237C4⋊Dic11—22no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—22no—
241C4⋊Dic11—22no—
242C4⋊Dic11C2×D411yescharacteristic
243C4⋊Dic11C2×D411yescharacteristic
244C4⋊Dic11C2414yes—
245C4⋊Dic11C2412yes—
246C4⋊Dic11C2412yes—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—22no—
254Dic11⋊C4—22no—
255Dic11⋊C4C2×D412yes—
256Dic11⋊C4C2×D412yes—
257C4×Dic11—24no—
258C4×Dic11—24no—
259C4×Dic11—22no—
260C4×Dic11C2×D412yes—
261C4×Dic11C2×D412yes—
262C4×Dic11C2412yes—
263C2×C11⋊C8C2×Q818yescomplemented
264C2×C11⋊C8C2412yes—
265C2×C11⋊C8C2412yes—
266#4313C2×Q8116yescomplemented
267C8×D11C2×Q8116yescomplemented
268#3503—111no—
269#3503—111no—
270#3165—112no—
271#3165—112no—
272#3165—111no—
273#3165D1111yescharacteristic, complemented
274#3164—118no—
275#3164—114no—
276#3160—112no—
277#3160—111no—
278C2×#500—112no—
279C2×#500—111no—
280#2913—114no—
281C4×#131—111no—
282C23×C11C22×D411yescharacteristic
283C22×D11C22×D412yes—
284Q8×C11—42no—
285Q8×C11—44no—
286Q8×C11—42no—
287Q8×C11—82no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—82no—
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×Q814yes—
300C2×C4×C11C2511yescharacteristic
301C22⋊D11C4⋊Q818yes—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—82no—
306C2×Dic11C22×D412yes—
307C2×Dic11C22×D412yes—
308C2×Dic11C22×D412yes—
309D44C4⋊Q814yes—
310C4×D11—24no—
311C4×D11—24no—
312C4×D11—84no—
313C4×D11—84no—
314C4×D11C22×Q818yes—
315Dic22—44no—
316Dic22—42no—
317Dic22—42no—
318Dic22—84no—
319Dic22—84no—
320Dic22—82no—
321Dic22C4⋊Q814yes—
322C8×C11C22×Q818yes—
323C11⋊C8C22×Q814yes—
324C11⋊C8C22×Q814yes—
325C2×#131—112no—
326Q82—221no—
327Q82—221no—
328#557—221no—
329#557—221no—
330#554—222no—
331#554—221no—
332#554—222no—
333#554—221no—
334D4×Q8—221no—
335D4×Q8—222no—
336D4×Q8—221no—
337D4×Q8—222no—
338#544—114no—
339#544—114no—
340#544—112no—
341#544—112no—
342#533—112no—
343#533—112no—
344#533—111no—
345#533C2×D1111yescharacteristic
346C2×C4⋊Q8—112no—
347C2×C4⋊Q8—112no—
348C2×C4⋊Q8—111no—
349C2×C4⋊Q8C2×D1111yescharacteristic
350#520—112no—
351#520—112no—
352C4×#41—111no—
353#501—118no—
354#501—118no—
355#501—114no—
356#501C2×D1114yes—
357#500—111no—
358#500—112no—
359#500—114no—
360#500—112no—
361#500—111no—
362#500—118no—
363#500—112no—
364#500C2×D1112yes—
365#499—114no—
366#499—118no—
367#498—111no—
368#498—111no—
369#498—112no—
370#498C2×D1112yes—
371#428—114no—
372#428—118no—
373#428—118no—
374#428C2×D1114yes—
375#427—114no—
376#427—118no—
377C2×#107—114no—
378C2×#107—118no—
379#405—112no—
380#405—114no—
381C4×M16—112no—
382C4×M16C2×D1111yescharacteristic
383C2×C4×C8—111no—
384C2×C4×C8—112no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11C2×C4⋊Q812yes—
388C22×C11C23×D411yescharacteristic
389C2×D11—22no—
390C2×D11—22no—
391C2×D11C2×C4⋊Q814yes—
392C4×C11—21no—
393C4×C11—21no—
394C4×C11—44no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11C2×C4⋊Q812yes—
398C4×C11#57612yes—
399C4×C11#57812yes—
400C4×C11C23×Q812yes—
401Dic11—22no—
402Dic11—22no—
403Dic11—42no—
404Dic11—44no—
405Dic11—42no—
406Dic11C2×C4⋊Q814yes—
407C2×#41—111no—
408C22×Q8—21no—
409C22×Q8—222no—
410C22×Q8—222no—
411C22×Q8—221no—
412#131—1116no—
413C2×M16—114no—
414C2×M16C22×D1112yes—
415C22×C8—112no—
416C22×C8—114no—
417C4⋊Q8—21no—
418C4⋊Q8—21no—
419C4⋊Q8—114no—
420C4⋊Q8—114no—
421C4⋊Q8—111no—
422C4⋊Q8—112no—
423C4⋊Q8—112no—
424C4⋊Q8—111no—
425C4⋊Q8—222no—
426C4⋊Q8—222no—
427C4⋊Q8—222no—
428C4⋊Q8—222no—
429C4⋊Q8—222no—
430C4⋊Q8—224no—
431C4⋊Q8—222no—
432C4⋊Q8—224no—
433C4⋊Q8—221no—
434C4⋊Q8—221no—
435C4⋊Q8C22×D1111yescharacteristic
436C4⋊Q8C22×D1112yes—
437C4⋊Q8C22×D1112yes—
438C4⋊Q8C22×D1111yescharacteristic
439#125—114no—
440#125—114no—
441#125—112no—
442#125—222no—
443#125—224no—
444#125—224no—
445#125—222no—
446#125C22×D1112yes—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—224no—
450C22⋊Q8—224no—
451C22⋊Q8—224no—
452C22⋊Q8—224no—
453C22⋊Q8—224no—
454C22⋊Q8—224no—
455C22⋊Q8—222no—
456C22⋊Q8—222no—
457C22⋊Q8—222no—
458C22⋊Q8—222no—
459C22⋊Q8—221no—
460C22⋊Q8—221no—
461C4×Q8—21no—
462C4×Q8—21no—
463C4×Q8—111no—
464C4×Q8—111no—
465C4×Q8—222no—
466C4×Q8—222no—
467C4×Q8—222no—
468C4×Q8—222no—
469C4×Q8—222no—
470C4×Q8—222no—
471C4×Q8—221no—
472C4×Q8—221no—
473C4×D4—112no—
474C4×D4—112no—
475C4×D4—111no—
476C4×D4—111no—
477C4×D4—222no—
478C4×D4—224no—
479C4×D4—222no—
480C4×D4—224no—
481#117—111no—
482#117—112no—
483#117—112no—
484#117—114no—
485#117—114no—
486#117C22×D1112yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4C22×D1112yes—
495C2×C42—112no—
496C2×C42C22×D1111yescharacteristic
497#107—118no—
498#107—114no—
499#107—118no—
500#107—118no—
501#107—114no—
502#107C22×D1118yes—
503#106—118no—
504#106—114no—
505#106—114no—
506#106C22×D1118yes—
507#97—114no—
508#97C22×D1112yes—
509C4×C8—114no—
510C4×C8—111no—
511C4×C8—111no—
512C4×C8—112no—
513C4×C8C22×D1112yes—
514C2×C11—22no—
515C2×C11C22×C4⋊Q811yescharacteristic
516C2×C11C2×#57611yescharacteristic
517C2×C11C2×#57811yescharacteristic
518D11—24no—
519#41—118no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—82no—
525C2×Q8—111no—
526C2×Q8—224no—
527C2×Q8—224no—
528C2×Q8—221no—
529C2×Q8—222no—
530C2×Q8—221no—
531C2×Q8—222no—
532C2×Q8—882no—
533C2×Q8—884no—
534C2×Q8—884no—
535C2×D4—112no—
536C2×D4—111no—
537C22×C4—22no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—224no—
542C22×C4—224no—
543C22×C4—222no—
544C22×C4D4×D1111yescharacteristic
545C22×C4D4×D1111yescharacteristic
546C22×C4C23×D1111yescharacteristic
547M16—1116no—
548M16Q8×D1118yescomplemented
549C2×C8—118no—
550C2×C8—112no—
551C2×C8—112no—
552C2×C8—1116no—
553C2×C8C23×D1114yes—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—112no—
562C4⋊C4—111no—
563C4⋊C4—112no—
564C4⋊C4—111no—
565C4⋊C4—112no—
566C4⋊C4—114no—
567C4⋊C4—112no—
568C4⋊C4—224no—
569C4⋊C4—224no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—224no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—224no—
576C4⋊C4—222no—
577C4⋊C4—221no—
578C4⋊C4—222no—
579C4⋊C4—222no—
580C4⋊C4—221no—
581C4⋊C4—222no—
582C4⋊C4—222no—
583C4⋊C4C23×D1112yes—
584C4⋊C4C23×D1112yes—
585C4⋊C4C23×D1114yes—
586C22⋊C4—22no—
587C22⋊C4—112no—
588C22⋊C4—112no—
589C22⋊C4—112no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—222no—
593C42—22no—
594C42—112no—
595C42—112no—
596C42—112no—
597C42—224no—
598C42—224no—
599C42—222no—
600C42D4×D1111yescharacteristic
601C42D4×D1111yescharacteristic
602C42C23×D1111yescharacteristic
603C42C23×D1111yescharacteristic
604C11#6066711yescharacteristic, complemented, Sylow
605C23—112no—
606C23C2×D4×D1111yescharacteristic
607Q8—44no—
608Q8—42no—
609Q8—42no—
610Q8—82no—
611Q8—114no—
612Q8—444no—
613Q8—442no—
614Q8—442no—
615Q8—882no—
616Q8—884no—
617Q8—884no—
618D4—118no—
619D4—114no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—82no—
626C2×C4—112no—
627C2×C4—118no—
628C2×C4—112no—
629C2×C4—112no—
630C2×C4—224no—
631C2×C4—224no—
632C2×C4—222no—
633C2×C4—224no—
634C2×C4—222no—
635C2×C4—884no—
636C2×C4—884no—
637C2×C4—882no—
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4C2×D4×D1111yescharacteristic
643C2×C4C2×Q8×D1114yes—
644C2×C4C24×D1111yescharacteristic
645C8—114no—
646C8—114no—
647C8C2×Q8×D1118yes—
648C22—21no—
649C22—21no—
650C22—114no—
651C22—222no—
652C22—222no—
653C22D11×C4⋊Q812yes—
654C22C22×D4×D1111yescharacteristic
655C4—21no—
656C4—21no—
657C4—44no—
658C4—42no—
659C4—42no—
660C4—114no—
661C4—222no—
662C4—222no—
663C4—442no—
664C4—444no—
665C4—442no—
666C4D11×C4⋊Q812yes—
667C4#1062330512yes—
668C4#1062331012yes—
669C4C22×Q8×D1112yes—
670C2—22no—
671C2—224no—
672C2C2×D11×C4⋊Q811yescharacteristic
673C2C2×#1062330511yescharacteristic
674C2C2×#1062331011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3165C2
socleC22×C11C23×D4
prime radicalC2×#4339C23
hypercenter#3165D11
hypocenterC11#60667
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #13079162C2semidirect
4. #13079159C2semidirect
5. #13079157C2semidirect
6. #13079154C2semidirect
7. #13079151C2semidirect
8. #13079126C2semidirect
9. #13079125C2semidirect
10. C2×#10622691C2semidirect
11. D11×#500C2semidirect
14. C11×#3165C2semidirect
115. #66960Q8semidirect
211. C11×M16C2×Q8semidirect
263. C2×C11⋊C8C2×Q8semidirect
266. #4313C2×Q8semidirect
267. C8×D11C2×Q8semidirect
273. #3165D11semidirect
548. M16Q8×D11semidirect
604. C11#60667semidirect

Maximal subgroups

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

subgroupindex
#130824322
#130824282
#130791622
#130791592
#130791572
#130791542
#130791512
#130791262
#130791252
C2×#106226912
D11×#5002
#130772152
C4×#669602
C11×#31652
#6066711