Finite Group Databasebeta

← #14781202

Subgroups — #14781202

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622618C211yesmaximal, characteristic
2C2×#10622618C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4#13069785C218yesmaximal, complemented
5C2×#10622171C211yesmaximal, characteristic, complemented
6#13068326C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C11×#3458C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C11×#544—22no—
11C11×#544—22no—
12C11×#544—22no—
13C11×#543—22no—
14C11×#533—22no—
15C11×#533—22no—
16C11×#533C2214yescomplemented
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10622619—22no—
24#10622619C2214yes—
25#10622618—22no—
26#10622618—22no—
27#10622618—22no—
28#10622618C2214yes—
29C2×#66870—22no—
30C2×#66869—22no—
31C2×#66869C2214yes—
32#10622171C2214yescomplemented
33#10622169C2214yescomplemented
34#10622161C2214yescomplemented
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C2×#4339—21no—
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×#4339—21no—
47C2×#4339Q812yescomplemented
48C2×#4339C2312yes—
49C22×D44Q811yescharacteristic, complemented
50C22×C4×D11—21no—
51C22×Dic22Q811yescharacteristic, complemented
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×#125—24no—
56C11×#125—24no—
57C11×#125—24no—
58C11×C22⋊Q8—28no—
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—28no—
61C4×Q8×C11—28no—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117D412yes—
69C11×#117D412yes—
70C11×#117D412yes—
71C11×#117D412yes—
72C11×#117C2312yes—
73C11×#117C2312yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D412yes—
80C2×C42×C11—21no—
81C2×C42×C11D412yes—
82C2×C42×C11C2312yes—
83C2×C22⋊Dic11—21no—
84#66979—21no—
85#66979—21no—
86#66979—21no—
87#66979C2312yes—
88C2×C4⋊Dic11—21no—
89C2×C4×Dic11—21no—
90C2×#4318—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318C2312yes—
101C2×#4318C2312yes—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104#66870—28no—
105#66869—28no—
106#66869—28no—
107#23472—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C2×Q8×C11—28no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×Q811yescharacteristic
120C22×C4×C11C2×Q811yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134C22×Dic11—21no—
135C22×Dic11—41no—
136#4339—22no—
137#4339—22no—
138#4339—22no—
139#4339—22no—
140#4339—22no—
141#4339—22no—
142#4339—22no—
143#4339—22no—
144#4339—41no—
145#4339—41no—
146#4339—41no—
147#4339—41no—
148#4339—41no—
149#4339—41no—
150#4339—41no—
151#4339—41no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C2×Q812yes—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C2×Q812yes—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4C2×D414yes—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11C2×D414yes—
190C42×C11C2×D414yes—
191C22⋊Dic11—22no—
192C22⋊Dic11—41no—
193C4⋊Dic11—22no—
194C4⋊Dic11—41no—
195C4×Dic11—22no—
196C4×Dic11—41no—
197#4318—22no—
198#4318—22no—
199#4318—22no—
200#4318—22no—
201#4318—41no—
202#4318—41no—
203#4318—41no—
204#4318—41no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—41no—
208C2×C11⋊C8—41no—
209C2×C11⋊C8—41no—
210C2×C11⋊C8—41no—
211#3458D1111yescharacteristic, complemented
212C2×#421—111no—
213C2×#421—111no—
214C2×#410—111no—
215#2031—118no—
216C2×#344—111no—
217#1733—111no—
218C2×H(3,ℤ/4)—111no—
219C23×C11—81no—
220C23×C11#12011yescharacteristic
221C23×C11#12011yescharacteristic
222C23×C11C22⋊Q811yescharacteristic
223C23×C11C22⋊Q811yescharacteristic
224C23×C11#12411yescharacteristic
225C23×C11#12411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231Q8×C11—88no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—82no—
236C2×C4×C11—82no—
237C2×C4×C11—82no—
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11C22⋊Q811yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11C22⋊Q811yescharacteristic
246C2×C4×C11C22⋊Q811yescharacteristic
247C2×C4×C11C22⋊Q811yescharacteristic
248C2×C4×C11C22⋊Q811yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11#12411yescharacteristic
251C2×C4×C11#12411yescharacteristic
252C2×C4×C11#12411yescharacteristic
253C2×C4×C11#12411yescharacteristic
254C2×C4×C11#12411yescharacteristic
255C2×C4×C11#12411yescharacteristic
256C2×C4×C11#12411yescharacteristic
257C2×C4×C11#12411yescharacteristic
258C2×C4×C11#12411yescharacteristic
259C2×C4×C11#12411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×Q811yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C22⋊D11—42no—
267C22⋊D11—42no—
268C22⋊D11—42no—
269C22⋊D11—42no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—82no—
275D44—22no—
276D44—22no—
277D44—41no—
278D44—41no—
279C4×D11—42no—
280C4×D11—42no—
281C4×D11—42no—
282C4×D11—42no—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289C22×#41—111no—
290C22×M16—111no—
291C22×M16—111no—
292#544—22no—
293#544—22no—
294#544—22no—
295#543—22no—
296#533—22no—
297#533—22no—
298#533C2×D1114yescomplemented
299C2×#117—111no—
300C2×#117C2×D1111yescharacteristic
301C2×#117C2×D1111yescharacteristic
302C2×#117C2×D1111yescharacteristic
303#421—114no—
304#421—222no—
305#421—222no—
306#421—222no—
307C2×#104—114no—
308C2×#104—222no—
309#410—114no—
310#410—222no—
311C2×#99—222no—
312#344—114no—
313#339—114no—
314H(3,ℤ/4)—114no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11#39311yescharacteristic
323C22×C11#39311yescharacteristic
324C22×C11#39311yescharacteristic
325C22×C11#39311yescharacteristic
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×C22⋊Q811yescharacteristic
328C22×C11C2×#12411yescharacteristic
329C2×D11—42no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C4×C11—44no—
334C4×C11—44no—
335C4×C11—44no—
336C4×C11#39311yescharacteristic
337C4×C11#39311yescharacteristic
338C4×C11#39311yescharacteristic
339C4×C11#39311yescharacteristic
340C4×C11C2×C22⋊Q811yescharacteristic
341C4×C11C2×C22⋊Q811yescharacteristic
342C4×C11C2×#12411yescharacteristic
343C4×C11C2×#12411yescharacteristic
344Dic11—42no—
345Dic11—82no—
346C2×#41—112no—
347C2×#41—112no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—221no—
354C2×#41—221no—
355C2×#41—221no—
356C2×#41—221no—
357C2×#41—221no—
358C22×Q8—111no—
359C22×D4—111no—
360C22×D4—221no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—112no—
364C2×M16—112no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16—221no—
375C22×C8—221no—
376C22×C8—221no—
377C4⋊Q8—24no—
378C4⋊Q8—24no—
379C4⋊Q8—24no—
380#125—24no—
381#125—24no—
382#125—24no—
383C22⋊Q8—28no—
384C22⋊Q8—28no—
385C22⋊Q8—28no—
386C4×Q8—28no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—112no—
394#117—221no—
395#117—221no—
396#117—221no—
397#117C22⋊D1112yes—
398#117C22⋊D1112yes—
399#117C22⋊D1112yes—
400#117C22⋊D1112yes—
401#117C22×D1112yes—
402#117C22×D1112yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—221no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4C22⋊D1112yes—
411C2×C42—21no—
412C2×C42—221no—
413C2×C42C22⋊D1112yes—
414C2×C42C22×D1112yes—
415#104—228no—
416#104—228no—
417#99—228no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11C2×#39311yescharacteristic
426D11—82no—
427C24—221no—
428C24C2×C22⋊D1111yescharacteristic
429#41—222no—
430#41—222no—
431#41—222no—
432#41—222no—
433#41—222no—
434#41—222no—
435#41—222no—
436#41—222no—
437#41—441no—
438#41—441no—
439#41—441no—
440#41—441no—
441#41—441no—
442#41—441no—
443#41—441no—
444#41—441no—
445C2×Q8—28no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×D4—112no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—441no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—221no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—441no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4Q8×D1111yescharacteristic
476C22×C4Q8×D1111yescharacteristic
477C22×C4#434311yescharacteristic
478C22×C4#434311yescharacteristic
479C22×C4#434311yescharacteristic
480C22×C4#434311yescharacteristic
481C22×C4#434311yescharacteristic
482C22×C4#434311yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—222no—
490M16—222no—
491M16—222no—
492M16—222no—
493M16—441no—
494M16—441no—
495M16—441no—
496M16—441no—
497C2×C8—222no—
498C2×C8—222no—
499C2×C8—441no—
500C2×C8—441no—
501C2×C8—441no—
502C2×C8—441no—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—222no—
513C4⋊C4—441no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—222no—
520C22⋊C4—441no—
521C22⋊C4C2×C22⋊D1114yes—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—222no—
527C42—441no—
528C42C2×C22⋊D1114yes—
529C42C2×C22⋊D1114yes—
530C11#2347211yescharacteristic, complemented, Sylow
531C23—81no—
532C23—222no—
533C23—441no—
534C23—441no—
535C23—882no—
536C23#6699911yescharacteristic
537C23#6699911yescharacteristic
538C23#6700011yescharacteristic
539C23#6700011yescharacteristic
540C23#6700611yescharacteristic
541C23#6700611yescharacteristic
542C23C22×C22⋊D1111yescharacteristic
543Q8—88no—
544Q8—222no—
545Q8—222no—
546Q8—441no—
547Q8—441no—
548D4—222no—
549D4—222no—
550D4—442no—
551D4—442no—
552D4—442no—
553D4—442no—
554D4—441no—
555D4—441no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—222no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—882no—
571C2×C4#6699911yescharacteristic
572C2×C4#6699911yescharacteristic
573C2×C4#6699911yescharacteristic
574C2×C4#6699911yescharacteristic
575C2×C4#6699911yescharacteristic
576C2×C4#6699911yescharacteristic
577C2×C4#6699911yescharacteristic
578C2×C4#6699911yescharacteristic
579C2×C4#6699911yescharacteristic
580C2×C4#6699911yescharacteristic
581C2×C4#6700011yescharacteristic
582C2×C4#6700011yescharacteristic
583C2×C4#6700011yescharacteristic
584C2×C4#6700011yescharacteristic
585C2×C4#6700011yescharacteristic
586C2×C4#6700011yescharacteristic
587C2×C4#6700011yescharacteristic
588C2×C4#6700011yescharacteristic
589C2×C4#6700011yescharacteristic
590C2×C4#6700011yescharacteristic
591C2×C4#6700611yescharacteristic
592C2×C4#6700611yescharacteristic
593C2×C4C2×Q8×D1111yescharacteristic
594C2×C4C2×#434311yescharacteristic
595C2×C4C2×#434311yescharacteristic
596C2×C4C2×#434311yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C8—442no—
600C8—442no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—442no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22#1062284411yescharacteristic
613C22#1062284411yescharacteristic
614C22#1062284411yescharacteristic
615C22#1062284411yescharacteristic
616C22C2×#6699911yescharacteristic
617C22C2×#6700011yescharacteristic
618C22C2×#6700611yescharacteristic
619C4—44no—
620C4—44no—
621C4—44no—
622C4—442no—
623C4—882no—
624C4#1062284411yescharacteristic
625C4#1062284411yescharacteristic
626C4#1062284411yescharacteristic
627C4#1062284411yescharacteristic
628C4C2×#6699911yescharacteristic
629C4C2×#6699911yescharacteristic
630C4C2×#6700011yescharacteristic
631C4C2×#6700011yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—882no—
640C2C2×#1062284411yescharacteristic
subgroupG/H
centerC4C2×#67000
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC2×C11C2×#393
prime radicalC22×#4339C22
hypercenter#3458D11
hypocenterC11#23472
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
4. #13069785C2semidirect
5. C2×#10622171C2semidirect
6. #13068326C2semidirect
7. C2×#10622169C2semidirect
8. C11×#3458C2semidirect
16. C11×#533C22semidirect
32. #10622171C22semidirect
33. #10622169C22semidirect
34. #10622161C22semidirect
47. C2×#4339Q8semidirect
49. C22×D44Q8semidirect
51. C22×Dic22Q8semidirect
211. #3458D11semidirect
298. #533C2×D11semidirect
530. C11#23472semidirect

Maximal subgroups

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

subgroupindex
C2×#106226182
C2×#106226192
#130697852
C2×#106221712
#130683262
C2×#106221692
C11×#34582
#2347211