Finite Group Databasebeta

← D11×#3228 #15625825

Subgroups — D11×#3228 #15625825

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic, complemented
2D11×#532C211yesmaximal, characteristic
3#13079755C211yesmaximal, characteristic, complemented
4#13079754C211yesmaximal, characteristic, complemented
5#13079753C211yesmaximal, characteristic, complemented
6#13079752C211yesmaximal, characteristic, complemented
7#13079751C214yesmaximal, complemented
8#13079750C214yesmaximal, complemented
9#13079749C211yesmaximal, characteristic, complemented
10#13079748C211yesmaximal, characteristic, complemented
11#13079747C211yesmaximal, characteristic, complemented
12D11×#500C211yesmaximal, characteristic, complemented
13D11×#498C211yesmaximal, characteristic, complemented
14D11×#486C211yesmaximal, characteristic, complemented
15D11×#486C211yesmaximal, characteristic, complemented
16D11×#482C214yesmaximal, complemented
17D11×#478C214yesmaximal, complemented
18D11×#431C211yesmaximal, characteristic, complemented
19C11×#3228C211yesmaximal, characteristic, complemented
20C2×#41×D11—21no—
21C11×#533C2211yescharacteristic, complemented
22C11×#532C2211yescharacteristic
23#10623363—21no—
24#10623259C2211yescharacteristic, complemented
25#10623259C2211yescharacteristic, complemented
26#10623256C2211yescharacteristic
27D11×C4⋊Q8C2211yescharacteristic
28D11×C4⋊Q8C2211yescharacteristic
29D11×C4⋊Q8C2211yescharacteristic
30#10623247C2211yescharacteristic
31D11×#127C2211yescharacteristic
32#10623219C2212yescomplemented
33D11×#125C2212yes—
34D11×#124—21no—
35#10623199—21no—
36D11×C22⋊Q8—21no—
37D11×C22⋊Q8—21no—
38#10623153—21no—
39#10623153—21no—
40D11×#121—21no—
41D11×#121C2212yes—
42#10623127—21no—
43#10623127C2212yes—
44#10623109—21no—
45#10623109—21no—
46C4×Q8×D11—21no—
47C4×Q8×D11—21no—
48#10623079—21no—
49#10623079C2212yes—
50C4×D4×D11—21no—
51C4×D4×D11C2212yes—
52D11×#117C2212yes—
53#10623048C2212yescomplemented
54#10623008C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56#10623001C2211yescharacteristic, complemented
57C11×#500C2211yescharacteristic, complemented
58C11×#498C2211yescharacteristic, complemented
59C11×#486C2211yescharacteristic, complemented
60C11×#486C2211yescharacteristic, complemented
61C11×#482C2214yescomplemented
62C11×#478C2214yescomplemented
63C11×#431C2211yescharacteristic, complemented
64#10622701C2211yescharacteristic, complemented
65#10622701C2211yescharacteristic, complemented
66#10622692C2211yescharacteristic, complemented
67#10622692C2211yescharacteristic, complemented
68#10622691C2211yescharacteristic, complemented
69#10622691C2211yescharacteristic, complemented
70#10622683C2211yescharacteristic, complemented
71#10622683C2211yescharacteristic, complemented
72#10622679C2214yescomplemented
73#10622648C2214yescomplemented
74#10622622C2214yescomplemented
75#10622616C2214yescomplemented
76#10622538C2211yescharacteristic, complemented
77#10622504C2214yescomplemented
78#10622498C2214yescomplemented
79D11×#107C2214yes—
80#10622487C2214yescomplemented
81#10622484C2214yescomplemented
82#10622479C2214yescomplemented
83D11×#106C2214yes—
84#10622468C2214yescomplemented
85#10622460C2214yescomplemented
86#10622446C2212yescomplemented
87D11×C4⋊C8C2212yes—
88#10622397C2214yescomplemented
89#10622392C2214yescomplemented
90D11×#102C2214yes—
91D11×#102C2214yes—
92#10622379C2214yescomplemented
93#10622376C2214yescomplemented
94#10622373C2214yescomplemented
95#10622373C2214yescomplemented
96#10622350C2214yescomplemented
97D11×C22⋊C8C2212yes—
98#10622331C2212yescomplemented
99#10622307C2211yescharacteristic, complemented
100#10622307C2211yescharacteristic, complemented
101#10622298C2211yescharacteristic, complemented
102#10622298C2211yescharacteristic, complemented
103C4×C8×D11C2211yescharacteristic
104C4×C8×D11C2211yescharacteristic
105#10622295C2211yescharacteristic, complemented
106#10622293C2211yescharacteristic, complemented
107C2×C11×#41—21no—
108#41×D11—48no—
109C2×#4343—21no—
110C2×Q8×D11—21no—
111C2×Q8×D11—21no—
112C2×Q8×D11—21no—
113C2×#4341—22no—
114C2×#4341—21no—
115C2×D4×D11—22no—
116C2×D4×D11—21no—
117C2×D4×D11—21no—
118C2×D4×D11C2312yes—
119C2×#4339—21no—
120C2×#4339—22no—
121C22×C4×D11—22no—
122C22×C4×D11D411yescharacteristic
123C22×C4×D11D411yescharacteristic
124C22×C4×D11C2311yescharacteristic
125C11×C4⋊Q8C2311yescharacteristic
126C11×C4⋊Q8C2311yescharacteristic
127C11×C4⋊Q8C2311yescharacteristic
128C11×#127C2311yescharacteristic
129C11×#125C2312yes—
130C11×#124—21no—
131C11×C22⋊Q8—21no—
132C11×C22⋊Q8—21no—
133C11×#121—21no—
134C11×#121C2312yes—
135C4×Q8×C11—21no—
136C4×Q8×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11C2312yes—
139C11×#117C2312yes—
140C2×C42×C11C2311yescharacteristic
141#67000—21no—
142#66999—21no—
143#66999—21no—
144Q8×Dic11—21no—
145Q8×Dic11—21no—
146#66997—21no—
147#66997—21no—
148#66997—21no—
149#66993—21no—
150#66993—21no—
151#66993C2312yes—
152#66992—22no—
153#66992—22no—
154#66991—21no—
155#66991C2312yes—
156#66989—21no—
157D4×Dic11—21no—
158D4×Dic11C2312yes—
159#66983—21no—
160#66983C2312yes—
161C4×C22⋊D11—22no—
162C4×C22⋊D11—22no—
163#66979C2312yes—
164#66977—21no—
165#66977—21no—
166C2×C4×Dic11D411yescharacteristic
167C2×C4×Dic11D411yescharacteristic
168C2×C4×Dic11C2311yescharacteristic
169C2×C8×D11C2312yes—
170C2×C8×D11C2312yes—
171#66950—21no—
172#66950—21no—
173#66949—22no—
174#66949—22no—
175#66948—21no—
176#66948C2312yes—
177#66946—21no—
178#66946C2312yes—
179#66945C2312yes—
180#66945C2312yes—
181C4⋊C4×D11—21no—
182C4⋊C4×D11—21no—
183C4⋊C4×D11—21no—
184C4⋊C4×D11—22no—
185C4⋊C4×D11—22no—
186C4⋊C4×D11C2312yes—
187C4⋊C4×D11C2312yes—
188C4⋊C4×D11C2312yes—
189#66943C2312yes—
190#66943C2312yes—
191#66942—22no—
192#66942—22no—
193#66941—21no—
194#66941—21no—
195#66941—21no—
196#66941C2312yes—
197#66941C2312yes—
198#66941C2312yes—
199#66940—21no—
200#66940—21no—
201#66940—22no—
202#66940—22no—
203#66938—22no—
204#66938—22no—
205#66937—22no—
206#66937—22no—
207(C22⋊D11)⋊C4—22no—
208(C22⋊D11)⋊C4—22no—
209C22⋊C4×D11—22no—
210C22⋊C4×D11—22no—
211C22⋊C4×D11—22no—
212#66931—22no—
213#66931—22no—
214#66930—22no—
215#66928—21no—
216#66927C2311yescharacteristic
217C4×D44—21no—
218C4×D44C2312yes—
219#66925—22no—
220C42×D11—22no—
221C42×D11D411yescharacteristic
222C42×D11D411yescharacteristic
223C42×D11D411yescharacteristic
224C42×D11D411yescharacteristic
225C42×D11C2311yescharacteristic
226C42×D11C2311yescharacteristic
227C42×D11C2311yescharacteristic
228C42×D11C2311yescharacteristic
229#66923C2312yes—
230#66922C2311yescharacteristic
231#66922C2311yescharacteristic
232#66922C2311yescharacteristic
233C4×Dic22—21no—
234C4×Dic22—21no—
235C4×Dic22—22no—
236C4×Dic22—22no—
237C11×#107C2314yes—
238C11×#106C2314yes—
239C11×C4⋊C8C2312yes—
240C11×#102C2314yes—
241C11×#102C2314yes—
242C11×C22⋊C8C2312yes—
243C4×C8×C11C2311yescharacteristic
244C4×C8×C11C2311yescharacteristic
245#66896C2314yes—
246#66896C2314yes—
247C22⋊(C11⋊C8)C2312yes—
248#66885C2314yes—
249#66885C2314yes—
250(C2×D11)⋊C8C2312yes—
251(C2×D11)⋊C8C2312yes—
252#66882C2314yes—
253#66881C2314yes—
254Dic11⋊C8C2312yes—
255Dic11⋊C8C2312yes—
256C8×Dic11C2312yes—
257C8×Dic11C2312yes—
258#66873C2314yes—
259#66873C2314yes—
260#66872C2314yes—
261#66872C2314yes—
262#66871C2314yes—
263#66871C2314yes—
264C4⋊(C11⋊C8)C2312yes—
265C4×C11⋊C8C2311yescharacteristic
266C4×C11⋊C8C2311yescharacteristic
267C2×#3228—111nomaximal, Sylow
268C23×D11—22no—
269C23×D11C2×D411yescharacteristic
270C11×#41—44no—
271C2×Q8×C11—21no—
272C2×Q8×C11—21no—
273C2×Q8×C11—21no—
274C2×D4×C11—22no—
275C2×D4×C11—21no—
276C2×D4×C11—21no—
277C2×D4×C11C2412yes—
278C22×C4×C11—22no—
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C2×C22⋊D11—22no—
283C2×C22⋊D11—22no—
284C2×C22⋊D11—22no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—22no—
287C22×Dic11—22no—
288C22×Dic11C2×D411yescharacteristic
289C22×Dic11C2×D411yescharacteristic
290C22×Dic11C2×D411yescharacteristic
291#4343—44no—
292Q8×D11—44no—
293Q8×D11—44no—
294Q8×D11—44no—
295#4341—44no—
296#4341—48no—
297D4×D11—28no—
298D4×D11—48no—
299D4×D11—44no—
300D4×D11—44no—
301#4339—44no—
302#4339—48no—
303C2×D44—22no—
304C2×D44—21no—
305C2×D44—21no—
306C2×D44C2412yes—
307C2×C4×D11—24no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—48no—
316C2×C4×D11C2×D411yescharacteristic
317C2×C4×D11C2×D411yescharacteristic
318C2×C4×D11C2×D411yescharacteristic
319C2×C4×D11C2×D411yescharacteristic
320C2×C4×D11C2×D411yescharacteristic
321C2×C4×D11C2×D411yescharacteristic
322C2×C4×D11C2×D411yescharacteristic
323C2×C4×D11C2×D411yescharacteristic
324C2×C4×D11C2×D411yescharacteristic
325C2×C4×D11C2×D411yescharacteristic
326C2×C4×D11C2411yescharacteristic
327C2×C4×D11C2411yescharacteristic
328C2×Dic22—22no—
329C2×Dic22—22no—
330C2×Dic22—22no—
331C2×Dic22—21no—
332C2×Dic22—21no—
333C2×Dic22—21no—
334C2×C8×C11C2412yes—
335C2×C8×C11C2412yes—
336C11×C4⋊C4—21no—
337C11×C4⋊C4—21no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—21no—
341C11×C4⋊C4C2412yes—
342C11×C4⋊C4C2412yes—
343C11×C4⋊C4C2412yes—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C42×C11—22no—
348C42×C11C2×D411yescharacteristic
349C42×C11C2×D411yescharacteristic
350C42×C11C2411yescharacteristic
351C42×C11C2411yescharacteristic
352C22⋊Dic11—22no—
353C22⋊Dic11—22no—
354C22⋊Dic11—22no—
355(C2×D11)⋊C4—22no—
356(C2×D11)⋊C4—22no—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—22no—
361C4⋊Dic11—22no—
362C4⋊Dic11—22no—
363C4⋊Dic11—21no—
364C4⋊Dic11—21no—
365C4⋊Dic11—21no—
366C4⋊Dic11C2412yes—
367C4⋊Dic11C2412yes—
368C4⋊Dic11C2412yes—
369Dic11⋊C4—22no—
370Dic11⋊C4—22no—
371Dic11⋊C4—22no—
372Dic11⋊C4—22no—
373Dic11⋊C4—22no—
374Dic11⋊C4—22no—
375Dic11⋊C4—22no—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378Dic11⋊C4—22no—
379C4×Dic11—22no—
380C4×Dic11—22no—
381C4×Dic11—22no—
382C4×Dic11C2×D411yescharacteristic
383C4×Dic11C2×D411yescharacteristic
384C4×Dic11C2×D411yescharacteristic
385C4×Dic11C2×D411yescharacteristic
386C4×Dic11C2×D411yescharacteristic
387C4×Dic11C2×D411yescharacteristic
388C4×Dic11C2×D411yescharacteristic
389C4×Dic11C2×D411yescharacteristic
390C4×Dic11C2×D411yescharacteristic
391C4×Dic11C2×D411yescharacteristic
392C4×Dic11C2411yescharacteristic
393C4×Dic11C2411yescharacteristic
394C2×C11⋊C8C2412yes—
395C2×C11⋊C8C2412yes—
396C8×D11—24no—
397C8×D11—24no—
398C2×#533—111no—
399C2×#532—111no—
400#3228—111no—
401#3228—111no—
402#3228—111no—
403#3228—111no—
404#3228—114no—
405#3228—114no—
406#3228—111no—
407#3228—111no—
408#3228—111no—
409#3228D1111yescharacteristic, direct product factor
410C2×#500—111no—
411C2×#498—111no—
412C2×#486—111no—
413C2×#486—111no—
414C2×#482—114no—
415C2×#478—114no—
416C2×#431—111no—
417C23×C11—22no—
418C23×C11C22×D411yescharacteristic
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—44no—
424C22×D11—44no—
425C22×D11—44no—
426C22×D11C22×D411yescharacteristic
427C22×D11C22×D411yescharacteristic
428Q8×C11—42no—
429Q8×C11—42no—
430Q8×C11—42no—
431D4×C11—24no—
432D4×C11—44no—
433D4×C11—42no—
434D4×C11—42no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—44no—
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C2511yescharacteristic
448C22⋊D11—44no—
449C22⋊D11—44no—
450C22⋊D11—44no—
451C22⋊D11—44no—
452C22⋊D11—44no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—44no—
460C2×Dic11C22×D411yescharacteristic
461C2×Dic11C22×D411yescharacteristic
462C2×Dic11C22×D411yescharacteristic
463C2×Dic11C22×D411yescharacteristic
464C2×Dic11C22×D411yescharacteristic
465C2×Dic11C22×D411yescharacteristic
466D44—24no—
467D44—44no—
468D44—42no—
469D44—42no—
470C4×D11—22no—
471C4×D11—22no—
472C4×D11—22no—
473C4×D11—22no—
474C4×D11—22no—
475C4×D11—22no—
476C4×D11—22no—
477C4×D11—22no—
478C4×D11—22no—
479C4×D11—44no—
480C4×D11—44no—
481C4×D11—44no—
482C4×D11—44no—
483C4×D11—44no—
484C4×D11#13514yes—
485C4×D11AGL(1,ℤ/8)14yes—
486C4×D112−1+414yes—
487Dic22—42no—
488Dic22—42no—
489Dic22—42no—
490Dic22—44no—
491Dic22—44no—
492Dic22—44no—
493C8×C11—22no—
494C8×C11—22no—
495C11⋊C8—22no—
496C11⋊C8—22no—
497C22×#41—221no—
498#533—111no—
499#533—111no—
500#533—112no—
501#533—112no—
502#533—111no—
503#533—221no—
504#533—221no—
505#533—221no—
506#533—221no—
507#533C2×D1111yescharacteristic, complemented
508#532—111no—
509#532—111no—
510#532—112no—
511#532—112no—
512#532—111no—
513#532—221no—
514#532—221no—
515#532—221no—
516#532—221no—
517#532C2×D1111yescharacteristic
518C2×C4⋊Q8—111no—
519C2×C4⋊Q8—111no—
520C2×C4⋊Q8—111no—
521C2×#127—111no—
522C2×#125—112no—
523C2×#124—221no—
524C2×C22⋊Q8—221no—
525C2×C22⋊Q8—221no—
526C2×#121—112no—
527C2×#121—221no—
528C2×C4×Q8—221no—
529C2×C4×Q8—221no—
530C2×C4×D4—112no—
531C2×C4×D4—221no—
532C2×#117—112no—
533C22×C42—111no—
534#500—111no—
535#500—111no—
536#500—114no—
537#500—111no—
538#500C2×D1111yescharacteristic, complemented
539#498—111no—
540#498—111no—
541#498—114no—
542#498—111no—
543#498C2×D1111yescharacteristic, complemented
544#486—111no—
545#486—111no—
546#486—111no—
547#486—111no—
548#486—114no—
549#486—114no—
550#486—111no—
551#486—111no—
552#486C2×D1111yescharacteristic, complemented
553#486C2×D1111yescharacteristic, complemented
554#482—114no—
555#482—114no—
556#482—114no—
557#482—114no—
558#482—114no—
559#482—114no—
560#482—114no—
561#482C2×D1114yescomplemented
562#478—114no—
563#478—114no—
564#478—114no—
565#478—114no—
566#478—114no—
567#478—114no—
568#478—114no—
569#478C2×D1114yescomplemented
570#431—111no—
571#431—112no—
572#431—112no—
573#431—111no—
574#431—111no—
575#431C2×D1111yescharacteristic, complemented
576C2×#107—114no—
577C2×#106—114no—
578C2×C4⋊C8—112no—
579C2×#102—114no—
580C2×#102—114no—
581C2×C22⋊C8—112no—
582C2×C4×C8—111no—
583C2×C4×C8—111no—
584C22×C11—21no—
585C22×C11—21no—
586C22×C11—21no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11C23×D411yescharacteristic
591C2×D11—21no—
592C2×D11—21no—
593C2×D11—21no—
594C2×D11—44no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—88no—
599C2×D11#53612yes—
600C2×D11C2×#13512yes—
601C2×D11C2×AGL(1,ℤ/8)12yes—
602C4×C11—21no—
603C4×C11—21no—
604C4×C11—21no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11C2×#13512yes—
609C4×C11C2×AGL(1,ℤ/8)12yes—
610C4×C11C2×2−1+412yes—
611Dic11—21no—
612Dic11—21no—
613Dic11—21no—
614Dic11—42no—
615Dic11—42no—
616Dic11—42no—
617Dic11#53612yes—
618Dic11C2×#13512yes—
619Dic11C2×AGL(1,ℤ/8)12yes—
620C2×#41—21no—
621C2×#41—222no—
622C2×#41—222no—
623C2×#41—221no—
624C2×#41—221no—
625C2×#41—221no—
626C2×#41—448no—
627C22×Q8—221no—
628C22×Q8—221no—
629C22×Q8—221no—
630C22×D4—112no—
631C22×D4—221no—
632C22×D4—221no—
633C22×D4—222no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—222no—
638C22×C8—112no—
639C22×C8—112no—
640C4⋊Q8—112no—
641C4⋊Q8—112no—
642C4⋊Q8—112no—
643C4⋊Q8—111no—
644C4⋊Q8—111no—
645C4⋊Q8—111no—
646C4⋊Q8—221no—
647C4⋊Q8—221no—
648C4⋊Q8—221no—
649C4⋊Q8—221no—
650C4⋊Q8—221no—
651C4⋊Q8—221no—
652C4⋊Q8C22×D1111yescharacteristic
653C4⋊Q8C22×D1111yescharacteristic
654C4⋊Q8C22×D1111yescharacteristic
655#127—112no—
656#127—111no—
657#127—221no—
658#127—221no—
659#127C22×D1111yescharacteristic
660#125—112no—
661#125—112no—
662#125—112no—
663#125—222no—
664#125—222no—
665#125C22×D1112yes—
666#124—21no—
667#124—222no—
668#124—222no—
669#124—221no—
670#124—221no—
671#124—221no—
672C22⋊Q8—21no—
673C22⋊Q8—21no—
674C22⋊Q8—222no—
675C22⋊Q8—222no—
676C22⋊Q8—222no—
677C22⋊Q8—222no—
678C22⋊Q8—221no—
679C22⋊Q8—221no—
680C22⋊Q8—221no—
681C22⋊Q8—221no—
682C22⋊Q8—221no—
683C22⋊Q8—221no—
684#121—21no—
685#121—112no—
686#121—112no—
687#121—112no—
688#121—222no—
689#121—222no—
690#121—221no—
691#121—222no—
692#121—221no—
693#121—222no—
694#121—221no—
695#121C22×D1112yes—
696C4×Q8—21no—
697C4×Q8—21no—
698C4×Q8—222no—
699C4×Q8—222no—
700C4×Q8—222no—
701C4×Q8—221no—
702C4×Q8—222no—
703C4×Q8—221no—
704C4×Q8—221no—
705C4×Q8—221no—
706C4×Q8—221no—
707C4×Q8—221no—
708C4×D4—21no—
709C4×D4—112no—
710C4×D4—112no—
711C4×D4—112no—
712C4×D4—222no—
713C4×D4—222no—
714C4×D4—221no—
715C4×D4—222no—
716C4×D4—222no—
717C4×D4—221no—
718C4×D4—221no—
719C4×D4C22×D1112yes—
720#117—112no—
721#117—112no—
722#117—112no—
723#117—222no—
724#117—222no—
725#117C22×D1112yes—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—112no—
728C2×C4⋊C4—112no—
729C2×C4⋊C4—221no—
730C2×C4⋊C4—222no—
731C2×C4⋊C4—222no—
732C2×C4⋊C4—221no—
733C2×C4⋊C4—221no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C42—111no—
738C2×C42—111no—
739C2×C42—111no—
740C2×C42—111no—
741C2×C42—111no—
742C2×C42—111no—
743C2×C42—111no—
744C2×C42—111no—
745C2×C42—111no—
746C2×C42—111no—
747C2×C42—111no—
748C2×C42—222no—
749C2×C42C22×D1111yescharacteristic
750#107—114no—
751#107—114no—
752#107—114no—
753#107C22×D1114yes—
754#106—114no—
755#106—114no—
756#106—114no—
757#106C22×D1114yes—
758C4⋊C8—112no—
759C4⋊C8—112no—
760C4⋊C8—112no—
761C4⋊C8C22×D1112yes—
762#102—114no—
763#102—114no—
764#102—114no—
765#102—114no—
766#102—114no—
767#102—114no—
768#102C22×D1114yes—
769#102C22×D1114yes—
770C22⋊C8—112no—
771C22⋊C8—112no—
772C22⋊C8—112no—
773C22⋊C8C22×D1112yes—
774C4×C8—112no—
775C4×C8—112no—
776C4×C8—111no—
777C4×C8—111no—
778C4×C8C22×D1111yescharacteristic
779C4×C8C22×D1111yescharacteristic
780C2×C11—41no—
781C2×C11—82no—
782C2×C11C2×#53611yescharacteristic
783C2×C11C22×#13511yescharacteristic
784C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
785D11—41no—
786D11—82no—
787D11#322814yesdirect product factor
788C24—111no—
789C24—222no—
790#41—44no—
791#41—444no—
792#41—448no—
793#41—448no—
794#41—444no—
795#41—444no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—222no—
800C2×Q8—222no—
801C2×Q8—222no—
802C2×Q8—221no—
803C2×Q8—221no—
804C2×Q8—221no—
805C2×Q8—444no—
806C2×Q8—444no—
807C2×Q8—444no—
808C2×D4—22no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—112no—
812C2×D4—222no—
813C2×D4—228no—
814C2×D4—222no—
815C2×D4—222no—
816C2×D4—222no—
817C2×D4—222no—
818C2×D4—222no—
819C2×D4—221no—
820C2×D4—221no—
821C2×D4—444no—
822C2×D4—444no—
823C2×D4—448no—
824C2×D4C23×D1112yes—
825C22×C4—22no—
826C22×C4—111no—
827C22×C4—111no—
828C22×C4—111no—
829C22×C4—111no—
830C22×C4—111no—
831C22×C4—111no—
832C22×C4—111no—
833C22×C4—111no—
834C22×C4—111no—
835C22×C4—111no—
836C22×C4—111no—
837C22×C4—111no—
838C22×C4—111no—
839C22×C4—111no—
840C22×C4—111no—
841C22×C4—224no—
842C22×C4—224no—
843C22×C4—224no—
844C22×C4—222no—
845C22×C4—222no—
846C22×C4—222no—
847C22×C4—222no—
848C22×C4—222no—
849C22×C4—222no—
850C22×C4—448no—
851C22×C4D4×D1111yescharacteristic
852C22×C4D4×D1111yescharacteristic
853C22×C4C23×D1111yescharacteristic
854C2×C8—112no—
855C2×C8—112no—
856C2×C8—224no—
857C2×C8—224no—
858C2×C8C23×D1112yes—
859C2×C8C23×D1112yes—
860C4⋊C4—21no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—112no—
866C4⋊C4—112no—
867C4⋊C4—112no—
868C4⋊C4—222no—
869C4⋊C4—222no—
870C4⋊C4—222no—
871C4⋊C4—222no—
872C4⋊C4—222no—
873C4⋊C4—222no—
874C4⋊C4—222no—
875C4⋊C4—222no—
876C4⋊C4—222no—
877C4⋊C4—222no—
878C4⋊C4—221no—
879C4⋊C4—222no—
880C4⋊C4—222no—
881C4⋊C4—221no—
882C4⋊C4—221no—
883C4⋊C4C23×D1112yes—
884C4⋊C4C23×D1112yes—
885C4⋊C4C23×D1112yes—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—222no—
890C22⋊C4—222no—
891C22⋊C4—222no—
892C22⋊C4—222no—
893C22⋊C4—222no—
894C22⋊C4—222no—
895C22⋊C4—222no—
896C22⋊C4—222no—
897C22⋊C4—222no—
898C42—22no—
899C42—111no—
900C42—111no—
901C42—111no—
902C42—111no—
903C42—111no—
904C42—111no—
905C42—111no—
906C42—111no—
907C42—111no—
908C42—111no—
909C42—111no—
910C42—111no—
911C42—222no—
912C42—222no—
913C42—222no—
914C42D4×D1111yescharacteristic
915C42D4×D1111yescharacteristic
916C42C23×D1111yescharacteristic
917C42C23×D1111yescharacteristic
918C11C2×#322811yescharacteristic, complemented, Sylow
919C23—22no—
920C23—111no—
921C23—111no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—444no—
927C23—444no—
928C23—444no—
929C23C2×D4×D1111yescharacteristic
930Q8—42no—
931Q8—42no—
932Q8—42no—
933Q8—444no—
934Q8—444no—
935Q8—444no—
936Q8—442no—
937Q8—442no—
938Q8—442no—
939D4—24no—
940D4—44no—
941D4—42no—
942D4—42no—
943D4—224no—
944D4—444no—
945D4—444no—
946D4—444no—
947D4—444no—
948D4—444no—
949D4—444no—
950D4—442no—
951D4—442no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—44no—
959C2×C4—111no—
960C2×C4—111no—
961C2×C4—111no—
962C2×C4—114no—
963C2×C4—114no—
964C2×C4—114no—
965C2×C4—111no—
966C2×C4—111no—
967C2×C4—111no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—444no—
984C2×C4—444no—
985C2×C4—444no—
986C2×C4—444no—
987C2×C4—444no—
988C2×C4—444no—
989C2×C4C2×D4×D1111yescharacteristic
990C2×C4C2×D4×D1111yescharacteristic
991C2×C4C2×D4×D1111yescharacteristic
992C2×C4C2×D4×D1111yescharacteristic
993C2×C4C2×D4×D1111yescharacteristic
994C2×C4C24×D1111yescharacteristic
995C8—22no—
996C8—22no—
997C8—222no—
998C8—222no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—112no—
1006C22—112no—
1007C22—112no—
1008C22—221no—
1009C22—221no—
1010C22—221no—
1011C22—444no—
1012C22—442no—
1013C22—442no—
1014C22—442no—
1015C22—888no—
1016C22C22×D4×D1111yescharacteristic
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—112no—
1024C4—112no—
1025C4—112no—
1026C4—221no—
1027C4—221no—
1028C4—221no—
1029C4—442no—
1030C4—442no—
1031C4—442no—
1032C4D11×#13512yes—
1033C4D11×AGL(1,ℤ/8)12yes—
1034C4D11×2−1+412yes—
1035C2—41no—
1036C2—82no—
1037C2—114no—
1038C2—441no—
1039C2—882no—
1040C2D11×#53611yescharacteristic
1041C2C2×D11×#13511yescharacteristic
1042C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3228C2
socleC22×C11C23×D4
prime radicalD11×#532C2
hypercenter#3228D11
hypocenterC11C2×#3228
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. D11×#533C2semidirect
3. #13079755C2semidirect
4. #13079754C2semidirect
5. #13079753C2semidirect
6. #13079752C2semidirect
7. #13079751C2semidirect
8. #13079750C2semidirect
9. #13079749C2semidirect
10. #13079748C2semidirect
11. #13079747C2semidirect
12. D11×#500C2semidirect
13. D11×#498C2semidirect
14. D11×#486C2semidirect
15. D11×#486C2semidirect
16. D11×#482C2semidirect
17. D11×#478C2semidirect
18. D11×#431C2semidirect
19. C11×#3228C2semidirect
21. C11×#533C22semidirect
24. #10623259C22semidirect
25. #10623259C22semidirect
32. #10623219C22semidirect
53. #10623048C22semidirect
56. #10623001C22semidirect
57. C11×#500C22semidirect
58. C11×#498C22semidirect
59. C11×#486C22semidirect
60. C11×#486C22semidirect
61. C11×#482C22semidirect
62. C11×#478C22semidirect
63. C11×#431C22semidirect
64. #10622701C22semidirect
65. #10622701C22semidirect
66. #10622692C22semidirect
67. #10622692C22semidirect
68. #10622691C22semidirect
69. #10622691C22semidirect
70. #10622683C22semidirect
71. #10622683C22semidirect
72. #10622679C22semidirect
73. #10622648C22semidirect
74. #10622622C22semidirect
75. #10622616C22semidirect
76. #10622538C22semidirect
77. #10622504C22semidirect
78. #10622498C22semidirect
80. #10622487C22semidirect
81. #10622484C22semidirect
82. #10622479C22semidirect
84. #10622468C22semidirect
85. #10622460C22semidirect
86. #10622446C22semidirect
88. #10622397C22semidirect
89. #10622392C22semidirect
92. #10622379C22semidirect
93. #10622376C22semidirect
94. #10622373C22semidirect
95. #10622373C22semidirect
96. #10622350C22semidirect
98. #10622331C22semidirect
99. #10622307C22semidirect
100. #10622307C22semidirect
101. #10622298C22semidirect
102. #10622298C22semidirect
105. #10622295C22semidirect
106. #10622293C22semidirect
409. #3228D11direct (N × H)
507. #533C2×D11semidirect
538. #500C2×D11semidirect
543. #498C2×D11semidirect
552. #486C2×D11semidirect
553. #486C2×D11semidirect
561. #482C2×D11semidirect
569. #478C2×D11semidirect
575. #431C2×D11semidirect
787. D11#3228direct (N × H)
918. C11C2×#3228semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#5322
#130797552
#130797542
#130797532
#130797522
#130797512
#130797502
#130797492
#130797482
#130797472
D11×#5002
D11×#4982
D11×#4862
D11×#4822
D11×#4782
D11×#4312
C11×#32282
C2×#322811