Finite Group Databasebeta

← #14781254

Subgroups — #14781254

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×#10622611C211yesmaximal, characteristic, complemented
3C2×#10622615C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#13069819C212yesmaximal, complemented
7#13069812C212yesmaximal, complemented
8#13069805C212yesmaximal, complemented
9#13069798C212yesmaximal, complemented
10#13068332C211yesmaximal, characteristic, complemented
11C11×#2280C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#67006—21no—
17#10623322—24no—
18#10623322—24no—
19C2×#66983C2212yes—
20C2×#66982—21no—
21C2×C4×C22⋊D11—22no—
22C2×#66979C2211yescharacteristic
23C2×#66977C2212yes—
24C23×C11⋊C8C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#381—21no—
27C11×#380C2212yes—
28C11×#380C2212yes—
29C11×#379—21no—
30C4×C11×C22⋊C4—22no—
31C2×C22⋊(C11⋊C8)—24no—
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622615—24no—
35#10622615—24no—
36#10622611—24no—
37C2×#66874C2211yescharacteristic, complemented
38C2×#66874C2212yescomplemented
39C2×#66874C2211yescharacteristic, complemented
40C2×#66873C2211yescharacteristic, complemented
41C2×#66873C2212yescomplemented
42C2×#66873C2211yescharacteristic, complemented
43C2×#66872C2212yescomplemented
44C2×#66871C2212yescomplemented
45#10622167C2212yescomplemented
46#10622167C2212yescomplemented
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
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82#67006—28no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—21no—
85#66983—24no—
86#66983—24no—
87#66982—28no—
88C4×C22⋊D11—216no—
89C2×(C2×D11)⋊C4—22no—
90#66979—22no—
91#66979D414yes—
92C2×C4⋊Dic11C2312yes—
93#66977—24no—
94#66977—24no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8D414yescomplemented
103C22×C11⋊C8C2312yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#95—22no—
107C11×#95—22no—
108C22⋊(C11⋊C8)—24no—
109C22⋊(C11⋊C8)—24no—
110#66874—24no—
111#66874—22no—
112#66874—22no—
113#66873—24no—
114#66873—22no—
115#66873—22no—
116#66872—24no—
117#66871—24no—
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—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—28no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—44no—
161C22×Dic11—22no—
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—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—44no—
192C42×C11—42no—
193C42×C11—42no—
194C22⋊Dic11—28no—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—28no—
197C4⋊Dic11—22no—
198C4⋊Dic11C2×D414yes—
199Dic11⋊C4—28no—
200C4×Dic11—24no—
201C2×C11⋊C8—28no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—44no—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8C2×D412yes—
212C2×#525—111no—
213C2×#427—111no—
214C2×#416—111no—
215C2×#416—111no—
216C22×C22⋊C8—111no—
217#2280D1111yescharacteristic, complemented
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—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11#12012yes—
263C2×C4×C11#12114yes—
264C2×C4×C11#12114yes—
265C2×C4×C11#12112yes—
266C2×C4×C11#12314yes—
267C2×C4×C11#12312yes—
268C2×C4×C11#12414yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C22⋊D11—416no—
276C22⋊D11—48no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
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—
292C11⋊C8—22no—
293C11⋊C8—22no—
294C11⋊C8—42no—
295C22×#41—111no—
296C24×C4C2×D1111yescharacteristic
297C23×C8—111no—
298C23×C8—111no—
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×#117C2×D1111yescharacteristic
308C2×#117C2×D1111yescharacteristic
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—112no—
321C2×C22⋊C8—112no—
322C2×C22⋊C8—224no—
323#381—21no—
324#380C2×D1112yes—
325#380C2×D1112yes—
326#379—21no—
327C4×C22⋊C4—22no—
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—82no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#39414yes—
358C4×C11C2×#12111yescharacteristic
359C4×C11C2×#12111yescharacteristic
360C4×C11C2×#12311yescharacteristic
361C4×C11C2×#12411yescharacteristic
362Dic11—42no—
363Dic11—44no—
364C25C22⋊D1111yescharacteristic
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×C4C22⋊D1111yescharacteristic
383C23×C4C22⋊D1112yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1111yescharacteristic
386C22×C8—114no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—112no—
390C22×C8—222no—
391C22×C8—222no—
392C22×C8—222no—
393C22×C8—222no—
394C22×C8—222no—
395#123—228no—
396C22⋊Q8—224no—
397C22⋊Q8—224no—
398#121—224no—
399#121—224no—
400#120—228no—
401C4×D4—2216no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—114no—
407#117—222no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1112yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—222no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—221no—
423#107—224no—
424#106—224no—
425#103—222no—
426#103—222no—
427#103—224no—
428#102—222no—
429#102—222no—
430#102—224no—
431C22⋊C8—224no—
432C22⋊C8—224no—
433#95—22no—
434#95—22no—
435C2×C11—24no—
436C2×C11—44no—
437C2×C11C2×#39411yescharacteristic
438C2×C11#300212yes—
439C2×C11#305011yescharacteristic
440C2×C11#305411yescharacteristic
441C2×C11#309112yes—
442D11—82no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—42no—
448C24—221no—
449C24C2×C22⋊D1112yes—
450C24C2×C22⋊D1111yescharacteristic
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—442no—
472C2×D4—444no—
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—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—224no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4#433912yes—
498C22×C4#433912yes—
499C22×C4D4×D1112yes—
500C22×C4D4×D1112yes—
501C22×C4D4×D1112yes—
502C22×C4#434112yes—
503C22×C4C2×C22⋊D1112yes—
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506C2×C8—112no—
507C2×C8—112no—
508C2×C8—228no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—222no—
514C2×C8—222no—
515C2×C8—222no—
516C2×C8—444no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—114no—
524C4⋊C4—228no—
525C4⋊C4—222no—
526C22⋊C4—44no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—44no—
530C22⋊C4—228no—
531C22⋊C4—228no—
532C22⋊C4—224no—
533C42—42no—
534C42—42no—
535C42—224no—
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—441no—
552C23—441no—
553C23—442no—
554C23—442no—
555C23#6698212yes—
556C23#6699012yes—
557C23#6699212yes—
558C23#6700314yes—
559C23C22×C22⋊D1111yescharacteristic
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—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—448no—
593C2×C4#6693614yes—
594C2×C4#6693714yes—
595C2×C4#6693714yes—
596C2×C4#6693814yes—
597C2×C4#6698212yes—
598C2×C4#6699012yes—
599C2×C4#6699212yes—
600C2×C4C2×#433911yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×D4×D1111yescharacteristic
604C2×C4C2×D4×D1111yescharacteristic
605C2×C4C2×#434111yescharacteristic
606C8—222no—
607C8—222no—
608C8—442no—
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#1062257214yes—
627C22C2×#6698211yescharacteristic
628C22C2×#6699011yescharacteristic
629C22C2×#6699211yescharacteristic
630C22C2×#6700312yes—
631C22#1062335312yes—
632C4—42no—
633C4—82no—
634C4—81no—
635C4—81no—
636C4—444no—
637C4—442no—
638C4#1062257214yes—
639C4C2×#6693611yescharacteristic
640C4C2×#6693711yescharacteristic
641C4C2×#6693711yescharacteristic
642C4C2×#6693811yescharacteristic
643C2—24no—
644C2—44no—
645C2—882no—
646C2C2×#1062257211yescharacteristic
647C2#1307783212yes—
648C2#1307819411yescharacteristic
649C2#1307822211yescharacteristic
650C2#1307852912yes—
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2280C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenter#2280D11
hypocenterC11#23479
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#10622611C2semidirect
3. C2×#10622615C2semidirect
4. C2×#10622615C2semidirect
5. C22×C22⋊(C11⋊C8)C2semidirect
6. #13069819C2semidirect
7. #13069812C2semidirect
8. #13069805C2semidirect
9. #13069798C2semidirect
10. #13068332C2semidirect
11. C11×#2280C2semidirect
37. C2×#66874C22semidirect
38. C2×#66874C22semidirect
39. C2×#66874C22semidirect
40. C2×#66873C22semidirect
41. C2×#66873C22semidirect
42. C2×#66873C22semidirect
43. C2×#66872C22semidirect
44. C2×#66871C22semidirect
45. #10622167C22semidirect
46. #10622167C22semidirect
102. C22×C11⋊C8D4semidirect
217. #2280D11semidirect
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×#106226112
C2×#106226152
C22×C22⋊(C11⋊C8)2
#130698192
#130698122
#130698052
#130697982
#130683322
C11×#22802
#2347911