Finite Group Databasebeta

← D11×#1513 #14721024

Subgroups — D11×#1513 #14721024

Order 2816.

1510 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic, complemented
3D11×#380C211yesmaximal, characteristic, complemented
4#13067160C211yesmaximal, characteristic, complemented
5#13067159C211yesmaximal, characteristic, complemented
6#13067158C212yesmaximal, complemented
7#13067157C211yesmaximal, characteristic, complemented
8#13067156C212yesmaximal, complemented
9D11×#328C212yesmaximal, complemented
10D11×#327C212yesmaximal, complemented
11C11×#1513C211yesmaximal, characteristic, complemented
12C2×#41×D11C411yescharacteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C11×#525C2211yescharacteristic
15#10623359C411yescharacteristic, complemented
16#10623322C2211yescharacteristic
17C2×M16×D11—21no—
18#10623187—21no—
19D11×#123—21no—
20#10623158C411yescharacteristic, complemented
21#10623158C2211yescharacteristic
22D11×C22⋊Q8C411yescharacteristic, complemented
23D11×C22⋊Q8C2211yescharacteristic
24#10623137C411yescharacteristic, complemented
25#10623137C2211yescharacteristic
26D11×#121C411yescharacteristic, complemented
27D11×#121C2211yescharacteristic
28D11×#120—21no—
29#10623117—21no—
30#10623078—21no—
31#10623078—21no—
32C4×D4×D11—21no—
33C4×D4×D11—21no—
34#10623055C411yescharacteristic, complemented
35D11×#117C411yescharacteristic, complemented
36C2×C4⋊C4×D11—21no—
37C2×C22⋊C4×D11—21no—
38C11×#407C2211yescharacteristic, complemented
39C11×#380C2211yescharacteristic, complemented
40#10622825C2211yescharacteristic, complemented
41#10622820C2211yescharacteristic, complemented
42#10622739—21no—
43#10622600—21no—
44#10622555—21no—
45#10622339—21no—
46#10622339C2212yescomplemented
47D11×C22⋊C8—21no—
48D11×C22⋊C8C2212yes—
49#10622280C2212yescomplemented
50D11×#95C2212yes—
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×C11C2311yescharacteristic
62C23×Dic11D411yescharacteristic
63#41×D11—44no—
64C2×#4343C2×C411yescharacteristic, complemented
65C2×Q8×D11C2×C411yescharacteristic
66C2×#4341—21no—
67C2×#4341C2×C411yescharacteristic, complemented
68C2×D4×D11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C2×D4×D11C2×C411yescharacteristic
72C2×#4339—21no—
73C2×#4339C2×C411yescharacteristic, complemented
74C22×C4×D11—21no—
75C22×C4×D11—22no—
76C22×C4×D11—44no—
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11D411yescharacteristic
82C22×C4×D11D411yescharacteristic
83C22×C4×D11D411yescharacteristic
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11D411yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C2×C11×M16—21no—
90C11×#123—21no—
91C11×C22⋊Q8C2×C411yescharacteristic, complemented
92C11×C22⋊Q8C2311yescharacteristic
93C11×#121C2×C411yescharacteristic, complemented
94C11×#121C2311yescharacteristic
95C11×#120—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C11×#117C2×C411yescharacteristic, complemented
99C2×C11×C4⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101#67006—21no—
102C2×C22⋊Dic11—21no—
103#66999C2×C411yescharacteristic
104#66999C2×C411yescharacteristic, complemented
105#66992—21no—
106#66992—21no—
107#66991C2×C411yescharacteristic
108#66991C2×C411yescharacteristic, complemented
109#66990—21no—
110#66990—21no—
111#66990—21no—
112#66988—21no—
113D4×Dic11—21no—
114D4×Dic11—21no—
115#66983C2×C411yescharacteristic, complemented
116#66983C2311yescharacteristic
117#66982—21no—
118C4×C22⋊D11—21no—
119C4×C22⋊D11—21no—
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C2×(C2×D11)⋊C4—22no—
123#66979C2×C411yescharacteristic, complemented
124C2×C4⋊Dic11—21no—
125#66977C2×C411yescharacteristic, complemented
126#66977C2311yescharacteristic
127C2×Dic11⋊C4—22no—
128C2×#4318—21no—
129M16×D11—44no—
130C2×#4313—22no—
131C2×C8×D11—22no—
132#66950C2×C411yescharacteristic
133#66950C2×C411yescharacteristic, complemented
134#66949—21no—
135#66949—21no—
136#66948C2×C411yescharacteristic
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×D11—44no—
147C4⋊C4×D11C2×C411yescharacteristic
148C4⋊C4×D11C2×C411yescharacteristic
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—
166C22⋊C4×D11—44no—
167#66931—21no—
168#66931—21no—
169#66930—21no—
170C4×D44—21no—
171C4×D44—21no—
172#66925—21no—
173C42×D11—21no—
174C11×C22⋊C8—21no—
175C11×C22⋊C8C2312yes—
176C11×#95C2312yes—
177C11⋊#95—22no—
178C11⋊#95C2312yes—
179C22⋊(C11⋊C8)—21no—
180C22⋊(C11⋊C8)C2312yes—
181(C2×D11)⋊C8—22no—
182(C2×D11)⋊C8—22no—
183C2×#1513—111nomaximal, Sylow
184C24×C11C2×D411yescharacteristic
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—21no—
188C23×D11—42no—
189C23×D11—42no—
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—21no—
203C22×C4×C11—22no—
204C22×C4×C11—42no—
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—21no—
212C2×C22⋊D11—21no—
213C2×C22⋊D11—21no—
214C2×C22⋊D11—21no—
215C2×C22⋊D11—21no—
216C2×C22⋊D11—21no—
217C2×C22⋊D11—21no—
218C22×Dic11—21no—
219C22×Dic11—22no—
220C22×Dic11—42no—
221C22×Dic11C22⋊C411yescharacteristic
222C22×Dic11C22⋊C411yescharacteristic
223C22×Dic11C22⋊C411yescharacteristic
224C22×Dic11C22⋊C411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227#4343—42no—
228Q8×D11—42no—
229#4341—42no—
230#4341—44no—
231D4×D11—44no—
232D4×D11—44no—
233D4×D11—42no—
234D4×D11—42no—
235D4×D11—42no—
236#4339—42no—
237#4339—44no—
238C2×D44—21no—
239C2×D44—21no—
240C2×D44—21no—
241C2×D44C22×C411yescharacteristic
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11—42no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—42no—
259C2×C4×D11—42no—
260C2×C4×D11—42no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11C22⋊C411yescharacteristic
264C2×C4×D11C22⋊C411yescharacteristic
265C2×C4×D11C22⋊C411yescharacteristic
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×D11C2×D411yescharacteristic
276C2×C4×D11C2×D411yescharacteristic
277C2×C4×D11C2×D411yescharacteristic
278C2×C4×D11C2×D411yescharacteristic
279C2×Dic22—21no—
280C2×Dic22C22×C411yescharacteristic
281C11×M16—42no—
282C2×C8×C11—22no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—42no—
286C11×C4⋊C4C22×C411yescharacteristic
287C11×C4⋊C4C22×C411yescharacteristic
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—42no—
294C42×C11—21no—
295C22⋊Dic11—21no—
296C22⋊Dic11—21no—
297C22⋊Dic11—21no—
298C22⋊Dic11—21no—
299C22⋊Dic11—21no—
300C22⋊Dic11—42no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
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—44no—
312C4⋊Dic11—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11—42no—
315C4⋊Dic11C22×C411yescharacteristic
316C4⋊Dic11C22×C411yescharacteristic
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323Dic11⋊C4—44no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—21no—
327#4318—42no—
328C2×C11⋊C8—22no—
329#4313—44no—
330C8×D11—44no—
331C2×#525—111no—
332C2×#407—111no—
333C2×#380—111no—
334#1513—111no—
335#1513—111no—
336#1513—112no—
337#1513—112no—
338#1513—111no—
339#1513D1111yescharacteristic, direct product factor
340C2×#328—112no—
341C2×#327—112no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11C2×C22⋊C411yescharacteristic
348C23×C11C2×C22⋊C411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—21no—
353C22×D11—21no—
354C22×D11—22no—
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—48no—
370C22×D11—48no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11C2×C22⋊C411yescharacteristic
375C22×D11C2×C22⋊C411yescharacteristic
376C22×D11C2×C22⋊C411yescharacteristic
377C22×D11C2×C22⋊C411yescharacteristic
378C22×D11AGL(1,ℤ/8)12yes—
379C22×D11#13712yes—
380Q8×C11—41no—
381D4×C11—41no—
382D4×C11—42no—
383D4×C11—42no—
384D4×C11—41no—
385D4×C11—41no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—42no—
399C2×C4×C11C2×C22⋊C411yescharacteristic
400C2×C4×C11C2×C22⋊C411yescharacteristic
401C2×C4×C11C23×C411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C22⋊D11—42no—
404C22⋊D11—42no—
405C22⋊D11—42no—
406C22⋊D11—42no—
407C22⋊D11—42no—
408C22⋊D11—41no—
409C22⋊D11—41no—
410C22⋊D11—42no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—42no—
421C2×Dic11—42no—
422C2×Dic11—42no—
423C2×Dic11—42no—
424C2×Dic11C2×C22⋊C411yescharacteristic
425C2×Dic11C2×C22⋊C411yescharacteristic
426C2×Dic11C2×C22⋊C411yescharacteristic
427C2×Dic11C2×C22⋊C411yescharacteristic
428D44—41no—
429D44—42no—
430D44—42no—
431D44—42no—
432C4×D11—22no—
433C4×D11—22no—
434C4×D11—22no—
435C4×D11—22no—
436C4×D11—22no—
437C4×D11—22no—
438C4×D11—22no—
439C4×D11—22no—
440C4×D11—22no—
441C4×D11—41no—
442C4×D11—41no—
443C4×D11—41no—
444C4×D11—41no—
445C4×D11—41no—
446C4×D11—41no—
447C4×D11—42no—
448C4×D11—42no—
449C4×D11—42no—
450C4×D11—42no—
451C4×D11—42no—
452C4×D11—88no—
453C4×D11#9914yes—
454Dic22—42no—
455Dic22—41no—
456C8×C11—42no—
457C11⋊C8—42no—
458C22×#41—111no—
459C24×C4—111no—
460C22×M16—221no—
461#525—111no—
462#525—111no—
463#525—111no—
464#525—111no—
465#525—111no—
466#525—111no—
467#525—111no—
468#525—221no—
469#525—221no—
470#525—221no—
471#525—221no—
472#525C2×D1111yescharacteristic
473C2×#123—221no—
474C2×C22⋊Q8—111no—
475C2×C22⋊Q8—111no—
476C2×#121—111no—
477C2×#121—111no—
478C2×#120—221no—
479C2×C4×D4—221no—
480C2×C4×D4—221no—
481C2×#117—111no—
482C22×C4⋊C4—221no—
483C22×C22⋊C4—221no—
484#407—111no—
485#407—112no—
486#407—221no—
487#407—221no—
488#407C2×D1111yescharacteristic, complemented
489C2×C22⋊C8—112no—
490C2×C22⋊C8—221no—
491#380—111no—
492#380—112no—
493#380—221no—
494#380—221no—
495#380C2×D1111yescharacteristic, complemented
496C2×#95—112no—
497#328—112no—
498#328—112no—
499#328—112no—
500#328C2×D1112yescomplemented
501#327—112no—
502#327—112no—
503#327—112no—
504#327C2×D1112yescomplemented
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11C22×C22⋊C411yescharacteristic
519C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
520C22×C11C2×#13711yescharacteristic
521C2×D11—21no—
522C2×D11—21no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—21no—
526C2×D11—21no—
527C2×D11—21no—
528C2×D11—21no—
529C2×D11—21no—
530C2×D11—21no—
531C2×D11—44no—
532C2×D11—44no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—44no—
536C2×D11—44no—
537C2×D11—41no—
538C2×D11—41no—
539C2×D11—41no—
540C2×D11—84no—
541C2×D11C2×#9912yes—
542C2×D11#41712yes—
543C2×D11#41712yes—
544C2×D11#42112yes—
545C4×C11—21no—
546C4×C11—21no—
547C4×C11—21no—
548C4×C11—41no—
549C4×C11—41no—
550C4×C11—41no—
551C4×C11—82no—
552C4×C11C2×#9912yes—
553Dic11—21no—
554Dic11—21no—
555Dic11—21no—
556Dic11—41no—
557Dic11—41no—
558Dic11—41no—
559Dic11—82no—
560Dic11C2×#9912yes—
561C25—111no—
562C2×#41—111no—
563C2×#41—111no—
564C2×#41—111no—
565C2×#41—221no—
566C2×#41—221no—
567C2×#41—444no—
568C2×#41C4×D1111yescharacteristic, complemented
569C22×Q8—111no—
570C22×D4—111no—
571C22×D4—221no—
572C22×D4—221no—
573C22×D4—221no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—111no—
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—221no—
588C23×C4—222no—
589C23×C4—444no—
590C23×C4C22×D1111yescharacteristic
591C2×M16—21no—
592C2×M16—222no—
593C2×M16—221no—
594C2×M16—444no—
595C22×C8—222no—
596#123—21no—
597#123—221no—
598#123—221no—
599#123—221no—
600#123—221no—
601#123—221no—
602#123—221no—
603#123—221no—
604C22⋊Q8—111no—
605C22⋊Q8—111no—
606C22⋊Q8—111no—
607C22⋊Q8—111no—
608C22⋊Q8—111no—
609C22⋊Q8—111no—
610C22⋊Q8—221no—
611C22⋊Q8—221no—
612C22⋊Q8—221no—
613C22⋊Q8—221no—
614C22⋊Q8C4×D1111yescharacteristic, complemented
615C22⋊Q8C22×D1111yescharacteristic
616#121—111no—
617#121—111no—
618#121—111no—
619#121—111no—
620#121—111no—
621#121—111no—
622#121—221no—
623#121—221no—
624#121—221no—
625#121—221no—
626#121C4×D1111yescharacteristic, complemented
627#121C22×D1111yescharacteristic
628#120—21no—
629#120—221no—
630#120—221no—
631#120—221no—
632#120—221no—
633#120—221no—
634#120—221no—
635#120—221no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—221no—
639C4×D4—221no—
640C4×D4—221no—
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—
652#117—111no—
653#117—111no—
654#117—111no—
655#117—221no—
656#117—221no—
657#117C4×D1111yescharacteristic, complemented
658C2×C4⋊C4—21no—
659C2×C4⋊C4—111no—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—221no—
662C2×C4⋊C4—221no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—221no—
665C2×C4⋊C4—444no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—221no—
668C2×C22⋊C4—221no—
669C2×C22⋊C4—221no—
670C2×C22⋊C4—221no—
671C2×C22⋊C4—221no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—221no—
674C2×C22⋊C4—444no—
675C2×C42—221no—
676C22⋊C8—21no—
677C22⋊C8—112no—
678C22⋊C8—222no—
679C22⋊C8—222no—
680C22⋊C8—221no—
681C22⋊C8C22×D1112yes—
682#95—112no—
683#95—222no—
684#95C22×D1112yes—
685C2×C11—21no—
686C2×C11—21no—
687C2×C11—41no—
688C2×C11—41no—
689C2×C11—81no—
690C2×C11C22×#9911yescharacteristic
691C2×C11C2×#41711yescharacteristic
692C2×C11C2×#42111yescharacteristic
693D11—22no—
694D11—41no—
695D11—41no—
696D11—81no—
697D11#151314yesdirect product factor
698C24—111no—
699C24—111no—
700C24—111no—
701C24—111no—
702C24—111no—
703C24—111no—
704C24—222no—
705C24—222no—
706C24—221no—
707C24—442no—
708C24—442no—
709C24D4×D1111yescharacteristic
710#41—42no—
711#41—442no—
712#41—444no—
713#41—444no—
714#41—442no—
715#41—442no—
716C2×Q8—111no—
717C2×Q8—221no—
718C2×Q8—442no—
719C2×Q8C2×C4×D1111yescharacteristic
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—111no—
724C2×D4—221no—
725C2×D4—221no—
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—442no—
735C2×D4—442no—
736C2×D4—442no—
737C2×D4—444no—
738C2×D4—444no—
739C2×D4C2×C4×D1111yescharacteristic
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—42no—
743C22×C4—111no—
744C22×C4—111no—
745C22×C4—111no—
746C22×C4—111no—
747C22×C4—111no—
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—224no—
766C22×C4—224no—
767C22×C4—224no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—222no—
775C22×C4—442no—
776C22×C4—442no—
777C22×C4—442no—
778C22×C4—444no—
779C22×C4—442no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4—442no—
785C22×C4—444no—
786C22×C4—444no—
787C22×C4—444no—
788C22×C4—442no—
789C22×C4C2×C4×D1111yescharacteristic
790C22×C4C2×C4×D1111yescharacteristic
791C22×C4D4×D1111yescharacteristic
792C22×C4D4×D1111yescharacteristic
793C22×C4D4×D1111yescharacteristic
794C22×C4C23×D1111yescharacteristic
795M16—42no—
796M16—444no—
797M16—442no—
798C2×C8—22no—
799C2×C8—222no—
800C2×C8—444no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—42no—
804C4⋊C4—111no—
805C4⋊C4—111no—
806C4⋊C4—221no—
807C4⋊C4—221no—
808C4⋊C4—221no—
809C4⋊C4—221no—
810C4⋊C4—221no—
811C4⋊C4—221no—
812C4⋊C4—221no—
813C4⋊C4—221no—
814C4⋊C4—442no—
815C4⋊C4—444no—
816C4⋊C4C2×C4×D1111yescharacteristic
817C4⋊C4C2×C4×D1111yescharacteristic
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—42no—
824C22⋊C4—221no—
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—221no—
834C22⋊C4—221no—
835C22⋊C4—221no—
836C22⋊C4—221no—
837C22⋊C4—221no—
838C22⋊C4—221no—
839C22⋊C4—444no—
840C22⋊C4—442no—
841C42—21no—
842C42—221no—
843C42—221no—
844C42—221no—
845C11C2×#151311yescharacteristic, complemented, Sylow
846C23—21no—
847C23—21no—
848C23—21no—
849C23—41no—
850C23—41no—
851C23—111no—
852C23—111no—
853C23—112no—
854C23—112no—
855C23—111no—
856C23—111no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—221no—
868C23—221no—
869C23—221no—
870C23—441no—
871C23—441no—
872C23—441no—
873C23—441no—
874C23—441no—
875C23—441no—
876C23—442no—
877C23—442no—
878C23—442no—
879C23—448no—
880C23—448no—
881C23C22⋊C4×D1111yescharacteristic
882C23C22⋊C4×D1111yescharacteristic
883C23C2×D4×D1111yescharacteristic
884Q8—41no—
885Q8—441no—
886Q8—442no—
887D4—41no—
888D4—42no—
889D4—42no—
890D4—41no—
891D4—41no—
892D4—441no—
893D4—442no—
894D4—442no—
895D4—442no—
896D4—442no—
897D4—442no—
898D4—442no—
899D4—442no—
900D4—442no—
901D4—442no—
902D4—441no—
903D4—441no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—111no—
918C2×C4—114no—
919C2×C4—111no—
920C2×C4—111no—
921C2×C4—111no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
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—221no—
935C2×C4—221no—
936C2×C4—221no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—442no—
944C2×C4—442no—
945C2×C4—442no—
946C2×C4—442no—
947C2×C4—442no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—442no—
952C2×C4—442no—
953C2×C4—442no—
954C2×C4—442no—
955C2×C4—888no—
956C2×C4C22⋊C4×D1111yescharacteristic
957C2×C4C22⋊C4×D1111yescharacteristic
958C2×C4C22×C4×D1111yescharacteristic
959C2×C4C2×D4×D1111yescharacteristic
960C8—42no—
961C8—442no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—42no—
971C22—42no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—112no—
976C22—112no—
977C22—112no—
978C22—112no—
979C22—224no—
980C22—224no—
981C22—221no—
982C22—221no—
983C22—221no—
984C22—221no—
985C22—221no—
986C22—221no—
987C22—221no—
988C22—221no—
989C22—442no—
990C22—442no—
991C22—444no—
992C22—444no—
993C22—444no—
994C22—444no—
995C22—441no—
996C22—441no—
997C22—441no—
998C22—884no—
999C22C2×C22⋊C4×D1111yescharacteristic
1000C22D11×AGL(1,ℤ/8)11yescharacteristic
1001C22D11×#13711yescharacteristic
1002C4—21no—
1003C4—21no—
1004C4—21no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—82no—
1009C4—112no—
1010C4—221no—
1011C4—221no—
1012C4—221no—
1013C4—441no—
1014C4—441no—
1015C4—441no—
1016C4—882no—
1017C4D11×#9912yes—
1018C2—21no—
1019C2—21no—
1020C2—41no—
1021C2—41no—
1022C2—81no—
1023C2—114no—
1024C2—222no—
1025C2—441no—
1026C2—441no—
1027C2—881no—
1028C2C2×D11×#9911yescharacteristic
1029C2D11×#41711yescharacteristic
1030C2D11×#42111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1513C2
socleC22×C11C22×C22⋊C4
prime radicalD11×#525C2
cosocleC22×C4×C11C24
hypercenter#1513D11
hypocenterC11C2×#1513
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. D11×#380C2semidirect
4. #13067160C2semidirect
5. #13067159C2semidirect
6. #13067158C2semidirect
7. #13067157C2semidirect
8. #13067156C2semidirect
9. D11×#328C2semidirect
10. D11×#327C2semidirect
11. C11×#1513C2semidirect
12. C2×#41×D11C4semidirect
15. #10623359C4semidirect
20. #10623158C4semidirect
22. D11×C22⋊Q8C4semidirect
24. #10623137C4semidirect
26. D11×#121C4semidirect
34. #10623055C4semidirect
35. D11×#117C4semidirect
38. C11×#407C22semidirect
39. C11×#380C22semidirect
40. #10622825C22semidirect
41. #10622820C22semidirect
46. #10622339C22semidirect
49. #10622280C22semidirect
51. C11×#328C22semidirect
52. C11×#327C22semidirect
53. #10622176C22semidirect
54. #10622175C22semidirect
55. #10622108C22semidirect
56. #10622105C22semidirect
57. #10622090C22semidirect
58. #10622089C22semidirect
60. C2×C11×#41C2×C4semidirect
64. C2×#4343C2×C4semidirect
67. C2×#4341C2×C4semidirect
73. C2×#4339C2×C4semidirect
91. C11×C22⋊Q8C2×C4semidirect
93. C11×#121C2×C4semidirect
98. C11×#117C2×C4semidirect
104. #66999C2×C4semidirect
108. #66991C2×C4semidirect
115. #66983C2×C4semidirect
123. #66979C2×C4semidirect
125. #66977C2×C4semidirect
133. #66950C2×C4semidirect
137. #66948C2×C4semidirect
142. #66945C2×C4semidirect
143. #66945C2×C4semidirect
339. #1513D11direct (N × H)
488. #407C2×D11semidirect
495. #380C2×D11semidirect
500. #328C2×D11semidirect
504. #327C2×D11semidirect
568. C2×#41C4×D11semidirect
614. C22⋊Q8C4×D11semidirect
626. #121C4×D11semidirect
657. #117C4×D11semidirect
697. D11#1513direct (N × H)
845. C11C2×#1513semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
D11×#4072
D11×#3802
#130671602
#130671592
#130671582
#130671572
#130671562
D11×#3282
D11×#3272
C11×#15132
C2×#151311