Finite Group Databasebeta

← #14720977

Subgroups — #14720977

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082667C211yesmaximal, characteristic
2#13077650C211yesmaximal, characteristic, complemented
3#13070978C211yesmaximal, characteristic, complemented
4#13067141C211yesmaximal, characteristic, complemented
5#13067134C212yesmaximal, complemented
6#13067127C211yesmaximal, characteristic, complemented
7#13067117C212yesmaximal, complemented
8#13067116C211yesmaximal, characteristic, complemented
9#13067104C212yesmaximal, complemented
10D11×#328C212yesmaximal, complemented
11C11×#1500C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13#10623238—22no—
14#10623225C412yescomplemented
15#10623208C412yescomplemented
16#10623189—22no—
17D11×C22⋊Q8C2212yes—
18#10623137C2212yes—
19#10623115C411yescharacteristic, complemented
20Q8×D44C411yescharacteristic, complemented
21#10623086C411yescharacteristic, complemented
22#10623082C411yescharacteristic, complemented
23#10623081—21no—
24#10623074—21no—
25#10623065—21no—
26#10623054—21no—
27C2×C4×D44—21no—
28C2×C4×D44C2211yescharacteristic
29#10623001C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C11×#376C2211yescharacteristic
32C4×C4⋊Dic11—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622539C2211yescharacteristic
35#10622449—22no—
36#10622339C2212yes—
37D11×C22⋊C8C2212yes—
38#10622301—21no—
39C8×D44—21no—
40#10622279—22no—
41#10622279C2212yes—
42D11×#95C2212yes—
43C11×#328C2211yescharacteristic
44C11×#328C2211yescharacteristic
45C11×#327C2211yescharacteristic
46C11×#327C2211yescharacteristic
47#10622176C2212yes—
48#10622175C2212yes—
49#10622105C2212yes—
50#10622105C2212yes—
51#10622090C2212yes—
52#10622090C2212yes—
53C2×Q8×D11C2×C412yescomplemented
54C2×#4341C2×C412yescomplemented
55C2×#4339—21no—
56C22×D44D411yescharacteristic
57C22×C4×D11—22no—
58C22×C4×D11C2312yes—
59C11×#126—21no—
60C11×#125C2×C411yescharacteristic, complemented
61C11×#124C2×C411yescharacteristic, complemented
62C11×#123—21no—
63C11×C22⋊Q8C2311yescharacteristic
64C11×#121C2311yescharacteristic
65C4×Q8×C11C2×C411yescharacteristic, complemented
66C4×D4×C11—21no—
67C4×D4×C11C2×C411yescharacteristic, complemented
68C11×#117—21no—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#66999C2×C412yescomplemented
72#66991C2×C412yescomplemented
73#66990—22no—
74D4×Dic11—22no—
75#66983—21no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4D412yes—
78#66979—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11D411yescharacteristic
82#66977—21no—
83#66977—21no—
84#66977C2312yes—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—22no—
87C2×#4313—22no—
88C2×C8×D11—22no—
89#66951—22no—
90#66951—22no—
91#66950—22no—
92#66950C2×C412yescomplemented
93#66950C2×C412yescomplemented
94#66949—22no—
95#66947—22no—
96#66945—22no—
97#66945C2×C412yescomplemented
98C4⋊C4×D11—22no—
99C4⋊C4×D11C2×C412yescomplemented
100#66943—22no—
101#66939—22no—
102#66938—22no—
103#66937—22no—
104#66936—22no—
105#66936—22no—
106(C22⋊D11)⋊C4—22no—
107(C22⋊D11)⋊C4—22no—
108C22⋊C4×D11—22no—
109#66931—22no—
110#66931—22no—
111#66928—21no—
112C4×D44—28no—
113C4×D44—21no—
114C4×D44C2×C411yescharacteristic
115C4×D44C2×C411yescharacteristic
116C4×D44C2×C412yes—
117C4×D44D412yes—
118C4×D44D411yescharacteristic
119C4×D44D411yescharacteristic
120#66923—21no—
121#66922—21no—
122#66922C2×C411yescharacteristic, complemented
123#66922C2×C411yescharacteristic, complemented
124C4×Dic22—21no—
125C4×Dic22—21no—
126C4×Dic22C2×C412yescomplemented
127C11×C4⋊C8—21no—
128C11×C22⋊C8C2311yescharacteristic
129C11×C22⋊C8C2311yescharacteristic
130C4×C8×C11—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134C11⋊#95—22no—
135C11⋊#95C2312yes—
136C22⋊(C11⋊C8)C2312yes—
137(C2×D11)⋊C8—22no—
138(C2×D11)⋊C8—22no—
139C4⋊(C11⋊C8)—21no—
140#66867—21no—
141#17548—111nomaximal, Sylow
142C23×D11C2×D412yes—
143C2×Q8×C11C22×C411yescharacteristic
144C2×D4×C11—21no—
145C2×D4×C11C22×C411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11C2×D412yes—
157Q8×D11—82no—
158#4341—82no—
159#4339—44no—
160C2×D44—24no—
161C2×D44C22⋊C411yescharacteristic
162C2×D44C22⋊C412yes—
163C2×D44C22⋊C411yescharacteristic
164C2×C4×D11—28no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—82no—
168C2×C4×D11—82no—
169C2×C4×D11—82no—
170C2×C4×D11C22×C412yes—
171C2×C4×D11C22×C412yes—
172C2×C4×D11C2×D412yes—
173C2×C4×D11C2×D412yes—
174C2×Dic22—22no—
175C2×Dic22—21no—
176C2×Dic22C22×C412yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C42×C11—24no—
191C42×C11—21no—
192C42×C11C22×C411yescharacteristic
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4C22⋊C412yes—
204(C2×D11)⋊C4C22⋊C412yes—
205(C2×D11)⋊C4C22⋊C412yes—
206(C2×D11)⋊C4C22⋊C412yes—
207C4⋊Dic11—24no—
208C4⋊Dic11—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11C22⋊C411yescharacteristic
214C4⋊Dic11C22⋊C411yescharacteristic
215C4⋊Dic11C22⋊C412yes—
216C4⋊Dic11C22×C412yes—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—22no—
221C4×Dic11—22no—
222C4×Dic11—22no—
223C4×Dic11—81no—
224C4×Dic11—82no—
225C2×C11⋊C8—22no—
226#4313—82no—
227C8×D11—82no—
228#3520—111no—
229#2974—111no—
230#2275—111no—
231#1509—111no—
232#1508—112no—
233#1506—111no—
234#1504—112no—
235#1503—111no—
236#1501—112no—
237#1500D1111yescharacteristic, complemented
238C2×#328—112no—
239C23×C11—21no—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—42no—
245C22×D11C2×C22⋊C412yes—
246C22×D11C2×C22⋊C412yes—
247Q8×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C22⋊D11—44no—
272C22⋊D11—82no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—82no—
280C2×Dic11C2×C22⋊C412yes—
281C2×Dic11C2×C22⋊C412yes—
282D44—24no—
283D44—22no—
284D44#10414yes—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—42no—
288C4×D11—42no—
289C4×D11—44no—
290C4×D11—82no—
291C4×D11—88no—
292Dic22—42no—
293Dic22—42no—
294Dic22—82no—
295C8×C11—41no—
296C8×C11—41no—
297C11⋊C8—42no—
298#556—111no—
299#554—221no—
300#552—112no—
301#551—222no—
302D4×Q8—111no—
303#548—112no—
304#547—111no—
305#547—111no—
306#546—221no—
307#542—221no—
308#539—222no—
309#533—111no—
310#529C2×D1111yescharacteristic
311#525—112no—
312C2×C22⋊Q8—112no—
313#520—221no—
314C2×C4×D4—111no—
315C2×C4×D4—221no—
316#436—221no—
317#435—222no—
318C8×D4—221no—
319#432—111no—
320#431C2×D1111yescharacteristic
321#407—112no—
322C2×C22⋊C8—112no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C22⋊C4—112no—
326C4×C22⋊C4—222no—
327#376C2×D1111yescharacteristic
328C2×#95—112no—
329#328—112no—
330#328—112no—
331#328—112no—
332#328—112no—
333#328—112no—
334#328C2×D1111yescharacteristic
335#328C2×D1111yescharacteristic
336#327—112no—
337#327C2×D1111yescharacteristic
338#327C2×D1111yescharacteristic
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C22×C22⋊C411yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57811yescharacteristic
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11C2×#10414yes—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11C2×#10412yes—
366Dic11—22no—
367Dic11—22no—
368Dic11—44no—
369Dic11—42no—
370Dic11—42no—
371C2×#41—112no—
372C2×#41—221no—
373C22×Q8—112no—
374C22×D4—111no—
375C23×C4—112no—
376C23×C4—222no—
377C2×M16—222no—
378C22×C8—222no—
379C4⋊Q8—111no—
380C4⋊Q8—111no—
381C4⋊Q8—221no—
382#126—21no—
383#126—222no—
384#126—222no—
385#125—222no—
386#125—221no—
387#125C4×D1111yescharacteristic, complemented
388#124—221no—
389#124—222no—
390#124C4×D1111yescharacteristic, complemented
391#123—21no—
392#123—222no—
393#123—222no—
394#123—222no—
395#123—222no—
396C22⋊Q8—112no—
397C22⋊Q8—112no—
398C22⋊Q8—112no—
399C22⋊Q8—112no—
400C22⋊Q8—222no—
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C22⋊Q8—221no—
405C22⋊Q8—221no—
406C22⋊Q8C22×D1111yescharacteristic
407#121—112no—
408#121—222no—
409#121—221no—
410#121C22×D1111yescharacteristic
411#120—222no—
412C4×Q8—112no—
413C4×Q8—221no—
414C4×Q8—221no—
415C4×Q8C4×D1111yescharacteristic, complemented
416C4×D4—21no—
417C4×D4—111no—
418C4×D4—111no—
419C4×D4—112no—
420C4×D4—111no—
421C4×D4—112no—
422C4×D4—111no—
423C4×D4—221no—
424C4×D4—228no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4C4×D1111yescharacteristic, complemented
429#117—21no—
430#117—112no—
431#117—222no—
432#117—221no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4—222no—
441C2×C42—21no—
442C2×C42—222no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—221no—
447C22⋊C8—112no—
448C22⋊C8—222no—
449C22⋊C8—222no—
450C22⋊C8C22×D1111yescharacteristic
451C22⋊C8C22×D1111yescharacteristic
452#97—221no—
453C4×C8—21no—
454#95—21no—
455#95—112no—
456#95—222no—
457#95C22×D1111yescharacteristic
458#95C22×D1111yescharacteristic
459C2×C11—21no—
460C2×C11—21no—
461C2×C11—81no—
462C2×C11#288311yescharacteristic
463C2×C11#289811yescharacteristic
464C2×C11C22×#10411yescharacteristic
465D11—24no—
466D11—42no—
467C24—112no—
468#41—444no—
469#41—882no—
470C2×Q8—112no—
471C2×Q8—222no—
472C2×Q8—221no—
473C2×Q8—882no—
474C2×Q8C2×C4×D1111yescharacteristic
475C2×D4—21no—
476C2×D4—111no—
477C2×D4—112no—
478C2×D4—111no—
479C2×D4—224no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4C2×C4×D1111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—228no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—882no—
497C22×C4—882no—
498C22×C4—882no—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502M16—882no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—222no—
506C2×C8—882no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—111no—
512C4⋊C4—112no—
513C4⋊C4—111no—
514C4⋊C4—112no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—224no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4C2×C4×D1111yescharacteristic
526C4⋊C4C2×C4×D1111yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—112no—
533C22⋊C4—112no—
534C22⋊C4—112no—
535C22⋊C4—112no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—228no—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C42—24no—
544C42—21no—
545C42—222no—
546C42—222no—
547C42—881no—
548C42—882no—
549C42C2×C4×D1111yescharacteristic
550C42C2×C4×D1111yescharacteristic
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C11#1754811yescharacteristic, complemented, Sylow
554C23—21no—
555C23—112no—
556C23—112no—
557C23—224no—
558C23—222no—
559C23—222no—
560C23—442no—
561C23C2×D4×D1111yescharacteristic
562Q8—41no—
563Q8—442no—
564Q8—442no—
565Q8—882no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—114no—
570D4—224no—
571D4—222no—
572D4—444no—
573D4—882no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—444no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—882no—
602C2×C4—888no—
603C2×C4—882no—
604C2×C4C22⋊C4×D1111yescharacteristic
605C2×C4C22⋊C4×D1111yescharacteristic
606C2×C4C22⋊C4×D1111yescharacteristic
607C2×C4C22⋊C4×D1111yescharacteristic
608C2×C4C22×C4×D1111yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C8—41no—
611C8—41no—
612C8—442no—
613C22—21no—
614C22—21no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—114no—
619C22—222no—
620C22—222no—
621C22—222no—
622C22—222no—
623C22—222no—
624C22—444no—
625C22—444no—
626C22C2×C22⋊C4×D1111yescharacteristic
627C22#1062330111yescharacteristic
628C22#1062330211yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—222no—
640C4—222no—
641C4—444no—
642C4—442no—
643C4—442no—
644C4D11×#10412yes—
645C2—21no—
646C2—21no—
647C2—81no—
648C2—224no—
649C2—442no—
650C2#1307707511yescharacteristic
651C2#1307714511yescharacteristic
652C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1500C2
socleC22×C11C22×C22⋊C4
prime radical#13082667C2
cosocleC22×C4×C11C24
hypercenter#1500D11
hypocenterC11#17548
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #13077650C2semidirect
3. #13070978C2semidirect
4. #13067141C2semidirect
5. #13067134C2semidirect
6. #13067127C2semidirect
7. #13067117C2semidirect
8. #13067116C2semidirect
9. #13067104C2semidirect
10. D11×#328C2semidirect
11. C11×#1500C2semidirect
14. #10623225C4semidirect
15. #10623208C4semidirect
19. #10623115C4semidirect
20. Q8×D44C4semidirect
21. #10623086C4semidirect
22. #10623082C4semidirect
53. C2×Q8×D11C2×C4semidirect
54. C2×#4341C2×C4semidirect
60. C11×#125C2×C4semidirect
61. C11×#124C2×C4semidirect
65. C4×Q8×C11C2×C4semidirect
67. C4×D4×C11C2×C4semidirect
71. #66999C2×C4semidirect
72. #66991C2×C4semidirect
92. #66950C2×C4semidirect
93. #66950C2×C4semidirect
97. #66945C2×C4semidirect
99. C4⋊C4×D11C2×C4semidirect
122. #66922C2×C4semidirect
123. #66922C2×C4semidirect
126. C4×Dic22C2×C4semidirect
237. #1500D11semidirect
387. #125C4×D11semidirect
390. #124C4×D11semidirect
415. C4×Q8C4×D11semidirect
428. C4×D4C4×D11semidirect
553. C11#17548semidirect

Maximal subgroups

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

subgroupindex
#130826672
#130776502
#130709782
#130671412
#130671342
#130671272
#130671172
#130671162
#130671042
D11×#3282
C11×#15002
#1754811