Finite Group Databasebeta

← D11×#3093 #15621556

Subgroups — D11×#3093 #15621556

Order 2816.

2346 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13078550C212yesmaximal, complemented
4#13078549C211yesmaximal, characteristic, complemented
5#13078548C214yesmaximal, complemented
6#13078547C211yesmaximal, characteristic, complemented
7#13078546C212yesmaximal, complemented
8#13078545C211yesmaximal, characteristic, complemented
9#13078544C214yesmaximal, complemented
10D11×#485C214yesmaximal, complemented
11D11×#482C214yesmaximal, complemented
12D11×#428C212yesmaximal, complemented
13D11×#417C212yesmaximal, complemented
14D11×#407C211yesmaximal, characteristic, complemented
15C11×#3093C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C11×#525C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic, complemented
20#10623359C2211yescharacteristic
21#10623322C2211yescharacteristic
22C2×#66979C2211yescharacteristic, complemented
23C2×M16×D11C2212yes—
24#10623187—21no—
25D11×#123—21no—
26#10623158C2212yes—
27D11×C22⋊Q8C2212yes—
28#10623137C2212yes—
29D11×#121C2212yes—
30D11×#120—21no—
31#10623117—21no—
32#10623078—22no—
33C4×D4×D11—22no—
34#10623055C2211yescharacteristic
35D11×#117—22no—
36D11×#117—22no—
37D11×#117C2214yes—
38D11×#117C2211yescharacteristic
39D11×#117C2214yescomplemented
40C2×#66945C2212yescomplemented
41C2×C4⋊C4×D11C2212yes—
42C2×C22⋊C4×D11—21no—
43C2×#66930—21no—
44C2×#66925—21no—
45C2×C42×D11—21no—
46C11×#485C2214yescomplemented
47C11×#482C2214yescomplemented
48C11×#428C2212yescomplemented
49C11×#417C2212yescomplemented
50C11×#407C2211yescharacteristic, complemented
51#10622845C2212yescomplemented
52#10622820C2211yescharacteristic, complemented
53#10622746C2212yescomplemented
54#10622739C2212yescomplemented
55#10622734C2212yescomplemented
56#10622658C2214yescomplemented
57#10622648C2214yescomplemented
58#10622616C2214yescomplemented
59#10622609C2214yescomplemented
60#10622608C2212yescomplemented
61#10622579C2212yescomplemented
62#10622577C2212yescomplemented
63#10622501C2214yescomplemented
64#10622498C2214yescomplemented
65#10622494C2214yescomplemented
66D11×#107C2214yescomplemented
67#10622480C2214yescomplemented
68#10622479C2214yescomplemented
69#10622474C2214yescomplemented
70D11×#106C2214yescomplemented
71#10622428C2214yescomplemented
72#10622427C2214yescomplemented
73#10622416C2214yescomplemented
74D11×#103C2214yescomplemented
75#10622397C2214yescomplemented
76#10622392C2214yescomplemented
77#10622384C2214yescomplemented
78D11×#102C2214yescomplemented
79#10622350C2214yescomplemented
80#10622339C2214yescomplemented
81D11×C22⋊C8C2214yes—
82#10622336C2214yescomplemented
83C24×D11D411yescharacteristic
84C2×C11×#41C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×Dic11D411yescharacteristic
87#41×D11—28no—
88C2×#4343C2311yescharacteristic
89C2×Q8×D11C2311yescharacteristic
90C2×#4341—21no—
91C2×#4341C2311yescharacteristic
92C2×D4×D11—22no—
93C2×D4×D11—21no—
94C2×D4×D11C2311yescharacteristic
95C2×#4339—21no—
96C2×#4339C2311yescharacteristic
97C22×C4×D11—28no—
98C22×C4×D11—22no—
99C22×C4×D11—21no—
100C22×C4×D11D411yescharacteristic
101C22×C4×D11D411yescharacteristic
102C22×C4×D11D412yes—
103C22×C4×D11D412yes—
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2312yes—
106C22×C4×D11C2312yes—
107C22×C4×D11C2311yescharacteristic
108C2×C11×M16C2312yes—
109C11×#123—21no—
110C11×C22⋊Q8C2312yes—
111C11×#121C2312yes—
112C11×#120—21no—
113C4×D4×C11—22no—
114C11×#117—22no—
115C11×#117C2314yes—
116C11×#117C2311yescharacteristic
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4—21no—
119C2×C42×C11—21no—
120#67006—21no—
121C2×C22⋊Dic11—21no—
122#66999C2312yes—
123#66992—22no—
124#66991C2312yes—
125#66990—22no—
126#66990—21no—
127#66988—21no—
128D4×Dic11—22no—
129#66983C2312yes—
130#66982—21no—
131C4×C22⋊D11—22no—
132C4×C22⋊D11—22no—
133C2×(C2×D11)⋊C4—22no—
134#66979—22no—
135#66979C2311yescharacteristic
136#66979C2314yes—
137C2×C4⋊Dic11C2312yes—
138#66977C2312yes—
139C2×Dic11⋊C4—22no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11—22no—
142C2×#4318C2312yes—
143M16×D11—28no—
144C2×#4313C2314yes—
145C2×C8×D11C2314yes—
146#66950C2312yes—
147#66949—22no—
148#66948C2312yes—
149#66947—22no—
150#66946—22no—
151#66945—22no—
152#66945—22no—
153#66945C2312yes—
154#66945C2314yes—
155#66945C2314yes—
156C4⋊C4×D11—22no—
157C4⋊C4×D11—22no—
158C4⋊C4×D11—22no—
159C4⋊C4×D11C2312yes—
160C4⋊C4×D11C2314yes—
161C4⋊C4×D11C2314yes—
162#66939—21no—
163#66937—22no—
164#66936—22no—
165#66935—21no—
166#66935—22no—
167(C22⋊D11)⋊C4—22no—
168(C22⋊D11)⋊C4—22no—
169C22⋊C4×D11—24no—
170C22⋊C4×D11—24no—
171C22⋊C4×D11—21no—
172C22⋊C4×D11—22no—
173C22⋊C4×D11—22no—
174#66931—22no—
175#66930—24no—
176#66930—24no—
177#66930—21no—
178C4×D44—22no—
179#66925—24no—
180#66925—24no—
181#66925—21no—
182C42×D11—24no—
183C42×D11—24no—
184C42×D11—21no—
185C11×#107C2314yescomplemented
186C11×#106C2314yescomplemented
187C11×#103C2314yescomplemented
188C11×#102C2314yescomplemented
189C11×C22⋊C8C2314yes—
190#66899C2314yescomplemented
191#66896C2314yescomplemented
192C22⋊(C11⋊C8)C2314yes—
193#66885C2314yescomplemented
194(C2×D11)⋊C8C2314yes—
195(C2×D11)⋊C8C2314yes—
196#66882C2314yescomplemented
197#66881C2314yescomplemented
198#66880C2314yescomplemented
199#66874C2314yescomplemented
200#66873C2314yescomplemented
201#66872C2314yescomplemented
202#66872C2314yescomplemented
203#66871C2314yescomplemented
204#66871C2314yescomplemented
205C2×#3093—111nomaximal, Sylow
206C24×C11C2×D411yescharacteristic
207C23×D11—24no—
208C23×D11—21no—
209C23×D11—44no—
210C23×D11C2×D412yes—
211C23×D11C2×D411yescharacteristic
212C23×D11C2×D412yes—
213C23×D11C2×D411yescharacteristic
214C11×#41—24no—
215C2×Q8×C11C2411yescharacteristic
216C2×D4×C11—22no—
217C2×D4×C11—21no—
218C2×D4×C11C2411yescharacteristic
219C22×C4×C11—24no—
220C22×C4×C11—22no—
221C22×C4×C11—21no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—21no—
227C2×C22⋊D11—22no—
228C2×C22⋊D11—21no—
229C2×C22⋊D11—22no—
230C2×C22⋊D11—21no—
231C22×Dic11—24no—
232C22×Dic11—21no—
233C22×Dic11—22no—
234C22×Dic11C2×D412yes—
235C22×Dic11C2×D412yes—
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238#4343—24no—
239Q8×D11—24no—
240#4341—24no—
241#4341—44no—
242D4×D11—24no—
243D4×D11—48no—
244D4×D11—44no—
245#4339—24no—
246#4339—44no—
247C2×D44—22no—
248C2×D44—21no—
249C2×D44C2411yescharacteristic
250C2×C4×D11—24no—
251C2×C4×D11—28no—
252C2×C4×D11—28no—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—21no—
256C2×C4×D11—24no—
257C2×C4×D11—24no—
258C2×C4×D11—24no—
259C2×C4×D11—22no—
260C2×C4×D11—21no—
261C2×C4×D11—21no—
262C2×C4×D11—24no—
263C2×C4×D11—48no—
264C2×C4×D11—44no—
265C2×C4×D11C2×D412yes—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2×D412yes—
268C2×C4×D11C2×D412yes—
269C2×C4×D11C2×D412yes—
270C2×C4×D11C2×D411yescharacteristic
271C2×C4×D11C2×D411yescharacteristic
272C2×C4×D11#4118yes—
273C2×C4×D11C2412yes—
274C2×C4×D11C2411yescharacteristic
275C2×C4×D11C2411yescharacteristic
276C2×Dic22—21no—
277C2×Dic22C2411yescharacteristic
278C11×M16—24no—
279C2×C8×C11C2414yes—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4C2412yes—
283C11×C4⋊C4C2414yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—22no—
288C42×C11—24no—
289C42×C11—21no—
290C22⋊Dic11—22no—
291C22⋊Dic11—24no—
292C22⋊Dic11—21no—
293C22⋊Dic11—22no—
294(C2×D11)⋊C4—22no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301C4⋊Dic11—22no—
302C4⋊Dic11—22no—
303C4⋊Dic11C2412yes—
304C4⋊Dic11C2414yes—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—22no—
308Dic11⋊C4—22no—
309Dic11⋊C4—22no—
310C4×Dic11—24no—
311C4×Dic11—24no—
312C4×Dic11—22no—
313C4×Dic11—24no—
314C4×Dic11—21no—
315#4318—24no—
316C2×C11⋊C8C2414yes—
317#4313—28no—
318C8×D11—28no—
319C2×#525—111no—
320C22×#117—111no—
321#3093—114no—
322#3093—114no—
323#3093—112no—
324#3093—112no—
325#3093—111no—
326#3093—111no—
327#3093—111no—
328#3093D1111yescharacteristic, direct product factor
329C2×#485—114no—
330C2×#482—114no—
331C2×#428—112no—
332C2×#417—112no—
333C2×#407—111no—
334C23×C11—22no—
335C23×C11—21no—
336C23×C11—42no—
337C23×C11C22×D412yes—
338C23×C11C22×D411yescharacteristic
339C22×D11—24no—
340C22×D11—22no—
341C22×D11—24no—
342C22×D11—24no—
343C22×D11—24no—
344C22×D11—24no—
345C22×D11—21no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—416no—
350C22×D11—42no—
351C22×D11—44no—
352C22×D11#12314yes—
353C22×D11C22×D412yes—
354C22×D11C22×D411yescharacteristic
355C22×D11C22×D411yescharacteristic
356Q8×C11—22no—
357D4×C11—22no—
358D4×C11—44no—
359D4×C11—42no—
360C2×C4×C11—22no—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—44no—
367C2×C4×C11—42no—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4114yes—
371C2×C4×C11C2511yescharacteristic
372C22⋊D11—44no—
373C22⋊D11—44no—
374C22⋊D11—42no—
375C22⋊D11—42no—
376C22⋊D11—42no—
377C2×Dic11—22no—
378C2×Dic11—24no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—22no—
382C2×Dic11—21no—
383C2×Dic11—44no—
384C2×Dic11—42no—
385C2×Dic11#12314yes—
386C2×Dic11C22×D412yes—
387C2×Dic11C22×D411yescharacteristic
388C2×Dic11C22×D411yescharacteristic
389D44—22no—
390D44—44no—
391D44—42no—
392C4×D11—24no—
393C4×D11—24no—
394C4×D11—24no—
395C4×D11—24no—
396C4×D11—24no—
397C4×D11—24no—
398C4×D11—48no—
399C4×D11—42no—
400C4×D11—48no—
401C4×D11—44no—
402C4×D11—42no—
403C4×D11—42no—
404C4×D11#12314yes—
405C4×D11#12314yes—
406C4×D11C2×#4114yes—
407C4×D11C2×#4114yes—
408Dic22—22no—
409Dic22—42no—
410C8×C11—24no—
411C11⋊C8—24no—
412C22×#41—111no—
413C24×C4—111no—
414C22×M16—112no—
415#525—111no—
416#525—111no—
417#525—112no—
418#525—112no—
419#525—111no—
420#525—222no—
421#525—221no—
422#525—221no—
423#525C2×D1111yescharacteristic
424C2×#123—221no—
425C2×C22⋊Q8—112no—
426C2×#121—112no—
427C2×#120—221no—
428C2×C4×D4—222no—
429C2×#117—111no—
430C2×#117—114no—
431C2×#117—114no—
432C2×#117—111no—
433C2×#117—112no—
434C2×#117—221no—
435C2×#117—221no—
436C2×#117—222no—
437C2×#117—222no—
438C2×#117C2×D1111yescharacteristic, complemented
439C22×C4⋊C4—112no—
440C22×C22⋊C4—221no—
441C22×C42—221no—
442#485—114no—
443#485—114no—
444#485—114no—
445#485—114no—
446#485—114no—
447#485—114no—
448#485—114no—
449#485C2×D1114yescomplemented
450#482—114no—
451#482—114no—
452#482—114no—
453#482—114no—
454#482—114no—
455#482—114no—
456#482—114no—
457#482C2×D1114yescomplemented
458#428—112no—
459#428—112no—
460#428—112no—
461#428—114no—
462#428—114no—
463#428C2×D1112yescomplemented
464C2×#107—114no—
465C2×#106—114no—
466#417—112no—
467#417—112no—
468#417—112no—
469#417—114no—
470#417—114no—
471#417C2×D1112yescomplemented
472C2×#103—114no—
473C2×#102—114no—
474#407—111no—
475#407—112no—
476#407—114no—
477#407C2×D1111yescharacteristic, complemented
478C2×C22⋊C8—114no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—44no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11C2×#12312yes—
487C22×C11C23×D411yescharacteristic
488C2×D11—22no—
489C2×D11—28no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—48no—
494C2×D11—44no—
495C2×D11—48no—
496C2×D11—41no—
497C2×D11—42no—
498C2×D11—84no—
499C2×D11C2×#12312yes—
500C2×D11C2×#12312yes—
501C2×D11#57514yes—
502C4×C11—22no—
503C4×C11—41no—
504C4×C11—44no—
505C4×C11—42no—
506C4×C11C2×#12312yes—
507C4×C11C22×#4112yes—
508Dic11—22no—
509Dic11—41no—
510Dic11—44no—
511Dic11—42no—
512Dic11C2×#12312yes—
513Dic11C2×#12312yes—
514C25—111no—
515C2×#41—111no—
516C2×#41—111no—
517C2×#41—111no—
518C2×#41—221no—
519C2×#41—221no—
520C2×#41—228no—
521C2×#41C22×D1111yescharacteristic
522C22×Q8—111no—
523C22×D4—111no—
524C22×D4—222no—
525C22×D4—221no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—112no—
529C23×C4—111no—
530C23×C4—112no—
531C23×C4—111no—
532C23×C4—112no—
533C23×C4—112no—
534C23×C4—111no—
535C23×C4—228no—
536C23×C4—221no—
537C23×C4—222no—
538C23×C4C22×D1111yescharacteristic
539C2×M16—112no—
540C2×M16—114no—
541C2×M16—228no—
542C2×M16C22×D1112yes—
543C22×C8—114no—
544#123—21no—
545#123—222no—
546#123—221no—
547#123—222no—
548#123—221no—
549#123—221no—
550C22⋊Q8—112no—
551C22⋊Q8—112no—
552C22⋊Q8—112no—
553C22⋊Q8—222no—
554C22⋊Q8—222no—
555C22⋊Q8C22×D1112yes—
556#121—112no—
557#121—112no—
558#121—112no—
559#121—222no—
560#121—222no—
561#121C22×D1112yes—
562#120—21no—
563#120—221no—
564#120—222no—
565#120—222no—
566#120—221no—
567#120—221no—
568C4×D4—22no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4—222no—
574C4×D4—222no—
575C4×D4—222no—
576#117—22no—
577#117—114no—
578#117—111no—
579#117—114no—
580#117—114no—
581#117—112no—
582#117—224no—
583#117—224no—
584#117—221no—
585#117—224no—
586#117—224no—
587#117—221no—
588#117—222no—
589#117—222no—
590#117—222no—
591#117C22×D1114yes—
592#117C22×D1111yescharacteristic
593C2×C4⋊C4—112no—
594C2×C4⋊C4—114no—
595C2×C4⋊C4—114no—
596C2×C4⋊C4—112no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4C22×D1112yes—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—224no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—221no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—221no—
610C2×C42—21no—
611C2×C42—224no—
612C2×C42—224no—
613C2×C42—221no—
614C2×C42—222no—
615C2×C42—221no—
616#107—114no—
617#107—114no—
618#107—114no—
619#107C22×D1114yescomplemented
620#106—114no—
621#106—114no—
622#106—114no—
623#106C22×D1114yescomplemented
624#103—114no—
625#103—114no—
626#103—114no—
627#103C22×D1114yescomplemented
628#102—114no—
629#102—114no—
630#102—114no—
631#102C22×D1114yescomplemented
632C22⋊C8—114no—
633C22⋊C8—114no—
634C22⋊C8—114no—
635C22⋊C8C22×D1114yes—
636C2×C11—22no—
637C2×C11—42no—
638C2×C11—81no—
639C2×C11C22×#12311yescharacteristic
640C2×C11C2×#57512yes—
641D11—22no—
642D11—42no—
643D11—81no—
644D11#309314yesdirect product factor
645C24—111no—
646C24—112no—
647C24—112no—
648C24—111no—
649C24—224no—
650C24—221no—
651C24—444no—
652C24D4×D1111yescharacteristic
653#41—24no—
654#41—224no—
655#41—224no—
656#41—224no—
657#41—444no—
658#41—444no—
659C2×Q8—111no—
660C2×Q8—221no—
661C2×Q8—224no—
662C2×Q8C23×D1111yescharacteristic
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—111no—
666C2×D4—222no—
667C2×D4—221no—
668C2×D4—224no—
669C2×D4—221no—
670C2×D4—222no—
671C2×D4—221no—
672C2×D4—222no—
673C2×D4—221no—
674C2×D4—444no—
675C2×D4—448no—
676C2×D4C23×D1111yescharacteristic
677C22×C4—24no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—111no—
681C22×C4—111no—
682C22×C4—111no—
683C22×C4—118no—
684C22×C4—111no—
685C22×C4—111no—
686C22×C4—111no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—224no—
696C22×C4—228no—
697C22×C4—228no—
698C22×C4—228no—
699C22×C4—228no—
700C22×C4—221no—
701C22×C4—224no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—222no—
705C22×C4—221no—
706C22×C4—224no—
707C22×C4—221no—
708C22×C4—224no—
709C22×C4—222no—
710C22×C4—221no—
711C22×C4—444no—
712C22×C4—448no—
713C22×C4D4×D1111yescharacteristic
714C22×C4D4×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717M16—24no—
718M16—228no—
719M16—224no—
720C2×C8—114no—
721C2×C8—228no—
722C2×C8C23×D1114yes—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—114no—
726C4⋊C4—112no—
727C4⋊C4—224no—
728C4⋊C4—224no—
729C4⋊C4—222no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4—222no—
734C4⋊C4C23×D1114yes—
735C4⋊C4C23×D1112yes—
736C22⋊C4—24no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—222no—
741C22⋊C4—224no—
742C22⋊C4—224no—
743C22⋊C4—222no—
744C22⋊C4—222no—
745C22⋊C4—222no—
746C22⋊C4—222no—
747C22⋊C4—224no—
748C22⋊C4—221no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C42—24no—
752C42—21no—
753C42—224no—
754C42—224no—
755C42—222no—
756C42—224no—
757C42—221no—
758C11C2×#309311yescharacteristic, complemented, Sylow
759C23—22no—
760C23—21no—
761C23—42no—
762C23—111no—
763C23—114no—
764C23—111no—
765C23—112no—
766C23—224no—
767C23—224no—
768C23—224no—
769C23—224no—
770C23—224no—
771C23—222no—
772C23—221no—
773C23—442no—
774C23—442no—
775C23—442no—
776C23—442no—
777C23—444no—
778C23—4416no—
779C23C2×D4×D1112yes—
780C23C2×D4×D1111yescharacteristic
781Q8—22no—
782Q8—222no—
783Q8—442no—
784D4—22no—
785D4—44no—
786D4—42no—
787D4—222no—
788D4—442no—
789D4—444no—
790D4—442no—
791D4—444no—
792D4—442no—
793D4—444no—
794D4—442no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—114no—
804C2×C4—111no—
805C2×C4—111no—
806C2×C4—114no—
807C2×C4—114no—
808C2×C4—114no—
809C2×C4—114no—
810C2×C4—112no—
811C2×C4—224no—
812C2×C4—224no—
813C2×C4—224no—
814C2×C4—224no—
815C2×C4—224no—
816C2×C4—224no—
817C2×C4—222no—
818C2×C4—224no—
819C2×C4—224no—
820C2×C4—224no—
821C2×C4—222no—
822C2×C4—221no—
823C2×C4—442no—
824C2×C4—442no—
825C2×C4—448no—
826C2×C4—444no—
827C2×C4—448no—
828C2×C4—442no—
829C2×C4—444no—
830C2×C4—442no—
831C2×C4C2×D4×D1112yes—
832C2×C4C2×D4×D1111yescharacteristic
833C2×C4#41×D1114yes—
834C2×C4C24×D1111yescharacteristic
835C8—24no—
836C8—224no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—44no—
842C22—42no—
843C22—41no—
844C22—114no—
845C22—112no—
846C22—112no—
847C22—228no—
848C22—222no—
849C22—222no—
850C22—222no—
851C22—222no—
852C22—444no—
853C22—448no—
854C22—448no—
855C22—442no—
856C22—441no—
857C22—884no—
858C22D11×#12312yes—
859C22C22×D4×D1111yescharacteristic
860C4—22no—
861C4—44no—
862C4—42no—
863C4—41no—
864C4—112no—
865C4—112no—
866C4—222no—
867C4—444no—
868C4—442no—
869C4—441no—
870C4D11×#12312yes—
871C4C2×#41×D1112yes—
872C2—22no—
873C2—42no—
874C2—81no—
875C2—114no—
876C2—222no—
877C2—442no—
878C2—881no—
879C2C2×D11×#12311yescharacteristic
880C2D11×#57512yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3093C2
socleC22×C11C23×D4
prime radicalD11×#525C2
hypercenter#3093D11
hypocenterC11C2×#3093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3093

Complements

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

NH ≅ G/Ntype
2. C2×D11×#117C2semidirect
3. #13078550C2semidirect
4. #13078549C2semidirect
5. #13078548C2semidirect
6. #13078547C2semidirect
7. #13078546C2semidirect
8. #13078545C2semidirect
9. #13078544C2semidirect
10. D11×#485C2semidirect
11. D11×#482C2semidirect
12. D11×#428C2semidirect
13. D11×#417C2semidirect
14. D11×#407C2semidirect
15. C11×#3093C2semidirect
19. C2×C11×#117C22semidirect
22. C2×#66979C22semidirect
39. D11×#117C22semidirect
40. C2×#66945C22semidirect
46. C11×#485C22semidirect
47. C11×#482C22semidirect
48. C11×#428C22semidirect
49. C11×#417C22semidirect
50. C11×#407C22semidirect
51. #10622845C22semidirect
52. #10622820C22semidirect
53. #10622746C22semidirect
54. #10622739C22semidirect
55. #10622734C22semidirect
56. #10622658C22semidirect
57. #10622648C22semidirect
58. #10622616C22semidirect
59. #10622609C22semidirect
60. #10622608C22semidirect
61. #10622579C22semidirect
62. #10622577C22semidirect
63. #10622501C22semidirect
64. #10622498C22semidirect
65. #10622494C22semidirect
66. D11×#107C22semidirect
67. #10622480C22semidirect
68. #10622479C22semidirect
69. #10622474C22semidirect
70. D11×#106C22semidirect
71. #10622428C22semidirect
72. #10622427C22semidirect
73. #10622416C22semidirect
74. D11×#103C22semidirect
75. #10622397C22semidirect
76. #10622392C22semidirect
77. #10622384C22semidirect
78. D11×#102C22semidirect
79. #10622350C22semidirect
80. #10622339C22semidirect
82. #10622336C22semidirect
185. C11×#107C23semidirect
186. C11×#106C23semidirect
187. C11×#103C23semidirect
188. C11×#102C23semidirect
190. #66899C23semidirect
191. #66896C23semidirect
193. #66885C23semidirect
196. #66882C23semidirect
197. #66881C23semidirect
198. #66880C23semidirect
199. #66874C23semidirect
200. #66873C23semidirect
201. #66872C23semidirect
202. #66872C23semidirect
203. #66871C23semidirect
204. #66871C23semidirect
328. #3093D11direct (N × H)
438. C2×#117C2×D11semidirect
449. #485C2×D11semidirect
457. #482C2×D11semidirect
463. #428C2×D11semidirect
471. #417C2×D11semidirect
477. #407C2×D11semidirect
619. #107C22×D11semidirect
623. #106C22×D11semidirect
627. #103C22×D11semidirect
631. #102C22×D11semidirect
644. D11#3093direct (N × H)
758. C11C2×#3093semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
C2×D11×#1172
#130785502
#130785492
#130785482
#130785472
#130785462
#130785452
#130785442
D11×#4852
D11×#4822
D11×#4282
D11×#4172
D11×#4072
C11×#30932
C2×#309311