Finite Group Databasebeta

← #14721582

Subgroups — #14721582

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13067170C212yesmaximal, complemented
4#13067152C212yesmaximal, complemented
5#13067148C211yesmaximal, characteristic, complemented
6#13067144C211yesmaximal, characteristic, complemented
7#13067139C212yesmaximal, complemented
8#13067135C211yesmaximal, characteristic, complemented
9#13067131C211yesmaximal, characteristic, complemented
10#13067105C212yesmaximal, complemented
11C11×#2357C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13#10623335—21no—
14#10623322C2212yes—
15C2×#66983C2211yescharacteristic
16C2×#66977C2211yescharacteristic
17#10623096C412yescomplemented
18#10623087—22no—
19#10623083C412yescomplemented
20#10623081C412yescomplemented
21#10623072C412yescomplemented
22#10623071—22no—
23#10623046—21no—
24#10623025—21no—
25#10623017—21no—
26#10623010C2212yes—
27C11×#390—21no—
28C11×#388—21no—
29C11×#388—21no—
30C11×#382C2211yescharacteristic, complemented
31C11×#381C2211yescharacteristic
32C11×#381C2211yescharacteristic, complemented
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4C2211yescharacteristic, complemented
35C4×C11×C22⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4C2211yescharacteristic, complemented
37#10622820C2211yescharacteristic
38#10622820C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2212yescomplemented
40#10622624—22no—
41#10622624—22no—
42#10622539C2212yescomplemented
43#10622090C2212yescomplemented
44#10622090C2212yescomplemented
45#10622090C2212yescomplemented
46#10622090C2212yescomplemented
47#10622089C2212yes—
48#10622089C2212yes—
49#10622089C2212yes—
50#10622089C2212yes—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C2×#4339C2×C412yes—
56C22×D44C2×C411yescharacteristic
57C22×Dic22C2×C411yescharacteristic
58C4×D4×C11C2×C412yes—
59C4×D4×C11C2×C412yes—
60C4×D4×C11D412yes—
61C4×D4×C11D412yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75#67006—22no—
76C2×C22⋊Dic11—21no—
77#66992—22no—
78#66992—22no—
79#66990—22no—
80#66988—22no—
81#66983—21no—
82#66983—21no—
83#66983C2×C412yes—
84#66983C2×C412yes—
85#66983C2312yes—
86#66982—22no—
87#66982—22no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C2×(C2×D11)⋊C4—21no—
92#66979C2×C412yes—
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95#66977—21no—
96#66977—21no—
97#66977C2×C412yes—
98#66977C2×C412yes—
99#66977C2312yes—
100C2×Dic11⋊C4—21no—
101C2×#4318—21no—
102C2×#4318—21no—
103C22×C11⋊C8—22no—
104#66951—22no—
105#66949—22no—
106#66947—22no—
107#66942—22no—
108#66938—22no—
109#66937—22no—
110#66936—22no—
111(C22⋊D11)⋊C4—22no—
112(C22⋊D11)⋊C4—22no—
113C22⋊C4×D11—22no—
114#66932—22no—
115#66930—22no—
116#66929—22no—
117#66928C2×C412yes—
118C4×D44C2×C412yes—
119#66925—22no—
120#66923C2×C412yes—
121C4×Dic22C2×C412yes—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95C2311yescharacteristic
126C11×#95C2311yescharacteristic
127C11×#95C2311yescharacteristic
128C11×#95C2311yescharacteristic
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—21no—
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)C2312yes—
133C22⋊(C11⋊C8)C2312yes—
134C4⋊(C11⋊C8)—22no—
135#66867—22no—
136#17625—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11C22⋊C412yes—
143C2×D4×C11C22⋊C412yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C412yes—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170#4339—82no—
171C2×D44—21no—
172C2×D44—81no—
173C2×D44C22×C412yes—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×Dic22—21no—
177C2×Dic22—81no—
178C2×Dic22C22×C412yes—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C22⋊C412yes—
182C11×C4⋊C4C22⋊C412yes—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—81no—
186C11×C22⋊C4—81no—
187C11×C22⋊C4C22⋊C412yes—
188C11×C22⋊C4C22⋊C412yes—
189C11×C22⋊C4C22⋊C412yes—
190C11×C22⋊C4C22⋊C412yes—
191C42×C11—42no—
192C42×C11—81no—
193C42×C11—81no—
194C42×C11C22×C412yes—
195C42×C11C2×D412yes—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218#4318—81no—
219#4318—81no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—82no—
223#3505—111no—
224#2973—111no—
225#2357D1111yescharacteristic, complemented
226#1516—112no—
227#1512—112no—
228#1511—111no—
229#1510—111no—
230#1509—112no—
231#1508—111no—
232#1507—111no—
233#1501—112no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C2×C22⋊C411yescharacteristic
243C23×C11C2×C22⋊C412yes—
244C23×C11C2×C22⋊C411yescharacteristic
245C23×C11C22×D411yescharacteristic
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—81no—
249C22×D11—81no—
250D4×C11—42no—
251D4×C11—42no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C411yescharacteristic
279C2×C4×C11C2×C22⋊C412yes—
280C2×C4×C11C2×C22⋊C411yescharacteristic
281C2×C4×C11C23×C411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C22⋊D11—44no—
284C22⋊D11—42no—
285C22⋊D11—42no—
286C22⋊D11—82no—
287C22⋊D11—82no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—42no—
292C2×Dic11—81no—
293C2×Dic11—81no—
294D44—42no—
295D44—81no—
296C4×D11—82no—
297C4×D11—82no—
298Dic22—42no—
299Dic22—81no—
300C11⋊C8—42no—
301C11⋊C8—42no—
302#553—112no—
303#553—222no—
304#552—112no—
305#551—222no—
306#548—112no—
307#546—112no—
308#539—221no—
309#538—221no—
310#534—221no—
311#529—112no—
312#525—112no—
313C2×C22⋊Q8—111no—
314C2×#121—111no—
315#518—221no—
316C2×C4×D4C2×D1111yescharacteristic
317#435—222no—
318#435—222no—
319#432—112no—
320#407—111no—
321#407—111no—
322C2×C22⋊C8—112no—
323#390—21no—
324#388—21no—
325#388—21no—
326#382C2×D1111yescharacteristic, complemented
327#381C2×D1111yescharacteristic
328#381C2×D1111yescharacteristic, complemented
329C4×C4⋊C4—21no—
330C4×C4⋊C4C2×D1111yescharacteristic, complemented
331C4×C22⋊C4C2×D1111yescharacteristic
332C4×C22⋊C4C2×D1111yescharacteristic, complemented
333#328—112no—
334#328—112no—
335#328—112no—
336#328—112no—
337#327—112no—
338#327—112no—
339#327—112no—
340#327—112no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—22no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—22no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11C22×C22⋊C411yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—162no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—22no—
367C4×C11—21no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11—81no—
374Dic11—42no—
375Dic11—42no—
376Dic11—42no—
377C2×#41—112no—
378C22×Q8—111no—
379C22×D4—111no—
380C22×D4—221no—
381C22×D4C22⋊D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×M16—221no—
385C2×M16—221no—
386C22×C8—222no—
387#126—222no—
388#126—222no—
389#126—222no—
390#125—112no—
391#125—222no—
392#124—112no—
393#124—222no—
394#123—222no—
395#123—222no—
396#123—222no—
397#123—222no—
398#123—222no—
399C22⋊Q8—112no—
400C22⋊Q8—112no—
401C22⋊Q8—112no—
402C22⋊Q8—221no—
403C22⋊Q8—221no—
404C22⋊Q8—222no—
405#121—112no—
406#121—112no—
407#121—112no—
408#121—222no—
409#121—222no—
410#121—221no—
411#121—221no—
412#121—222no—
413#120—222no—
414#120—222no—
415C4×Q8—112no—
416C4×D4—112no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4C4×D1112yes—
423C4×D4C4×D1112yes—
424C4×D4D4412yes—
425C4×D4D4412yes—
426#117—112no—
427#117—222no—
428#117—222no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4C22⋊D1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—222no—
442C2×C22⋊C4C22⋊D1111yescharacteristic
443C2×C22⋊C4C22⋊D1111yescharacteristic
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C22×D1111yescharacteristic
448C4⋊C8—222no—
449C22⋊C8—112no—
450C22⋊C8—112no—
451C22⋊C8—222no—
452C22⋊C8—221no—
453C22⋊C8—221no—
454#97—222no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95C22×D1111yescharacteristic
459#95C22×D1111yescharacteristic
460#95C22×D1111yescharacteristic
461#95C22×D1111yescharacteristic
462C2×C11—21no—
463C2×C11—21no—
464C2×C11—41no—
465C2×C11—41no—
466C2×C11—42no—
467C2×C11#288311yescharacteristic
468C2×C11#289611yescharacteristic
469C2×C11#290111yescharacteristic
470D11—82no—
471C24—221no—
472C24C2×C22⋊D1111yescharacteristic
473C24C2×C22⋊D1111yescharacteristic
474#41—882no—
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—881no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—112no—
481C2×D4—222no—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—222no—
485C2×D4—221no—
486C2×D4—442no—
487C2×D4—442no—
488C2×D4—881no—
489C2×D4(C2×D11)⋊C412yes—
490C2×D4(C2×D11)⋊C412yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4C2×C4×D1111yescharacteristic
503C22×C4C2×C4×D1111yescharacteristic
504C22×C4C2×C4×D1112yes—
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4412yes—
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513M16—881no—
514M16—881no—
515C2×C8—222no—
516C2×C8—222no—
517C2×C8—882no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—112no—
521C4⋊C4—112no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4(C2×D11)⋊C412yes—
531C4⋊C4(C2×D11)⋊C412yes—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4(C2×D11)⋊C412yes—
547C22⋊C4(C2×D11)⋊C412yes—
548C22⋊C4(C2×D11)⋊C412yes—
549C22⋊C4(C2×D11)⋊C412yes—
550C42—42no—
551C42—81no—
552C42—81no—
553C42—222no—
554C42—222no—
555C42C2×C4×D1112yes—
556C42C2×D4412yes—
557C11#1762511yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—222no—
567C23—442no—
568C23—881no—
569C23—881no—
570C23C2×(C2×D11)⋊C411yescharacteristic
571C23C2×(C2×D11)⋊C412yes—
572C23C2×(C2×D11)⋊C411yescharacteristic
573C23C22×C22⋊D1111yescharacteristic
574Q8—442no—
575Q8—881no—
576D4—42no—
577D4—42no—
578D4—442no—
579D4—444no—
580D4—442no—
581D4—442no—
582D4—881no—
583D4—882no—
584D4—882no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—442no—
613C2×C4—882no—
614C2×C4—882no—
615C2×C4—881no—
616C2×C4—881no—
617C2×C4C2×(C2×D11)⋊C412yes—
618C2×C4C2×(C2×D11)⋊C412yes—
619C2×C4C2×(C2×D11)⋊C412yes—
620C2×C4C2×(C2×D11)⋊C411yescharacteristic
621C2×C4C2×(C2×D11)⋊C411yescharacteristic
622C2×C4C22×C4×D1111yescharacteristic
623C2×C4C22×D4411yescharacteristic
624C8—442no—
625C8—442no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—22no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—22no—
634C22—21no—
635C22—22no—
636C22—21no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—442no—
642C22—442no—
643C22—442no—
644C22—1762no—
645C22C22×(C2×D11)⋊C411yescharacteristic
646C22#1062335311yescharacteristic
647C22#1062335311yescharacteristic
648C4—21no—
649C4—21no—
650C4—22no—
651C4—21no—
652C4—21no—
653C4—22no—
654C4—22no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—442no—
660C4—442no—
661C4—442no—
662C2—21no—
663C2—21no—
664C2—41no—
665C2—41no—
666C2—42no—
667C2—882no—
668C2#1307707611yescharacteristic
669C2#1307713311yescharacteristic
670C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2357C2
socleC22×C11C22×C22⋊C4
prime radical#13082455C2
cosocleC22×C4×C11C24
hypercenter#2357D11
hypocenterC11#17625
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13067170C2semidirect
4. #13067152C2semidirect
5. #13067148C2semidirect
6. #13067144C2semidirect
7. #13067139C2semidirect
8. #13067135C2semidirect
9. #13067131C2semidirect
10. #13067105C2semidirect
11. C11×#2357C2semidirect
17. #10623096C4semidirect
19. #10623083C4semidirect
20. #10623081C4semidirect
21. #10623072C4semidirect
30. C11×#382C22semidirect
32. C11×#381C22semidirect
34. C4×C11×C4⋊C4C22semidirect
36. C4×C11×C22⋊C4C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
42. #10622539C22semidirect
43. #10622090C22semidirect
44. #10622090C22semidirect
45. #10622090C22semidirect
46. #10622090C22semidirect
225. #2357D11semidirect
326. #382C2×D11semidirect
328. #381C2×D11semidirect
330. C4×C4⋊C4C2×D11semidirect
332. C4×C22⋊C4C2×D11semidirect
557. C11#17625semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130776452
#130671702
#130671522
#130671482
#130671442
#130671392
#130671352
#130671312
#130671052
C11×#23572
#1762511