Finite Group Databasebeta

← #14781256

Subgroups — #14781256

Order 2816.

1610 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10622719C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic, complemented
4C2×#10622726C211yesmaximal, characteristic, complemented
5#13070999C211yesmaximal, characteristic, complemented
6#13069820C212yesmaximal, complemented
7#13069813C212yesmaximal, complemented
8#13069806C212yesmaximal, complemented
9#13069799C212yesmaximal, complemented
10#13068333C211yesmaximal, characteristic, complemented
11C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×#67006—21no—
17#10623322—24no—
18#10623322—24no—
19C2×#66983C2212yes—
20C2×#66982—21no—
21C2×C4×C22⋊D11—22no—
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C2×#66977C2212yes—
26C2×C11×C22⋊C8—24no—
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29#10622860—21no—
30#10622825C2212yes—
31#10622825C2212yes—
32#10622824—21no—
33C4×C22⋊Dic11—22no—
34#10622726—24no—
35#10622726—24no—
36C2×#66885C2211yescharacteristic, complemented
37C2×#66885C2212yescomplemented
38C2×#66885C2211yescharacteristic, complemented
39#10622719—24no—
40C2×#66882C2212yescomplemented
41C2×#66881C2212yescomplemented
42C2×#66880C2211yescharacteristic, complemented
43C2×#66880C2212yescomplemented
44C2×#66880C2211yescharacteristic, complemented
45#10622189C2212yescomplemented
46#10622189C2212yescomplemented
47C25×C11D411yescharacteristic
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11D412yes—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—22no—
59C22×C22⋊D11—21no—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339D414yes—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11D414yescomplemented
75C22×C8×C11C2312yes—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78#67006—28no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85#66983—24no—
86#66983—24no—
87#66982—28no—
88C4×C22⋊D11—216no—
89C2×(C2×D11)⋊C4—22no—
90#66979—22no—
91#66979—22no—
92#66979—22no—
93#66979—22no—
94#66979—22no—
95#66979D414yes—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100#66977—24no—
101#66977—24no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C11×C22⋊C8—24no—
107C11×C22⋊C8—24no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110#66885—24no—
111#66885—22no—
112#66885—22no—
113#66882—24no—
114#66881—24no—
115#66880—24no—
116#66880—22no—
117#66880—22no—
118#23479—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—24no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—42no—
124C24×C11C2×D412yes—
125C24×C11C2×D411yescharacteristic
126C23×D11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—44no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—28no—
153C2×C22⋊D11—24no—
154C2×C22⋊D11—44no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—44no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163#4339—28no—
164#4339—28no—
165#4339—44no—
166#4339—44no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44C2×D412yes—
173C2×C4×D11—24no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22C2×D412yes—
182C2×C8×C11—28no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—22no—
190C2×C8×C11—44no—
191C2×C8×C11C2×D412yes—
192C2×C8×C11C2×D412yes—
193C22⋊Dic11—28no—
194C22⋊Dic11—24no—
195C22⋊Dic11—44no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—44no—
199(C2×D11)⋊C4—28no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—22no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2×D414yes—
208Dic11⋊C4—28no—
209C4×Dic11—24no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C2×#525—111no—
213C2×#427—111no—
214C2×#416—111no—
215C2×#416—111no—
216C22×C22⋊C8D1111yescharacteristic, complemented
217#2280—111no—
218#2036—112no—
219#2035—112no—
220#2034—112no—
221#2033—112no—
222#1735—111no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—28no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11—44no—
235C23×C11—44no—
236C23×C11#12012yes—
237C23×C11#12112yes—
238C23×C11#12312yes—
239C23×C11#13514yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—42no—
245C22×D11—42no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—48no—
255C2×C4×C11#12012yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12114yes—
258C2×C4×C11#12114yes—
259C2×C4×C11#12314yes—
260C2×C4×C11#12312yes—
261C2×C4×C11#12414yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C22⋊D11—416no—
269C22⋊D11—48no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283D44—22no—
284D44—22no—
285D44—41no—
286D44—41no—
287C4×D11—48no—
288Dic22—22no—
289Dic22—22no—
290Dic22—41no—
291Dic22—41no—
292C8×C11—22no—
293C8×C11—22no—
294C8×C11—42no—
295C22×#41—111no—
296C24×C4C2×D1111yescharacteristic
297C23×C8C2×D1111yescharacteristic
298C23×C8C2×D1111yescharacteristic
299#525—224no—
300#525—224no—
301C2×#123—221no—
302C2×C22⋊Q8—112no—
303C2×#121—112no—
304C2×#120—221no—
305C2×C4×D4—222no—
306C2×#117—111no—
307C2×#117—111no—
308C2×#117—111no—
309#427—224no—
310C2×#107—112no—
311C2×#106—112no—
312#416—224no—
313#416—224no—
314C2×#103—111no—
315C2×#103—112no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102—112no—
319C2×#102—111no—
320C2×C22⋊C8—24no—
321C2×C22⋊C8C2×D1112yes—
322C2×C22⋊C8C2×D1112yes—
323#381—221no—
324#380—112no—
325#380—112no—
326#379—221no—
327C4×C22⋊C4—222no—
328#340—112no—
329#340—112no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—24no—
337C22×C11—416no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11#39414yes—
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×#12111yescharacteristic
345C22×C11C2×#12311yescharacteristic
346C22×C11C2×#13512yes—
347C22×C11#57512yes—
348C2×D11—42no—
349C2×D11—44no—
350C2×D11—82no—
351C2×D11—81no—
352C2×D11—81no—
353C4×C11—42no—
354C4×C11#39414yes—
355C4×C11C2×#12111yescharacteristic
356C4×C11C2×#12111yescharacteristic
357C4×C11C2×#12311yescharacteristic
358C4×C11C2×#12411yescharacteristic
359Dic11—42no—
360Dic11—44no—
361Dic11—82no—
362Dic11—81no—
363Dic11—81no—
364C25D4411yescharacteristic
365C2×#41—114no—
366C2×#41—222no—
367C2×#41—222no—
368C2×#41—222no—
369C2×#41—222no—
370C2×#41—222no—
371C22×Q8—111no—
372C22×D4—111no—
373C22×D4—222no—
374C22×D4—221no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—221no—
382C23×C4D4411yescharacteristic
383C23×C4D4412yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1111yescharacteristic
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8C22⋊D1114yescomplemented
392C22×C8C22×D1112yes—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#123—228no—
396C22⋊Q8—224no—
397C22⋊Q8—224no—
398#121—224no—
399#121—224no—
400#120—228no—
401C4×D4—2216no—
402#117—114no—
403#117—222no—
404#117—222no—
405#117—222no—
406#117—222no—
407#117—222no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—222no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—222no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42—221no—
423#107—224no—
424#106—224no—
425#103—224no—
426#103—222no—
427#103—222no—
428#102—224no—
429#102—222no—
430#102—222no—
431C22⋊C8—24no—
432C22⋊C8—24no—
433#95—222no—
434#95—222no—
435C2×C11—24no—
436C2×C11—44no—
437C2×C11C2×#39411yescharacteristic
438C2×C11#300212yes—
439C2×C11#305011yescharacteristic
440C2×C11#305411yescharacteristic
441C2×C11#309112yes—
442D11—82no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—42no—
448C24—221no—
449C24C2×D4412yes—
450C24C2×D4411yescharacteristic
451#41—228no—
452#41—228no—
453#41—444no—
454#41—444no—
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×D4—112no—
462C2×D4—228no—
463C2×D4—224no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—444no—
470C2×D4—442no—
471C2×D4—444no—
472C2×D4—442no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—222no—
490C22×C4—221no—
491C22×C4—224no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—221no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4C2×D4412yes—
498C22×C4C2×D4411yescharacteristic
499C22×C4#433912yes—
500C22×C4D4×D1112yes—
501C22×C4D4×D1112yes—
502C22×C4#434112yes—
503C22×C4#434112yes—
504C22×C4C2×C22⋊D1112yes—
505C22×C4C23×D1111yescharacteristic
506C2×C8—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—44no—
515C2×C8C2×C22⋊D1112yes—
516C2×C8C2×C22⋊D1112yes—
517C4⋊C4—114no—
518C4⋊C4—228no—
519C4⋊C4—222no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C22⋊C4—228no—
527C22⋊C4—228no—
528C22⋊C4—224no—
529C22⋊C4—444no—
530C22⋊C4—442no—
531C22⋊C4—444no—
532C22⋊C4—442no—
533C42—224no—
534C42—442no—
535C42—442no—
536C11#2347911yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—28no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—48no—
547C23—48no—
548C23—44no—
549C23—44no—
550C23—222no—
551C23—442no—
552C23—441no—
553C23—442no—
554C23—441no—
555C23#6693512yes—
556C23#6693912yes—
557C23#6695714yes—
558C23#6698312yes—
559C23C22×D4411yescharacteristic
560Q8—222no—
561Q8—222no—
562Q8—441no—
563Q8—441no—
564D4—222no—
565D4—222no—
566D4—4416no—
567D4—448no—
568D4—441no—
569D4—441no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—48no—
579C2×C4—224no—
580C2×C4—222no—
581C2×C4—442no—
582C2×C4—441no—
583C2×C4—442no—
584C2×C4—441no—
585C2×C4—448no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4#6693512yes—
594C2×C4#6693614yes—
595C2×C4#6693814yes—
596C2×C4#6693912yes—
597C2×C4#6698312yes—
598C2×C4#6699114yes—
599C2×C4#6699214yes—
600C2×C4C2×#433911yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—22no—
607C8—22no—
608C8—42no—
609C22—24no—
610C22—24no—
611C22—22no—
612C22—22no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—416no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—444no—
622C22—442no—
623C22—882no—
624C22—881no—
625C22—881no—
626C22#1062257414yes—
627C22C2×#6693511yescharacteristic
628C22C2×#6693911yescharacteristic
629C22C2×#6695712yes—
630C22#1062327912yes—
631C22C2×#6698311yescharacteristic
632C4—42no—
633C4—444no—
634C4—442no—
635C4—882no—
636C4—881no—
637C4—881no—
638C4#1062257414yes—
639C4C2×#6693611yescharacteristic
640C4C2×#6693811yescharacteristic
641C4C2×#6699111yescharacteristic
642C4C2×#6699211yescharacteristic
643C2—24no—
644C2—44no—
645C2—882no—
646C2C2×#1062257411yescharacteristic
647C2#1307783812yes—
648C2#1307819711yescharacteristic
649C2#1307822511yescharacteristic
650C2#1307853112yes—
subgroupG/H
centerC22×C4C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC22×C22⋊C8D11
hypocenterC11#23479
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622719C2semidirect
3. C2×#10622726C2semidirect
4. C2×#10622726C2semidirect
5. #13070999C2semidirect
6. #13069820C2semidirect
7. #13069813C2semidirect
8. #13069806C2semidirect
9. #13069799C2semidirect
10. #13068333C2semidirect
11. C22×C11×C22⋊C8C2semidirect
36. C2×#66885C22semidirect
37. C2×#66885C22semidirect
38. C2×#66885C22semidirect
40. C2×#66882C22semidirect
41. C2×#66881C22semidirect
42. C2×#66880C22semidirect
43. C2×#66880C22semidirect
44. C2×#66880C22semidirect
45. #10622189C22semidirect
46. #10622189C22semidirect
74. C22×C8×C11D4semidirect
216. C22×C22⋊C8D11semidirect
391. C22×C8C22⋊D11semidirect
536. C11#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106227192
C2×#106227262
#130709992
#130698202
#130698132
#130698062
#130697992
#130683332
C22×C11×C22⋊C82
#2347911