Finite Group Databasebeta

← D11×#3165 #15623416

Subgroups — D11×#3165 #15623416

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079163C211yesmaximal, characteristic, complemented
4#13079162C211yesmaximal, characteristic, complemented
5#13079161C214yesmaximal, complemented
6#13079160C214yesmaximal, complemented
7#13079159C212yesmaximal, complemented
8#13079158C211yesmaximal, characteristic, complemented
9#13079157C212yesmaximal, complemented
10D11×#501C214yesmaximal, complemented
11D11×#500C212yesmaximal, complemented
12D11×#498C212yesmaximal, complemented
13D11×#428C214yesmaximal
14C4×M16×D11C211yesmaximal, characteristic
15C11×#3165C211yesmaximal, characteristic, complemented
16C22×Q8×D11—21no—
17C11×#533C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×#66997—21no—
20C2×M16×D11C2212yes—
21#10623259C2211yescharacteristic
22#10623259C2211yescharacteristic
23D11×C4⋊Q8—21no—
24D11×C4⋊Q8—21no—
25D11×C4⋊Q8—21no—
26D11×C4⋊Q8—21no—
27D11×C4⋊Q8C2212yes—
28D11×C4⋊Q8C2212yes—
29D11×C4⋊Q8C2212yes—
30D11×C4⋊Q8C2212yes—
31D11×C4⋊Q8C2211yescharacteristic
32D11×C4⋊Q8C2211yescharacteristic
33#10623219C2212yes—
34D11×#125C2212yes—
35D11×C22⋊Q8—21no—
36D11×C22⋊Q8—21no—
37#10623153—21no—
38#10623153—21no—
39#10623109—21no—
40#10623109—21no—
41C4×Q8×D11—21no—
42C4×Q8×D11—21no—
43D11×#117C2212yes—
44#10623048C2212yes—
45C2×C4⋊C4×D11—21no—
46C2×C4⋊C4×D11C2212yes—
47C2×#66941—21no—
48C2×#66941C2212yes—
49C2×C42×D11C2211yescharacteristic
50#10623001C2211yescharacteristic
51C2×#66922C2211yescharacteristic
52C11×#501C2214yescomplemented
53C11×#500C2212yescomplemented
54C11×#498C2212yescomplemented
55C11×#428C2214yes—
56C4×C11×M16C2211yescharacteristic
57#10622734C2214yes—
58M16×Dic11C2212yes—
59#10622693C2214yescomplemented
60#10622692C2212yescomplemented
61#10622692C2212yescomplemented
62#10622691C2212yescomplemented
63#10622691C2212yescomplemented
64#10622678C2214yescomplemented
65#10622608C2214yes—
66#10622577C2214yes—
67C4×#4318C2211yescharacteristic
68#10622494C2218yes—
69D11×#107C2218yes—
70#10622489C2218yescomplemented
71#10622487C2218yescomplemented
72#10622474C2218yes—
73D11×#106C2218yes—
74#10622469C2218yescomplemented
75#10622468C2218yescomplemented
76#10622320C2212yes—
77D11×#97C2212yes—
78#10622315C2214yescomplemented
79C4×#4313C2212yes—
80C4×C8×D11C2212yes—
81#10622295C2212yescomplemented
82#10622293C2212yescomplemented
83C22×Q8×C11—21no—
84C2×Q8×D11—22no—
85C2×Q8×D11—22no—
86C2×Q8×D11—22no—
87C2×Q8×D11—22no—
88C2×Q8×D11—21no—
89C2×Q8×D11—21no—
90C2×Q8×D11—48no—
91C22×C4×D11—22no—
92C22×C4×D11D411yescharacteristic
93C22×C4×D11D411yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22—22no—
97C2×C11×M16C2312yes—
98C11×C4⋊Q8—21no—
99C11×C4⋊Q8—21no—
100C11×C4⋊Q8C2311yescharacteristic
101C11×C4⋊Q8C2312yes—
102C11×C4⋊Q8C2311yescharacteristic
103C11×C4⋊Q8C2312yes—
104C11×#125C2312yes—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C11×#117C2312yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2312yes—
112C2×C42×C11C2311yescharacteristic
113#66999—21no—
114#66999—21no—
115Q8×Dic11—21no—
116Q8×Dic11—21no—
117#66997—22no—
118#66997—22no—
119#66997—22no—
120#66997—22no—
121#66997—21no—
122#66997—21no—
123#66979C2312yes—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11C2312yes—
126#66977—21no—
127#66977—21no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×C4×Dic11D411yescharacteristic
131C2×C4×Dic11D411yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×#4318C2312yes—
134M16×D11Q8116yescomplemented
135C2×#4313C2314yes—
136C2×C8×D11C2314yes—
137#66950—21no—
138#66950—21no—
139#66949—22no—
140#66949—22no—
141#66945C2312yes—
142#66945C2312yes—
143C4⋊C4×D11—22no—
144C4⋊C4×D11—22no—
145C4⋊C4×D11—22no—
146C4⋊C4×D11—22no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11—21no—
150C4⋊C4×D11—21no—
151C4⋊C4×D11—22no—
152C4⋊C4×D11—22no—
153C4⋊C4×D11C2312yes—
154C4⋊C4×D11C2314yes—
155C4⋊C4×D11C2314yes—
156C4⋊C4×D11C2312yes—
157#66943C2312yes—
158#66943C2312yes—
159#66942—22no—
160#66942—22no—
161#66941—22no—
162#66941—22no—
163#66941—22no—
164#66941—22no—
165#66941—22no—
166#66941—22no—
167#66941—21no—
168#66941—21no—
169#66941C2312yes—
170#66941C2314yes—
171#66941C2314yes—
172#66941C2312yes—
173#66940—21no—
174#66940—21no—
175#66940—22no—
176#66940—22no—
177C22⋊C4×D11—22no—
178#66931—22no—
179#66931—22no—
180#66930—22no—
181#66925—22no—
182C42×D11—22no—
183C42×D11D411yescharacteristic
184C42×D11D411yescharacteristic
185C42×D11D411yescharacteristic
186C42×D11D411yescharacteristic
187C42×D11C2311yescharacteristic
188C42×D11C2311yescharacteristic
189C42×D11C2311yescharacteristic
190C42×D11C2311yescharacteristic
191#66923C2312yes—
192#66922—21no—
193#66922—21no—
194#66922C2312yes—
195#66922C2312yes—
196#66922C2311yescharacteristic
197#66922C2311yescharacteristic
198C4×Dic22—21no—
199C4×Dic22—21no—
200C4×Dic22—22no—
201C4×Dic22—22no—
202C11×#107C2318yes—
203C11×#106C2318yes—
204C11×#97C2312yes—
205C4×C8×C11C2312yes—
206#66882C2318yes—
207#66881C2318yes—
208#66879C2314yes—
209C8×Dic11C2314yes—
210#66872C2318yes—
211#66872C2318yes—
212#66871C2318yes—
213#66871C2318yes—
214#66867C2312yes—
215C4×C11⋊C8C2312yes—
216C2×#3165—111nomaximal, Sylow
217C23×D11C2×D411yescharacteristic
218C2×Q8×C11—22no—
219C2×Q8×C11—22no—
220C2×Q8×C11—21no—
221C2×Q8×C11—21no—
222C2×Q8×C11—44no—
223C22×C4×C11—22no—
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2411yescharacteristic
227C22×Dic11—22no—
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231Q8×D11—48no—
232Q8×D11—48no—
233Q8×D11—48no—
234Q8×D11—44no—
235Q8×D11—48no—
236Q8×D11—44no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—48no—
244C2×C4×D11C2×D411yescharacteristic
245C2×C4×D11C2×D411yescharacteristic
246C2×C4×D11C2×D411yescharacteristic
247C2×C4×D11C2×D411yescharacteristic
248C2×C4×D11C2×D411yescharacteristic
249C2×C4×D11C2×D411yescharacteristic
250C2×C4×D11C2×D411yescharacteristic
251C2×C4×D11C2×D411yescharacteristic
252C2×C4×D11C2×D411yescharacteristic
253C2×C4×D11C2×D411yescharacteristic
254C2×C4×D11C2×Q818yes—
255C2×C4×D11C2411yescharacteristic
256C2×C4×D11C2411yescharacteristic
257C2×Dic22—22no—
258C2×Dic22—22no—
259C2×Dic22—24no—
260C2×Dic22—24no—
261C2×Dic22—21no—
262C2×Dic22—21no—
263C2×Dic22—22no—
264C2×Dic22—22no—
265C2×Dic22—44no—
266C2×Dic22—48no—
267C11×M16C2×Q818yescomplemented
268C2×C8×C11C2414yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2414yes—
278C11×C4⋊C4C2412yes—
279C11×C22⋊C4—22no—
280C42×C11—22no—
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2411yescharacteristic
284C42×C11C2411yescharacteristic
285C22⋊Dic11—22no—
286(C2×D11)⋊C4—22no—
287(C2×D11)⋊C4—22no—
288C4⋊Dic11—22no—
289C4⋊Dic11—22no—
290C4⋊Dic11—21no—
291C4⋊Dic11—21no—
292C4⋊Dic11—22no—
293C4⋊Dic11—22no—
294C4⋊Dic11—22no—
295C4⋊Dic11C2412yes—
296C4⋊Dic11C2414yes—
297C4⋊Dic11C2412yes—
298Dic11⋊C4—22no—
299Dic11⋊C4—22no—
300Dic11⋊C4—22no—
301Dic11⋊C4—22no—
302Dic11⋊C4—22no—
303Dic11⋊C4—22no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—22no—
309Dic11⋊C4—22no—
310C4×Dic11—22no—
311C4×Dic11—22no—
312C4×Dic11—22no—
313C4×Dic11C2×D411yescharacteristic
314C4×Dic11C2×D411yescharacteristic
315C4×Dic11C2×D411yescharacteristic
316C4×Dic11C2×D411yescharacteristic
317C4×Dic11C2×D411yescharacteristic
318C4×Dic11C2×D411yescharacteristic
319C4×Dic11C2×D411yescharacteristic
320C4×Dic11C2×D411yescharacteristic
321C4×Dic11C2×D411yescharacteristic
322C4×Dic11C2×D411yescharacteristic
323C4×Dic11C2411yescharacteristic
324C4×Dic11C2411yescharacteristic
325#4318C2×Q818yescomplemented
326C2×C11⋊C8C2414yes—
327#4313C2×Q8116yescomplemented
328C8×D11C2×Q8116yescomplemented
329C2×#533—111no—
330C22×C4⋊Q8—111no—
331#3165—114no—
332#3165—112no—
333#3165—112no—
334#3165—114no—
335#3165—111no—
336#3165—111no—
337#3165—111no—
338#3165D1111yescharacteristic, direct product factor
339C2×#501—114no—
340C2×#500—112no—
341C2×#498—112no—
342C2×#428—114no—
343C2×C4×M16—111no—
344C23×C11C22×D411yescharacteristic
345C22×D11—22no—
346C22×D11—22no—
347C22×D11C4⋊Q814yes—
348C22×D11C22×D411yescharacteristic
349C22×D11C22×D411yescharacteristic
350Q8×C11—44no—
351Q8×C11—44no—
352Q8×C11—42no—
353Q8×C11—42no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—24no—
359C2×C4×C11—44no—
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×Q814yes—
366C2×C4×C11C2511yescharacteristic
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—24no—
372C2×Dic11—44no—
373C2×Dic11C4⋊Q814yes—
374C2×Dic11C22×D411yescharacteristic
375C2×Dic11C22×D411yescharacteristic
376C2×Dic11C22×D411yescharacteristic
377C2×Dic11C22×D411yescharacteristic
378C2×Dic11C22×D411yescharacteristic
379C2×Dic11C22×D411yescharacteristic
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—48no—
387C4×D11—48no—
388C4×D11—44no—
389C4×D11—44no—
390C4×D11C4⋊Q814yes—
391C4×D11C4⋊Q814yes—
392C4×D11AGL(1,ℤ/8)14yes—
393C4×D11#13714yes—
394C4×D11C22×Q814yes—
395C4×D11C22×Q814yes—
396Dic22—48no—
397Dic22—44no—
398Dic22—44no—
399Dic22—42no—
400Dic22—42no—
401Dic22—48no—
402Dic22—44no—
403Dic22—44no—
404C8×C11C22×Q818yescomplemented
405C11⋊C8C22×Q818yescomplemented
406C23×Q8—221no—
407C22×M16—112no—
408#533—111no—
409#533—111no—
410#533—112no—
411#533—112no—
412#533—111no—
413#533—221no—
414#533—221no—
415#533—221no—
416#533—221no—
417#533C2×D1111yescharacteristic
418C2×C4⋊Q8—111no—
419C2×C4⋊Q8—112no—
420C2×C4⋊Q8—111no—
421C2×C4⋊Q8—112no—
422C2×C4⋊Q8—112no—
423C2×C4⋊Q8—112no—
424C2×C4⋊Q8—112no—
425C2×C4⋊Q8—111no—
426C2×C4⋊Q8—221no—
427C2×C4⋊Q8—221no—
428C2×C4⋊Q8—221no—
429C2×C4⋊Q8—221no—
430C2×C4⋊Q8—221no—
431C2×C4⋊Q8—221no—
432C2×C4⋊Q8C2×D1111yescharacteristic
433C2×#125—112no—
434C2×C22⋊Q8—221no—
435C2×C22⋊Q8—221no—
436C2×C4×Q8—221no—
437C2×C4×Q8—221no—
438C2×#117—112no—
439C22×C4⋊C4—112no—
440C22×C4⋊C4—221no—
441C22×C42—111no—
442#501—114no—
443#501—114no—
444#501—118no—
445#501—118no—
446#501—114no—
447#501C2×D1114yescomplemented
448#500—112no—
449#500—112no—
450#500—118no—
451#500—112no—
452#500C2×D1112yescomplemented
453#498—112no—
454#498—112no—
455#498—118no—
456#498—112no—
457#498C2×D1112yescomplemented
458#428—114no—
459#428—114no—
460#428—114no—
461#428—118no—
462#428—118no—
463#428C2×D1114yes—
464C2×#107—118no—
465C2×#106—118no—
466C4×M16—112no—
467C4×M16—111no—
468C4×M16—112no—
469C4×M16—112no—
470C4×M16C2×D1111yescharacteristic
471C2×#97—112no—
472C2×C4×C8—112no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11C2×C4⋊Q812yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—21no—
478C2×D11—21no—
479C2×D11—28no—
480C2×D11C2×C4⋊Q812yes—
481C2×D11C2×C4⋊Q812yes—
482C2×D11C2×AGL(1,ℤ/8)12yes—
483C2×D11C2×#13712yes—
484C4×C11—21no—
485C4×C11—21no—
486C4×C11—44no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11C2×C4⋊Q812yes—
490C4×C11C2×AGL(1,ℤ/8)12yes—
491C4×C11C2×#13712yes—
492C4×C11C23×Q812yes—
493Dic11—21no—
494Dic11—21no—
495Dic11—44no—
496Dic11—42no—
497Dic11—42no—
498Dic11C2×C4⋊Q812yes—
499Dic11C2×C4⋊Q812yes—
500Dic11C2×AGL(1,ℤ/8)12yes—
501Dic11C2×#13712yes—
502C22×Q8—21no—
503C22×Q8—222no—
504C22×Q8—221no—
505C22×Q8—221no—
506C22×Q8—222no—
507C22×Q8—222no—
508C22×Q8—222no—
509C22×Q8—222no—
510C22×Q8—221no—
511C22×Q8—448no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—222no—
516C2×M16—112no—
517C2×M16—1116no—
518C2×M16—114no—
519C2×M16C22×D1112yes—
520C22×C8—114no—
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8—114no—
524C4⋊Q8—114no—
525C4⋊Q8—112no—
526C4⋊Q8—112no—
527C4⋊Q8—112no—
528C4⋊Q8—112no—
529C4⋊Q8—111no—
530C4⋊Q8—111no—
531C4⋊Q8—222no—
532C4⋊Q8—222no—
533C4⋊Q8—222no—
534C4⋊Q8—222no—
535C4⋊Q8—222no—
536C4⋊Q8—222no—
537C4⋊Q8—221no—
538C4⋊Q8—221no—
539C4⋊Q8—222no—
540C4⋊Q8—222no—
541C4⋊Q8—222no—
542C4⋊Q8—222no—
543C4⋊Q8—221no—
544C4⋊Q8—221no—
545C4⋊Q8—221no—
546C4⋊Q8—221no—
547C4⋊Q8C22×D1112yes—
548C4⋊Q8C22×D1112yes—
549C4⋊Q8C22×D1111yescharacteristic
550C4⋊Q8C22×D1111yescharacteristic
551#125—112no—
552#125—112no—
553#125—112no—
554#125—222no—
555#125—222no—
556#125C22×D1112yes—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—222no—
560C22⋊Q8—222no—
561C22⋊Q8—222no—
562C22⋊Q8—222no—
563C22⋊Q8—221no—
564C22⋊Q8—221no—
565C22⋊Q8—221no—
566C22⋊Q8—221no—
567C22⋊Q8—221no—
568C22⋊Q8—221no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—222no—
572C4×Q8—222no—
573C4×Q8—222no—
574C4×Q8—222no—
575C4×Q8—221no—
576C4×Q8—221no—
577C4×Q8—221no—
578C4×Q8—221no—
579C4×Q8—221no—
580C4×Q8—221no—
581#117—112no—
582#117—112no—
583#117—112no—
584#117—222no—
585#117—222no—
586#117C22×D1112yes—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—112no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—112no—
592C2×C4⋊C4—112no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4C22×D1112yes—
607C2×C22⋊C4—222no—
608C2×C42—111no—
609C2×C42—111no—
610C2×C42—111no—
611C2×C42—111no—
612C2×C42—111no—
613C2×C42—111no—
614C2×C42—111no—
615C2×C42—111no—
616C2×C42—111no—
617C2×C42—111no—
618C2×C42—111no—
619C2×C42—222no—
620C2×C42C22×D1111yescharacteristic
621#107—118no—
622#107—118no—
623#107—118no—
624#107C22×D1118yes—
625#106—118no—
626#106—118no—
627#106—118no—
628#106C22×D1118yes—
629#97—114no—
630#97—112no—
631#97C22×D1112yes—
632C4×C8—114no—
633C4×C8—112no—
634C4×C8C22×D1112yes—
635C2×C11—22no—
636C2×C11C22×C4⋊Q811yescharacteristic
637C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
638C2×C11C22×#13711yescharacteristic
639D11—22no—
640D11#316514yesdirect product factor
641C24—111no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—44no—
647C2×Q8—222no—
648C2×Q8—222no—
649C2×Q8—224no—
650C2×Q8—224no—
651C2×Q8—221no—
652C2×Q8—221no—
653C2×Q8—222no—
654C2×Q8—222no—
655C2×Q8—444no—
656C2×Q8—448no—
657C2×Q8—448no—
658C2×Q8—444no—
659C2×Q8—444no—
660C2×Q8—448no—
661C2×Q8—448no—
662C2×Q8—448no—
663C22×C4—22no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—111no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—118no—
670C22×C4—111no—
671C22×C4—111no—
672C22×C4—111no—
673C22×C4—111no—
674C22×C4—111no—
675C22×C4—111no—
676C22×C4—111no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—111no—
680C22×C4—224no—
681C22×C4—224no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—224no—
685C22×C4—224no—
686C22×C4—222no—
687C22×C4—448no—
688C22×C4D4×D1111yescharacteristic
689C22×C4D4×D1111yescharacteristic
690C22×C4C23×D1111yescharacteristic
691M16—118no—
692M16—1116no—
693M16Q8×D1118yescomplemented
694C2×C8—114no—
695C2×C8—1116no—
696C2×C8C23×D1114yes—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—112no—
705C4⋊C4—114no—
706C4⋊C4—112no—
707C4⋊C4—224no—
708C4⋊C4—224no—
709C4⋊C4—222no—
710C4⋊C4—222no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—222no—
714C4⋊C4—222no—
715C4⋊C4—222no—
716C4⋊C4—222no—
717C4⋊C4—222no—
718C4⋊C4—222no—
719C4⋊C4—222no—
720C4⋊C4—222no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4C23×D1112yes—
727C4⋊C4C23×D1114yes—
728C4⋊C4C23×D1112yes—
729C22⋊C4—22no—
730C22⋊C4—222no—
731C22⋊C4—222no—
732C22⋊C4—222no—
733C42—22no—
734C42—111no—
735C42—111no—
736C42—111no—
737C42—111no—
738C42—111no—
739C42—111no—
740C42—111no—
741C42—111no—
742C42—111no—
743C42—111no—
744C42—111no—
745C42—111no—
746C42—222no—
747C42—222no—
748C42—222no—
749C42D4×D1111yescharacteristic
750C42D4×D1111yescharacteristic
751C42C23×D1111yescharacteristic
752C42C23×D1111yescharacteristic
753C11C2×#316511yescharacteristic, complemented, Sylow
754C23—111no—
755C23—114no—
756C23—111no—
757C23—222no—
758C23—222no—
759C23C2×D4×D1111yescharacteristic
760Q8—44no—
761Q8—44no—
762Q8—42no—
763Q8—42no—
764Q8—444no—
765Q8—448no—
766Q8—444no—
767Q8—444no—
768Q8—448no—
769Q8—444no—
770Q8—442no—
771Q8—442no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—44no—
778C2×C4—114no—
779C2×C4—111no—
780C2×C4—111no—
781C2×C4—111no—
782C2×C4—111no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—114no—
789C2×C4—111no—
790C2×C4—111no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—224no—
802C2×C4—448no—
803C2×C4—444no—
804C2×C4—444no—
805C2×C4—448no—
806C2×C4—444no—
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4C2×D4×D1111yescharacteristic
809C2×C4C2×D4×D1111yescharacteristic
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4C2×D4×D1111yescharacteristic
812C2×C4C2×Q8×D1114yes—
813C2×C4C24×D1111yescharacteristic
814C8—118no—
815C8C2×Q8×D1118yescomplemented
816C22—21no—
817C22—21no—
818C22—112no—
819C22—112no—
820C22—112no—
821C22—112no—
822C22—228no—
823C22—221no—
824C22—221no—
825C22D11×C4⋊Q812yes—
826C22C22×D4×D1111yescharacteristic
827C4—21no—
828C4—21no—
829C4—44no—
830C4—42no—
831C4—42no—
832C4—112no—
833C4—112no—
834C4—112no—
835C4—112no—
836C4—221no—
837C4—221no—
838C4—444no—
839C4—442no—
840C4—442no—
841C4D11×C4⋊Q812yes—
842C4D11×AGL(1,ℤ/8)12yes—
843C4D11×#13712yes—
844C4C22×Q8×D1112yes—
845C2—22no—
846C2—114no—
847C2—222no—
848C2C2×D11×C4⋊Q811yescharacteristic
849C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
850C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3165C2
socleC22×C11C23×D4
prime radicalC23×D11C2×D4
hypercenter#3165D11
hypocenterC11C2×#3165
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #13079163C2semidirect
4. #13079162C2semidirect
5. #13079161C2semidirect
6. #13079160C2semidirect
7. #13079159C2semidirect
8. #13079158C2semidirect
9. #13079157C2semidirect
10. D11×#501C2semidirect
11. D11×#500C2semidirect
12. D11×#498C2semidirect
15. C11×#3165C2semidirect
52. C11×#501C22semidirect
53. C11×#500C22semidirect
54. C11×#498C22semidirect
59. #10622693C22semidirect
60. #10622692C22semidirect
61. #10622692C22semidirect
62. #10622691C22semidirect
63. #10622691C22semidirect
64. #10622678C22semidirect
70. #10622489C22semidirect
71. #10622487C22semidirect
74. #10622469C22semidirect
75. #10622468C22semidirect
78. #10622315C22semidirect
81. #10622295C22semidirect
82. #10622293C22semidirect
134. M16×D11Q8semidirect
267. C11×M16C2×Q8semidirect
325. #4318C2×Q8semidirect
327. #4313C2×Q8semidirect
328. C8×D11C2×Q8semidirect
338. #3165D11direct (N × H)
404. C8×C11C22×Q8semidirect
405. C11⋊C8C22×Q8semidirect
447. #501C2×D11semidirect
452. #500C2×D11semidirect
457. #498C2×D11semidirect
640. D11#3165direct (N × H)
693. M16Q8×D11semidirect
753. C11C2×#3165semidirect
815. C8C2×Q8×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
C2×D11×C4⋊Q82
#130791632
#130791622
#130791612
#130791602
#130791592
#130791582
#130791572
D11×#5012
D11×#5002
D11×#4982
D11×#4282
C4×M16×D112
C11×#31652
C2×#316511