Finite Group Databasebeta

← D11×#1504 #14720909

Subgroups — D11×#1504 #14720909

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic, complemented
3C2×D11×#95C211yesmaximal, characteristic, complemented
4#13067121C211yesmaximal, characteristic, complemented
5#13067120C211yesmaximal, characteristic, complemented
6#13067119C212yesmaximal, complemented
7#13067118C211yesmaximal, characteristic, complemented
8#13067117C212yesmaximal, complemented
9D11×#328C212yesmaximal, complemented
10D11×#327C212yesmaximal, complemented
11C11×#1504C211yesmaximal, characteristic, complemented
12C2×#41×D11C411yescharacteristic, complemented
13C23×C4×D11—21no—
14C23×C4×D11C2211yescharacteristic
15C11×#525C2211yescharacteristic
16#10623359C411yescharacteristic, complemented
17#10623322C2211yescharacteristic
18C2×M16×D11—21no—
19#10623187—21no—
20D11×#123—21no—
21#10623158C411yescharacteristic, complemented
22#10623158C2211yescharacteristic
23D11×C22⋊Q8C411yescharacteristic, complemented
24D11×C22⋊Q8C2211yescharacteristic
25#10623137C411yescharacteristic, complemented
26#10623137C2211yescharacteristic
27D11×#121C411yescharacteristic, complemented
28D11×#121C2211yescharacteristic
29D11×#120—21no—
30#10623117—21no—
31#10623078—21no—
32#10623078—21no—
33C4×D4×D11—21no—
34C4×D4×D11—21no—
35#10623055C411yescharacteristic, complemented
36D11×#117C411yescharacteristic, complemented
37C11×#407C2211yescharacteristic, complemented
38C2×C11×#95C2211yescharacteristic, complemented
39C2×C11⋊#95—21no—
40C2×C11⋊#95C2211yescharacteristic, complemented
41#10622820C2211yescharacteristic, complemented
42#10622739—21no—
43#10622339—21no—
44#10622339C2212yescomplemented
45D11×C22⋊C8—21no—
46D11×C22⋊C8C2212yes—
47D11×#95—21no—
48D11×#95—21no—
49D11×#95C2212yes—
50D11×#95C2212yescomplemented
51C11×#328C2212yescomplemented
52C11×#327C2212yescomplemented
53#10622176C2212yescomplemented
54#10622175C2212yescomplemented
55#10622108C2212yescomplemented
56#10622105C2212yescomplemented
57#10622090C2212yescomplemented
58#10622089C2212yescomplemented
59C24×D11D411yescharacteristic
60C2×C11×#41C2×C411yescharacteristic, complemented
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C23×Dic11D411yescharacteristic
65#41×D11—44no—
66C2×#4343C2×C411yescharacteristic, complemented
67C2×Q8×D11C2×C411yescharacteristic, complemented
68C2×#4341—21no—
69C2×#4341C2×C411yescharacteristic, complemented
70C2×D4×D11—21no—
71C2×D4×D11—21no—
72C2×D4×D11—21no—
73C2×D4×D11C2×C411yescharacteristic, complemented
74C2×#4339—21no—
75C2×#4339C2×C411yescharacteristic, complemented
76C22×C4×D11—28no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—21no—
80C22×C4×D11—44no—
81C22×C4×D11—44no—
82C22×C4×D11—44no—
83C22×C4×D11C2×C411yescharacteristic
84C22×C4×D11C2×C411yescharacteristic
85C22×C4×D11C2×C411yescharacteristic
86C22×C4×D11C2×C411yescharacteristic
87C22×C4×D11D411yescharacteristic
88C22×C4×D11D411yescharacteristic
89C22×C4×D11D411yescharacteristic
90C22×C4×D11D411yescharacteristic
91C22×C4×D11D411yescharacteristic
92C22×C4×D11D411yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C2×C11×M16—21no—
96C11×#123—21no—
97C11×C22⋊Q8C2×C411yescharacteristic, complemented
98C11×C22⋊Q8C2311yescharacteristic
99C11×#121C2×C411yescharacteristic, complemented
100C11×#121C2311yescharacteristic
101C11×#120—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C11×#117C2×C411yescharacteristic, complemented
105#67006—21no—
106#66999C2×C411yescharacteristic, complemented
107#66999C2×C411yescharacteristic, complemented
108#66992—21no—
109#66992—21no—
110#66991C2×C411yescharacteristic, complemented
111#66991C2×C411yescharacteristic, complemented
112#66990—21no—
113#66990—21no—
114#66990—21no—
115#66988—21no—
116D4×Dic11—21no—
117D4×Dic11—21no—
118#66983C2×C411yescharacteristic, complemented
119#66983C2311yescharacteristic
120#66982—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11—21no—
123C4×C22⋊D11—21no—
124C4×C22⋊D11—21no—
125#66979C2×C411yescharacteristic, complemented
126#66977C2×C411yescharacteristic, complemented
127#66977C2311yescharacteristic
128C2×#4318—21no—
129M16×D11—44no—
130C2×#4313—22no—
131C2×C8×D11—22no—
132#66950C2×C411yescharacteristic, complemented
133#66950C2×C411yescharacteristic, complemented
134#66949—21no—
135#66949—21no—
136#66948C2×C411yescharacteristic, complemented
137#66948C2×C411yescharacteristic, complemented
138#66947—21no—
139#66947—21no—
140#66946—21no—
141#66946—21no—
142#66945C2×C411yescharacteristic, complemented
143#66945C2×C411yescharacteristic, complemented
144C4⋊C4×D11—21no—
145C4⋊C4×D11—21no—
146C4⋊C4×D11C2×C411yescharacteristic, complemented
147C4⋊C4×D11C2×C411yescharacteristic, complemented
148#66939—21no—
149#66937—21no—
150#66937—21no—
151#66936—21no—
152#66936—21no—
153#66935—21no—
154#66935—21no—
155#66935—21no—
156(C22⋊D11)⋊C4—21no—
157(C22⋊D11)⋊C4—21no—
158(C22⋊D11)⋊C4—21no—
159(C22⋊D11)⋊C4—21no—
160C22⋊C4×D11—21no—
161C22⋊C4×D11—21no—
162C22⋊C4×D11—21no—
163C22⋊C4×D11—21no—
164C22⋊C4×D11—21no—
165#66931—21no—
166#66931—21no—
167#66930—21no—
168C4×D44—21no—
169C4×D44—21no—
170#66925—21no—
171C42×D11—21no—
172C11×C22⋊C8—21no—
173C11×C22⋊C8C2312yes—
174C11×#95—21no—
175C11×#95C2312yes—
176C11⋊#95—21no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95C2312yes—
180C22⋊(C11⋊C8)—21no—
181C22⋊(C11⋊C8)C2312yes—
182(C2×D11)⋊C8—22no—
183(C2×D11)⋊C8—22no—
184C2×#1504—111nomaximal, Sylow
185C24×C11C2×D411yescharacteristic
186C23×D11—24no—
187C23×D11—24no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—21no—
191C23×D11C22⋊C411yescharacteristic
192C23×D11C22⋊C411yescharacteristic
193C23×D11C22⋊C411yescharacteristic
194C23×D11C22⋊C411yescharacteristic
195C23×D11C2×D411yescharacteristic
196C23×D11C2×D411yescharacteristic
197C11×#41—42no—
198C2×Q8×C11C22×C411yescharacteristic, complemented
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11C22×C411yescharacteristic, complemented
203C22×C4×C11—24no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—21no—
216C2×C22⋊D11—21no—
217C2×C22⋊D11—21no—
218C2×C22⋊D11—21no—
219C2×C22⋊D11—21no—
220C2×C22⋊D11—21no—
221C2×C22⋊D11—21no—
222C22×Dic11—24no—
223C22×Dic11—21no—
224C22×Dic11—22no—
225C22×Dic11—42no—
226C22×Dic11—42no—
227C22×Dic11—42no—
228C22×Dic11C22⋊C411yescharacteristic
229C22×Dic11C22⋊C411yescharacteristic
230C22×Dic11C22⋊C411yescharacteristic
231C22×Dic11C22⋊C411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—42no—
235Q8×D11—42no—
236#4341—42no—
237#4341—44no—
238D4×D11—44no—
239D4×D11—44no—
240D4×D11—42no—
241D4×D11—42no—
242D4×D11—42no—
243#4339—42no—
244#4339—44no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44C22×C411yescharacteristic, complemented
249C2×C4×D11—28no—
250C2×C4×D11—28no—
251C2×C4×D11—21no—
252C2×C4×D11—24no—
253C2×C4×D11—24no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—42no—
259C2×C4×D11—42no—
260C2×C4×D11—42no—
261C2×C4×D11—42no—
262C2×C4×D11—42no—
263C2×C4×D11—42no—
264C2×C4×D11—42no—
265C2×C4×D11—42no—
266C2×C4×D11—42no—
267C2×C4×D11—42no—
268C2×C4×D11—432no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11C22⋊C411yescharacteristic
275C2×C4×D11C22⋊C411yescharacteristic
276C2×C4×D11C22⋊C411yescharacteristic
277C2×C4×D11C22⋊C411yescharacteristic
278C2×C4×D11C22⋊C411yescharacteristic
279C2×C4×D11C22⋊C411yescharacteristic
280C2×C4×D11C22⋊C411yescharacteristic
281C2×C4×D11C22⋊C411yescharacteristic
282C2×C4×D11C22×C411yescharacteristic
283C2×C4×D11C22×C411yescharacteristic
284C2×C4×D11C22×C411yescharacteristic
285C2×C4×D11C22×C411yescharacteristic
286C2×C4×D11C2×D411yescharacteristic
287C2×C4×D11C2×D411yescharacteristic
288C2×C4×D11C2×D411yescharacteristic
289C2×C4×D11C2×D411yescharacteristic
290C2×Dic22—21no—
291C2×Dic22C22×C411yescharacteristic, complemented
292C11×M16—42no—
293C2×C8×C11—22no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C22×C411yescharacteristic, complemented
297C11×C4⋊C4C22×C411yescharacteristic, complemented
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C42×C11—21no—
304C22⋊Dic11—21no—
305C22⋊Dic11—21no—
306C22⋊Dic11—21no—
307C22⋊Dic11—21no—
308C22⋊Dic11—21no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—21no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—21no—
314(C2×D11)⋊C4—21no—
315(C2×D11)⋊C4—21no—
316(C2×D11)⋊C4—21no—
317(C2×D11)⋊C4—21no—
318(C2×D11)⋊C4—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11C22×C411yescharacteristic, complemented
322C4⋊Dic11C22×C411yescharacteristic, complemented
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325Dic11⋊C4—21no—
326Dic11⋊C4—21no—
327Dic11⋊C4—21no—
328Dic11⋊C4—21no—
329C4×Dic11—21no—
330C4×Dic11—21no—
331C4×Dic11—21no—
332#4318—42no—
333C2×C11⋊C8—22no—
334#4313—44no—
335C8×D11—44no—
336C2×#525—111no—
337C2×#407—111no—
338C22×#95—111no—
339#1504—111no—
340#1504—111no—
341#1504—112no—
342#1504—112no—
343#1504—111no—
344#1504D1111yescharacteristic, direct product factor
345C2×#328—112no—
346C2×#327—112no—
347C23×C11—21no—
348C23×C11—21no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—21no—
352C23×C11C2×C22⋊C411yescharacteristic
353C23×C11C2×C22⋊C411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C22×D11—216no—
356C22×D11—216no—
357C22×D11—21no—
358C22×D11—21no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—21no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11#9914yes—
378C22×D11#10414yes—
379C22×D11C2×C22⋊C411yescharacteristic
380C22×D11C2×C22⋊C411yescharacteristic
381C22×D11C2×C22⋊C411yescharacteristic
382C22×D11C2×C22⋊C411yescharacteristic
383C22×D11AGL(1,ℤ/8)12yes—
384C22×D11#13712yes—
385Q8×C11—41no—
386D4×C11—41no—
387D4×C11—41no—
388D4×C11—41no—
389D4×C11—42no—
390D4×C11—42no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—48no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11C2×C22⋊C411yescharacteristic
406C2×C4×C11C2×C22⋊C411yescharacteristic
407C2×C4×C11C23×C411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C22⋊D11—42no—
410C22⋊D11—41no—
411C22⋊D11—41no—
412C22⋊D11—42no—
413C22⋊D11—42no—
414C22⋊D11—42no—
415C22⋊D11—42no—
416C22⋊D11—42no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—24no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—42no—
428C2×Dic11—48no—
429C2×Dic11—42no—
430C2×Dic11—42no—
431C2×Dic11C2×C22⋊C411yescharacteristic
432C2×Dic11C2×C22⋊C411yescharacteristic
433C2×Dic11C2×C22⋊C411yescharacteristic
434C2×Dic11C2×C22⋊C411yescharacteristic
435D44—41no—
436D44—42no—
437D44—42no—
438D44—42no—
439C4×D11—22no—
440C4×D11—22no—
441C4×D11—22no—
442C4×D11—22no—
443C4×D11—22no—
444C4×D11—22no—
445C4×D11—22no—
446C4×D11—22no—
447C4×D11—41no—
448C4×D11—41no—
449C4×D11—41no—
450C4×D11—41no—
451C4×D11—41no—
452C4×D11—41no—
453C4×D11—41no—
454C4×D11—41no—
455C4×D11—42no—
456C4×D11—42no—
457C4×D11—416no—
458C4×D11—416no—
459C4×D11—42no—
460C4×D11—42no—
461C4×D11—42no—
462Dic22—42no—
463Dic22—41no—
464C8×C11—42no—
465C11⋊C8—42no—
466C22×#41—111no—
467C24×C4—111no—
468C24×C4—221no—
469C22×M16—221no—
470#525—111no—
471#525—111no—
472#525—111no—
473#525—111no—
474#525—111no—
475#525—111no—
476#525—111no—
477#525—221no—
478#525—221no—
479#525—221no—
480#525—221no—
481#525C2×D1111yescharacteristic
482C2×#123—221no—
483C2×C22⋊Q8—111no—
484C2×C22⋊Q8—111no—
485C2×#121—111no—
486C2×#121—111no—
487C2×#120—221no—
488C2×C4×D4—221no—
489C2×C4×D4—221no—
490C2×#117—111no—
491#407—111no—
492#407—112no—
493#407—221no—
494#407—221no—
495#407C2×D1111yescharacteristic, complemented
496C2×C22⋊C8—112no—
497C2×C22⋊C8—221no—
498C2×#95—111no—
499C2×#95—112no—
500C2×#95—112no—
501C2×#95—221no—
502C2×#95—221no—
503C2×#95—221no—
504C2×#95C2×D1111yescharacteristic, complemented
505#328—112no—
506#328—112no—
507#328—112no—
508#328C2×D1112yescomplemented
509#327—112no—
510#327—112no—
511#327—112no—
512#327C2×D1112yescomplemented
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—41no—
524C22×C11C2×#9912yes—
525C22×C11C2×#10412yes—
526C22×C11C22×C22⋊C411yescharacteristic
527C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
528C22×C11C2×#13711yescharacteristic
529C2×D11—28no—
530C2×D11—24no—
531C2×D11—28no—
532C2×D11—24no—
533C2×D11—21no—
534C2×D11—21no—
535C2×D11—21no—
536C2×D11—21no—
537C2×D11—21no—
538C2×D11—21no—
539C2×D11—28no—
540C2×D11—28no—
541C2×D11—24no—
542C2×D11—24no—
543C2×D11—41no—
544C2×D11—41no—
545C2×D11—41no—
546C2×D11—84no—
547C2×D11C2×#9912yes—
548C2×D11C2×#9912yes—
549C2×D11#41712yes—
550C2×D11#41712yes—
551C2×D11C2×#10412yes—
552C2×D11C2×#10412yes—
553C4×C11—21no—
554C4×C11—21no—
555C4×C11—21no—
556C4×C11—21no—
557C4×C11—44no—
558C4×C11—41no—
559C4×C11—41no—
560C4×C11—41no—
561Dic11—21no—
562Dic11—21no—
563Dic11—21no—
564Dic11—21no—
565Dic11—44no—
566Dic11—41no—
567Dic11—41no—
568Dic11—41no—
569C25—111no—
570C2×#41—111no—
571C2×#41—111no—
572C2×#41—111no—
573C2×#41—221no—
574C2×#41—221no—
575C2×#41—444no—
576C2×#41C4×D1111yescharacteristic, complemented
577C22×Q8—111no—
578C22×D4—111no—
579C22×D4—221no—
580C22×D4—221no—
581C22×D4—221no—
582C23×C4—21no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—221no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4—228no—
600C23×C4—221no—
601C23×C4—444no—
602C23×C4—444no—
603C23×C4—444no—
604C23×C4C22×D1111yescharacteristic
605C2×M16—21no—
606C2×M16—222no—
607C2×M16—221no—
608C2×M16—444no—
609C22×C8—222no—
610#123—21no—
611#123—221no—
612#123—221no—
613#123—221no—
614#123—221no—
615#123—221no—
616#123—221no—
617#123—221no—
618C22⋊Q8—111no—
619C22⋊Q8—111no—
620C22⋊Q8—111no—
621C22⋊Q8—111no—
622C22⋊Q8—111no—
623C22⋊Q8—111no—
624C22⋊Q8—221no—
625C22⋊Q8—221no—
626C22⋊Q8—221no—
627C22⋊Q8—221no—
628C22⋊Q8C4×D1111yescharacteristic, complemented
629C22⋊Q8C22×D1111yescharacteristic
630#121—111no—
631#121—111no—
632#121—111no—
633#121—111no—
634#121—111no—
635#121—111no—
636#121—221no—
637#121—221no—
638#121—221no—
639#121—221no—
640#121C4×D1111yescharacteristic, complemented
641#121C22×D1111yescharacteristic
642#120—21no—
643#120—221no—
644#120—221no—
645#120—221no—
646#120—221no—
647#120—221no—
648#120—221no—
649#120—221no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—221no—
653C4×D4—221no—
654C4×D4—221no—
655C4×D4—221no—
656C4×D4—221no—
657C4×D4—221no—
658C4×D4—221no—
659C4×D4—221no—
660C4×D4—221no—
661C4×D4—221no—
662C4×D4—221no—
663C4×D4—221no—
664C4×D4—221no—
665C4×D4—221no—
666#117—111no—
667#117—111no—
668#117—111no—
669#117—221no—
670#117—221no—
671#117C4×D1111yescharacteristic, complemented
672C2×C4⋊C4—111no—
673C2×C4⋊C4—111no—
674C2×C4⋊C4—221no—
675C2×C4⋊C4—221no—
676C2×C22⋊C4—221no—
677C2×C22⋊C4—221no—
678C2×C22⋊C4—221no—
679C2×C22⋊C4—221no—
680C2×C22⋊C4—221no—
681C2×C42—221no—
682C22⋊C8—21no—
683C22⋊C8—112no—
684C22⋊C8—222no—
685C22⋊C8—222no—
686C22⋊C8—221no—
687C22⋊C8C22×D1112yes—
688#95—21no—
689#95—112no—
690#95—222no—
691#95—222no—
692#95—221no—
693#95C22×D1112yes—
694C2×C11—21no—
695C2×C11—21no—
696C2×C11—22no—
697C2×C11—22no—
698C2×C11—81no—
699C2×C11C22×#9911yescharacteristic
700C2×C11C2×#41711yescharacteristic
701C2×C11C22×#10411yescharacteristic
702D11—22no—
703D11—22no—
704D11—22no—
705D11—81no—
706D11#150414yesdirect product factor
707C24—111no—
708C24—111no—
709C24—111no—
710C24—111no—
711C24—111no—
712C24—111no—
713C24—224no—
714C24—222no—
715C24—224no—
716C24—222no—
717C24—221no—
718C24D4×D1111yescharacteristic
719#41—42no—
720#41—442no—
721#41—444no—
722#41—444no—
723#41—442no—
724#41—442no—
725C2×Q8—111no—
726C2×Q8—221no—
727C2×Q8—442no—
728C2×Q8C2×C4×D1111yescharacteristic, complemented
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—111no—
733C2×D4—221no—
734C2×D4—221no—
735C2×D4—221no—
736C2×D4—221no—
737C2×D4—221no—
738C2×D4—221no—
739C2×D4—221no—
740C2×D4—221no—
741C2×D4—221no—
742C2×D4—221no—
743C2×D4—442no—
744C2×D4—444no—
745C2×D4—442no—
746C2×D4—442no—
747C2×D4—444no—
748C2×D4C2×C4×D1111yescharacteristic, complemented
749C22×C4—24no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—111no—
756C22×C4—111no—
757C22×C4—111no—
758C22×C4—111no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—111no—
764C22×C4—111no—
765C22×C4—111no—
766C22×C4—111no—
767C22×C4—111no—
768C22×C4—111no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—111no—
777C22×C4—221no—
778C22×C4—224no—
779C22×C4—224no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—228no—
784C22×C4—228no—
785C22×C4—221no—
786C22×C4—224no—
787C22×C4—222no—
788C22×C4—221no—
789C22×C4—442no—
790C22×C4—442no—
791C22×C4—442no—
792C22×C4—442no—
793C22×C4—442no—
794C22×C4—442no—
795C22×C4—442no—
796C22×C4—442no—
797C22×C4—442no—
798C22×C4—442no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—444no—
802C22×C4—444no—
803C22×C4—4432no—
804C22×C4—444no—
805C22×C4—442no—
806C22×C4—442no—
807C22×C4—442no—
808C22×C4C2×C4×D1111yescharacteristic
809C22×C4C2×C4×D1111yescharacteristic
810C22×C4D4×D1111yescharacteristic
811C22×C4D4×D1111yescharacteristic
812C22×C4D4×D1111yescharacteristic
813C22×C4C23×D1111yescharacteristic
814M16—42no—
815M16—444no—
816M16—442no—
817C2×C8—22no—
818C2×C8—222no—
819C2×C8—444no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—111no—
823C4⋊C4—111no—
824C4⋊C4—221no—
825C4⋊C4—221no—
826C4⋊C4—221no—
827C4⋊C4—221no—
828C4⋊C4—221no—
829C4⋊C4—221no—
830C4⋊C4—221no—
831C4⋊C4—221no—
832C4⋊C4C2×C4×D1111yescharacteristic, complemented
833C4⋊C4C2×C4×D1111yescharacteristic, complemented
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—221no—
840C22⋊C4—221no—
841C22⋊C4—221no—
842C22⋊C4—221no—
843C22⋊C4—221no—
844C22⋊C4—221no—
845C22⋊C4—221no—
846C22⋊C4—221no—
847C22⋊C4—221no—
848C22⋊C4—221no—
849C22⋊C4—221no—
850C22⋊C4—221no—
851C22⋊C4—221no—
852C22⋊C4—221no—
853C22⋊C4—221no—
854C42—21no—
855C42—221no—
856C42—221no—
857C42—221no—
858C11C2×#150411yescharacteristic, complemented, Sylow
859C23—21no—
860C23—21no—
861C23—22no—
862C23—22no—
863C23—21no—
864C23—111no—
865C23—111no—
866C23—111no—
867C23—111no—
868C23—112no—
869C23—112no—
870C23—114no—
871C23—114no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—2216no—
885C23—2216no—
886C23—221no—
887C23—221no—
888C23—222no—
889C23—222no—
890C23—221no—
891C23—442no—
892C23—442no—
893C23—442no—
894C23C22⋊C4×D1111yescharacteristic
895C23C22⋊C4×D1111yescharacteristic
896C23C2×D4×D1111yescharacteristic
897Q8—41no—
898Q8—441no—
899Q8—442no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—42no—
904D4—42no—
905D4—441no—
906D4—442no—
907D4—442no—
908D4—442no—
909D4—442no—
910D4—442no—
911D4—442no—
912D4—442no—
913D4—441no—
914D4—441no—
915D4—442no—
916D4—442no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—48no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—111no—
932C2×C4—111no—
933C2×C4—111no—
934C2×C4—111no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—224no—
946C2×C4—221no—
947C2×C4—221no—
948C2×C4—221no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—442no—
958C2×C4—442no—
959C2×C4—442no—
960C2×C4—442no—
961C2×C4—442no—
962C2×C4—4416no—
963C2×C4—4416no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—442no—
969C2×C4—448no—
970C2×C4—442no—
971C2×C4—442no—
972C2×C4C22⋊C4×D1111yescharacteristic
973C2×C4C22⋊C4×D1111yescharacteristic
974C2×C4C22×C4×D1111yescharacteristic
975C2×C4C2×D4×D1111yescharacteristic
976C8—42no—
977C8—442no—
978C22—24no—
979C22—24no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—112no—
990C22—112no—
991C22—112no—
992C22—112no—
993C22—112no—
994C22—112no—
995C22—224no—
996C22—224no—
997C22—228no—
998C22—228no—
999C22—224no—
1000C22—224no—
1001C22—228no—
1002C22—228no—
1003C22—221no—
1004C22—221no—
1005C22—221no—
1006C22—221no—
1007C22—221no—
1008C22—221no—
1009C22—441no—
1010C22—441no—
1011C22—441no—
1012C22—884no—
1013C22D11×#9912yes—
1014C22D11×#10412yes—
1015C22C2×C22⋊C4×D1111yescharacteristic
1016C22D11×AGL(1,ℤ/8)11yescharacteristic
1017C22D11×#13711yescharacteristic
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—44no—
1023C4—41no—
1024C4—41no—
1025C4—41no—
1026C4—221no—
1027C4—221no—
1028C4—221no—
1029C4—221no—
1030C4—444no—
1031C4—441no—
1032C4—441no—
1033C4—441no—
1034C2—21no—
1035C2—21no—
1036C2—22no—
1037C2—22no—
1038C2—81no—
1039C2—114no—
1040C2—222no—
1041C2—222no—
1042C2—222no—
1043C2—881no—
1044C2C2×D11×#9911yescharacteristic
1045C2D11×#41711yescharacteristic
1046C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1504C2
socleC22×C11C22×C22⋊C4
prime radicalD11×#525C2
cosocleC22×C4×C11C24
hypercenter#1504D11
hypocenterC11C2×#1504
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. C2×D11×#95C2semidirect
4. #13067121C2semidirect
5. #13067120C2semidirect
6. #13067119C2semidirect
7. #13067118C2semidirect
8. #13067117C2semidirect
9. D11×#328C2semidirect
10. D11×#327C2semidirect
11. C11×#1504C2semidirect
12. C2×#41×D11C4semidirect
16. #10623359C4semidirect
21. #10623158C4semidirect
23. D11×C22⋊Q8C4semidirect
25. #10623137C4semidirect
27. D11×#121C4semidirect
35. #10623055C4semidirect
36. D11×#117C4semidirect
37. C11×#407C22semidirect
38. C2×C11×#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. #10622820C22semidirect
44. #10622339C22semidirect
50. D11×#95C22semidirect
51. C11×#328C22semidirect
52. C11×#327C22semidirect
53. #10622176C22semidirect
54. #10622175C22semidirect
55. #10622108C22semidirect
56. #10622105C22semidirect
57. #10622090C22semidirect
58. #10622089C22semidirect
60. C2×C11×#41C2×C4semidirect
66. C2×#4343C2×C4semidirect
67. C2×Q8×D11C2×C4semidirect
69. C2×#4341C2×C4semidirect
73. C2×D4×D11C2×C4semidirect
75. C2×#4339C2×C4semidirect
97. C11×C22⋊Q8C2×C4semidirect
99. C11×#121C2×C4semidirect
104. C11×#117C2×C4semidirect
106. #66999C2×C4semidirect
107. #66999C2×C4semidirect
110. #66991C2×C4semidirect
111. #66991C2×C4semidirect
118. #66983C2×C4semidirect
125. #66979C2×C4semidirect
126. #66977C2×C4semidirect
132. #66950C2×C4semidirect
133. #66950C2×C4semidirect
136. #66948C2×C4semidirect
137. #66948C2×C4semidirect
142. #66945C2×C4semidirect
143. #66945C2×C4semidirect
146. C4⋊C4×D11C2×C4semidirect
147. C4⋊C4×D11C2×C4semidirect
198. C2×Q8×C11C22×C4semidirect
202. C2×D4×C11C22×C4semidirect
248. C2×D44C22×C4semidirect
291. C2×Dic22C22×C4semidirect
296. C11×C4⋊C4C22×C4semidirect
297. C11×C4⋊C4C22×C4semidirect
321. C4⋊Dic11C22×C4semidirect
322. C4⋊Dic11C22×C4semidirect
344. #1504D11direct (N × H)
495. #407C2×D11semidirect
504. C2×#95C2×D11semidirect
508. #328C2×D11semidirect
512. #327C2×D11semidirect
576. C2×#41C4×D11semidirect
628. C22⋊Q8C4×D11semidirect
640. #121C4×D11semidirect
671. #117C4×D11semidirect
706. D11#1504direct (N × H)
728. C2×Q8C2×C4×D11semidirect
748. C2×D4C2×C4×D11semidirect
832. C4⋊C4C2×C4×D11semidirect
833. C4⋊C4C2×C4×D11semidirect
858. C11C2×#1504semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
D11×#4072
C2×D11×#952
#130671212
#130671202
#130671192
#130671182
#130671172
D11×#3282
D11×#3272
C11×#15042
C2×#150411