Finite Group Databasebeta

← #14755280

Subgroups — #14755280

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C22×#66901C211yesmaximal, characteristic, complemented
3#13077133C211yesmaximal, characteristic, complemented
4#13071104C211yesmaximal, characteristic, complemented
5#13068992C214yesmaximal, complemented
6#13068985C214yesmaximal, complemented
7#13068355C211yesmaximal, characteristic, complemented
8C2×#10622170C211yesmaximal, characteristic, complemented
9C11×#3428C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C11×#520—22no—
13C11×#520C2214yes—
14C11×#519—21no—
15C11×#518—21no—
16C11×#518—22no—
17C4×C11×#41—22no—
18C4×C11×#41—22no—
19C2×C11×#117—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×#67004C2212yes—
23#10623353—24no—
24#10623353C418yescomplemented
25C2×#67003—22no—
26C2×#67002C2212yes—
27C2×#66995—21no—
28C2×#66985—21no—
29C22×C4×Dic11C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C2×#66901—24no—
33C2×#66901C2214yes—
34#10622617C2212yescomplemented
35#10622615—22no—
36#10622614C2212yescomplemented
37#10622601C2212yescomplemented
38#10622587C2212yescomplemented
39#10622579—22no—
40#10622571—22no—
41C4×(C2×D11)⋊C4—22no—
42#10622170C2214yescomplemented
43#10622168C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41C2×C414yes—
49C2×C11×#41D414yes—
50C2×C11×#41D412yes—
51C2×C11×#41C2312yes—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C23×Dic11—21no—
59C2×#4339—22no—
60C2×#4339—21no—
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—22no—
64C2×#4339—21no—
65C2×#4339—22no—
66C2×#4339C2×C414yescomplemented
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×Dic22C2311yescharacteristic
70C4×Q8×C11—24no—
71C4×Q8×C11—24no—
72C4×D4×C11—28no—
73C4×D4×C11—24no—
74C4×D4×C11—24no—
75C4×D4×C11—28no—
76C11×#117—24no—
77C11×#117—24no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117—24no—
85C11×#117D412yes—
86C11×#117C2312yes—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4D412yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—24no—
94C2×C42×C11—21no—
95C2×C42×C11D412yes—
96#67004—24no—
97#67004C2×C418yescomplemented
98#67003—216no—
99#67002—24no—
100#67002C2×C418yescomplemented
101C2×#4326—22no—
102#66995—28no—
103C2×#4325—22no—
104C2×#4324—22no—
105#66985—28no—
106C2×#4323—22no—
107C2×(C2×D11)⋊C4—24no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11C2312yes—
112C2×#4318—21no—
113C2×#4318—22no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318C2×C414yescomplemented
118C2×#4318C2312yes—
119C2×#4318C2312yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66901—28no—
123C11⋊#95—24no—
124#66874—24no—
125#66873—24no—
126#20942—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C11×#41—24no—
131C11×#41—24no—
132C11×#41—24no—
133C11×#41—24no—
134C11×#41—24no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41C22⋊C418yescomplemented
138C11×#41C22×C414yes—
139C11×#41C2×D414yes—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11C22⋊C414yescomplemented
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—24no—
145C2×D4×C11—22no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11C22⋊C414yescomplemented
151C2×D4×C11C2×D412yes—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—24no—
156C22×C4×C11—22no—
157C22×C4×C11—28no—
158C22×C4×C11—22no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—24no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11—42no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—44no—
177C22×Dic11—42no—
178#4339—24no—
179#4339—24no—
180#4339—24no—
181#4339—24no—
182#4339—42no—
183#4339—42no—
184#4339—42no—
185#4339—42no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44C22×C412yes—
192C2×C4×D11—24no—
193C2×C4×D11—41no—
194C2×C4×D11—41no—
195C2×C4×D11—42no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22C22×C412yes—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4C2×D414yes—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C42×C11—28no—
213C42×C11—22no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—22no—
217#4326—28no—
218#4325—28no—
219#4324—28no—
220#4323—28no—
221(C2×D11)⋊C4—48no—
222C4×Dic11—22no—
223C4×Dic11—22no—
224C4×Dic11—42no—
225#4318—24no—
226#4318—22no—
227#4318—22no—
228#4318—22no—
229#4318—42no—
230#4318C22×C414yes—
231C2×C11⋊C8—24no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—42no—
235C2×#575—111no—
236#3428D1111yescharacteristic, complemented
237C22×#104—111no—
238#2896—111no—
239#2297—111no—
240#1883—114no—
241#1882—114no—
242#1742—111no—
243C2×#339—111no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—42no—
247C23×C11—82no—
248C23×C11C4×D412yes—
249C23×C11#12011yescharacteristic
250C23×C11#12011yescharacteristic
251C23×C11#12112yes—
252C23×C11C22×D411yescharacteristic
253C22×D11—22no—
254C22×D11—44no—
255C22×D11—41no—
256C22×D11—41no—
257Q8×C11—22no—
258Q8×C11—24no—
259Q8×C11C2×C22⋊C414yes—
260D4×C11—24no—
261D4×C11—24no—
262D4×C11—28no—
263D4×C11—22no—
264D4×C11—24no—
265D4×C11C2×C22⋊C414yes—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—28no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—44no—
274C2×C4×C11—82no—
275C2×C4×C11—88no—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C4×D412yes—
279C2×C4×C11C4×D412yes—
280C2×C4×C11C4×D412yes—
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11#12112yes—
284C2×C4×C11#12112yes—
285C2×C4×C11#12112yes—
286C2×C4×C11#12312yes—
287C2×C4×C11#12312yes—
288C2×C4×C11C23×C411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C22⋊D11—44no—
295C22⋊D11—44no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—42no—
299C2×Dic11—48no—
300C2×Dic11—41no—
301C2×Dic11—42no—
302C2×Dic11—41no—
303D44—22no—
304D44—22no—
305D44—41no—
306D44—41no—
307C4×D11—44no—
308C4×D11—44no—
309Dic22—22no—
310Dic22—22no—
311Dic22—41no—
312Dic22—41no—
313C11⋊C8—24no—
314C11⋊C8—42no—
315C22×#41—111no—
316C22×#41C2×D1111yescharacteristic
317#575—118no—
318#575—224no—
319C2×#137—112no—
320C2×#137—221no—
321C2×AGL(1,ℤ/8)—112no—
322C2×AGL(1,ℤ/8)—221no—
323C2×#135—222no—
324C22×M16—111no—
325C22×M16—111no—
326#520—22no—
327#520C2×D1114yes—
328#519—21no—
329#518—21no—
330#518—22no—
331C4×#41—22no—
332C4×#41—22no—
333C2×#117—22no—
334C2×#117C2×D1111yescharacteristic
335C2×#117C2×D1111yescharacteristic
336C22×C42—111no—
337C2×#104—114no—
338C2×#104—224no—
339#419—112no—
340#418—112no—
341#417—222no—
342#416—222no—
343#391—112no—
344#390—112no—
345#386—222no—
346C4×C22⋊C4—222no—
347#343—114no—
348#339—114no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—24no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—44no—
356C22×C11—84no—
357C22×C11#38612yes—
358C22×C11#38612yes—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C2×D11—44no—
363C2×D11—42no—
364C2×D11—82no—
365C2×D11—82no—
366C4×C11—24no—
367C4×C11—44no—
368C4×C11—44no—
369C4×C11#38612yes—
370C4×C11#38612yes—
371C4×C11C22×C22⋊C411yescharacteristic
372C4×C11C2×C4×D411yescharacteristic
373C4×C11C2×#12111yescharacteristic
374C4×C11C2×#12311yescharacteristic
375Dic11—44no—
376Dic11—42no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—114no—
382C2×#41—222no—
383C2×#41—222no—
384C2×#41—222no—
385C2×#41—221no—
386C2×#41—221no—
387C2×#41—221no—
388C2×#41—221no—
389C2×#41C4×D1114yes—
390C2×#41D4414yes—
391C2×#41C22⋊D1112yes—
392C2×#41C22×D1112yes—
393C22×Q8—111no—
394C22×Q8C22⋊D1111yescharacteristic
395C22×D4—21no—
396C22×D4—111no—
397C22×D4—221no—
398C22×D4C22⋊D1111yescharacteristic
399C23×C4—21no—
400C23×C4—221no—
401C23×C4—221no—
402C23×C4C22×D1111yescharacteristic
403#137—118no—
404#137—224no—
405#137—228no—
406AGL(1,ℤ/8)—118no—
407AGL(1,ℤ/8)—224no—
408AGL(1,ℤ/8)—228no—
409#135—2216no—
410C2×Q16—222no—
411C2×SD16—222no—
412C2×SD16—222no—
413C2×D8—222no—
414C2×M16—114no—
415C2×M16—112no—
416C2×M16—112no—
417C2×M16—222no—
418C2×M16—221no—
419C2×M16—221no—
420C2×M16—222no—
421C2×M16—222no—
422C22×C8—221no—
423C22×C8—221no—
424C4×Q8—24no—
425C4×Q8—24no—
426C4×D4—28no—
427C4×D4—24no—
428C4×D4—24no—
429C4×D4—28no—
430#117—24no—
431#117—24no—
432#117—21no—
433#117—21no—
434#117—21no—
435#117—21no—
436#117—21no—
437#117—21no—
438#117—24no—
439#117C22⋊D1112yes—
440#117C22×D1112yes—
441C2×C4⋊C4—24no—
442C2×C4⋊C4C22⋊D1112yes—
443C2×C4⋊C4C22×D1112yes—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—224no—
447C2×C22⋊C4C22⋊D1112yes—
448C2×C42—24no—
449C2×C42—21no—
450C2×C42—112no—
451C2×C42—222no—
452C2×C42—222no—
453C2×C42—221no—
454C2×C42C22⋊D1112yes—
455#104—228no—
456#103—224no—
457#102—224no—
458#95—224no—
459C2×C11—21no—
460C2×C11—21no—
461C2×C11—22no—
462C2×C11—22no—
463C2×C11—44no—
464C2×C11C2×#38611yescharacteristic
465C2×C11#301812yes—
466D11—82no—
467C24—21no—
468C24—221no—
469C24C2×C22⋊D1111yescharacteristic
470#41—24no—
471#41—24no—
472#41—24no—
473#41—24no—
474#41—24no—
475#41—22no—
476#41—22no—
477#41—224no—
478#41—224no—
479#41—224no—
480#41—224no—
481#41—442no—
482#41—442no—
483#41—442no—
484#41—442no—
485#41(C2×D11)⋊C418yescomplemented
486#41C2×C4×D1114yes—
487#41C2×D4414yes—
488C2×Q8—22no—
489C2×Q8—21no—
490C2×Q8—112no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8(C2×D11)⋊C414yescomplemented
497C2×Q8C2×C22⋊D1112yes—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—112no—
505C2×D4—224no—
506C2×D4—221no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—221no—
511C2×D4—442no—
512C2×D4—441no—
513C2×D4—441no—
514C2×D4(C2×D11)⋊C414yescomplemented
515C2×D4C2×C22⋊D1112yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—221no—
524C22×C4—222no—
525C22×C4—224no—
526C22×C4—444no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4—441no—
530C22×C4—441no—
531C22×C4C2×C4×D1112yes—
532C22×C4C2×D4412yes—
533C22×C4#433912yes—
534C22×C4#433912yes—
535C22×C4C2×C22⋊D1114yes—
536C22×C4C2×C22⋊D1111yescharacteristic
537C22×C4C2×C22⋊D1111yescharacteristic
538C22×C4C2×C22⋊D1111yescharacteristic
539C22×C4C2×C22⋊D1111yescharacteristic
540C22×C4C2×C22⋊D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542Q16—228no—
543SD16—228no—
544SD16—228no—
545D8—228no—
546M16—114no—
547M16—224no—
548M16—222no—
549M16—222no—
550M16—222no—
551M16—442no—
552C2×C8—224no—
553C2×C8—222no—
554C2×C8—222no—
555C2×C8—442no—
556C4⋊C4—28no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4C2×C22⋊D1114yes—
561C22⋊C4—28no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—448no—
567C42—28no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—222no—
573C42—222no—
574C42—442no—
575C11#2094211yescharacteristic, complemented, Sylow
576C23—22no—
577C23—24no—
578C23—42no—
579C23—82no—
580C23—222no—
581C23—444no—
582C23—441no—
583C23—441no—
584C23C4×C22⋊D1112yes—
585C23#6698312yes—
586C23#6700611yescharacteristic
587C23#6700611yescharacteristic
588C23C22×C22⋊D1111yescharacteristic
589Q8—22no—
590Q8—24no—
591Q8—222no—
592Q8—222no—
593Q8—441no—
594Q8—441no—
595Q8C2×(C2×D11)⋊C414yes—
596D4—24no—
597D4—24no—
598D4—28no—
599D4—22no—
600D4—24no—
601D4—222no—
602D4—222no—
603D4—444no—
604D4—444no—
605D4—441no—
606D4—441no—
607D4C2×(C2×D11)⋊C414yes—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—28no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—44no—
616C2×C4—82no—
617C2×C4—88no—
618C2×C4—224no—
619C2×C4—222no—
620C2×C4—442no—
621C2×C4—448no—
622C2×C4—442no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—444no—
626C2×C4—444no—
627C2×C4C2×(C2×D11)⋊C412yes—
628C2×C4C2×(C2×D11)⋊C412yes—
629C2×C4C4×C22⋊D1112yes—
630C2×C4C4×C22⋊D1112yes—
631C2×C4C4×C22⋊D1112yes—
632C2×C4#6698212yes—
633C2×C4#6698212yes—
634C2×C4#6698312yes—
635C2×C4#6698312yes—
636C2×C4#6698312yes—
637C2×C4#6700611yescharacteristic
638C2×C4#6700611yescharacteristic
639C2×C4C22×C4×D1111yescharacteristic
640C2×C4C22×D4411yescharacteristic
641C2×C4C2×#433911yescharacteristic
642C2×C4C2×#433911yescharacteristic
643C2×C4C22×C22⋊D1111yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C8—224no—
646C8—442no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—44no—
654C22—84no—
655C22—444no—
656C22—442no—
657C22—882no—
658C22—882no—
659C22#1062282612yes—
660C22#1062282612yes—
661C22C2×C4×C22⋊D1111yescharacteristic
662C22C2×#6698311yescharacteristic
663C22C2×#6700611yescharacteristic
664C4—24no—
665C4—44no—
666C4—44no—
667C4—444no—
668C4—442no—
669C4#1062282612yes—
670C4#1062282612yes—
671C4C22×(C2×D11)⋊C411yescharacteristic
672C4C2×C4×C22⋊D1111yescharacteristic
673C4C2×#6698211yescharacteristic
674C4C2×#6698311yescharacteristic
675C2—21no—
676C2—22no—
677C2—21no—
678C2—22no—
679C2—44no—
680C2—882no—
681C2C2×#1062282611yescharacteristic
682C2#1307796512yes—
subgroupG/H
centerC2×C4#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3428C2
socleC22×C11C2×#120
prime radicalC2×#10623353C2
cosocleC22×C4×C11C24
hypercenter#3428D11
hypocenterC11#20942
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3428

Complements

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

NH ≅ G/Ntype
2. C22×#66901C2semidirect
3. #13077133C2semidirect
4. #13071104C2semidirect
5. #13068992C2semidirect
6. #13068985C2semidirect
7. #13068355C2semidirect
8. C2×#10622170C2semidirect
9. C11×#3428C2semidirect
24. #10623353C4semidirect
34. #10622617C22semidirect
36. #10622614C22semidirect
37. #10622601C22semidirect
38. #10622587C22semidirect
42. #10622170C22semidirect
43. #10622168C22semidirect
66. C2×#4339C2×C4semidirect
97. #67004C2×C4semidirect
100. #67002C2×C4semidirect
117. C2×#4318C2×C4semidirect
137. C11×#41C22⋊C4semidirect
142. C2×Q8×C11C22⋊C4semidirect
150. C2×D4×C11C22⋊C4semidirect
236. #3428D11semidirect
485. #41(C2×D11)⋊C4semidirect
496. C2×Q8(C2×D11)⋊C4semidirect
514. C2×D4(C2×D11)⋊C4semidirect
575. C11#20942semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C22×#669012
#130771332
#130711042
#130689922
#130689852
#130683552
C2×#106221702
C11×#34282
#2094211