Finite Group Databasebeta

← #14720934

Subgroups — #14720934

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic, complemented
4#13067134C212yesmaximal, complemented
5#13067130C212yesmaximal, complemented
6#13067121C211yesmaximal, characteristic, complemented
7#13067120C211yesmaximal, characteristic, complemented
8#13067118C211yesmaximal, characteristic, complemented
9#13067106C212yesmaximal, complemented
10#13067104C212yesmaximal, complemented
11C11×#1504C211yesmaximal, characteristic, complemented
12C2×#41×D11C411yescharacteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C11×#525C2211yescharacteristic
15#10623359C411yescharacteristic, complemented
16#10623322C2211yescharacteristic
17C22×(C2×D11)⋊C4—21no—
18C22×C4×Dic11—21no—
19C2×M16×D11—21no—
20#10623187—21no—
21D11×#123—21no—
22#10623158C411yescharacteristic, complemented
23#10623158C2211yescharacteristic
24D11×C22⋊Q8C411yescharacteristic, complemented
25D11×C22⋊Q8C2211yescharacteristic
26#10623137C411yescharacteristic, complemented
27#10623137C2211yescharacteristic
28D11×#121C411yescharacteristic, complemented
29D11×#121C2211yescharacteristic
30D11×#120—21no—
31#10623117—21no—
32#10623078—21no—
33#10623078—21no—
34C4×D4×D11—21no—
35C4×D4×D11—21no—
36#10623055C411yescharacteristic, complemented
37D11×#117C411yescharacteristic, complemented
38C11×#407C2211yescharacteristic, complemented
39C2×C11×#95C2211yescharacteristic, complemented
40C2×C11⋊#95C2211yescharacteristic, complemented
41#10622820C2211yescharacteristic, complemented
42#10622739—21no—
43#10622339—21no—
44#10622339C2212yes—
45D11×C22⋊C8—21no—
46D11×C22⋊C8C2212yescomplemented
47#10622279—21no—
48#10622279—21no—
49#10622279C2212yes—
50#10622279C2212yescomplemented
51C11×#328C2212yescomplemented
52C11×#327C2212yescomplemented
53#10622176C2212yescomplemented
54#10622175C2212yescomplemented
55#10622108C2212yescomplemented
56#10622105C2212yescomplemented
57#10622090C2212yescomplemented
58#10622089C2212yescomplemented
59C24×D11D411yescharacteristic
60C2×C11×#41C2×C411yescharacteristic
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
76C22×C4×D11—21no—
77C22×C4×D11—44no—
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11D411yescharacteristic
83C22×C4×D11D411yescharacteristic
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11D411yescharacteristic
87C22×C4×D11D411yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C2×C11×M16—21no—
91C11×#123—21no—
92C11×C22⋊Q8C2×C411yescharacteristic
93C11×C22⋊Q8C2311yescharacteristic
94C11×#121C2×C411yescharacteristic
95C11×#121C2311yescharacteristic
96C11×#120—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C11×#117C2×C411yescharacteristic
100#67006—21no—
101#66999C2×C411yescharacteristic, complemented
102#66999C2×C411yescharacteristic, complemented
103#66992—21no—
104#66992—21no—
105#66991C2×C411yescharacteristic, complemented
106#66991C2×C411yescharacteristic, complemented
107#66990—21no—
108#66990—21no—
109#66990—21no—
110#66988—21no—
111D4×Dic11—21no—
112D4×Dic11—21no—
113#66983C2×C411yescharacteristic
114#66983C2311yescharacteristic
115#66982—21no—
116C4×C22⋊D11—21no—
117C4×C22⋊D11—21no—
118C4×C22⋊D11—21no—
119C4×C22⋊D11—21no—
120C2×(C2×D11)⋊C4—28no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123#66979C2×C411yescharacteristic
124#66977C2×C411yescharacteristic
125#66977C2311yescharacteristic
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—44no—
129C2×#4318—21no—
130M16×D11—44no—
131C2×#4313—22no—
132C2×C8×D11—22no—
133#66950C2×C411yescharacteristic, complemented
134#66950C2×C411yescharacteristic, complemented
135#66949—21no—
136#66949—21no—
137#66948C2×C411yescharacteristic, complemented
138#66948C2×C411yescharacteristic, complemented
139#66947—21no—
140#66947—21no—
141#66946—21no—
142#66946—21no—
143#66945C2×C411yescharacteristic, complemented
144#66945C2×C411yescharacteristic, complemented
145C4⋊C4×D11—21no—
146C4⋊C4×D11—21no—
147C4⋊C4×D11C2×C411yescharacteristic, complemented
148C4⋊C4×D11C2×C411yescharacteristic, complemented
149#66939—21no—
150#66937—21no—
151#66937—21no—
152#66936—21no—
153#66936—21no—
154#66935—21no—
155#66935—21no—
156#66935—21no—
157(C22⋊D11)⋊C4—21no—
158(C22⋊D11)⋊C4—21no—
159(C22⋊D11)⋊C4—21no—
160(C22⋊D11)⋊C4—21no—
161C22⋊C4×D11—21no—
162C22⋊C4×D11—21no—
163C22⋊C4×D11—21no—
164C22⋊C4×D11—21no—
165C22⋊C4×D11—21no—
166#66931—21no—
167#66931—21no—
168#66930—21no—
169C4×D44—21no—
170C4×D44—21no—
171#66925—21no—
172C42×D11—21no—
173C11×C22⋊C8—21no—
174C11×C22⋊C8C2312yes—
175C11×#95—21no—
176C11×#95C2312yes—
177C11⋊#95—21no—
178C11⋊#95C2312yes—
179C22⋊(C11⋊C8)—21no—
180C22⋊(C11⋊C8)C2312yes—
181(C2×D11)⋊C8—22no—
182(C2×D11)⋊C8—22no—
183#17542—111nomaximal, Sylow
184C24×C11C2×D411yescharacteristic
185C23×D11—24no—
186C23×D11—21no—
187C23×D11—42no—
188C23×D11—41no—
189C23×D11—41no—
190C23×D11C22⋊C411yescharacteristic
191C23×D11C22⋊C411yescharacteristic
192C23×D11C22⋊C411yescharacteristic
193C23×D11C22⋊C411yescharacteristic
194C23×D11C2×D411yescharacteristic
195C23×D11C2×D411yescharacteristic
196C11×#41—42no—
197C2×Q8×C11C22×C411yescharacteristic
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11C22×C411yescharacteristic
202C22×C4×C11—24no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—21no—
215C2×C22⋊D11—21no—
216C2×C22⋊D11—21no—
217C2×C22⋊D11—21no—
218C2×C22⋊D11—21no—
219C2×C22⋊D11—21no—
220C2×C22⋊D11—21no—
221C22×Dic11—24no—
222C22×Dic11—24no—
223C22×Dic11—21no—
224C22×Dic11—22no—
225C22×Dic11—42no—
226C22×Dic11—42no—
227C22×Dic11C22⋊C411yescharacteristic
228C22×Dic11C22⋊C411yescharacteristic
229C22×Dic11C22⋊C411yescharacteristic
230C22×Dic11C22⋊C411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233#4343—42no—
234Q8×D11—42no—
235#4341—42no—
236#4341—44no—
237D4×D11—42no—
238D4×D11—42no—
239D4×D11—44no—
240D4×D11—42no—
241D4×D11—44no—
242#4339—42no—
243#4339—44no—
244C2×D44—21no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44C22×C411yescharacteristic
248C2×C4×D11—24no—
249C2×C4×D11—24no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C2×C4×D11—42no—
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—44no—
266C2×C4×D11C22⋊C411yescharacteristic
267C2×C4×D11C22⋊C411yescharacteristic
268C2×C4×D11C22⋊C411yescharacteristic
269C2×C4×D11C22⋊C411yescharacteristic
270C2×C4×D11C22⋊C411yescharacteristic
271C2×C4×D11C22⋊C411yescharacteristic
272C2×C4×D11C22⋊C411yescharacteristic
273C2×C4×D11C22⋊C411yescharacteristic
274C2×C4×D11C22×C411yescharacteristic
275C2×C4×D11C22×C411yescharacteristic
276C2×C4×D11C22×C411yescharacteristic
277C2×C4×D11C22×C411yescharacteristic
278C2×C4×D11C2×D411yescharacteristic
279C2×C4×D11C2×D411yescharacteristic
280C2×C4×D11C2×D411yescharacteristic
281C2×C4×D11C2×D411yescharacteristic
282C2×Dic22—21no—
283C2×Dic22C22×C411yescharacteristic
284C11×M16—42no—
285C2×C8×C11—22no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C22×C411yescharacteristic
289C11×C4⋊C4C22×C411yescharacteristic
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—21no—
295C42×C11—21no—
296C22⋊Dic11—21no—
297C22⋊Dic11—21no—
298C22⋊Dic11—21no—
299C22⋊Dic11—21no—
300C22⋊Dic11—21no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—21no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—21no—
312(C2×D11)⋊C4—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11C22×C411yescharacteristic
316C4⋊Dic11C22×C411yescharacteristic
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323C4×Dic11—21no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—44no—
327C4×Dic11—44no—
328#4318—42no—
329C2×C11⋊C8—22no—
330#4313—44no—
331C8×D11—44no—
332C2×#525—111no—
333C2×#407—111no—
334C2×C4×C22⋊C4—111no—
335#1508—112no—
336#1507—112no—
337#1504—111no—
338#1504—111no—
339#1504—111no—
340#1504D1111yescharacteristic, complemented
341#1501—112no—
342#1501—112no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—21no—
348C23×C11C2×C22⋊C411yescharacteristic
349C23×C11C2×C22⋊C411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C22×D11—21no—
352C22×D11—21no—
353C22×D11—21no—
354C22×D11—21no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—21no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—48no—
374C22×D11—48no—
375C22×D11—42no—
376C22×D11#10414yes—
377C22×D11C2×C22⋊C411yescharacteristic
378C22×D11C2×C22⋊C411yescharacteristic
379C22×D11C2×C22⋊C411yescharacteristic
380C22×D11C2×C22⋊C411yescharacteristic
381Q8×C11—41no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—42no—
386D4×C11—42no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—24no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—42no—
398C2×C4×C11—42no—
399C2×C4×C11—48no—
400C2×C4×C11—42no—
401C2×C4×C11C2×C22⋊C411yescharacteristic
402C2×C4×C11C2×C22⋊C411yescharacteristic
403C2×C4×C11C23×C411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C22⋊D11—42no—
406C22⋊D11—42no—
407C22⋊D11—41no—
408C22⋊D11—41no—
409C22⋊D11—42no—
410C22⋊D11—42no—
411C22⋊D11—42no—
412C22⋊D11—42no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—24no—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—42no—
423C2×Dic11—48no—
424C2×Dic11—42no—
425C2×Dic11—42no—
426C2×Dic11#9914yes—
427C2×Dic11C2×C22⋊C411yescharacteristic
428C2×Dic11C2×C22⋊C411yescharacteristic
429C2×Dic11C2×C22⋊C411yescharacteristic
430C2×Dic11C2×C22⋊C411yescharacteristic
431D44—41no—
432D44—42no—
433D44—42no—
434D44—42no—
435C4×D11—22no—
436C4×D11—22no—
437C4×D11—22no—
438C4×D11—22no—
439C4×D11—22no—
440C4×D11—22no—
441C4×D11—22no—
442C4×D11—22no—
443C4×D11—41no—
444C4×D11—41no—
445C4×D11—41no—
446C4×D11—41no—
447C4×D11—41no—
448C4×D11—41no—
449C4×D11—41no—
450C4×D11—41no—
451C4×D11—42no—
452C4×D11—42no—
453C4×D11—42no—
454C4×D11—42no—
455C4×D11—42no—
456Dic22—42no—
457Dic22—41no—
458C8×C11—42no—
459C11⋊C8—42no—
460C22×#41—111no—
461C24×C4—111no—
462C22×M16—221no—
463#525—111no—
464#525—111no—
465#525—111no—
466#525—111no—
467#525—111no—
468#525—111no—
469#525—111no—
470#525—221no—
471#525—221no—
472#525—221no—
473#525—221no—
474#525C2×D1111yescharacteristic
475C2×#123—221no—
476C2×C22⋊Q8—111no—
477C2×C22⋊Q8—111no—
478C2×#121—111no—
479C2×#121—111no—
480C2×#120—221no—
481C2×C4×D4—221no—
482C2×C4×D4—221no—
483C2×#117—111no—
484C22×C22⋊C4—221no—
485C22×C42—221no—
486#407—111no—
487#407—112no—
488#407—221no—
489#407—221no—
490#407C2×D1111yescharacteristic, complemented
491C2×C22⋊C8—112no—
492C2×C22⋊C8—221no—
493C4×C22⋊C4—112no—
494C4×C22⋊C4—112no—
495C4×C22⋊C4—221no—
496C4×C22⋊C4—221no—
497C2×#95—111no—
498C2×#95C2×D1111yescharacteristic, complemented
499#328—112no—
500#328—112no—
501#328—112no—
502#328C2×D1112yescomplemented
503#327—112no—
504#327—112no—
505#327—112no—
506#327C2×D1112yescomplemented
507C22×C11—24no—
508C22×C11—24no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11C2×#9912yes—
519C22×C11C2×#10412yes—
520C22×C11C22×C22⋊C411yescharacteristic
521C22×C11#57511yescharacteristic
522C22×C11#57511yescharacteristic
523C2×D11—21no—
524C2×D11—21no—
525C2×D11—21no—
526C2×D11—21no—
527C2×D11—21no—
528C2×D11—21no—
529C2×D11—21no—
530C2×D11—21no—
531C2×D11—21no—
532C2×D11—21no—
533C2×D11—44no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—44no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—44no—
540C2×D11—44no—
541C2×D11—41no—
542C2×D11—41no—
543C2×D11—41no—
544C2×D11—84no—
545C2×D11C2×#10412yes—
546C2×D11C2×#10412yes—
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—21no—
550C4×C11—21no—
551C4×C11—44no—
552C4×C11—41no—
553C4×C11—41no—
554C4×C11—41no—
555Dic11—21no—
556Dic11—21no—
557Dic11—44no—
558Dic11—41no—
559Dic11—41no—
560Dic11—41no—
561Dic11C2×#9912yes—
562Dic11C2×#9912yes—
563C25—111no—
564C2×#41—111no—
565C2×#41—111no—
566C2×#41—111no—
567C2×#41—221no—
568C2×#41—221no—
569C2×#41—444no—
570C2×#41C4×D1111yescharacteristic
571C22×Q8—111no—
572C22×D4—111no—
573C22×D4—221no—
574C22×D4—221no—
575C22×D4—221no—
576C23×C4—21no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—221no—
591C23×C4—221no—
592C23×C4—444no—
593C23×C4C22×D1111yescharacteristic
594C2×M16—21no—
595C2×M16—222no—
596C2×M16—221no—
597C2×M16—444no—
598C22×C8—222no—
599#123—21no—
600#123—221no—
601#123—221no—
602#123—221no—
603#123—221no—
604#123—221no—
605#123—221no—
606#123—221no—
607C22⋊Q8—111no—
608C22⋊Q8—111no—
609C22⋊Q8—111no—
610C22⋊Q8—111no—
611C22⋊Q8—111no—
612C22⋊Q8—111no—
613C22⋊Q8—221no—
614C22⋊Q8—221no—
615C22⋊Q8—221no—
616C22⋊Q8—221no—
617C22⋊Q8C4×D1111yescharacteristic
618C22⋊Q8C22×D1111yescharacteristic
619#121—111no—
620#121—111no—
621#121—111no—
622#121—111no—
623#121—111no—
624#121—111no—
625#121—221no—
626#121—221no—
627#121—221no—
628#121—221no—
629#121C4×D1111yescharacteristic
630#121C22×D1111yescharacteristic
631#120—21no—
632#120—221no—
633#120—221no—
634#120—221no—
635#120—221no—
636#120—221no—
637#120—221no—
638#120—221no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—221no—
642C4×D4—221no—
643C4×D4—221no—
644C4×D4—221no—
645C4×D4—221no—
646C4×D4—221no—
647C4×D4—221no—
648C4×D4—221no—
649C4×D4—221no—
650C4×D4—221no—
651C4×D4—221no—
652C4×D4—221no—
653C4×D4—221no—
654C4×D4—221no—
655#117—111no—
656#117—111no—
657#117—111no—
658#117—221no—
659#117—221no—
660#117C4×D1111yescharacteristic
661C2×C4⋊C4—111no—
662C2×C4⋊C4—111no—
663C2×C4⋊C4—221no—
664C2×C4⋊C4—221no—
665C2×C22⋊C4—221no—
666C2×C22⋊C4—221no—
667C2×C22⋊C4—221no—
668C2×C22⋊C4—221no—
669C2×C22⋊C4—221no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—228no—
673C2×C42—221no—
674C2×C42—222no—
675C2×C42—222no—
676C2×C42—444no—
677C22⋊C8—21no—
678C22⋊C8—112no—
679C22⋊C8—222no—
680C22⋊C8—222no—
681C22⋊C8—221no—
682C22⋊C8C22×D1112yes—
683#95—21no—
684#95—112no—
685#95—221no—
686#95C22×D1112yes—
687C2×C11—21no—
688C2×C11—21no—
689C2×C11—22no—
690C2×C11—22no—
691C2×C11—81no—
692C2×C11C22×#9911yescharacteristic
693C2×C11#289611yescharacteristic
694C2×C11C22×#10411yescharacteristic
695D11—22no—
696D11—22no—
697D11—41no—
698D11—41no—
699D11—81no—
700C24—111no—
701C24—111no—
702C24—111no—
703C24—111no—
704C24—111no—
705C24—111no—
706C24—224no—
707C24—221no—
708C24—442no—
709C24—441no—
710C24—441no—
711C24D4×D1111yescharacteristic
712#41—42no—
713#41—442no—
714#41—444no—
715#41—444no—
716#41—442no—
717#41—442no—
718C2×Q8—111no—
719C2×Q8—221no—
720C2×Q8—442no—
721C2×Q8C2×C4×D1111yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—111no—
726C2×D4—221no—
727C2×D4—221no—
728C2×D4—221no—
729C2×D4—221no—
730C2×D4—221no—
731C2×D4—221no—
732C2×D4—221no—
733C2×D4—221no—
734C2×D4—221no—
735C2×D4—221no—
736C2×D4—442no—
737C2×D4—444no—
738C2×D4—444no—
739C2×D4—442no—
740C2×D4—442no—
741C2×D4C2×C4×D1111yescharacteristic
742C22×C4—24no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
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—224no—
771C22×C4—224no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—224no—
777C22×C4—221no—
778C22×C4—224no—
779C22×C4—222no—
780C22×C4—221no—
781C22×C4—442no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4—442no—
785C22×C4—442no—
786C22×C4—442no—
787C22×C4—442no—
788C22×C4—442no—
789C22×C4—442no—
790C22×C4—442no—
791C22×C4—444no—
792C22×C4—442no—
793C22×C4—442no—
794C22×C4C2×C4×D1111yescharacteristic
795C22×C4C2×C4×D1111yescharacteristic
796C22×C4D4×D1111yescharacteristic
797C22×C4D4×D1111yescharacteristic
798C22×C4D4×D1111yescharacteristic
799C22×C4C23×D1111yescharacteristic
800M16—42no—
801M16—444no—
802M16—442no—
803C2×C8—22no—
804C2×C8—222no—
805C2×C8—444no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—111no—
809C4⋊C4—111no—
810C4⋊C4—221no—
811C4⋊C4—221no—
812C4⋊C4—221no—
813C4⋊C4—221no—
814C4⋊C4—221no—
815C4⋊C4—221no—
816C4⋊C4—221no—
817C4⋊C4—221no—
818C4⋊C4C2×C4×D1111yescharacteristic
819C4⋊C4C2×C4×D1111yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—221no—
826C22⋊C4—221no—
827C22⋊C4—221no—
828C22⋊C4—221no—
829C22⋊C4—221no—
830C22⋊C4—221no—
831C22⋊C4—221no—
832C22⋊C4—221no—
833C22⋊C4—228no—
834C22⋊C4—228no—
835C22⋊C4—221no—
836C22⋊C4—221no—
837C22⋊C4—221no—
838C22⋊C4—221no—
839C22⋊C4—221no—
840C22⋊C4—221no—
841C22⋊C4—221no—
842C42—21no—
843C42—221no—
844C42—221no—
845C42—221no—
846C42—444no—
847C42—444no—
848C11#1754211yescharacteristic, complemented, Sylow
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—21no—
854C23—111no—
855C23—111no—
856C23—114no—
857C23—111no—
858C23—111no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—221no—
864C23—221no—
865C23—221no—
866C23—221no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—221no—
871C23—441no—
872C23—441no—
873C23—441no—
874C23—441no—
875C23—441no—
876C23—441no—
877C23—441no—
878C23—441no—
879C23—448no—
880C23—448no—
881C23—442no—
882C23—442no—
883C23—442no—
884C23C22⋊C4×D1111yescharacteristic
885C23C22⋊C4×D1111yescharacteristic
886C23C2×D4×D1111yescharacteristic
887Q8—41no—
888Q8—441no—
889Q8—442no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—42no—
894D4—42no—
895D4—441no—
896D4—442no—
897D4—442no—
898D4—442no—
899D4—442no—
900D4—442no—
901D4—442no—
902D4—442no—
903D4—441no—
904D4—441no—
905D4—442no—
906D4—442no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—48no—
920C2×C4—42no—
921C2×C4—111no—
922C2×C4—111no—
923C2×C4—114no—
924C2×C4—111no—
925C2×C4—111no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—224no—
940C2×C4—221no—
941C2×C4—221no—
942C2×C4—221no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—442no—
952C2×C4—442no—
953C2×C4—442no—
954C2×C4—442no—
955C2×C4—442no—
956C2×C4—442no—
957C2×C4—442no—
958C2×C4—448no—
959C2×C4—442no—
960C2×C4C22⋊C4×D1111yescharacteristic
961C2×C4C22⋊C4×D1111yescharacteristic
962C2×C4C22×C4×D1111yescharacteristic
963C2×C4C2×D4×D1111yescharacteristic
964C8—42no—
965C8—442no—
966C22—24no—
967C22—24no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—41no—
975C22—41no—
976C22—41no—
977C22—112no—
978C22—112no—
979C22—221no—
980C22—221no—
981C22—221no—
982C22—221no—
983C22—221no—
984C22—221no—
985C22—221no—
986C22—221no—
987C22—221no—
988C22—221no—
989C22—444no—
990C22—442no—
991C22—442no—
992C22—442no—
993C22—442no—
994C22—444no—
995C22—444no—
996C22—444no—
997C22—441no—
998C22—441no—
999C22—441no—
1000C22—884no—
1001C22D11×#9912yes—
1002C22D11×#10412yes—
1003C22C2×C22⋊C4×D1111yescharacteristic
1004C22#1062330411yescharacteristic
1005C22#1062330811yescharacteristic
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—44no—
1011C4—41no—
1012C4—41no—
1013C4—41no—
1014C4—112no—
1015C4—112no—
1016C4—221no—
1017C4—221no—
1018C4—444no—
1019C4—441no—
1020C4—441no—
1021C4—441no—
1022C2—21no—
1023C2—21no—
1024C2—22no—
1025C2—22no—
1026C2—81no—
1027C2—222no—
1028C2—222no—
1029C2—441no—
1030C2—441no—
1031C2—881no—
1032C2C2×D11×#9911yescharacteristic
1033C2#1307713211yescharacteristic
1034C2C2×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
hypocenterC11#17542
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×#10622279C2semidirect
4. #13067134C2semidirect
5. #13067130C2semidirect
6. #13067121C2semidirect
7. #13067120C2semidirect
8. #13067118C2semidirect
9. #13067106C2semidirect
10. #13067104C2semidirect
11. C11×#1504C2semidirect
12. C2×#41×D11C4semidirect
15. #10623359C4semidirect
22. #10623158C4semidirect
24. D11×C22⋊Q8C4semidirect
26. #10623137C4semidirect
28. D11×#121C4semidirect
36. #10623055C4semidirect
37. D11×#117C4semidirect
38. C11×#407C22semidirect
39. C2×C11×#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. #10622820C22semidirect
46. D11×C22⋊C8C22semidirect
50. #10622279C22semidirect
51. C11×#328C22semidirect
52. C11×#327C22semidirect
53. #10622176C22semidirect
54. #10622175C22semidirect
55. #10622108C22semidirect
56. #10622105C22semidirect
57. #10622090C22semidirect
58. #10622089C22semidirect
66. C2×#4343C2×C4semidirect
67. C2×Q8×D11C2×C4semidirect
69. C2×#4341C2×C4semidirect
73. C2×D4×D11C2×C4semidirect
101. #66999C2×C4semidirect
102. #66999C2×C4semidirect
105. #66991C2×C4semidirect
106. #66991C2×C4semidirect
133. #66950C2×C4semidirect
134. #66950C2×C4semidirect
137. #66948C2×C4semidirect
138. #66948C2×C4semidirect
143. #66945C2×C4semidirect
144. #66945C2×C4semidirect
147. C4⋊C4×D11C2×C4semidirect
148. C4⋊C4×D11C2×C4semidirect
340. #1504D11semidirect
490. #407C2×D11semidirect
498. C2×#95C2×D11semidirect
502. #328C2×D11semidirect
506. #327C2×D11semidirect
848. C11#17542semidirect

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×#106222792
#130671342
#130671302
#130671212
#130671202
#130671182
#130671062
#130671042
C11×#15042
#1754211