Finite Group Databasebeta

← D11×#3200 #15624441

Subgroups — D11×#3200 #15624441

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#536C211yesmaximal, characteristic, complemented
2D11×#535C211yesmaximal, characteristic
3#13079490C212yesmaximal, complemented
4#13079489C211yesmaximal, characteristic, complemented
5#13079488C211yesmaximal, characteristic, complemented
6#13079487C212yesmaximal, complemented
7#13079486C212yesmaximal, complemented
8#13079485C212yesmaximal, complemented
9#13079484C212yesmaximal, complemented
10#13079483C211yesmaximal, characteristic, complemented
11#13079482C212yesmaximal, complemented
12D11×#485C212yesmaximal, complemented
13D11×#482C212yesmaximal, complemented
14D11×#468C212yesmaximal, complemented
15D11×#465C212yesmaximal, complemented
16D11×#448C212yesmaximal, complemented
17D11×#450C212yesmaximal, complemented
18D11×#408C211yesmaximal, characteristic, complemented
19C11×#3200C211yesmaximal, characteristic, complemented
20C2×#41×D11C2211yescharacteristic
21C22×Q8×D11C2211yescharacteristic, complemented
22C22×D4×D11C2211yescharacteristic
23C11×#536C2211yescharacteristic, complemented
24C11×#535C2211yescharacteristic
25#10623361C2211yescharacteristic
26#10623356C2211yescharacteristic, complemented
27#10623347C2211yescharacteristic, complemented
28#10623336C2211yescharacteristic
29C2×SD16×D11C2212yes—
30C2×SD16×D11C2212yes—
31C2×M16×D11C2211yescharacteristic, complemented
32C22×C8×D11C2211yescharacteristic, complemented
33#10623255—21no—
34D11×C4⋊Q8—21no—
35#10623246—21no—
36D11×#127—21no—
37#10623206—21no—
38#10623205—21no—
39D11×#124—21no—
40D11×#124—21no—
41D11×#123—21no—
42D11×#123—21no—
43#10623179—21no—
44#10623179—21no—
45#10623159C2212yescomplemented
46#10623159C2212yescomplemented
47D11×C22⋊Q8C2212yes—
48D11×C22⋊Q8C2212yescomplemented
49#10623138C2212yes—
50#10623138C2212yes—
51D11×#121C2212yes—
52D11×#121C2212yes—
53#10623123—21no—
54#10623123—21no—
55D11×#120—21no—
56D11×#120—21no—
57#10623057C2211yescharacteristic, complemented
58#10623056C2211yescharacteristic
59D11×#117C2211yescharacteristic
60D11×#117C2211yescharacteristic, complemented
61C11×#485C2212yescomplemented
62C11×#482C2212yescomplemented
63C11×#468C2212yescomplemented
64C11×#465C2212yescomplemented
65C11×#450C2212yescomplemented
66C11×#448C2212yescomplemented
67C11×#408C2211yescharacteristic, complemented
68#10622847C2211yescharacteristic, complemented
69#10622840C2212yescomplemented
70#10622831C2212yescomplemented
71#10622787C2212yescomplemented
72#10622784C2212yescomplemented
73#10622783C2212yescomplemented
74#10622783C2212yescomplemented
75#10622782C2212yescomplemented
76#10622782C2212yescomplemented
77#10622747C2212yescomplemented
78#10622742C2211yescharacteristic, complemented
79#10622727C2212yescomplemented
80#10622723C2211yescharacteristic, complemented
81#10622662C2212yescomplemented
82#10622661C2212yescomplemented
83#10622659C2212yescomplemented
84#10622658C2212yescomplemented
85#10622655C2212yescomplemented
86#10622654C2212yescomplemented
87#10622653C2212yescomplemented
88#10622648C2212yescomplemented
89#10622616C2212yescomplemented
90#10622609C2212yescomplemented
91#10622501C2212yescomplemented
92#10622499C2212yescomplemented
93#10622498C2212yescomplemented
94D11×#107C2212yescomplemented
95#10622480C2212yescomplemented
96#10622479C2212yescomplemented
97#10622477C2212yescomplemented
98D11×#106C2212yescomplemented
99#10622428C2212yescomplemented
100#10622427C2212yescomplemented
101#10622425C2212yescomplemented
102#10622420C2212yescomplemented
103#10622419C2212yescomplemented
104#10622419C2212yescomplemented
105D11×#103C2212yescomplemented
106D11×#103C2212yescomplemented
107#10622397C2212yescomplemented
108#10622393C2212yescomplemented
109#10622392C2212yescomplemented
110#10622391C2212yescomplemented
111#10622389C2212yescomplemented
112#10622389C2212yescomplemented
113D11×#102C2212yes—
114D11×#102C2212yes—
115#10622351C2212yescomplemented
116#10622350C2212yescomplemented
117#10622344C2212yescomplemented
118#10622340C2212yescomplemented
119#10622340C2212yescomplemented
120D11×C22⋊C8C2212yes—
121D11×C22⋊C8C2212yescomplemented
122#10622336C2212yescomplemented
123C24×D11—21no—
124C2×C11×#41C2311yescharacteristic
125C22×Q8×C11C2311yescharacteristic, complemented
126C22×D4×C11C2311yescharacteristic
127C22×C22⋊D11—21no—
128#41×D11—42no—
129#41×D11—42no—
130C2×#4343D411yescharacteristic
131C2×Q8×D11—21no—
132C2×Q8×D11—21no—
133C2×Q8×D11—42no—
134C2×Q8×D11—42no—
135C2×Q8×D11D411yescharacteristic
136C2×Q8×D11C2312yes—
137C2×Q8×D11C2312yescomplemented
138C2×#4341D411yescharacteristic
139C2×#4341D411yescharacteristic
140C2×#4341D411yescharacteristic
141C2×D4×D11—22no—
142C2×D4×D11—22no—
143C2×D4×D11—21no—
144C2×D4×D11—21no—
145C2×D4×D11—42no—
146C2×D4×D11—42no—
147C2×D4×D11D411yescharacteristic
148C2×D4×D11D411yescharacteristic
149C2×D4×D11D411yescharacteristic
150C2×D4×D11C2312yes—
151C2×D4×D11C2312yes—
152C2×#4339C2311yescharacteristic
153C2×#4339C2311yescharacteristic
154C2×#4339C2311yescharacteristic
155C22×D44C2311yescharacteristic
156C22×C4×D11—21no—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×Dic22—21no—
161C22×Dic22C2311yescharacteristic, complemented
162C2×C11×SD16C2312yes—
163C2×C11×SD16C2312yes—
164C2×C11×M16C2311yescharacteristic, complemented
165C22×C8×C11C2311yescharacteristic, complemented
166C11×C4⋊Q8—21no—
167C11×#127—21no—
168C11×#124—21no—
169C11×#124—21no—
170C11×#123—21no—
171C11×#123—21no—
172C11×C22⋊Q8C2312yes—
173C11×C22⋊Q8C2312yescomplemented
174C11×#121C2312yes—
175C11×#121C2312yes—
176C11×#120—21no—
177C11×#120—21no—
178C11×#117C2311yescharacteristic
179C11×#117C2311yescharacteristic, complemented
180#67006—21no—
181#67006—21no—
182#67000—21no—
183#67000—21no—
184#66999C2312yes—
185#66999C2312yescomplemented
186#66997—21no—
187#66997—21no—
188C2×#4325C2312yes—
189C2×#4325C2312yes—
190#66993—21no—
191#66993—22no—
192#66993—22no—
193#66993—21no—
194#66992—22no—
195#66992—22no—
196#66991C2312yes—
197#66991C2312yes—
198#66990—21no—
199#66990—21no—
200#66990—22no—
201#66990—22no—
202#66989—21no—
203#66989—21no—
204#66988—21no—
205#66988—21no—
206C2×#4324C2312yes—
207C2×#4324C2312yes—
208#66983C2312yes—
209#66983C2312yes—
210#66982—21no—
211#66982—21no—
212#66979C2311yescharacteristic
213#66979C2311yescharacteristic, complemented
214#66977C2312yes—
215#66977C2312yescomplemented
216C2×#4318C2311yescharacteristic, complemented
217C22×C11⋊C8C2311yescharacteristic, complemented
218SD16×D11—44no—
219SD16×D11—44no—
220M16×D11—42no—
221C2×#4314C2312yes—
222C2×#4314C2312yes—
223C2×#4313C2312yescomplemented
224C2×C8×D11—42no—
225C2×C8×D11C2312yes—
226C2×C8×D11C2312yes—
227C2×C8×D11C2312yescomplemented
228#66950C2312yes—
229#66950C2312yescomplemented
230#66949—22no—
231#66949—22no—
232#66948C2312yes—
233#66948C2312yes—
234#66947—22no—
235#66947—22no—
236#66945C2312yes—
237#66945C2312yescomplemented
238C4⋊C4×D11—22no—
239C4⋊C4×D11—22no—
240C4⋊C4×D11C2312yes—
241C4⋊C4×D11C2312yes—
242#66941—22no—
243#66941—22no—
244#66939—21no—
245#66939—21no—
246#66938—22no—
247#66938—22no—
248#66938—22no—
249#66938—22no—
250#66937—22no—
251#66937—22no—
252#66936—22no—
253#66936—22no—
254#66935—21no—
255#66935—21no—
256#66935—22no—
257#66935—22no—
258C22⋊C4×D11—21no—
259C22⋊C4×D11—21no—
260C22⋊C4×D11—22no—
261C22⋊C4×D11—22no—
262C22⋊C4×D11—22no—
263C22⋊C4×D11—22no—
264#66931—22no—
265#66931—22no—
266#66930—21no—
267#66930—21no—
268#66928—21no—
269#66928—21no—
270#66927—21no—
271#66925—21no—
272#66925—21no—
273C42×D11—21no—
274C42×D11—21no—
275#66922—21no—
276C11×#107C2312yescomplemented
277C11×#106C2312yescomplemented
278C11×#103C2312yescomplemented
279C11×#103C2312yescomplemented
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2312yescomplemented
284#66899C2312yescomplemented
285#66899C2312yescomplemented
286#66896C2312yes—
287#66896C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yescomplemented
290#66885C2312yes—
291#66885C2312yes—
292(C2×D11)⋊C8C2312yes—
293(C2×D11)⋊C8C2312yes—
294(C2×D11)⋊C8C2312yescomplemented
295(C2×D11)⋊C8C2312yescomplemented
296#66882C2312yescomplemented
297#66881C2312yescomplemented
298#66880C2312yescomplemented
299#66880C2312yescomplemented
300#66874C2312yescomplemented
301#66874C2312yescomplemented
302#66873C2312yes—
303#66873C2312yes—
304#66872C2312yescomplemented
305#66872C2312yescomplemented
306#66871C2312yescomplemented
307#66871C2312yescomplemented
308C2×#3200—111nomaximal, Sylow
309C24×C11—21no—
310C23×D11—21no—
311C23×D11—22no—
312C23×D11—22no—
313C23×D11—44no—
314C23×D11—84no—
315C23×D11C2×D411yescharacteristic
316C23×D11C2×D411yescharacteristic
317C23×D11C2×D411yescharacteristic
318C11×#41—41no—
319C11×#41—41no—
320C2×Q8×C11—21no—
321C2×Q8×C11—41no—
322C2×Q8×C11—41no—
323C2×Q8×C11C2×D411yescharacteristic
324C2×Q8×C11C2412yes—
325C2×D4×C11—22no—
326C2×D4×C11—22no—
327C2×D4×C11—21no—
328C2×D4×C11—41no—
329C2×D4×C11—41no—
330C2×D4×C11C2×D411yescharacteristic
331C2×D4×C11C2×D411yescharacteristic
332C2×D4×C11C2×D411yescharacteristic
333C2×D4×C11C2412yes—
334C22×C4×C11—21no—
335C22×C4×C11C2411yescharacteristic
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2411yescharacteristic
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—22no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—44no—
345C2×C22⋊D11C2×D411yescharacteristic
346C2×C22⋊D11C2×D411yescharacteristic
347C2×C22⋊D11C2×D411yescharacteristic
348C2×C22⋊D11C2×D411yescharacteristic
349C2×C22⋊D11C2×D411yescharacteristic
350C2×C22⋊D11C2×D411yescharacteristic
351C22×Dic11—21no—
352C22×Dic11C2×D411yescharacteristic
353C22×Dic11C2×D411yescharacteristic
354C22×Dic11C2×D411yescharacteristic
355#4343—42no—
356Q8×D11—24no—
357Q8×D11—24no—
358Q8×D11—42no—
359Q8×D11—42no—
360Q8×D11—42no—
361Q8×D11—44no—
362Q8×D11—44no—
363#4341—42no—
364#4341—42no—
365#4341—42no—
366D4×D11—24no—
367D4×D11—24no—
368D4×D11—42no—
369D4×D11—42no—
370D4×D11—42no—
371D4×D11—42no—
372D4×D11—42no—
373D4×D11—44no—
374D4×D11—44no—
375D4×D11—84no—
376D4×D11—84no—
377#4339—41no—
378#4339—41no—
379#4339—41no—
380#4339—41no—
381#4339—41no—
382#4339—41no—
383C2×D44—22no—
384C2×D44—22no—
385C2×D44—21no—
386C2×D44—41no—
387C2×D44—41no—
388C2×D44C2×D411yescharacteristic
389C2×D44C2×D411yescharacteristic
390C2×D44C2×D411yescharacteristic
391C2×D44C2412yes—
392C2×C4×D11—22no—
393C2×C4×D11—22no—
394C2×C4×D11—22no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—22no—
399C2×C4×D11—22no—
400C2×C4×D11—22no—
401C2×C4×D11—22no—
402C2×C4×D11—44no—
403C2×C4×D11C2×D411yescharacteristic
404C2×C4×D11C2×D411yescharacteristic
405C2×C4×D11C2×D411yescharacteristic
406C2×C4×D11C2×D411yescharacteristic
407C2×C4×D11C2×D411yescharacteristic
408C2×C4×D11C2×D411yescharacteristic
409C2×C4×D11C2411yescharacteristic
410C2×C4×D11C2411yescharacteristic
411C2×C4×D11C2411yescharacteristic
412C2×C4×D11C2411yescharacteristic
413C2×Dic22—22no—
414C2×Dic22—22no—
415C2×Dic22—21no—
416C2×Dic22—41no—
417C2×Dic22—41no—
418C2×Dic22—44no—
419C2×Dic22C2×D411yescharacteristic
420C2×Dic22C2×D411yescharacteristic
421C2×Dic22C2×D411yescharacteristic
422C2×Dic22C2412yes—
423C11×SD16—42no—
424C11×SD16—42no—
425C11×M16—41no—
426C2×C8×C11—41no—
427C2×C8×C11C2412yes—
428C2×C8×C11C2412yes—
429C11×C4⋊C4—22no—
430C11×C4⋊C4—22no—
431C11×C4⋊C4C2412yes—
432C11×C4⋊C4C2412yes—
433C11×C22⋊C4—21no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C42×C11—21no—
440C42×C11—21no—
441C22⋊Dic11—22no—
442C22⋊Dic11—22no—
443C22⋊Dic11—21no—
444C22⋊Dic11—21no—
445C22⋊Dic11—22no—
446C22⋊Dic11—22no—
447#4325—42no—
448#4325—42no—
449#4324—42no—
450#4324—42no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4—22no—
458(C2×D11)⋊C4—22no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461C4⋊Dic11—22no—
462C4⋊Dic11—22no—
463C4⋊Dic11C2412yes—
464C4⋊Dic11C2412yes—
465Dic11⋊C4—22no—
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468Dic11⋊C4—22no—
469Dic11⋊C4—22no—
470Dic11⋊C4—22no—
471C4×Dic11—22no—
472C4×Dic11—22no—
473C4×Dic11—21no—
474C4×Dic11—21no—
475#4318—41no—
476C2×C11⋊C8—41no—
477C2×C11⋊C8C2412yes—
478C2×C11⋊C8C2412yes—
479#4314—42no—
480#4314—42no—
481#4313—42no—
482C8×D11—24no—
483C8×D11—24no—
484C8×D11—42no—
485C2×#536—111no—
486C2×#535—111no—
487#3200—112no—
488#3200—112no—
489#3200—112no—
490#3200—112no—
491#3200—112no—
492#3200—112no—
493#3200—111no—
494#3200—111no—
495#3200—111no—
496#3200D1111yescharacteristic, direct product factor
497C2×#485—112no—
498C2×#482—112no—
499C2×#468—112no—
500C2×#465—112no—
501C2×#448—112no—
502C2×#450—112no—
503C2×#408—111no—
504C23×C11—22no—
505C23×C11—42no—
506C23×C11—82no—
507C23×C11C22×D411yescharacteristic
508C23×C11C22×D411yescharacteristic
509C23×C11C22×D411yescharacteristic
510C22×D11—22no—
511C22×D11—22no—
512C22×D11—22no—
513C22×D11—24no—
514C22×D11—24no—
515C22×D11—24no—
516C22×D11—22no—
517C22×D11—44no—
518C22×D11—42no—
519C22×D11—44no—
520C22×D11—44no—
521C22×D11—44no—
522C22×D11—82no—
523C22×D11—82no—
524C22×D11—82no—
525C22×D11—816no—
526C22×D11C22×D411yescharacteristic
527C22×D11C22×D411yescharacteristic
528C22×D11C22×D411yescharacteristic
529C22×D11C22×D411yescharacteristic
530Q8×C11—22no—
531Q8×C11—22no—
532Q8×C11—41no—
533Q8×C11—42no—
534D4×C11—22no—
535D4×C11—22no—
536D4×C11—41no—
537D4×C11—41no—
538D4×C11—41no—
539D4×C11—42no—
540D4×C11—82no—
541D4×C11—82no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—22no—
549C2×C4×C11—22no—
550C2×C4×C11—22no—
551C2×C4×C11—42no—
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C2511yescharacteristic
556C22⋊D11—41no—
557C22⋊D11—41no—
558C22⋊D11—41no—
559C22⋊D11—41no—
560C22⋊D11—41no—
561C22⋊D11—41no—
562C22⋊D11—44no—
563C22⋊D11—44no—
564C22⋊D11—82no—
565C22⋊D11—82no—
566C22⋊D11—82no—
567C22⋊D11—82no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—42no—
575C2×Dic11C22×D411yescharacteristic
576C2×Dic11C22×D411yescharacteristic
577C2×Dic11C22×D411yescharacteristic
578C2×Dic11C22×D411yescharacteristic
579D44—22no—
580D44—22no—
581D44—41no—
582D44—41no—
583D44—41no—
584D44—42no—
585D44—82no—
586D44—82no—
587C4×D11—22no—
588C4×D11—22no—
589C4×D11—22no—
590C4×D11—21no—
591C4×D11—21no—
592C4×D11—21no—
593C4×D11—21no—
594C4×D11—21no—
595C4×D11—21no—
596C4×D11—22no—
597C4×D11—22no—
598C4×D11—22no—
599C4×D11—44no—
600C4×D11—44no—
601C4×D11—44no—
602C4×D11—44no—
603C4×D11H(5,𝔽2)12yes—
604C4×D11H(5,𝔽2)12yes—
605Dic22—22no—
606Dic22—22no—
607Dic22—41no—
608Dic22—41no—
609Dic22—41no—
610Dic22—44no—
611Dic22—42no—
612Dic22—44no—
613C8×C11—22no—
614C8×C11—22no—
615C11⋊C8—22no—
616C11⋊C8—22no—
617C22×#41—111no—
618C23×Q8—111no—
619C23×D4—111no—
620C22×SD16—112no—
621C22×SD16—112no—
622C22×M16—111no—
623C23×C8—111no—
624#536—111no—
625#536—111no—
626#536—112no—
627#536—112no—
628#536—111no—
629#536—221no—
630#536—221no—
631#536—221no—
632#536—221no—
633#536C2×D1111yescharacteristic, complemented
634#535—111no—
635#535—111no—
636#535—112no—
637#535—112no—
638#535—111no—
639#535—221no—
640#535—221no—
641#535—221no—
642#535—221no—
643#535C2×D1111yescharacteristic
644C2×C4⋊Q8—221no—
645C2×#127—221no—
646C2×#124—221no—
647C2×#124—221no—
648C2×#123—221no—
649C2×#123—221no—
650C2×C22⋊Q8—112no—
651C2×C22⋊Q8—112no—
652C2×#121—112no—
653C2×#121—112no—
654C2×#120—221no—
655C2×#120—221no—
656C2×#117—111no—
657C2×#117—111no—
658#485—112no—
659#485—112no—
660#485—112no—
661#485—112no—
662#485—112no—
663#485—112no—
664#485—112no—
665#485C2×D1112yescomplemented
666#482—112no—
667#482—112no—
668#482—112no—
669#482—112no—
670#482—112no—
671#482—112no—
672#482—112no—
673#482C2×D1112yescomplemented
674#468—112no—
675#468—112no—
676#468—112no—
677#468—112no—
678#468—112no—
679#468—112no—
680#468—112no—
681#468C2×D1112yescomplemented
682#465—112no—
683#465—112no—
684#465—112no—
685#465—112no—
686#465—112no—
687#465—112no—
688#465—112no—
689#465C2×D1112yescomplemented
690#450—112no—
691#450—112no—
692#450—112no—
693#450—112no—
694#450—112no—
695#450—112no—
696#450—112no—
697#450C2×D1112yescomplemented
698#448—112no—
699#448—112no—
700#448—112no—
701#448—112no—
702#448—112no—
703#448—112no—
704#448—112no—
705#448C2×D1112yescomplemented
706C2×#107—112no—
707C2×#106—112no—
708C2×#103—112no—
709C2×#103—112no—
710C2×#102—112no—
711C2×#102—112no—
712#408—111no—
713#408—111no—
714#408—111no—
715#408—112no—
716#408—112no—
717#408C2×D1111yescharacteristic, complemented
718C2×C22⋊C8—112no—
719C2×C22⋊C8—112no—
720C22×C11—21no—
721C22×C11—21no—
722C22×C11—21no—
723C22×C11—22no—
724C22×C11—22no—
725C22×C11—22no—
726C22×C11—42no—
727C22×C11—42no—
728C22×C11—42no—
729C22×C11—84no—
730C22×C11C23×D411yescharacteristic
731C2×D11—21no—
732C2×D11—21no—
733C2×D11—21no—
734C2×D11—22no—
735C2×D11—22no—
736C2×D11—22no—
737C2×D11—44no—
738C2×D11—44no—
739C2×D11—44no—
740C2×D11—42no—
741C2×D11—42no—
742C2×D11—42no—
743C2×D11—88no—
744C2×D11—84no—
745C2×D11—88no—
746C2×D11#53412yes—
747C2×D11#57714yes—
748C4×C11—21no—
749C4×C11—21no—
750C4×C11—21no—
751C4×C11—42no—
752C4×C11—42no—
753C4×C11—42no—
754C4×C11C2×H(5,𝔽2)11yescharacteristic
755C4×C11C2×H(5,𝔽2)11yescharacteristic
756Dic11—21no—
757Dic11—21no—
758Dic11—21no—
759Dic11—42no—
760Dic11—42no—
761Dic11—42no—
762Dic11#53412yes—
763C25—221no—
764C2×#41—111no—
765C2×#41—111no—
766C2×#41—111no—
767C2×#41—111no—
768C2×#41—111no—
769C2×#41—111no—
770C2×#41—111no—
771C2×#41—442no—
772C2×#41—442no—
773C2×#41C22×D1111yescharacteristic
774C22×Q8—111no—
775C22×Q8—112no—
776C22×Q8—112no—
777C22×Q8—111no—
778C22×Q8—221no—
779C22×Q8—221no—
780C22×Q8—221no—
781C22×Q8—442no—
782C22×Q8—442no—
783C22×Q8C22×D1111yescharacteristic, complemented
784C22×D4—111no—
785C22×D4—111no—
786C22×D4—111no—
787C22×D4—112no—
788C22×D4—112no—
789C22×D4—111no—
790C22×D4—221no—
791C22×D4—221no—
792C22×D4—221no—
793C22×D4—222no—
794C22×D4—222no—
795C22×D4—442no—
796C22×D4—442no—
797C22×D4C22×D1111yescharacteristic
798C23×C4—111no—
799C23×C4—111no—
800C23×C4—111no—
801C23×C4—221no—
802C2×SD16—112no—
803C2×SD16—112no—
804C2×SD16—112no—
805C2×SD16—112no—
806C2×SD16—112no—
807C2×SD16—112no—
808C2×SD16—444no—
809C2×SD16—444no—
810C2×SD16C22×D1112yes—
811C2×SD16C22×D1112yes—
812C2×M16—111no—
813C2×M16—112no—
814C2×M16—442no—
815C2×M16C22×D1111yescharacteristic, complemented
816C22×C8—111no—
817C22×C8—112no—
818C22×C8—112no—
819C22×C8—112no—
820C22×C8—442no—
821C22×C8C22×D1111yescharacteristic, complemented
822C4⋊Q8—21no—
823C4⋊Q8—221no—
824C4⋊Q8—222no—
825C4⋊Q8—222no—
826C4⋊Q8—221no—
827C4⋊Q8—221no—
828#127—21no—
829#127—221no—
830#127—222no—
831#127—222no—
832#127—221no—
833#127—221no—
834#124—21no—
835#124—21no—
836#124—221no—
837#124—221no—
838#124—222no—
839#124—222no—
840#124—222no—
841#124—222no—
842#124—221no—
843#124—221no—
844#124—221no—
845#124—221no—
846#123—21no—
847#123—21no—
848#123—222no—
849#123—222no—
850#123—221no—
851#123—221no—
852#123—222no—
853#123—222no—
854#123—221no—
855#123—221no—
856#123—221no—
857#123—221no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—112no—
863C22⋊Q8—112no—
864C22⋊Q8—222no—
865C22⋊Q8—222no—
866C22⋊Q8—222no—
867C22⋊Q8—222no—
868C22⋊Q8C22×D1112yes—
869C22⋊Q8C22×D1112yescomplemented
870#121—112no—
871#121—112no—
872#121—112no—
873#121—112no—
874#121—112no—
875#121—112no—
876#121—222no—
877#121—222no—
878#121—222no—
879#121—222no—
880#121C22×D1112yes—
881#121C22×D1112yes—
882#120—21no—
883#120—21no—
884#120—221no—
885#120—221no—
886#120—222no—
887#120—222no—
888#120—222no—
889#120—222no—
890#120—221no—
891#120—221no—
892#120—221no—
893#120—221no—
894#117—111no—
895#117—111no—
896#117—112no—
897#117—112no—
898#117—221no—
899#117—221no—
900#117—221no—
901#117—221no—
902#117C22×D1111yescharacteristic
903#117C22×D1111yescharacteristic, complemented
904C2×C4⋊C4—112no—
905C2×C4⋊C4—112no—
906C2×C4⋊C4—222no—
907C2×C4⋊C4—222no—
908C2×C22⋊C4—222no—
909C2×C22⋊C4—222no—
910C2×C22⋊C4—221no—
911C2×C22⋊C4—221no—
912C2×C22⋊C4—222no—
913C2×C22⋊C4—222no—
914C2×C42—221no—
915C2×C42—221no—
916#107—112no—
917#107—112no—
918#107—112no—
919#107C22×D1112yescomplemented
920#106—112no—
921#106—112no—
922#106—112no—
923#106C22×D1112yescomplemented
924#103—112no—
925#103—112no—
926#103—112no—
927#103—112no—
928#103—112no—
929#103—112no—
930#103C22×D1112yescomplemented
931#103C22×D1112yescomplemented
932#102—112no—
933#102—112no—
934#102—112no—
935#102—112no—
936#102—112no—
937#102—112no—
938#102C22×D1112yes—
939#102C22×D1112yes—
940C22⋊C8—112no—
941C22⋊C8—112no—
942C22⋊C8—112no—
943C22⋊C8—112no—
944C22⋊C8—112no—
945C22⋊C8—112no—
946C22⋊C8C22×D1112yes—
947C22⋊C8C22×D1112yescomplemented
948C2×C11—41no—
949C2×C11—41no—
950C2×C11—41no—
951C2×C11—82no—
952C2×C11C2×#53411yescharacteristic
953C2×C11C2×#57712yes—
954D11—41no—
955D11—41no—
956D11—41no—
957D11—82no—
958D11#320014yesdirect product factor
959C24—21no—
960C24—111no—
961C24—111no—
962C24—111no—
963C24—222no—
964C24—222no—
965C24—221no—
966C24—444no—
967C24—884no—
968#41—41no—
969#41—41no—
970#41—441no—
971#41—441no—
972#41—441no—
973#41—441no—
974#41—441no—
975#41—441no—
976#41—442no—
977#41—442no—
978#41—442no—
979#41—442no—
980C2×Q8—21no—
981C2×Q8—41no—
982C2×Q8—41no—
983C2×Q8—111no—
984C2×Q8—111no—
985C2×Q8—111no—
986C2×Q8—112no—
987C2×Q8—222no—
988C2×Q8—222no—
989C2×Q8—224no—
990C2×Q8—224no—
991C2×Q8—221no—
992C2×Q8—441no—
993C2×Q8—441no—
994C2×Q8—444no—
995C2×Q8—442no—
996C2×Q8—442no—
997C2×Q8—442no—
998C2×Q8—444no—
999C2×Q8—444no—
1000C2×Q8D4×D1111yescharacteristic
1001C2×Q8C23×D1112yes—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—41no—
1006C2×D4—41no—
1007C2×D4—111no—
1008C2×D4—111no—
1009C2×D4—111no—
1010C2×D4—111no—
1011C2×D4—111no—
1012C2×D4—111no—
1013C2×D4—111no—
1014C2×D4—111no—
1015C2×D4—111no—
1016C2×D4—112no—
1017C2×D4—222no—
1018C2×D4—222no—
1019C2×D4—224no—
1020C2×D4—224no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—222no—
1026C2×D4—222no—
1027C2×D4—221no—
1028C2×D4—441no—
1029C2×D4—441no—
1030C2×D4—442no—
1031C2×D4—442no—
1032C2×D4—442no—
1033C2×D4—442no—
1034C2×D4—442no—
1035C2×D4—444no—
1036C2×D4—444no—
1037C2×D4—444no—
1038C2×D4—884no—
1039C2×D4—884no—
1040C2×D4D4×D1111yescharacteristic
1041C2×D4D4×D1111yescharacteristic
1042C2×D4D4×D1111yescharacteristic
1043C2×D4C23×D1112yes—
1044C22×C4—21no—
1045C22×C4—111no—
1046C22×C4—111no—
1047C22×C4—111no—
1048C22×C4—111no—
1049C22×C4—111no—
1050C22×C4—111no—
1051C22×C4—111no—
1052C22×C4—111no—
1053C22×C4—111no—
1054C22×C4—111no—
1055C22×C4—111no—
1056C22×C4—111no—
1057C22×C4—111no—
1058C22×C4—222no—
1059C22×C4—222no—
1060C22×C4—222no—
1061C22×C4—222no—
1062C22×C4—222no—
1063C22×C4—222no—
1064C22×C4—222no—
1065C22×C4—222no—
1066C22×C4—222no—
1067C22×C4—222no—
1068C22×C4—221no—
1069C22×C4—444no—
1070C22×C4C23×D1111yescharacteristic
1071C22×C4C23×D1111yescharacteristic
1072C22×C4C23×D1111yescharacteristic
1073SD16—42no—
1074SD16—42no—
1075SD16—442no—
1076SD16—442no—
1077SD16—442no—
1078SD16—442no—
1079SD16—442no—
1080SD16—442no—
1081M16—41no—
1082M16—442no—
1083M16—441no—
1084C2×C8—41no—
1085C2×C8—112no—
1086C2×C8—112no—
1087C2×C8—224no—
1088C2×C8—224no—
1089C2×C8—442no—
1090C2×C8—441no—
1091C2×C8C23×D1112yes—
1092C2×C8C23×D1112yes—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—112no—
1096C4⋊C4—112no—
1097C4⋊C4—222no—
1098C4⋊C4—222no—
1099C4⋊C4—222no—
1100C4⋊C4—222no—
1101C4⋊C4—222no—
1102C4⋊C4—222no—
1103C4⋊C4—222no—
1104C4⋊C4—222no—
1105C4⋊C4C23×D1112yes—
1106C4⋊C4C23×D1112yes—
1107C22⋊C4—21no—
1108C22⋊C4—21no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—222no—
1114C22⋊C4—222no—
1115C22⋊C4—222no—
1116C22⋊C4—222no—
1117C22⋊C4—222no—
1118C22⋊C4—222no—
1119C22⋊C4—222no—
1120C22⋊C4—222no—
1121C22⋊C4—222no—
1122C22⋊C4—222no—
1123C22⋊C4—221no—
1124C22⋊C4—221no—
1125C22⋊C4—222no—
1126C22⋊C4—222no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C42—21no—
1130C42—21no—
1131C42—222no—
1132C42—222no—
1133C42—221no—
1134C42—221no—
1135C11C2×#320011yescharacteristic, complemented, Sylow
1136C23—22no—
1137C23—42no—
1138C23—82no—
1139C23—111no—
1140C23—111no—
1141C23—111no—
1142C23—111no—
1143C23—222no—
1144C23—222no—
1145C23—222no—
1146C23—224no—
1147C23—224no—
1148C23—224no—
1149C23—222no—
1150C23—442no—
1151C23—444no—
1152C23—444no—
1153C23—444no—
1154C23—444no—
1155C23—882no—
1156C23—882no—
1157C23—882no—
1158C23—8816no—
1159C23C2×D4×D1111yescharacteristic
1160C23C2×D4×D1111yescharacteristic
1161C23C2×D4×D1111yescharacteristic
1162Q8—22no—
1163Q8—22no—
1164Q8—41no—
1165Q8—42no—
1166Q8—222no—
1167Q8—222no—
1168Q8—441no—
1169Q8—441no—
1170Q8—441no—
1171Q8—442no—
1172Q8—444no—
1173Q8—444no—
1174D4—22no—
1175D4—22no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—42no—
1180D4—82no—
1181D4—82no—
1182D4—222no—
1183D4—222no—
1184D4—441no—
1185D4—441no—
1186D4—441no—
1187D4—442no—
1188D4—444no—
1189D4—441no—
1190D4—441no—
1191D4—441no—
1192D4—441no—
1193D4—441no—
1194D4—441no—
1195D4—444no—
1196D4—882no—
1197D4—882no—
1198D4—882no—
1199D4—882no—
1200D4—882no—
1201D4—882no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—42no—
1212C2×C4—111no—
1213C2×C4—112no—
1214C2×C4—112no—
1215C2×C4—111no—
1216C2×C4—111no—
1217C2×C4—111no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—222no—
1223C2×C4—222no—
1224C2×C4—222no—
1225C2×C4—222no—
1226C2×C4—222no—
1227C2×C4—221no—
1228C2×C4—221no—
1229C2×C4—221no—
1230C2×C4—221no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—222no—
1236C2×C4—444no—
1237C2×C4—444no—
1238C2×C4—444no—
1239C2×C4—444no—
1240C2×C4—442no—
1241C2×C4C2×D4×D1111yescharacteristic
1242C2×C4C2×D4×D1111yescharacteristic
1243C2×C4C2×D4×D1111yescharacteristic
1244C2×C4C24×D1111yescharacteristic
1245C8—22no—
1246C8—22no—
1247C8—222no—
1248C8—222no—
1249C22—21no—
1250C22—21no—
1251C22—21no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—84no—
1259C22—112no—
1260C22—114no—
1261C22—221no—
1262C22—221no—
1263C22—221no—
1264C22—222no—
1265C22—222no—
1266C22—222no—
1267C22—444no—
1268C22—444no—
1269C22—444no—
1270C22—442no—
1271C22—442no—
1272C22—442no—
1273C22—884no—
1274C22—888no—
1275C22—888no—
1276C22C22×D4×D1111yescharacteristic
1277C4—21no—
1278C4—21no—
1279C4—21no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—112no—
1284C4—221no—
1285C4—221no—
1286C4—221no—
1287C4—442no—
1288C4—442no—
1289C4—442no—
1290C4D11×H(5,𝔽2)11yescharacteristic
1291C4D11×H(5,𝔽2)11yescharacteristic
1292C2—41no—
1293C2—41no—
1294C2—41no—
1295C2—82no—
1296C2—114no—
1297C2—441no—
1298C2—441no—
1299C2—441no—
1300C2—882no—
1301C2D11×#53411yescharacteristic
1302C2D11×#57712yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3200C2
socleC22×C11C23×D4
prime radicalD11×#535C2
hypercenter#3200D11
hypocenterC11C2×#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3200

Complements

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

NH ≅ G/Ntype
1. D11×#536C2semidirect
3. #13079490C2semidirect
4. #13079489C2semidirect
5. #13079488C2semidirect
6. #13079487C2semidirect
7. #13079486C2semidirect
8. #13079485C2semidirect
9. #13079484C2semidirect
10. #13079483C2semidirect
11. #13079482C2semidirect
12. D11×#485C2semidirect
13. D11×#482C2semidirect
14. D11×#468C2semidirect
15. D11×#465C2semidirect
16. D11×#448C2semidirect
17. D11×#450C2semidirect
18. D11×#408C2semidirect
19. C11×#3200C2semidirect
21. C22×Q8×D11C22semidirect
23. C11×#536C22semidirect
26. #10623356C22semidirect
27. #10623347C22semidirect
31. C2×M16×D11C22semidirect
32. C22×C8×D11C22semidirect
45. #10623159C22semidirect
46. #10623159C22semidirect
48. D11×C22⋊Q8C22semidirect
57. #10623057C22semidirect
60. D11×#117C22semidirect
61. C11×#485C22semidirect
62. C11×#482C22semidirect
63. C11×#468C22semidirect
64. C11×#465C22semidirect
65. C11×#450C22semidirect
66. C11×#448C22semidirect
67. C11×#408C22semidirect
68. #10622847C22semidirect
69. #10622840C22semidirect
70. #10622831C22semidirect
71. #10622787C22semidirect
72. #10622784C22semidirect
73. #10622783C22semidirect
74. #10622783C22semidirect
75. #10622782C22semidirect
76. #10622782C22semidirect
77. #10622747C22semidirect
78. #10622742C22semidirect
79. #10622727C22semidirect
80. #10622723C22semidirect
81. #10622662C22semidirect
82. #10622661C22semidirect
83. #10622659C22semidirect
84. #10622658C22semidirect
85. #10622655C22semidirect
86. #10622654C22semidirect
87. #10622653C22semidirect
88. #10622648C22semidirect
89. #10622616C22semidirect
90. #10622609C22semidirect
91. #10622501C22semidirect
92. #10622499C22semidirect
93. #10622498C22semidirect
94. D11×#107C22semidirect
95. #10622480C22semidirect
96. #10622479C22semidirect
97. #10622477C22semidirect
98. D11×#106C22semidirect
99. #10622428C22semidirect
100. #10622427C22semidirect
101. #10622425C22semidirect
102. #10622420C22semidirect
103. #10622419C22semidirect
104. #10622419C22semidirect
105. D11×#103C22semidirect
106. D11×#103C22semidirect
107. #10622397C22semidirect
108. #10622393C22semidirect
109. #10622392C22semidirect
110. #10622391C22semidirect
111. #10622389C22semidirect
112. #10622389C22semidirect
115. #10622351C22semidirect
116. #10622350C22semidirect
117. #10622344C22semidirect
118. #10622340C22semidirect
119. #10622340C22semidirect
121. D11×C22⋊C8C22semidirect
122. #10622336C22semidirect
125. C22×Q8×C11C23semidirect
137. C2×Q8×D11C23semidirect
161. C22×Dic22C23semidirect
164. C2×C11×M16C23semidirect
165. C22×C8×C11C23semidirect
173. C11×C22⋊Q8C23semidirect
179. C11×#117C23semidirect
185. #66999C23semidirect
213. #66979C23semidirect
215. #66977C23semidirect
216. C2×#4318C23semidirect
217. C22×C11⋊C8C23semidirect
223. C2×#4313C23semidirect
227. C2×C8×D11C23semidirect
229. #66950C23semidirect
237. #66945C23semidirect
276. C11×#107C23semidirect
277. C11×#106C23semidirect
278. C11×#103C23semidirect
279. C11×#103C23semidirect
283. C11×C22⋊C8C23semidirect
284. #66899C23semidirect
285. #66899C23semidirect
289. C22⋊(C11⋊C8)C23semidirect
294. (C2×D11)⋊C8C23semidirect
295. (C2×D11)⋊C8C23semidirect
296. #66882C23semidirect
297. #66881C23semidirect
298. #66880C23semidirect
299. #66880C23semidirect
300. #66874C23semidirect
301. #66874C23semidirect
304. #66872C23semidirect
305. #66872C23semidirect
306. #66871C23semidirect
307. #66871C23semidirect
496. #3200D11direct (N × H)
633. #536C2×D11semidirect
665. #485C2×D11semidirect
673. #482C2×D11semidirect
681. #468C2×D11semidirect
689. #465C2×D11semidirect
697. #450C2×D11semidirect
705. #448C2×D11semidirect
717. #408C2×D11semidirect
783. C22×Q8C22×D11semidirect
815. C2×M16C22×D11semidirect
821. C22×C8C22×D11semidirect
869. C22⋊Q8C22×D11semidirect
903. #117C22×D11semidirect
919. #107C22×D11semidirect
923. #106C22×D11semidirect
930. #103C22×D11semidirect
931. #103C22×D11semidirect
947. C22⋊C8C22×D11semidirect
958. D11#3200direct (N × H)
1135. C11C2×#3200semidirect

Maximal subgroups

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

subgroupindex
D11×#5362
D11×#5352
#130794902
#130794892
#130794882
#130794872
#130794862
#130794852
#130794842
#130794832
#130794822
D11×#4852
D11×#4822
D11×#4682
D11×#4652
D11×#4482
D11×#4502
D11×#4082
C11×#32002
C2×#320011