Finite Group Databasebeta

← #14660204

Subgroups — #14660204

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622618C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4C2×#10622171C211yesmaximal, characteristic, complemented
5#13068335C211yesmaximal, characteristic, complemented
6C2×#10622169C211yesmaximal, characteristic, complemented
7C11×#2274C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C4×C11×C4⋊C4—22no—
16C4×C11×C4⋊C4—22no—
17C4×C11×C22⋊C4—22no—
18#10622619—22no—
19#10622619C414yescomplemented
20#10622618—22no—
21#10622618C414yescomplemented
22C2×#66874C412yescomplemented
23#10622579—22no—
24#10622579—22no—
25C2×#66873C412yescomplemented
26C2×#66870—22no—
27C2×#66869—22no—
28#10622171—22no—
29#10622169—22no—
30#10622167—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C2×#4339—21no—
35C2×#4339—21no—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339C2×C412yes—
45C2×#4339C2×C412yes—
46C22×D44C2×C411yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22C2×C411yescharacteristic
49C11×#117—21no—
50C11×#117—21no—
51C11×#117—21no—
52C11×#117—21no—
53C11×#117C2×C412yes—
54C11×#117C2×C412yes—
55C11×#117D412yes—
56C11×#117D412yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2×C412yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11—21no—
68C2×C42×C11—24no—
69C2×C42×C11D412yes—
70C2×C22⋊Dic11—21no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979C2×C412yes—
75C2×C4⋊Dic11—21no—
76C2×C4×Dic11—21no—
77C2×#4318—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318C2×C412yes—
89C22×C11⋊C8—21no—
90C22×C11⋊C8C2×C412yes—
91C11×#95—24no—
92#66874—24no—
93#66873—24no—
94#66870—28no—
95#66869—28no—
96#10954—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C23×D11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—82no—
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×C22⋊D11—22no—
120C2×C22⋊D11—22no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11—21no—
126C22×Dic11—41no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—22no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142#4339—41no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C4212yescomplemented
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C4212yescomplemented
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C22⋊C414yes—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4C22⋊C414yes—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—84no—
177C42×C11C22⋊C414yes—
178C22⋊Dic11—22no—
179C22⋊Dic11—41no—
180C4⋊Dic11—22no—
181C4⋊Dic11—41no—
182C4×Dic11—22no—
183C4×Dic11—41no—
184#4318—22no—
185#4318—22no—
186#4318—41no—
187#4318—41no—
188#4318—41no—
189#4318—41no—
190#4318—41no—
191#4318—41no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×#421—111no—
199C2×#417—111no—
200C2×#410—111no—
201#2274D1111yescharacteristic, complemented
202C2×#344—111no—
203#1736—111no—
204C2×H(3,ℤ/4)—111no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C2×C22⋊C411yescharacteristic
208C23×C11C4×D411yescharacteristic
209C23×C11C4×D411yescharacteristic
210C23×C11#12011yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11#12311yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—81no—
218C22×D11—81no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—82no—
228C2×C4×C11—82no—
229C2×C4×C11C2×C4211yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11#11711yescharacteristic
233C2×C4×C11#11711yescharacteristic
234C2×C4×C11#11711yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12411yescharacteristic
252C2×C4×C11#12411yescharacteristic
253C2×C4×C11#12411yescharacteristic
254C2×C4×C11#12611yescharacteristic
255C2×C4×C11#12611yescharacteristic
256C2×C4×C11#12711yescharacteristic
257C22⋊D11—42no—
258C22⋊D11—42no—
259C22⋊D11—42no—
260C22⋊D11—42no—
261C2×Dic11—22no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—42no—
265C2×Dic11—81no—
266C2×Dic11—81no—
267D44—22no—
268D44—22no—
269D44—41no—
270D44—41no—
271C4×D11—42no—
272C4×D11—42no—
273C4×D11—42no—
274C4×D11—42no—
275Dic22—22no—
276Dic22—22no—
277Dic22—41no—
278Dic22—41no—
279C11⋊C8—42no—
280C11⋊C8—42no—
281C22×#41—111no—
282C22×M16—111no—
283C22×M16—111no—
284C2×#117—111no—
285C2×#117C2×D1111yescharacteristic
286C2×#117C2×D1111yescharacteristic
287C22×C4⋊C4C2×D1111yescharacteristic
288#421—114no—
289#421—222no—
290C2×#104—222no—
291#417—222no—
292#417—222no—
293C2×#103—112no—
294C2×#102—112no—
295#410—114no—
296#410—222no—
297C2×#99—222no—
298C4×C4⋊C4—22no—
299C4×C4⋊C4—22no—
300C4×C22⋊C4—22no—
301#344—222no—
302#340—222no—
303H(3,ℤ/4)—222no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—41no—
314C22×C11C4×C22⋊C411yescharacteristic
315C22×C11#38611yescharacteristic
316C22×C11#38611yescharacteristic
317C22×C11#38611yescharacteristic
318C22×C11#38811yescharacteristic
319C22×C11#38811yescharacteristic
320C22×C11#39011yescharacteristic
321C2×D11—42no—
322C2×D11—82no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—82no—
326C4×C11—44no—
327C4×C11—44no—
328C4×C11—44no—
329C4×C11C4×C22⋊C411yescharacteristic
330C4×C11C4×C22⋊C411yescharacteristic
331C4×C11#38811yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#38811yescharacteristic
335C4×C11#39011yescharacteristic
336C4×C11#39011yescharacteristic
337Dic11—42no—
338Dic11—82no—
339C2×#41—112no—
340C2×#41—112no—
341C2×#41—221no—
342C2×#41—221no—
343C2×#41—221no—
344C2×#41—221no—
345C2×#41—221no—
346C2×#41—221no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C22×Q8—111no—
352C22×D4—111no—
353C22×D4—221no—
354C23×C4—21no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357C2×M16—112no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C22×C8—112no—
370C22×C8—221no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—112no—
376#117—221no—
377#117—221no—
378#117—221no—
379#117C4×D1112yes—
380#117C4×D1112yes—
381#117D4412yes—
382#117D4412yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C4×D1112yes—
390C2×C4⋊C4D4412yes—
391C2×C4⋊C4C22⋊D1112yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4C22⋊D1112yes—
395C2×C42—21no—
396C2×C42—24no—
397C2×C42—221no—
398C2×C42C22⋊D1112yes—
399#104—228no—
400#103—224no—
401#102—224no—
402#99—228no—
403#95—24no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11#143711yescharacteristic
411C2×C11#190411yescharacteristic
412C2×C11#190511yescharacteristic
413D11—82no—
414C24—221no—
415C24C2×C22⋊D1111yescharacteristic
416#41—222no—
417#41—222no—
418#41—222no—
419#41—222no—
420#41—222no—
421#41—222no—
422#41—222no—
423#41—222no—
424#41—441no—
425#41—441no—
426#41—441no—
427#41—441no—
428#41—441no—
429#41—441no—
430#41—441no—
431#41—441no—
432C2×Q8—112no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×D4—112no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—82no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4—441no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4#433911yescharacteristic
471C22×C4#433911yescharacteristic
472C22×C4#433911yescharacteristic
473C22×C4#433911yescharacteristic
474C22×C4#433911yescharacteristic
475C22×C4#433911yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478M16—222no—
479M16—222no—
480M16—441no—
481M16—441no—
482M16—441no—
483M16—441no—
484M16—441no—
485M16—441no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—222no—
489C2×C8—222no—
490C2×C8—441no—
491C2×C8—441no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—222no—
500C4⋊C4—441no—
501C4⋊C4(C2×D11)⋊C414yes—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—222no—
506C22⋊C4—441no—
507C22⋊C4(C2×D11)⋊C414yes—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—84no—
512C42—222no—
513C42—441no—
514C42(C2×D11)⋊C414yes—
515C11#1095411yescharacteristic, complemented, Sylow
516C23—41no—
517C23—41no—
518C23—222no—
519C23—441no—
520C23—441no—
521C23—881no—
522C23—881no—
523C23C2×(C2×D11)⋊C411yescharacteristic
524C23C4×C22⋊D1111yescharacteristic
525C23C4×C22⋊D1111yescharacteristic
526C23#6698211yescharacteristic
527C23#6698311yescharacteristic
528C23#6698311yescharacteristic
529C23#6700611yescharacteristic
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534D4—222no—
535D4—222no—
536D4—442no—
537D4—442no—
538D4—442no—
539D4—442no—
540D4—441no—
541D4—441no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—222no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—881no—
561C2×C4—881no—
562C2×C4C42×D1111yescharacteristic
563C2×C4#6692511yescharacteristic
564C2×C4#6692511yescharacteristic
565C2×C4#6692511yescharacteristic
566C2×C4C4×D4411yescharacteristic
567C2×C4C4×D4411yescharacteristic
568C2×C4C4×D4411yescharacteristic
569C2×C4C4×D4411yescharacteristic
570C2×C4C4×D4411yescharacteristic
571C2×C4C4×D4411yescharacteristic
572C2×C4#6692711yescharacteristic
573C2×C4#6692811yescharacteristic
574C2×C4#6692811yescharacteristic
575C2×C4#6692811yescharacteristic
576C2×C4#6692911yescharacteristic
577C2×C4#6692911yescharacteristic
578C2×C4C2×(C2×D11)⋊C411yescharacteristic
579C2×C4C2×(C2×D11)⋊C411yescharacteristic
580C2×C4C4×C22⋊D1111yescharacteristic
581C2×C4C4×C22⋊D1111yescharacteristic
582C2×C4C4×C22⋊D1111yescharacteristic
583C2×C4C4×C22⋊D1111yescharacteristic
584C2×C4#6698211yescharacteristic
585C2×C4#6698211yescharacteristic
586C2×C4#6698311yescharacteristic
587C2×C4#6698311yescharacteristic
588C2×C4#6698311yescharacteristic
589C2×C4#6698311yescharacteristic
590C8—442no—
591C8—442no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—442no—
603C22—882no—
604C22—882no—
605C22—881no—
606C22—881no—
607C22C4×(C2×D11)⋊C411yescharacteristic
608C22#1062255211yescharacteristic
609C22#1062255311yescharacteristic
610C22#1062255311yescharacteristic
611C22#1062282611yescharacteristic
612C22#1062282611yescharacteristic
613C22#1062282611yescharacteristic
614C4—44no—
615C4—44no—
616C4—44no—
617C4—442no—
618C4—882no—
619C4C4×(C2×D11)⋊C411yescharacteristic
620C4C4×(C2×D11)⋊C411yescharacteristic
621C4#1062255211yescharacteristic
622C4#1062255211yescharacteristic
623C4#1062255311yescharacteristic
624C4#1062255311yescharacteristic
625C4#1062255311yescharacteristic
626C4#1062255311yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—882no—
634C2#1306685411yescharacteristic
635C2#1306910311yescharacteristic
636C2#1306911011yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#2274C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#2274D11
hypocenterC11#10954
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
4. C2×#10622171C2semidirect
5. #13068335C2semidirect
6. C2×#10622169C2semidirect
7. C11×#2274C2semidirect
19. #10622619C4semidirect
21. #10622618C4semidirect
22. C2×#66874C4semidirect
25. C2×#66873C4semidirect
148. C2×D44C42semidirect
160. C2×Dic22C42semidirect
201. #2274D11semidirect
515. C11#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#106226182
C2×#106225792
C2×#106226192
C2×#106221712
#130683352
C2×#106221692
C11×#22742
#1095411