Finite Group Databasebeta

← #15633932

Subgroups — #15633932

Order 2816.

1852 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082493C211yesmaximal, characteristic, complemented
2#13081384C214yesmaximal, complemented
3#13081369C214yesmaximal, complemented
4#13081345C214yesmaximal, complemented
5#13081323C214yesmaximal, complemented
6#13078975C212yesmaximal, complemented
7C2×#10622680C211yesmaximal, characteristic, complemented
8#13078441C212yesmaximal, complemented
9#13078434C211yesmaximal, characteristic, complemented
10#13078155C212yesmaximal, complemented
11#13078096C211yesmaximal, characteristic, complemented
12#13077557C211yesmaximal, characteristic, complemented
13#13077444C212yesmaximal, complemented
14#13077414C211yesmaximal, characteristic, complemented
15C11×#3504C211yesmaximal, characteristic, complemented
16C11×#557C2214yescomplemented
17C11×#554—24no—
18C11×#554C2214yescomplemented
19C11×#544—22no—
20C11×#544C2212yes—
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C2×C11×#125—21no—
24C2×C11×#125C2211yescharacteristic
25C11×#520C2212yes—
26C4×C11×#41C2211yescharacteristic
27C2×#67003C2211yescharacteristic
28C2×#67002C2212yes—
29#10623256—22no—
30#10623229—21no—
31#10623229—21no—
32#10623161—24no—
33#10623116C2214yes—
34#10623108C2214yes—
35#10623056C2212yes—
36#10623052C2212yes—
37C2×#66927C2211yescharacteristic
38C4×#4339C2211yescharacteristic
39#10622846C2211yescharacteristic
40#10622702C2214yescomplemented
41#10622701C2214yescomplemented
42#10622700C2214yescomplemented
43#10622697C2214yescomplemented
44#10622681C2214yescomplemented
45#10622680C2214yes—
46#10622680C2214yes—
47#10622680C2214yescomplemented
48#10622679C2214yescomplemented
49#10622679C2214yescomplemented
50#10622679C2214yescomplemented
51#10622676C2214yescomplemented
52#10622643C2212yescomplemented
53#10622641C2214yescomplemented
54#10622640C2214yes—
55#10622640C2214yescomplemented
56#10622639C2212yescomplemented
57#10622639C2214yescomplemented
58C4×#4325C2214yescomplemented
59#10622637C2214yescomplemented
60#10622637C2214yescomplemented
61#10622631C2212yescomplemented
62#10622629C2214yescomplemented
63#10622628C2214yes—
64#10622628C2214yescomplemented
65#10622627C2214yescomplemented
66#10622627C2212yescomplemented
67C4×#4323C2214yescomplemented
68#10622615C2211yescharacteristic
69#10622614C2212yes—
70#10622612C2212yes—
71#10622611C2211yescharacteristic
72#10622610C2212yes—
73#10622579C2212yes—
74C2×#66873C2212yes—
75C2×#66873C2212yes—
76#10622577C2212yes—
77#10622537C2211yescharacteristic
78C2×#66867C2211yescharacteristic
79C2×C11×#41C2311yescharacteristic
80C2×#4343—24no—
81C2×#4339C2311yescharacteristic
82C22×D44—22no—
83C22×D44C2312yes—
84C11×C4⋊Q8—24no—
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8D412yes—
87C11×C4⋊Q8C2314yes—
88C11×#125—22no—
89C11×#125—24no—
90C11×#125—24no—
91C11×#125—21no—
92C11×#125—21no—
93C11×#125D411yescharacteristic
94C11×#125D411yescharacteristic
95C11×#125C2314yes—
96C11×#125C2314yes—
97C11×C22⋊Q8—24no—
98C11×C22⋊Q8—24no—
99C11×C22⋊Q8—24no—
100C11×C22⋊Q8—24no—
101C11×C22⋊Q8D414yes—
102C4×Q8×C11—24no—
103C4×Q8×C11C2312yes—
104C4×Q8×C11C2314yes—
105C4×Q8×C11C2314yes—
106C4×D4×C11—22no—
107C4×D4×C11—24no—
108C4×D4×C11C2312yes—
109C4×D4×C11C2314yes—
110C11×#117—22no—
111C11×#117—21no—
112C11×#117C2311yescharacteristic
113C11×#117C2312yes—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4C2312yes—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120#67003—24no—
121#67002—28no—
122#67000—24no—
123C2×#4326C2311yescharacteristic
124C2×#4325C2314yes—
125C2×#4325C2311yescharacteristic
126C2×#4324C2311yescharacteristic
127C2×#4323C2314yes—
128C2×#4323C2311yescharacteristic
129C4×C22⋊D11—22no—
130#66979C2311yescharacteristic
131C2×#4318C2312yes—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134#66948—22no—
135#66948—22no—
136#66948—24no—
137#66948—24no—
138#66948—24no—
139#66947—24no—
140#66947—24no—
141#66946—22no—
142#66946—22no—
143#66946—24no—
144#66935—24no—
145C22⋊C4×D11—24no—
146#66928C2314yes—
147#66927—21no—
148#66927—21no—
149#66927C2314yes—
150#66927C2314yes—
151C4×D44C2312yes—
152C4×D44C2314yes—
153C4×D44C2314yes—
154#66925—21no—
155C42×D11—21no—
156C4×Dic22C2312yes—
157#66899C2312yes—
158#66896C2312yes—
159#66874C2314yes—
160#66874C2312yes—
161#66873C2314yes—
162#66873C2314yes—
163#66873C2314yes—
164#66873C2314yes—
165#66873C2314yes—
166#66873C2314yes—
167#66873C2314yes—
168#66873C2312yes—
169#66872C2314yes—
170#66872C2312yes—
171#66871C2314yes—
172#66871C2312yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176#66867C2312yes—
177#66867C2312yes—
178#66867C2314yes—
179C4×C11⋊C8C2314yes—
180#61337—111nomaximal, Sylow
181C23×D11—22no—
182C11×#41—22no—
183C11×#41#4114yescomplemented
184C2×Q8×C11—24no—
185C2×Q8×C11C2×D414yes—
186C2×Q8×C11C2411yescharacteristic
187C2×D4×C11—21no—
188C2×D4×C11C2411yescharacteristic
189C22×C4×C11—21no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—24no—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—21no—
196#4343—88no—
197#4339—22no—
198#4339—22no—
199C2×D44—22no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—24no—
204C2×D44—24no—
205C2×D44—24no—
206C2×D44—84no—
207C2×D44C2411yescharacteristic
208C2×D44C2414yes—
209C2×C4×D11—21no—
210C2×C4×D11—22no—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×Dic22C2411yescharacteristic
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4C2×D412yes—
223C11×C4⋊C4C2×D412yes—
224C11×C4⋊C4C2×D414yes—
225C11×C4⋊C4C2×D414yes—
226C11×C4⋊C4C2×D414yes—
227C11×C4⋊C4C2414yes—
228C11×C4⋊C4C2412yes—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4C2×D414yes—
233C42×C11—21no—
234C42×C11—22no—
235C42×C11—24no—
236C42×C11C2×D411yescharacteristic
237C42×C11C2×D411yescharacteristic
238C42×C11C2414yes—
239C42×C11C2412yes—
240C22⋊Dic11—21no—
241#4326—22no—
242#4325—28no—
243#4325—22no—
244#4324—22no—
245#4323—28no—
246#4323—22no—
247(C2×D11)⋊C4—22no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252C4⋊Dic11C2412yes—
253Dic11⋊C4—22no—
254C4×Dic11—22no—
255C4×Dic11—21no—
256#4318—24no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2414yes—
261C2×C11⋊C8C2411yescharacteristic
262C2×C11⋊C8C2411yescharacteristic
263#3508—111no—
264#3504D1111yescharacteristic, complemented
265#3371—114no—
266#3370—114no—
267#3368—114no—
268#3366—114no—
269#3136—112no—
270C2×#490—111no—
271#3081—112no—
272#3080—111no—
273#3045—112no—
274#3038—111no—
275#2961—111no—
276#2946—112no—
277#2943—111no—
278C23×C11—21no—
279C23×C11C22×D411yescharacteristic
280C22×D11—24no—
281C22×D11—21no—
282C22×D11—44no—
283C22×D11—82no—
284C22×D11—82no—
285Q8×C11—21no—
286Q8×C11—44no—
287Q8×C11—84no—
288Q8×C11C2×#4112yes—
289D4×C11—24no—
290D4×C11—21no—
291D4×C11C2×#4112yes—
292C2×C4×C11—21no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—42no—
297C2×C4×C11—82no—
298C2×C4×C11—84no—
299C2×C4×C11—82no—
300C2×C4×C11C22×D412yes—
301C2×C4×C11C22×D412yes—
302C2×C4×C11C22×D414yes—
303C2×C4×C11C22×D414yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4112yes—
306C2×C4×C112−1+412yes—
307C2×C4×C11C2511yescharacteristic
308C22⋊D11—42no—
309C2×Dic11—21no—
310C2×Dic11—22no—
311D44—24no—
312D44—21no—
313D44—24no—
314D44—21no—
315D44—48no—
316D44—44no—
317D44—84no—
318D44—84no—
319D44—84no—
320C4×D11—44no—
321C4×D11—42no—
322C4×D11—84no—
323C4×D11—84no—
324Dic22—21no—
325Dic22—21no—
326C11⋊C8—21no—
327C11⋊C8—21no—
328C11⋊C8—24no—
329C11⋊C8—22no—
330C2×AGL(1,ℤ/8)—112no—
331C2×#135—111no—
332#559—114no—
333#557C2×D1114yescomplemented
334#554—24no—
335#554C2×D1114yescomplemented
336#550—114no—
337#546—224no—
338#544—22no—
339#544C2×D1112yes—
340#540—221no—
341#540—221no—
342#535—112no—
343#533—21no—
344#533C2×D1111yescharacteristic
345#532—222no—
346C2×#127—111no—
347C2×#125—21no—
348C2×#125C2×D1111yescharacteristic
349#520C2×D1112yes—
350#518—112no—
351C4×#41—111no—
352C4×#41C2×D1111yescharacteristic
353#490—114no—
354#490—114no—
355#490—114no—
356#489—114no—
357#488—114no—
358#486—114no—
359#479—114no—
360#478—114no—
361#478—114no—
362#478—114no—
363#476—114no—
364#474—114no—
365#464—114no—
366#463—114no—
367#460—114no—
368#460—114no—
369#459—114no—
370#459—114no—
371#446—114no—
372#446—114no—
373#442—112no—
374#442—114no—
375#441—112no—
376#440—112no—
377#440—114no—
378#440—112no—
379C4×SD16—114no—
380C4×D8—114no—
381#428—112no—
382#427—111no—
383#424—112no—
384#423—111no—
385#418—112no—
386#417—112no—
387#416—111no—
388#416—111no—
389C2×#102—112no—
390C2×#102—112no—
391#405—112no—
392C2×#97—111no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—42no—
396C22×C11#54812yes—
397C22×C11C23×D411yescharacteristic
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—42no—
401C2×D11—44no—
402C2×D11—41no—
403C2×D11—164no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—24no—
407C4×C11—24no—
408C4×C11—22no—
409C4×C11—44no—
410C4×C11—42no—
411C4×C11#54812yes—
412C4×C11C22×#4111yescharacteristic
413C4×C11C2×2−1+411yescharacteristic
414Dic11—42no—
415Dic11—41no—
416C2×#41—111no—
417C2×#41—224no—
418C2×#41C22×D1111yescharacteristic
419C22×D4—112no—
420C22×D4—222no—
421AGL(1,ℤ/8)—228no—
422#135—224no—
423C2×Q16—111no—
424C2×SD16—111no—
425C2×SD16—114no—
426C2×SD16—111no—
427C2×D8—111no—
428C2×D8—114no—
429C2×M16—112no—
430C22×C8—111no—
431C22×C8—111no—
432C4⋊Q8—24no—
433C4⋊Q8—22no—
434C4⋊Q8C22⋊D1112yes—
435C4⋊Q8C22×D1114yes—
436#127—114no—
437#127—114no—
438#127—221no—
439#127—221no—
440#125—22no—
441#125—24no—
442#125—24no—
443#125—21no—
444#125—21no—
445#125C22⋊D1111yescharacteristic
446#125C22⋊D1111yescharacteristic
447#125C22×D1114yes—
448#125C22×D1114yes—
449#124—114no—
450#124—224no—
451#123—224no—
452#123—224no—
453C22⋊Q8—24no—
454C22⋊Q8—24no—
455C22⋊Q8—24no—
456C22⋊Q8—24no—
457C22⋊Q8C22⋊D1114yes—
458#121—222no—
459#121—222no—
460#121—224no—
461#121—224no—
462#121—224no—
463#120—224no—
464C4×Q8—24no—
465C4×Q8—112no—
466C4×Q8C22×D1112yes—
467C4×Q8C22×D1114yes—
468C4×Q8C22×D1114yes—
469C4×D4—22no—
470C4×D4—24no—
471C4×D4—112no—
472C4×D4—114no—
473C4×D4—114no—
474C4×D4—222no—
475C4×D4—222no—
476C4×D4—222no—
477C4×D4—224no—
478C4×D4C22×D1112yes—
479C4×D4C22×D1114yes—
480#117—22no—
481#117—21no—
482#117—111no—
483#117—221no—
484#117C22×D1111yescharacteristic
485#117C22×D1112yes—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4C22×D1112yes—
490C2×C22⋊C4—224no—
491C2×C42—21no—
492C2×C42—221no—
493C2×C42C22×D1111yescharacteristic
494#107—112no—
495#107—114no—
496#106—112no—
497#106—114no—
498C4⋊C8—114no—
499C4⋊C8—114no—
500C4⋊C8—114no—
501#103—112no—
502#103—112no—
503#103—114no—
504#102—112no—
505#102—114no—
506#102—114no—
507#102—114no—
508#102—114no—
509#102—112no—
510#102—114no—
511#102—114no—
512#102—114no—
513#97—112no—
514#97—112no—
515#97—114no—
516C4×C8—114no—
517C2×C11—22no—
518C2×C11—42no—
519C2×C11C2×#54811yescharacteristic
520C2×C11#358512yes—
521D11—81no—
522D11—84no—
523C24—222no—
524#41—22no—
525#41—222no—
526#41—222no—
527#41—888no—
528#41#434314yescomplemented
529C2×Q8—24no—
530C2×Q8—111no—
531C2×Q8C2×C22⋊D1114yes—
532C2×Q8C23×D1111yescharacteristic
533C2×D4—21no—
534C2×D4—114no—
535C2×D4—111no—
536C2×D4—221no—
537C2×D4—224no—
538C2×D4—224no—
539C2×D4—222no—
540C2×D4—224no—
541C2×D4—224no—
542C2×D4—224no—
543C2×D4—224no—
544C2×D4—884no—
545C2×D4C23×D1111yescharacteristic
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—221no—
551C22×C4—222no—
552C22×C4—224no—
553C22×C4—224no—
554C22×C4C2×C22⋊D1112yes—
555C22×C4C23×D1111yescharacteristic
556Q16—222no—
557SD16—222no—
558SD16—228no—
559SD16—222no—
560D8—222no—
561D8—228no—
562M16—224no—
563C2×C8—112no—
564C2×C8—114no—
565C2×C8—111no—
566C2×C8—111no—
567C2×C8—222no—
568C2×C8—222no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—112no—
578C4⋊C4—222no—
579C4⋊C4C2×C22⋊D1112yes—
580C4⋊C4C2×C22⋊D1114yes—
581C4⋊C4C2×C22⋊D1112yes—
582C4⋊C4C2×C22⋊D1114yes—
583C4⋊C4C2×C22⋊D1114yes—
584C4⋊C4C23×D1114yes—
585C4⋊C4C23×D1112yes—
586C22⋊C4—21no—
587C22⋊C4—22no—
588C22⋊C4—24no—
589C22⋊C4—221no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—222no—
593C22⋊C4—224no—
594C22⋊C4—224no—
595C22⋊C4C2×C22⋊D1114yes—
596C42—21no—
597C42—22no—
598C42—24no—
599C42—221no—
600C42—222no—
601C42C2×C22⋊D1111yescharacteristic
602C42C2×C22⋊D1111yescharacteristic
603C42C23×D1114yes—
604C42C23×D1112yes—
605C11#6133711yescharacteristic, complemented, Sylow
606C23—21no—
607C23—224no—
608C23—221no—
609C23—444no—
610C23—882no—
611C23—882no—
612C23C22×C22⋊D1111yescharacteristic
613Q8—21no—
614Q8—44no—
615Q8—84no—
616Q8—221no—
617Q8—221no—
618Q8C2×#434312yes—
619D4—24no—
620D4—21no—
621D4—224no—
622D4—221no—
623D4—224no—
624D4—221no—
625D4—448no—
626D4—442no—
627D4—444no—
628D4—884no—
629D4—884no—
630D4—884no—
631D4C2×#434312yes—
632C2×C4—21no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—42no—
637C2×C4—82no—
638C2×C4—84no—
639C2×C4—82no—
640C2×C4—221no—
641C2×C4—222no—
642C2×C4—444no—
643C2×C4—442no—
644C2×C4—884no—
645C2×C4—884no—
646C2×C4C2×#434312yes—
647C2×C4#6704012yes—
648C2×C4C22×C22⋊D1112yes—
649C2×C4C22×C22⋊D1114yes—
650C2×C4C22×C22⋊D1112yes—
651C2×C4C22×C22⋊D1114yes—
652C2×C4C22×C22⋊D1111yescharacteristic
653C2×C4C24×D1111yescharacteristic
654C8—221no—
655C8—221no—
656C8—224no—
657C8—222no—
658C22—22no—
659C22—22no—
660C22—42no—
661C22—442no—
662C22—444no—
663C22—444no—
664C22—441no—
665C22—444no—
666C22—1764no—
667C22#1062334812yes—
668C22C23×C22⋊D1111yescharacteristic
669C4—22no—
670C4—22no—
671C4—24no—
672C4—24no—
673C4—22no—
674C4—44no—
675C4—42no—
676C4—442no—
677C4—441no—
678C4#1062334812yes—
679C4C22×#434311yescharacteristic
680C4C2×#6704011yescharacteristic
681C2—22no—
682C2—42no—
683C2—884no—
684C2—881no—
685C2C2×#1062334811yescharacteristic
686C2#1308339512yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3504C2
socleC22×C11C23×D4
hypercenter#3504D11
hypocenterC11#61337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #13082493C2semidirect
2. #13081384C2semidirect
3. #13081369C2semidirect
4. #13081345C2semidirect
5. #13081323C2semidirect
6. #13078975C2semidirect
7. C2×#10622680C2semidirect
8. #13078441C2semidirect
9. #13078434C2semidirect
10. #13078155C2semidirect
11. #13078096C2semidirect
12. #13077557C2semidirect
13. #13077444C2semidirect
14. #13077414C2semidirect
15. C11×#3504C2semidirect
16. C11×#557C22semidirect
18. C11×#554C22semidirect
40. #10622702C22semidirect
41. #10622701C22semidirect
42. #10622700C22semidirect
43. #10622697C22semidirect
44. #10622681C22semidirect
47. #10622680C22semidirect
48. #10622679C22semidirect
49. #10622679C22semidirect
50. #10622679C22semidirect
51. #10622676C22semidirect
52. #10622643C22semidirect
53. #10622641C22semidirect
55. #10622640C22semidirect
56. #10622639C22semidirect
57. #10622639C22semidirect
58. C4×#4325C22semidirect
59. #10622637C22semidirect
60. #10622637C22semidirect
61. #10622631C22semidirect
62. #10622629C22semidirect
64. #10622628C22semidirect
65. #10622627C22semidirect
66. #10622627C22semidirect
67. C4×#4323C22semidirect
183. C11×#41#41semidirect
264. #3504D11semidirect
333. #557C2×D11semidirect
335. #554C2×D11semidirect
528. #41#4343semidirect
605. C11#61337semidirect

Maximal subgroups

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

subgroupindex
#130824932
#130813842
#130813692
#130813452
#130813232
#130789752
C2×#106226802
#130784412
#130784342
#130781552
#130780962
#130775572
#130774442
#130774142
C11×#35042
#6133711