Finite Group Databasebeta

← #14721566

Subgroups — #14721566

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic
2#13071556C211yesmaximal, characteristic, complemented
3#13067194C212yesmaximal, complemented
4#13067160C212yesmaximal, complemented
5#13067150C211yesmaximal, characteristic, complemented
6#13067146C211yesmaximal, characteristic, complemented
7#13067137C211yesmaximal, characteristic, complemented
8#13067133C211yesmaximal, characteristic, complemented
9#13067121C212yesmaximal, complemented
10#13067103C212yesmaximal, complemented
11C11×#2975C211yesmaximal, 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×#436—22no—
28C11×#436—22no—
29C11×#431C2212yescomplemented
30C11×#407C2211yescharacteristic
31C11×#407C2211yescharacteristic
32C11×#407C2212yescomplemented
33#10622833—21no—
34#10622825C2211yescharacteristic, complemented
35#10622824C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic, complemented
38#10622594—21no—
39#10622564—21no—
40C22⋊C4×Dic11—21no—
41#10622550C2211yescharacteristic, complemented
42#10622545C2211yescharacteristic, complemented
43#10622108C2212yes—
44#10622108C2212yes—
45#10622108C2212yes—
46#10622108C2212yes—
47#10622105C2212yescomplemented
48#10622105C2212yescomplemented
49#10622105C2212yescomplemented
50#10622105C2212yescomplemented
51C22×D4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C23×Dic11—21no—
56C2×#4339C2×C412yes—
57C22×D44C2×C411yescharacteristic, complemented
58C22×Dic22C2×C411yescharacteristic, complemented
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—22no—
62C4×D4×C11C2×C412yes—
63C4×D4×C11C2×C412yes—
64C4×D4×C11D412yes—
65C4×D4×C11D412yes—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70#67006—22no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66992—22no—
76#66992—22no—
77#66990—22no—
78#66988—22no—
79#66983—21no—
80#66983—21no—
81#66983C2×C412yes—
82#66983C2×C412yescomplemented
83#66983C2312yes—
84#66982—22no—
85#66982—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C2×(C2×D11)⋊C4—21no—
90#66979C2×C412yes—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2×C411yescharacteristic, complemented
93C2×C4⋊Dic11C2×C411yescharacteristic, complemented
94#66977—21no—
95#66977—21no—
96#66977C2×C412yes—
97#66977C2×C412yescomplemented
98#66977C2312yes—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102#66951—22no—
103#66949—22no—
104#66947—22no—
105#66942—22no—
106#66938—22no—
107#66937—22no—
108#66936—22no—
109(C22⋊D11)⋊C4—22no—
110(C22⋊D11)⋊C4—22no—
111C22⋊C4×D11—22no—
112#66932—22no—
113#66930—22no—
114#66929—22no—
115#66928C2×C412yescomplemented
116C4×D44C2×C412yescomplemented
117#66925—22no—
118#66923C2×C412yescomplemented
119C4×Dic22C2×C412yescomplemented
120C11×C4⋊C8—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8C2312yes—
125C11×C22⋊C8C2312yes—
126C4×C8×C11—22no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95C2311yescharacteristic
133C11⋊#95C2311yescharacteristic
134C11⋊#95C2311yescharacteristic
135C11⋊#95C2311yescharacteristic
136#17623—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—81no—
145C22×C4×C11—81no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—22no—
160C2×C22⋊D11—22no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—81no—
173#4339—82no—
174C2×D44—21no—
175C2×D44—81no—
176C2×D44C22×C412yes—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×Dic22—21no—
180C2×Dic22—81no—
181C2×Dic22C22×C412yes—
182C11×M16—81no—
183C11×M16—81no—
184C11×M16—82no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C412yes—
189C11×C22⋊C4C22⋊C412yes—
190C11×C22⋊C4C22⋊C412yes—
191C11×C22⋊C4C22⋊C412yes—
192C11×C22⋊C4C22⋊C412yes—
193C42×C11C22×C412yes—
194C42×C11C2×D412yes—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11—42no—
200C22⋊Dic11—42no—
201C22⋊Dic11—81no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—22no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—81no—
211C4⋊Dic11C22×C412yes—
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221C4×Dic11—42no—
222C4×Dic11—81no—
223#3505—111no—
224#2975D1111yescharacteristic, complemented
225#2353—111no—
226#1521—112no—
227#1513—112no—
228#1511—111no—
229#1510—111no—
230#1508—111no—
231#1507—111no—
232#1504—112no—
233#1500—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—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C22⋊D11—44no—
272C22⋊D11—42no—
273C22⋊D11—42no—
274C22⋊D11—82no—
275C22⋊D11—82no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—81no—
293C2×Dic11—81no—
294C2×Dic11—84no—
295D44—42no—
296D44—81no—
297C4×D11—82no—
298C4×D11—82no—
299Dic22—42no—
300Dic22—81no—
301C8×C11—42no—
302C8×C11—42no—
303#553—112no—
304#553—222no—
305#552—112no—
306#551—222no—
307#548—112no—
308#546—112no—
309#539—221no—
310#538—221no—
311#534—221no—
312#529—112no—
313#525—112no—
314C2×C22⋊Q8—111no—
315C2×#121—111no—
316#518—221no—
317C2×C4×D4C2×D1111yescharacteristic
318#436—22no—
319#436—22no—
320#431C2×D1112yescomplemented
321#407C2×D1111yescharacteristic
322#407C2×D1111yescharacteristic
323#407C2×D1112yescomplemented
324#388—221no—
325#387—221no—
326#386—221no—
327#383—111no—
328#381—111no—
329#380—111no—
330C4×C22⋊C4—111no—
331C4×C22⋊C4—221no—
332#376—111no—
333C2×#95—111no—
334#328—112no—
335#328—112no—
336#328—112no—
337#328—112no—
338#327—112no—
339#327—112no—
340#327—112no—
341#327—112no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—22no—
347C22×C11—21no—
348C22×C11—22no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—22no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11C22×C22⋊C411yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57511yescharacteristic
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—162no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—22no—
368C4×C11—21no—
369C4×C11—22no—
370C4×C11—22no—
371Dic11—42no—
372Dic11—42no—
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C2×#41—112no—
379C22×Q8—111no—
380C22×D4—111no—
381C22×D4—221no—
382C22×D4D4411yescharacteristic
383C23×C4—221no—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—22no—
389#126—222no—
390#126—222no—
391#126—222no—
392#125—112no—
393#125—222no—
394#124—112no—
395#124—222no—
396#123—222no—
397#123—222no—
398#123—222no—
399#123—222no—
400#123—222no—
401C22⋊Q8—112no—
402C22⋊Q8—112no—
403C22⋊Q8—112no—
404C22⋊Q8—221no—
405C22⋊Q8—221no—
406C22⋊Q8—222no—
407#121—112no—
408#121—112no—
409#121—112no—
410#121—222no—
411#121—222no—
412#121—221no—
413#121—221no—
414#121—222no—
415#120—222no—
416#120—222no—
417C4×Q8—112no—
418C4×D4—112no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—222no—
424C4×D4C4×D1112yes—
425C4×D4C4×D1112yes—
426C4×D4C22⋊D1112yes—
427C4×D4C22⋊D1112yes—
428#117—112no—
429#117—222no—
430#117—222no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4D4411yescharacteristic
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4D4411yescharacteristic
443C2×C22⋊C4D4411yescharacteristic
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C4⋊C8—22no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—22no—
451C22⋊C8C22×D1112yes—
452C22⋊C8C22×D1112yes—
453C4×C8—22no—
454#95—111no—
455#95—111no—
456#95—111no—
457#95—111no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11—21no—
464C2×C11—21no—
465C2×C11—41no—
466C2×C11—42no—
467C2×C11—41no—
468C2×C11#288311yescharacteristic
469C2×C11#289611yescharacteristic
470C2×C11#290111yescharacteristic
471D11—82no—
472C24—221no—
473C24C2×D4411yescharacteristic
474C24C2×D4411yescharacteristic
475#41—882no—
476C2×Q8—112no—
477C2×Q8—221no—
478C2×Q8—881no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—112no—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—221no—
487C2×D4—442no—
488C2×D4—442no—
489C2×D4—881no—
490C2×D4(C2×D11)⋊C412yes—
491C2×D4(C2×D11)⋊C412yes—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—881no—
506C22×C4C2×C4×D1111yescharacteristic
507C22×C4C2×C4×D1111yescharacteristic
508C22×C4C2×C4×D1112yes—
509C22×C4C2×D4411yescharacteristic
510C22×C4C2×D4411yescharacteristic
511C22×C4C2×D4411yescharacteristic
512C22×C4C2×D4411yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1112yes—
516C22×C4C23×D1111yescharacteristic
517M16—81no—
518M16—81no—
519M16—82no—
520C2×C8—22no—
521C2×C8—22no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—881no—
533C4⋊C4(C2×D11)⋊C412yes—
534C4⋊C4(C2×D11)⋊C412yes—
535C22⋊C4—222no—
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—442no—
546C22⋊C4—442no—
547C22⋊C4—881no—
548C22⋊C4(C2×D11)⋊C412yes—
549C22⋊C4(C2×D11)⋊C412yes—
550C22⋊C4(C2×D11)⋊C412yes—
551C22⋊C4(C2×D11)⋊C412yes—
552C42—222no—
553C42—222no—
554C42—442no—
555C42—881no—
556C42C2×C4×D1112yes—
557C42C2×C22⋊D1112yes—
558C11#1762311yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—222no—
568C23—442no—
569C23—881no—
570C23—881no—
571C23C2×(C2×D11)⋊C411yescharacteristic
572C23C2×(C2×D11)⋊C412yes—
573C23C2×(C2×D11)⋊C411yescharacteristic
574C23C22×D4411yescharacteristic
575Q8—442no—
576Q8—881no—
577D4—42no—
578D4—42no—
579D4—442no—
580D4—444no—
581D4—442no—
582D4—442no—
583D4—881no—
584D4—882no—
585D4—882no—
586C2×C4—21no—
587C2×C4—21no—
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—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—442no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—882no—
615C2×C4—882no—
616C2×C4—881no—
617C2×C4—881no—
618C2×C4—884no—
619C2×C4C2×(C2×D11)⋊C412yes—
620C2×C4C2×(C2×D11)⋊C412yes—
621C2×C4C2×(C2×D11)⋊C412yes—
622C2×C4C2×(C2×D11)⋊C411yescharacteristic
623C2×C4C2×(C2×D11)⋊C411yescharacteristic
624C2×C4C22×C4×D1111yescharacteristic
625C2×C4C22×C22⋊D1111yescharacteristic
626C8—42no—
627C8—42no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—22no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—22no—
636C22—21no—
637C22—22no—
638C22—21no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—442no—
644C22—442no—
645C22—442no—
646C22—1762no—
647C22#1062327911yescharacteristic
648C22#1062327911yescharacteristic
649C22C22×(C2×D11)⋊C411yescharacteristic
650C4—21no—
651C4—21no—
652C4—22no—
653C4—21no—
654C4—21no—
655C4—22no—
656C4—22no—
657C4—442no—
658C4—442no—
659C4—442no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4—881no—
664C2—21no—
665C2—21no—
666C2—42no—
667C2—41no—
668C2—41no—
669C2—882no—
670C2#1307707611yescharacteristic
671C2#1307713611yescharacteristic
672C2#1307716111yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2975C2
socleC22×C11C22×C22⋊C4
prime radical#13082455C2
cosocleC22×C4×C11C24
hypercenter#2975D11
hypocenterC11#17623
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13071556C2semidirect
3. #13067194C2semidirect
4. #13067160C2semidirect
5. #13067150C2semidirect
6. #13067146C2semidirect
7. #13067137C2semidirect
8. #13067133C2semidirect
9. #13067121C2semidirect
10. #13067103C2semidirect
11. C11×#2975C2semidirect
17. #10623096C4semidirect
19. #10623083C4semidirect
20. #10623081C4semidirect
21. #10623072C4semidirect
29. C11×#431C22semidirect
32. C11×#407C22semidirect
34. #10622825C22semidirect
37. C2×C11⋊#95C22semidirect
41. #10622550C22semidirect
42. #10622545C22semidirect
47. #10622105C22semidirect
48. #10622105C22semidirect
49. #10622105C22semidirect
50. #10622105C22semidirect
57. C22×D44C2×C4semidirect
58. C22×Dic22C2×C4semidirect
82. #66983C2×C4semidirect
92. C2×C4⋊Dic11C2×C4semidirect
93. C2×C4⋊Dic11C2×C4semidirect
97. #66977C2×C4semidirect
115. #66928C2×C4semidirect
116. C4×D44C2×C4semidirect
118. #66923C2×C4semidirect
119. C4×Dic22C2×C4semidirect
224. #2975D11semidirect
320. #431C2×D11semidirect
323. #407C2×D11semidirect
558. C11#17623semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130715562
#130671942
#130671602
#130671502
#130671462
#130671372
#130671332
#130671212
#130671032
C11×#29752
#1762311