Finite Group Databasebeta

← #14659209

Subgroups — #14659209

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2C2×#10622745C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4#13068335C211yesmaximal, characteristic, complemented
5#13068327C211yesmaximal, characteristic, complemented
6#13068326C211yesmaximal, characteristic, complemented
7C11×#1736C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×C4×C22⋊D11—22no—
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623035—22no—
17#10623035—22no—
18#10623035—22no—
19#10623035—22no—
20C2×#66946—21no—
21C2×#66945C412yescomplemented
22C2×C4⋊C4×D11C412yescomplemented
23C2×#66940—21no—
24C2×#66888—21no—
25#10622745—22no—
26#10622745C414yescomplemented
27C2×#66887—21no—
28#10622619—22no—
29#10622619C414yescomplemented
30C2×#66870—22no—
31C11×#340—22no—
32#10622193—22no—
33#10622167—22no—
34#10622161—22no—
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11D412yes—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339C2×C412yes—
47C2×#4339C2×C412yes—
48C2×#4339D412yes—
49C2×#4339Q812yes—
50C22×D44D411yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11C2×C412yes—
53C22×Dic22D411yescharacteristic
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16C2×C412yescomplemented
60C22×C8×C11—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117C2×C412yescomplemented
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4D412yes—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C4×C22⋊D11—28no—
77C4×C22⋊D11—28no—
78C2×(C2×D11)⋊C4—22no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979—21no—
83#66979—21no—
84#66979C2×C412yescomplemented
85#66979D412yes—
86#66979D412yes—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×C4⋊Dic11C2×C411yescharacteristic
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318C2×C412yescomplemented
100C22×C11⋊C8—21no—
101#66946—24no—
102#66946—24no—
103#66945—24no—
104#66945—24no—
105C4⋊C4×D11—24no—
106C4⋊C4×D11—24no—
107#66940—24no—
108#66940—24no—
109#66888—24no—
110#66887—24no—
111#66870—28no—
112#10765—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11C22⋊C412yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—41no—
119C22×C4×C11—82no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q811yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C2×C22⋊D11—22no—
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—22no—
138C2×C22⋊D11C22⋊C414yes—
139C2×C22⋊D11C4⋊C414yes—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—41no—
143C22×Dic11C22⋊C412yes—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149#4339—22no—
150#4339—22no—
151#4339—22no—
152#4339—22no—
153#4339—22no—
154#4339—22no—
155#4339—22no—
156#4339—22no—
157#4339—22no—
158#4339—22no—
159#4339—22no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C22⋊C412yes—
165C2×D44C4⋊C412yes—
166C2×C4×D11—28no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—84no—
172C2×C4×D11C4214yes—
173C2×C4×D11C4⋊C414yes—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22C22⋊C412yes—
179C2×Dic22C4⋊C412yes—
180C11×M16—22no—
181C11×M16—22no—
182C11×M16—41no—
183C11×M16—41no—
184C2×C8×C11—22no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4C22⋊C414yes—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—41no—
195C42×C11—22no—
196C42×C11—41no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11—22no—
200C22⋊Dic11—41no—
201(C2×D11)⋊C4—28no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—22no—
205C4⋊Dic11—41no—
206C4⋊Dic11C22⋊C412yes—
207C4⋊Dic11C22⋊C412yes—
208Dic11⋊C4—28no—
209C4×Dic11—28no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11—41no—
214#4318—22no—
215#4318—22no—
216#4318—41no—
217#4318—41no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—41no—
220C2×C11⋊C8—41no—
221C2×#520—111no—
222C2×#413—111no—
223C2×#410—111no—
224#1736—111no—
225#1736D1111yescharacteristic, complemented
226#1733—111no—
227#1733—111no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C2×C22⋊C411yescharacteristic
231C23×C11C2×C22⋊C411yescharacteristic
232C23×C11C2×C4⋊C411yescharacteristic
233C23×C11#12011yescharacteristic
234C23×C11#12011yescharacteristic
235C23×C11#12311yescharacteristic
236C23×C11#12311yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11#9514yes—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11—81no—
248C2×C4×C11—81no—
249C2×C4×C11C2×C4211yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C4⋊C411yescharacteristic
254C2×C4×C11C2×C4⋊C411yescharacteristic
255C2×C4×C11#11711yescharacteristic
256C2×C4×C11#11711yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11C22⋊Q811yescharacteristic
272C2×C4×C11C22⋊Q811yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11#12311yescharacteristic
276C2×C4×C11#12311yescharacteristic
277C22⋊D11—24no—
278C22⋊D11—24no—
279C22⋊D11—24no—
280C22⋊D11—24no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—81no—
289C2×Dic11—81no—
290C2×Dic11#9514yes—
291D44—22no—
292D44—22no—
293D44—22no—
294D44—22no—
295C4×D11—24no—
296C4×D11—24no—
297C4×D11—24no—
298C4×D11—24no—
299C4×D11—88no—
300Dic22—22no—
301Dic22—22no—
302Dic22—22no—
303Dic22—22no—
304C8×C11—42no—
305C11⋊C8—42no—
306C22×#41—111no—
307C22×M16—111no—
308C22×M16C2×D1111yescharacteristic
309#520—222no—
310#520—222no—
311#520—222no—
312#520—222no—
313C2×C4×Q8—221no—
314C2×C4×D4—221no—
315C2×C4×D4—222no—
316C2×#117—111no—
317C2×#117—112no—
318C2×#117—111no—
319C2×#117C2×D1111yescharacteristic
320C22×C4⋊C4—112no—
321C22×C4⋊C4C2×D1111yescharacteristic
322#413—114no—
323#413—222no—
324C2×#101—221no—
325C2×#100—221no—
326#410—114no—
327#410—222no—
328C2×#99—222no—
329#340—22no—
330#340—222no—
331#339—222no—
332#339—222no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×#9511yescharacteristic
344C22×C11#37911yescharacteristic
345C22×C11#38111yescharacteristic
346C22×C11#38511yescharacteristic
347C22×C11#38511yescharacteristic
348C22×C11#38611yescharacteristic
349C22×C11#38611yescharacteristic
350C2×D11—24no—
351C2×D11—44no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—44no—
355C4×C11—44no—
356C4×C11—82no—
357C4×C11C4×C22⋊C411yescharacteristic
358C4×C11C4×C22⋊C411yescharacteristic
359C4×C11#38011yescharacteristic
360C4×C11#38011yescharacteristic
361C4×C11#38511yescharacteristic
362C4×C11#38511yescharacteristic
363C4×C11#38611yescharacteristic
364C4×C11#38611yescharacteristic
365Dic11—24no—
366Dic11—42no—
367Dic11—42no—
368Dic11—82no—
369C2×#41—112no—
370C2×#41—112no—
371C2×#41—112no—
372C2×#41—112no—
373C2×#41—221no—
374C2×#41—221no—
375C2×#41—221no—
376C2×#41—221no—
377C2×#41—221no—
378C2×#41—221no—
379C2×#41—221no—
380C2×#41—221no—
381C22×Q8—111no—
382C22×D4—112no—
383C22×D4—111no—
384C23×C4—21no—
385C23×C4—112no—
386C23×C4—222no—
387C23×C4C22×D1111yescharacteristic
388C2×M16—21no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—112no—
394C2×M16—221no—
395C2×M16—221no—
396C2×M16—221no—
397C2×M16—221no—
398C2×M16—221no—
399C2×M16C4×D1112yescomplemented
400C22×C8—21no—
401C22×C8—221no—
402C4×Q8—224no—
403C4×Q8—224no—
404C4×D4—224no—
405C4×D4—224no—
406C4×D4—228no—
407C4×D4—228no—
408#117—21no—
409#117—21no—
410#117—21no—
411#117—112no—
412#117—112no—
413#117—112no—
414#117—224no—
415#117—221no—
416#117—221no—
417#117—224no—
418#117—221no—
419#117—221no—
420#117—221no—
421#117C4×D1112yescomplemented
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—224no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—224no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C4×D1112yes—
433C2×C4⋊C4D4412yes—
434C2×C4⋊C4C22⋊D1112yes—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C42—21no—
440C2×C42—222no—
441C2×C42—221no—
442C2×C42—221no—
443#101—224no—
444#100—224no—
445#99—228no—
446C2×C11—21no—
447C2×C11—21no—
448C2×C11—21no—
449C2×C11—21no—
450C2×C11—21no—
451C2×C11—21no—
452C2×C11C22⋊#9511yescharacteristic
453C2×C11#179511yescharacteristic
454C2×C11#179611yescharacteristic
455D11—44no—
456C24—112no—
457C24D4×D1111yescharacteristic
458#41—222no—
459#41—222no—
460#41—222no—
461#41—222no—
462#41—222no—
463#41—222no—
464#41—222no—
465#41—222no—
466#41—222no—
467#41—222no—
468#41—222no—
469#41—222no—
470#41—222no—
471#41—222no—
472#41—222no—
473#41—222no—
474C2×Q8—112no—
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×D4—114no—
481C2×D4—114no—
482C2×D4—112no—
483C2×D4—112no—
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—222no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—41no—
496C22×C4—82no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—114no—
500C22×C4—228no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—441no—
508C22×C4—884no—
509C22×C4C2×C4×D1111yescharacteristic
510C22×C4C2×C4×D1111yescharacteristic
511C22×C4C2×C4×D1111yescharacteristic
512C22×C4C2×D4411yescharacteristic
513C22×C4#433911yescharacteristic
514C22×C4#433911yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4D4×D1111yescharacteristic
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4#434111yescharacteristic
520C22×C4Q8×D1111yescharacteristic
521C22×C4#434311yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523M16—22no—
524M16—22no—
525M16—41no—
526M16—41no—
527M16—222no—
528M16—222no—
529M16—441no—
530M16—441no—
531C2×C8—22no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—222no—
535C2×C8—441no—
536C2×C8—441no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—41no—
542C4⋊C4—112no—
543C4⋊C4—112no—
544C4⋊C4—228no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—222no—
548C4⋊C4—441no—
549C4⋊C4(C2×D11)⋊C414yes—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—228no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—222no—
556C22⋊C4—441no—
557C42—22no—
558C42—41no—
559C42—228no—
560C42—222no—
561C42—222no—
562C42—222no—
563C42—441no—
564C11#1076511yescharacteristic, complemented, Sylow
565C23—41no—
566C23—41no—
567C23—114no—
568C23—222no—
569C23—222no—
570C23—442no—
571C23—442no—
572C23C22⋊C4×D1111yescharacteristic
573C23C22⋊C4×D1111yescharacteristic
574C23#6693511yescharacteristic
575C23#6693611yescharacteristic
576C23C4⋊C4×D1111yescharacteristic
577C23#6694711yescharacteristic
578C23#6699011yescharacteristic
579Q8—222no—
580Q8—222no—
581Q8—222no—
582Q8—222no—
583D4—224no—
584D4—224no—
585D4—224no—
586D4—224no—
587D4—222no—
588D4—222no—
589D4—222no—
590D4—222no—
591C2×C4—24no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—114no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—888no—
611C2×C4—881no—
612C2×C4—881no—
613C2×C4C42×D1111yescharacteristic
614C2×C4#6692511yescharacteristic
615C2×C4C4×D4411yescharacteristic
616C2×C4C4×D4411yescharacteristic
617C2×C4C22⋊C4×D1111yescharacteristic
618C2×C4C22⋊C4×D1111yescharacteristic
619C2×C4(C22⋊D11)⋊C411yescharacteristic
620C2×C4(C22⋊D11)⋊C411yescharacteristic
621C2×C4#6693511yescharacteristic
622C2×C4#6693611yescharacteristic
623C2×C4#6693711yescharacteristic
624C2×C4#6693711yescharacteristic
625C2×C4C4⋊C4×D1111yescharacteristic
626C2×C4C4⋊C4×D1111yescharacteristic
627C2×C4#6694511yescharacteristic
628C2×C4#6694611yescharacteristic
629C2×C4#6694611yescharacteristic
630C2×C4#6694711yescharacteristic
631C2×C4#6694811yescharacteristic
632C2×C4#6694911yescharacteristic
633C2×C4#6694911yescharacteristic
634C2×C4#6695011yescharacteristic
635C2×C4C2×(C2×D11)⋊C411yescharacteristic
636C2×C4C4×C22⋊D1111yescharacteristic
637C2×C4C4×C22⋊D1111yescharacteristic
638C2×C4#6699011yescharacteristic
639C2×C4#6699111yescharacteristic
640C2×C4#6699911yescharacteristic
641C8—42no—
642C8—442no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—224no—
654C22—444no—
655C22—444no—
656C22—442no—
657C22—442no—
658C22D11×#9511yescharacteristic
659C22#1062227711yescharacteristic
660C22#1062227811yescharacteristic
661C22#1062228111yescharacteristic
662C22#1062256811yescharacteristic
663C22#1062256911yescharacteristic
664C22#1062260211yescharacteristic
665C4—44no—
666C4—82no—
667C4—224no—
668C4—442no—
669C4—442no—
670C4—882no—
671C4#1062227811yescharacteristic
672C4#1062227911yescharacteristic
673C4#1062228011yescharacteristic
674C4#1062228111yescharacteristic
675C4C4×(C2×D11)⋊C411yescharacteristic
676C4#1062256911yescharacteristic
677C4#1062260011yescharacteristic
678C4#1062260211yescharacteristic
679C2—21no—
680C2—21no—
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—444no—
686C2(C2×D11)⋊#9511yescharacteristic
687C2#1306858311yescharacteristic
688C2#1306858811yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1736C2
socleC22×C11#379
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#1736D11
hypocenterC11#10765
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13068335C2semidirect
5. #13068327C2semidirect
6. #13068326C2semidirect
7. C11×#1736C2semidirect
21. C2×#66945C4semidirect
22. C2×C4⋊C4×D11C4semidirect
26. #10622745C4semidirect
29. #10622619C4semidirect
59. C2×C11×M16C2×C4semidirect
64. C11×#117C2×C4semidirect
84. #66979C2×C4semidirect
99. C2×#4318C2×C4semidirect
225. #1736D11semidirect
399. C2×M16C4×D11semidirect
421. #117C4×D11semidirect
564. C11#10765semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
C2×#106227452
C2×#106226192
#130683352
#130683272
#130683262
C11×#17362
#1076511