Finite Group Databasebeta

← #15624529

Subgroups — #15624529

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2C22×#66950C211yesmaximal, characteristic, complemented
3#13079451C212yesmaximal, complemented
4#13079445C212yesmaximal, complemented
5#13079439C212yesmaximal, complemented
6#13079424C212yesmaximal, complemented
7#13079402C212yesmaximal, complemented
8#13079396C212yesmaximal, complemented
9#13079390C212yesmaximal, complemented
10#13079375C212yesmaximal, complemented
11#13078566C212yesmaximal, complemented
12#13078539C211yesmaximal, characteristic, complemented
13#13078249C212yesmaximal, complemented
14#13078247C212yesmaximal, complemented
15#13077877C212yesmaximal, complemented
16#13077853C211yesmaximal, characteristic, complemented
17#13077849C211yesmaximal, characteristic, complemented
18D11×#407C211yesmaximal, characteristic, complemented
19C11×#3092C211yesmaximal, characteristic, complemented
20C2×#41×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic, complemented
23C11×#525C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25#10623359C2211yescharacteristic
26C2×#67004C2212yescomplemented
27#10623322C2211yescharacteristic
28C22×(C2×D11)⋊C4—21no—
29C22×C4⋊Dic11—21no—
30C2×#66962C2212yescomplemented
31C2×M16×D11C2212yescomplemented
32#10623187—21no—
33D11×#123—21no—
34#10623158C2211yescharacteristic
35#10623158C2211yescharacteristic
36D11×C22⋊Q8C2211yescharacteristic
37D11×C22⋊Q8C2211yescharacteristic
38#10623137C2211yescharacteristic
39#10623137C2211yescharacteristic
40D11×#121C2211yescharacteristic
41D11×#121C2211yescharacteristic
42D11×#120—21no—
43#10623117—21no—
44#10623078—21no—
45#10623078—21no—
46C4×D4×D11—21no—
47C4×D4×D11—21no—
48#10623055C2211yescharacteristic
49D11×#117C2211yescharacteristic
50C2×#66950—21no—
51C2×#66950—21no—
52C2×#66950—21no—
53C2×#66950—21no—
54C2×#66950—21no—
55C2×#66950—21no—
56C2×#66950C2212yes—
57C2×#66950C2212yes—
58C2×#66950C2212yes—
59C2×#66950C2212yescomplemented
60C2×#66950C2212yescomplemented
61C2×#66950C2212yescomplemented
62C11×#484C2212yescomplemented
63C11×#483C2212yescomplemented
64C11×#481C2212yescomplemented
65C11×#480C2212yescomplemented
66C11×#428C2212yescomplemented
67C11×#417C2212yescomplemented
68C11×#407C2211yescharacteristic, complemented
69#10622820C2211yescharacteristic, complemented
70#10622739C2212yes—
71#10622733C2212yescomplemented
72#10622663C2212yescomplemented
73#10622663C2212yescomplemented
74#10622653C2212yescomplemented
75#10622653C2212yescomplemented
76#10622617C2212yescomplemented
77#10622584C2212yescomplemented
78#10622583C2212yescomplemented
79#10622581C2212yescomplemented
80#10622580C2212yescomplemented
81#10622579C2212yescomplemented
82#10622577C2212yescomplemented
83#10622501C2214yescomplemented
84#10622500C2214yescomplemented
85#10622499C2214yescomplemented
86#10622497C2214yescomplemented
87#10622481C2214yescomplemented
88#10622480C2214yescomplemented
89#10622477C2214yescomplemented
90#10622475C2214yescomplemented
91#10622429C2214yescomplemented
92#10622426C2214yescomplemented
93#10622423C2214yescomplemented
94#10622421C2214yescomplemented
95#10622396C2214yescomplemented
96#10622393C2214yescomplemented
97#10622391C2214yescomplemented
98#10622389C2214yescomplemented
99#10622352C2212yescomplemented
100#10622352C2212yescomplemented
101#10622351C2212yescomplemented
102#10622351C2212yescomplemented
103#10622339C2212yes—
104#10622339C2212yescomplemented
105D11×C22⋊C8C2212yes—
106D11×C22⋊C8C2212yescomplemented
107C24×D11D411yescharacteristic
108C2×C11×#41C2311yescharacteristic
109C23×C4×C11—21no—
110C23×C4×C11C2311yescharacteristic
111C23×Dic11—21no—
112C23×Dic11D411yescharacteristic
113#41×D11—44no—
114C2×#4343C2311yescharacteristic
115C2×Q8×D11C2311yescharacteristic
116C2×#4341—21no—
117C2×#4341C2311yescharacteristic
118C2×D4×D11—21no—
119C2×D4×D11—21no—
120C2×D4×D11—21no—
121C2×D4×D11C2311yescharacteristic
122C2×#4339—21no—
123C2×#4339C2311yescharacteristic
124C22×C4×D11—21no—
125C22×C4×D11—44no—
126C22×C4×D11D411yescharacteristic
127C22×C4×D11D411yescharacteristic
128C22×C4×D11D411yescharacteristic
129C22×C4×D11D411yescharacteristic
130C22×C4×D11D411yescharacteristic
131C22×C4×D11D411yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×Dic22—21no—
139C22×Dic22—21no—
140C22×Dic22—21no—
141C22×Dic22—44no—
142C22×Dic22C2312yes—
143C22×Dic22C2312yes—
144C22×Dic22C2312yes—
145C2×C11×M16C2312yes—
146C11×#123—21no—
147C11×C22⋊Q8C2311yescharacteristic
148C11×C22⋊Q8C2311yescharacteristic
149C11×#121C2311yescharacteristic
150C11×#121C2311yescharacteristic
151C11×#120—21no—
152C4×D4×C11—21no—
153C4×D4×C11—21no—
154C11×#117C2311yescharacteristic
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2312yes—
161#67006—21no—
162#67004—44no—
163#66999C2311yescharacteristic
164#66999C2311yescharacteristic
165C2×#4326C2314yescomplemented
166#66992—21no—
167#66992—21no—
168#66991C2311yescharacteristic
169#66991C2311yescharacteristic
170#66990—21no—
171#66990—21no—
172#66990—21no—
173#66988—21no—
174D4×Dic11—21no—
175D4×Dic11—21no—
176C2×#4324C2314yescomplemented
177#66983C2311yescharacteristic
178#66983C2311yescharacteristic
179#66982—21no—
180C4×C22⋊D11—21no—
181C4×C22⋊D11—21no—
182C4×C22⋊D11—21no—
183C4×C22⋊D11—21no—
184C2×(C2×D11)⋊C4—22no—
185C2×(C2×D11)⋊C4—22no—
186C2×(C2×D11)⋊C4—22no—
187C2×(C2×D11)⋊C4—22no—
188C2×(C2×D11)⋊C4—22no—
189C2×(C2×D11)⋊C4—22no—
190#66979C2311yescharacteristic
191C2×C4⋊Dic11—22no—
192C2×C4⋊Dic11—22no—
193C2×C4⋊Dic11—22no—
194C2×C4⋊Dic11—22no—
195C2×C4⋊Dic11—22no—
196C2×C4⋊Dic11—22no—
197#66977C2311yescharacteristic
198#66977C2311yescharacteristic
199C2×#4318C2312yes—
200#66962—44no—
201M16×D11—44no—
202C2×Dic44C2314yescomplemented
203C2×#4314C2314yescomplemented
204C2×#4313C2314yes—
205C2×C8×D11C2314yes—
206#66950—22no—
207#66950—22no—
208#66950—22no—
209#66950—22no—
210#66950—22no—
211#66950—22no—
212#66950—22no—
213#66950—22no—
214#66950—22no—
215#66950—22no—
216#66950—22no—
217#66950—22no—
218#66950C2314yes—
219#66950C2314yes—
220#66950C2314yes—
221#66950C2311yescharacteristic
222#66950C2314yes—
223#66950C2311yescharacteristic
224#66949—21no—
225#66949—21no—
226#66948C2311yescharacteristic
227#66948C2311yescharacteristic
228#66947—21no—
229#66947—21no—
230#66946—21no—
231#66946—21no—
232#66945C2311yescharacteristic
233#66945C2311yescharacteristic
234C4⋊C4×D11—21no—
235C4⋊C4×D11—21no—
236C4⋊C4×D11C2311yescharacteristic
237C4⋊C4×D11C2311yescharacteristic
238#66939—21no—
239#66937—21no—
240#66937—21no—
241#66936—21no—
242#66936—21no—
243#66935—21no—
244#66935—21no—
245#66935—21no—
246(C22⋊D11)⋊C4—21no—
247(C22⋊D11)⋊C4—21no—
248(C22⋊D11)⋊C4—21no—
249(C22⋊D11)⋊C4—21no—
250C22⋊C4×D11—21no—
251C22⋊C4×D11—21no—
252C22⋊C4×D11—21no—
253C22⋊C4×D11—21no—
254C22⋊C4×D11—21no—
255#66931—21no—
256#66931—21no—
257#66930—21no—
258C4×D44—21no—
259C4×D44—21no—
260#66925—21no—
261C42×D11—21no—
262C11×#107C2314yescomplemented
263C11×#106C2314yescomplemented
264C11×#103C2314yescomplemented
265C11×#102C2314yescomplemented
266C11×C22⋊C8C2312yes—
267C11×C22⋊C8C2312yes—
268C22⋊(C11⋊C8)C2312yes—
269C22⋊(C11⋊C8)C2312yes—
270(C2×D11)⋊C8C2314yes—
271(C2×D11)⋊C8C2314yes—
272#66880C2314yescomplemented
273#66880C2314yescomplemented
274#66874C2314yescomplemented
275#66874C2314yescomplemented
276#66874C2314yescomplemented
277#66873C2314yescomplemented
278#66872C2314yescomplemented
279#66871C2314yescomplemented
280#60751—111nomaximal, Sylow
281C24×C11C2×D411yescharacteristic
282C23×D11—24no—
283C23×D11—21no—
284C23×D11—42no—
285C23×D11—42no—
286C23×D11C2×D411yescharacteristic
287C23×D11C2×D411yescharacteristic
288C23×D11C2×D411yescharacteristic
289C23×D11C2×D411yescharacteristic
290C23×D11C2×D411yescharacteristic
291C23×D11C2×D411yescharacteristic
292C11×#41—24no—
293C2×Q8×C11C2411yescharacteristic
294C2×D4×C11—21no—
295C2×D4×C11—21no—
296C2×D4×C11—21no—
297C2×D4×C11C2411yescharacteristic
298C22×C4×C11—24no—
299C22×C4×C11—22no—
300C22×C4×C11—22no—
301C22×C4×C11—22no—
302C22×C4×C11—21no—
303C22×C4×C11—44no—
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2×D411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C2×C22⋊D11—21no—
311C2×C22⋊D11—21no—
312C2×C22⋊D11—21no—
313C2×C22⋊D11—21no—
314C2×C22⋊D11—21no—
315C2×C22⋊D11—21no—
316C2×C22⋊D11—21no—
317C22×Dic11—21no—
318C22×Dic11—22no—
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11—42no—
322C22×Dic11—44no—
323C22×Dic11C2×D411yescharacteristic
324C22×Dic11C2×D411yescharacteristic
325C22×Dic11C2×D411yescharacteristic
326C22×Dic11C2×D411yescharacteristic
327C22×Dic11C2×D411yescharacteristic
328C22×Dic11C2×D411yescharacteristic
329#4343—42no—
330Q8×D11—42no—
331#4341—42no—
332#4341—44no—
333D4×D11—42no—
334D4×D11—44no—
335D4×D11—44no—
336D4×D11—44no—
337#4339—24no—
338#4339—44no—
339C2×D44—21no—
340C2×D44—21no—
341C2×D44—21no—
342C2×D44C2411yescharacteristic
343C2×C4×D11—21no—
344C2×C4×D11—21no—
345C2×C4×D11—21no—
346C2×C4×D11—21no—
347C2×C4×D11—21no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11—44no—
361C2×C4×D11C2×D411yescharacteristic
362C2×C4×D11C2×D411yescharacteristic
363C2×C4×D11C2×D411yescharacteristic
364C2×C4×D11C2×D411yescharacteristic
365C2×C4×D11C2×D411yescharacteristic
366C2×C4×D11C2×D411yescharacteristic
367C2×C4×D11C2×D411yescharacteristic
368C2×C4×D11C2×D411yescharacteristic
369C2×C4×D11C2×D411yescharacteristic
370C2×C4×D11C2×D411yescharacteristic
371C2×C4×D11C2×D411yescharacteristic
372C2×C4×D11C2×D411yescharacteristic
373C2×C4×D11C2411yescharacteristic
374C2×C4×D11C2411yescharacteristic
375C2×C4×D11C2411yescharacteristic
376C2×C4×D11C2411yescharacteristic
377C2×Dic22—21no—
378C2×Dic22—22no—
379C2×Dic22—22no—
380C2×Dic22—22no—
381C2×Dic22—24no—
382C2×Dic22—24no—
383C2×Dic22—44no—
384C2×Dic22—44no—
385C2×Dic22—44no—
386C2×Dic22—44no—
387C2×Dic22—44no—
388C2×Dic22C2411yescharacteristic
389C2×Dic22C2414yes—
390C11×M16—24no—
391C2×C8×C11C2414yes—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4C2414yes—
398C11×C4⋊C4C2411yescharacteristic
399C11×C4⋊C4C2411yescharacteristic
400C11×C22⋊C4—21no—
401C11×C22⋊C4—21no—
402C11×C22⋊C4—21no—
403C11×C22⋊C4—21no—
404C11×C22⋊C4—21no—
405C42×C11—21no—
406C22⋊Dic11—21no—
407C22⋊Dic11—21no—
408C22⋊Dic11—21no—
409C22⋊Dic11—21no—
410C22⋊Dic11—21no—
411#4326—44no—
412#4324—44no—
413(C2×D11)⋊C4—21no—
414(C2×D11)⋊C4—21no—
415(C2×D11)⋊C4—21no—
416(C2×D11)⋊C4—21no—
417(C2×D11)⋊C4—21no—
418(C2×D11)⋊C4—21no—
419(C2×D11)⋊C4—21no—
420(C2×D11)⋊C4—21no—
421(C2×D11)⋊C4—24no—
422(C2×D11)⋊C4—24no—
423(C2×D11)⋊C4—24no—
424(C2×D11)⋊C4—24no—
425(C2×D11)⋊C4—21no—
426(C2×D11)⋊C4—21no—
427C4⋊Dic11—21no—
428C4⋊Dic11—21no—
429C4⋊Dic11—24no—
430C4⋊Dic11—24no—
431C4⋊Dic11—24no—
432C4⋊Dic11—24no—
433C4⋊Dic11C2411yescharacteristic
434C4⋊Dic11C2411yescharacteristic
435Dic11⋊C4—21no—
436Dic11⋊C4—21no—
437Dic11⋊C4—21no—
438Dic11⋊C4—21no—
439Dic11⋊C4—21no—
440Dic11⋊C4—21no—
441C4×Dic11—21no—
442C4×Dic11—21no—
443C4×Dic11—21no—
444#4318—24no—
445C2×C11⋊C8C2414yes—
446Dic44—44no—
447#4314—44no—
448#4313—44no—
449C8×D11—44no—
450C2×#525—111no—
451C22×C22⋊Q8—111no—
452#3196—112no—
453#3196—112no—
454#3195—112no—
455#3193—112no—
456#3190—112no—
457#3190—112no—
458#3189—112no—
459#3187—112no—
460#3095—112no—
461#3092—111no—
462#3092D1111yescharacteristic, complemented
463#3056—112no—
464#3056—112no—
465#3007—112no—
466#3004—111no—
467#3004—111no—
468C2×#407—111no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—22no—
472C23×C11—21no—
473C23×C11C22×D411yescharacteristic
474C23×C11C22×D411yescharacteristic
475C23×C11C22×D411yescharacteristic
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—42no—
495C22×D11—42no—
496C22×D11—416no—
497C22×D11—42no—
498C22×D11#13714yescomplemented
499C22×D11C22×D411yescharacteristic
500C22×D11C22×D411yescharacteristic
501C22×D11C22×D411yescharacteristic
502C22×D11C22×D411yescharacteristic
503Q8×C11—22no—
504D4×C11—22no—
505D4×C11—42no—
506D4×C11—42no—
507D4×C11—42no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—24no—
517C2×C4×C11—44no—
518C2×C4×C11—44no—
519C2×C4×C11—44no—
520C2×C4×C11—42no—
521C2×C4×C11C22×D411yescharacteristic
522C2×C4×C11C22×D411yescharacteristic
523C2×C4×C11C22×D411yescharacteristic
524C2×C4×C11H(5,𝔽2)14yes—
525C2×C4×C11C2511yescharacteristic
526C22⋊D11—42no—
527C22⋊D11—42no—
528C22⋊D11—42no—
529C22⋊D11—42no—
530C22⋊D11—42no—
531C22⋊D11—42no—
532C22⋊D11—42no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—24no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—41no—
543C2×Dic11—42no—
544C2×Dic11—44no—
545C2×Dic11—44no—
546C2×Dic11—44no—
547C2×Dic11C22×D411yescharacteristic
548C2×Dic11C22×D411yescharacteristic
549C2×Dic11C22×D411yescharacteristic
550C2×Dic11C22×D411yescharacteristic
551D44—22no—
552D44—42no—
553D44—42no—
554D44—42no—
555C4×D11—22no—
556C4×D11—22no—
557C4×D11—22no—
558C4×D11—22no—
559C4×D11—22no—
560C4×D11—22no—
561C4×D11—22no—
562C4×D11—22no—
563C4×D11—41no—
564C4×D11—41no—
565C4×D11—41no—
566C4×D11—41no—
567C4×D11—41no—
568C4×D11—41no—
569C4×D11—41no—
570C4×D11—41no—
571C4×D11—42no—
572C4×D11—42no—
573C4×D11—42no—
574C4×D11—42no—
575C4×D11—42no—
576Dic22—24no—
577Dic22—22no—
578Dic22—24no—
579Dic22—42no—
580Dic22—44no—
581Dic22—44no—
582Dic22—44no—
583C8×C11—24no—
584C11⋊C8—24no—
585C22×#41—111no—
586C23×Q8—111no—
587C24×C4—111no—
588C2×#137—112no—
589C2×#137—112no—
590C22×M16—112no—
591#525—111no—
592#525—111no—
593#525—111no—
594#525—111no—
595#525—111no—
596#525—111no—
597#525—111no—
598#525—221no—
599#525—221no—
600#525—221no—
601#525—221no—
602#525C2×D1111yescharacteristic
603C2×#123—221no—
604C2×C22⋊Q8—111no—
605C2×C22⋊Q8—111no—
606C2×C22⋊Q8—112no—
607C2×C22⋊Q8—112no—
608C2×C22⋊Q8—112no—
609C2×C22⋊Q8—112no—
610C2×C22⋊Q8—112no—
611C2×C22⋊Q8—112no—
612C2×C22⋊Q8—221no—
613C2×C22⋊Q8—221no—
614C2×C22⋊Q8—221no—
615C2×C22⋊Q8—221no—
616C2×C22⋊Q8—221no—
617C2×C22⋊Q8—221no—
618C2×#121—111no—
619C2×#121—111no—
620C2×#120—221no—
621C2×C4×D4—221no—
622C2×C4×D4—221no—
623C2×#117—111no—
624C22×C4⋊C4—221no—
625C22×C4⋊C4C2×D1111yescharacteristic, complemented
626C22×C22⋊C4—221no—
627#485—114no—
628#485—114no—
629#484—112no—
630#484—114no—
631#484C2×D1112yescomplemented
632#483—112no—
633#483—114no—
634#483C2×D1112yescomplemented
635#481—112no—
636#481C2×D1112yescomplemented
637#480—112no—
638#480C2×D1112yescomplemented
639#470—114no—
640#470—114no—
641#468—114no—
642#468—114no—
643#467—114no—
644#467—114no—
645#465—114no—
646#465—114no—
647#452—114no—
648#452—114no—
649#451—112no—
650#451—112no—
651#451—114no—
652#451—112no—
653#451—112no—
654#450—114no—
655#448—112no—
656#448—112no—
657#448—112no—
658#448—112no—
659#428—112no—
660#428C2×D1112yescomplemented
661#419—112no—
662#419—112no—
663#417—112no—
664#417C2×D1112yescomplemented
665#407—111no—
666#407—112no—
667#407—112no—
668#407—112no—
669#407C2×D1111yescharacteristic, complemented
670C2×C22⋊C8—112no—
671C2×C22⋊C8—112no—
672C22×C11—28no—
673C22×C11—21no—
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—41no—
680C22×C11—41no—
681C22×C11—41no—
682C22×C11#53412yes—
683C22×C11C2×#13712yes—
684C22×C11#57512yes—
685C22×C11C23×D411yescharacteristic
686C2×D11—21no—
687C2×D11—21no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—21no—
691C2×D11—21no—
692C2×D11—21no—
693C2×D11—21no—
694C2×D11—21no—
695C2×D11—21no—
696C2×D11—44no—
697C2×D11—44no—
698C2×D11—44no—
699C2×D11—44no—
700C2×D11—44no—
701C2×D11—44no—
702C2×D11—41no—
703C2×D11—41no—
704C2×D11—41no—
705C2×D11—84no—
706C2×D11C2×#13712yes—
707C2×D11C2×#13712yes—
708C4×C11—21no—
709C4×C11—21no—
710C4×C11—41no—
711C4×C11—41no—
712C4×C11—44no—
713C4×C11—41no—
714C4×C11#53412yes—
715C4×C11C2×H(5,𝔽2)12yes—
716Dic11—21no—
717Dic11—21no—
718Dic11—21no—
719Dic11—21no—
720Dic11—44no—
721Dic11—41no—
722Dic11—41no—
723Dic11—41no—
724C25—111no—
725C2×#41—111no—
726C2×#41—111no—
727C2×#41—111no—
728C2×#41—221no—
729C2×#41—221no—
730C2×#41—444no—
731C2×#41C22×D1111yescharacteristic
732C22×Q8—111no—
733C22×Q8—112no—
734C22×Q8—112no—
735C22×Q8—112no—
736C22×Q8—221no—
737C22×Q8—221no—
738C22×Q8—221no—
739C22×Q8—444no—
740C22×D4—111no—
741C22×D4—221no—
742C22×D4—221no—
743C22×D4—221no—
744C23×C4—21no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—221no—
759C23×C4—221no—
760C23×C4—444no—
761C23×C4C22×D1111yescharacteristic
762#137—444no—
763#137—444no—
764C2×Q16—114no—
765C2×Q16—114no—
766C2×SD16—114no—
767C2×SD16—114no—
768C2×M16—112no—
769C2×M16—114no—
770C2×M16—444no—
771C2×M16C22×D1112yes—
772C22×C8—114no—
773#123—21no—
774#123—221no—
775#123—221no—
776#123—221no—
777#123—221no—
778#123—221no—
779#123—221no—
780#123—221no—
781C22⋊Q8—111no—
782C22⋊Q8—111no—
783C22⋊Q8—111no—
784C22⋊Q8—111no—
785C22⋊Q8—114no—
786C22⋊Q8—114no—
787C22⋊Q8—114no—
788C22⋊Q8—114no—
789C22⋊Q8—111no—
790C22⋊Q8—111no—
791C22⋊Q8—221no—
792C22⋊Q8—221no—
793C22⋊Q8—222no—
794C22⋊Q8—222no—
795C22⋊Q8—222no—
796C22⋊Q8—222no—
797C22⋊Q8—222no—
798C22⋊Q8—222no—
799C22⋊Q8—222no—
800C22⋊Q8—222no—
801C22⋊Q8—222no—
802C22⋊Q8—222no—
803C22⋊Q8—222no—
804C22⋊Q8—222no—
805C22⋊Q8—221no—
806C22⋊Q8—221no—
807C22⋊Q8C22×D1111yescharacteristic
808C22⋊Q8C22×D1111yescharacteristic
809#121—111no—
810#121—111no—
811#121—111no—
812#121—111no—
813#121—111no—
814#121—111no—
815#121—221no—
816#121—221no—
817#121—221no—
818#121—221no—
819#121C22×D1111yescharacteristic
820#121C22×D1111yescharacteristic
821#120—21no—
822#120—221no—
823#120—221no—
824#120—221no—
825#120—221no—
826#120—221no—
827#120—221no—
828#120—221no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—221no—
832C4×D4—221no—
833C4×D4—221no—
834C4×D4—221no—
835C4×D4—221no—
836C4×D4—221no—
837C4×D4—221no—
838C4×D4—221no—
839C4×D4—221no—
840C4×D4—221no—
841C4×D4—221no—
842C4×D4—221no—
843C4×D4—221no—
844C4×D4—221no—
845#117—111no—
846#117—111no—
847#117—111no—
848#117—221no—
849#117—221no—
850#117C22×D1111yescharacteristic
851C2×C4⋊C4—21no—
852C2×C4⋊C4—21no—
853C2×C4⋊C4—21no—
854C2×C4⋊C4—111no—
855C2×C4⋊C4—111no—
856C2×C4⋊C4—221no—
857C2×C4⋊C4—221no—
858C2×C4⋊C4—222no—
859C2×C4⋊C4—222no—
860C2×C4⋊C4—222no—
861C2×C4⋊C4—222no—
862C2×C4⋊C4—222no—
863C2×C4⋊C4—222no—
864C2×C4⋊C4C22×D1112yes—
865C2×C4⋊C4C22×D1112yes—
866C2×C4⋊C4C22×D1112yes—
867C2×C22⋊C4—221no—
868C2×C22⋊C4—221no—
869C2×C22⋊C4—221no—
870C2×C22⋊C4—221no—
871C2×C22⋊C4—221no—
872C2×C22⋊C4—222no—
873C2×C22⋊C4—222no—
874C2×C22⋊C4—222no—
875C2×C22⋊C4—222no—
876C2×C22⋊C4—222no—
877C2×C22⋊C4—222no—
878C2×C42—221no—
879#107—114no—
880#107C22×D1114yescomplemented
881#106—114no—
882#106C22×D1114yescomplemented
883#103—114no—
884#103—114no—
885#103—114no—
886#103—114no—
887#103—114no—
888#103C22×D1114yescomplemented
889#102—114no—
890#102C22×D1114yescomplemented
891C22⋊C8—112no—
892C22⋊C8—112no—
893C22⋊C8—114no—
894C22⋊C8—114no—
895C22⋊C8C22×D1112yes—
896C22⋊C8C22×D1112yes—
897C2×C11—22no—
898C2×C11—22no—
899C2×C11—22no—
900C2×C11—81no—
901C2×C11C2×#53411yescharacteristic
902C2×C11C22×#13711yescharacteristic
903C2×C11C2×#57511yescharacteristic
904D11—22no—
905D11—22no—
906D11—41no—
907D11—41no—
908D11—81no—
909C24—111no—
910C24—111no—
911C24—111no—
912C24—111no—
913C24—111no—
914C24—111no—
915C24—224no—
916C24—221no—
917C24—442no—
918C24—442no—
919C24D4×D1111yescharacteristic
920#41—24no—
921#41—224no—
922#41—444no—
923#41—442no—
924#41—444no—
925#41—442no—
926C2×Q8—114no—
927C2×Q8—111no—
928C2×Q8—221no—
929C2×Q8—222no—
930C2×Q8—222no—
931C2×Q8—222no—
932C2×Q8—224no—
933C2×Q8—224no—
934C2×Q8—444no—
935C2×Q8—444no—
936C2×Q8—444no—
937C2×Q8—444no—
938C2×Q8—444no—
939C2×Q8—442no—
940C2×Q8C23×D1111yescharacteristic
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—111no—
945C2×D4—221no—
946C2×D4—221no—
947C2×D4—221no—
948C2×D4—221no—
949C2×D4—221no—
950C2×D4—221no—
951C2×D4—221no—
952C2×D4—221no—
953C2×D4—221no—
954C2×D4—221no—
955C2×D4—442no—
956C2×D4—444no—
957C2×D4—444no—
958C2×D4—444no—
959C2×D4C23×D1111yescharacteristic
960C22×C4—24no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—21no—
965C22×C4—44no—
966C22×C4—111no—
967C22×C4—111no—
968C22×C4—111no—
969C22×C4—111no—
970C22×C4—111no—
971C22×C4—111no—
972C22×C4—111no—
973C22×C4—111no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—111no—
977C22×C4—111no—
978C22×C4—111no—
979C22×C4—111no—
980C22×C4—111no—
981C22×C4—111no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—111no—
985C22×C4—111no—
986C22×C4—111no—
987C22×C4—111no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—224no—
994C22×C4—224no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—221no—
999C22×C4—442no—
1000C22×C4—442no—
1001C22×C4—442no—
1002C22×C4—442no—
1003C22×C4—442no—
1004C22×C4—442no—
1005C22×C4—442no—
1006C22×C4—442no—
1007C22×C4—442no—
1008C22×C4—442no—
1009C22×C4—444no—
1010C22×C4—442no—
1011C22×C4—444no—
1012C22×C4D4×D1111yescharacteristic
1013C22×C4D4×D1111yescharacteristic
1014C22×C4D4×D1111yescharacteristic
1015C22×C4C23×D1111yescharacteristic
1016C22×C4C23×D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018Q16—444no—
1019Q16—444no—
1020SD16—444no—
1021SD16—444no—
1022M16—24no—
1023M16—224no—
1024M16—444no—
1025C2×C8—114no—
1026C2×C8—444no—
1027C2×C8C23×D1114yes—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—111no—
1034C4⋊C4—111no—
1035C4⋊C4—221no—
1036C4⋊C4—221no—
1037C4⋊C4—224no—
1038C4⋊C4—224no—
1039C4⋊C4—224no—
1040C4⋊C4—224no—
1041C4⋊C4—221no—
1042C4⋊C4—221no—
1043C4⋊C4—221no—
1044C4⋊C4—221no—
1045C4⋊C4—221no—
1046C4⋊C4—221no—
1047C4⋊C4C23×D1114yes—
1048C4⋊C4C23×D1111yescharacteristic
1049C4⋊C4C23×D1111yescharacteristic
1050C22⋊C4—21no—
1051C22⋊C4—21no—
1052C22⋊C4—21no—
1053C22⋊C4—21no—
1054C22⋊C4—21no—
1055C22⋊C4—221no—
1056C22⋊C4—221no—
1057C22⋊C4—224no—
1058C22⋊C4—224no—
1059C22⋊C4—224no—
1060C22⋊C4—224no—
1061C22⋊C4—221no—
1062C22⋊C4—221no—
1063C22⋊C4—221no—
1064C22⋊C4—221no—
1065C22⋊C4—221no—
1066C22⋊C4—221no—
1067C22⋊C4—221no—
1068C22⋊C4—221no—
1069C22⋊C4—221no—
1070C22⋊C4—221no—
1071C22⋊C4—221no—
1072C22⋊C4—221no—
1073C22⋊C4—221no—
1074C42—21no—
1075C42—221no—
1076C42—221no—
1077C42—221no—
1078C11#6075111yescharacteristic, complemented, Sylow
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—21no—
1083C23—111no—
1084C23—111no—
1085C23—114no—
1086C23—111no—
1087C23—111no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—221no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—4416no—
1107C23—442no—
1108C23—442no—
1109C23—442no—
1110C23C2×D4×D1111yescharacteristic
1111C23C2×D4×D1111yescharacteristic
1112C23C2×D4×D1111yescharacteristic
1113Q8—22no—
1114Q8—224no—
1115Q8—224no—
1116Q8—222no—
1117Q8—444no—
1118Q8—444no—
1119Q8—442no—
1120Q8—444no—
1121D4—22no—
1122D4—42no—
1123D4—42no—
1124D4—42no—
1125D4—222no—
1126D4—442no—
1127D4—442no—
1128D4—442no—
1129D4—442no—
1130D4—442no—
1131D4—442no—
1132D4—442no—
1133D4—442no—
1134D4—442no—
1135D4—442no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—24no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—42no—
1149C2×C4—111no—
1150C2×C4—111no—
1151C2×C4—111no—
1152C2×C4—111no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—222no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—221no—
1164C2×C4—221no—
1165C2×C4—221no—
1166C2×C4—224no—
1167C2×C4—441no—
1168C2×C4—441no—
1169C2×C4—441no—
1170C2×C4—441no—
1171C2×C4—441no—
1172C2×C4—441no—
1173C2×C4—441no—
1174C2×C4—441no—
1175C2×C4—442no—
1176C2×C4—442no—
1177C2×C4—442no—
1178C2×C4—442no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—442no—
1184C2×C4—444no—
1185C2×C4—444no—
1186C2×C4—444no—
1187C2×C4—442no—
1188C2×C4C2×D4×D1111yescharacteristic
1189C2×C4C2×D4×D1111yescharacteristic
1190C2×C4C2×D4×D1111yescharacteristic
1191C2×C4#6704214yes—
1192C2×C4C24×D1111yescharacteristic
1193C8—24no—
1194C8—224no—
1195C22—28no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—112no—
1206C22—112no—
1207C22—221no—
1208C22—221no—
1209C22—221no—
1210C22—221no—
1211C22—221no—
1212C22—221no—
1213C22—221no—
1214C22—221no—
1215C22—221no—
1216C22—221no—
1217C22—444no—
1218C22—444no—
1219C22—444no—
1220C22—444no—
1221C22—444no—
1222C22—444no—
1223C22—441no—
1224C22—441no—
1225C22—441no—
1226C22—884no—
1227C22#1062318412yes—
1228C22#1062330412yes—
1229C22D11×#13712yes—
1230C22C22×D4×D1111yescharacteristic
1231C4—21no—
1232C4—21no—
1233C4—41no—
1234C4—41no—
1235C4—44no—
1236C4—41no—
1237C4—221no—
1238C4—221no—
1239C4—221no—
1240C4—221no—
1241C4—441no—
1242C4—444no—
1243C4—441no—
1244C4—441no—
1245C4#1062318412yes—
1246C4C2×#6704212yes—
1247C2—22no—
1248C2—22no—
1249C2—22no—
1250C2—81no—
1251C2—222no—
1252C2—222no—
1253C2—441no—
1254C2—441no—
1255C2—881no—
1256C2C2×#1062318411yescharacteristic
1257C2C2×D11×#13711yescharacteristic
1258C2C2×#1062330411yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3092C2
socleC22×C11C23×D4
prime radicalD11×#525C2
hypercenter#3092D11
hypocenterC11#60751
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
2. C22×#66950C2semidirect
3. #13079451C2semidirect
4. #13079445C2semidirect
5. #13079439C2semidirect
6. #13079424C2semidirect
7. #13079402C2semidirect
8. #13079396C2semidirect
9. #13079390C2semidirect
10. #13079375C2semidirect
11. #13078566C2semidirect
12. #13078539C2semidirect
13. #13078249C2semidirect
14. #13078247C2semidirect
15. #13077877C2semidirect
16. #13077853C2semidirect
17. #13077849C2semidirect
18. D11×#407C2semidirect
19. C11×#3092C2semidirect
22. C23×Dic22C22semidirect
24. C22×C11×C4⋊C4C22semidirect
26. C2×#67004C22semidirect
30. C2×#66962C22semidirect
31. C2×M16×D11C22semidirect
59. C2×#66950C22semidirect
60. C2×#66950C22semidirect
61. C2×#66950C22semidirect
62. C11×#484C22semidirect
63. C11×#483C22semidirect
64. C11×#481C22semidirect
65. C11×#480C22semidirect
66. C11×#428C22semidirect
67. C11×#417C22semidirect
68. C11×#407C22semidirect
69. #10622820C22semidirect
71. #10622733C22semidirect
72. #10622663C22semidirect
73. #10622663C22semidirect
74. #10622653C22semidirect
75. #10622653C22semidirect
76. #10622617C22semidirect
77. #10622584C22semidirect
78. #10622583C22semidirect
79. #10622581C22semidirect
80. #10622580C22semidirect
81. #10622579C22semidirect
82. #10622577C22semidirect
83. #10622501C22semidirect
84. #10622500C22semidirect
85. #10622499C22semidirect
86. #10622497C22semidirect
87. #10622481C22semidirect
88. #10622480C22semidirect
89. #10622477C22semidirect
90. #10622475C22semidirect
91. #10622429C22semidirect
92. #10622426C22semidirect
93. #10622423C22semidirect
94. #10622421C22semidirect
95. #10622396C22semidirect
96. #10622393C22semidirect
97. #10622391C22semidirect
98. #10622389C22semidirect
99. #10622352C22semidirect
100. #10622352C22semidirect
101. #10622351C22semidirect
102. #10622351C22semidirect
104. #10622339C22semidirect
106. D11×C22⋊C8C22semidirect
165. C2×#4326C23semidirect
176. C2×#4324C23semidirect
202. C2×Dic44C23semidirect
203. C2×#4314C23semidirect
262. C11×#107C23semidirect
263. C11×#106C23semidirect
264. C11×#103C23semidirect
265. C11×#102C23semidirect
272. #66880C23semidirect
273. #66880C23semidirect
274. #66874C23semidirect
275. #66874C23semidirect
276. #66874C23semidirect
277. #66873C23semidirect
278. #66872C23semidirect
279. #66871C23semidirect
462. #3092D11semidirect
498. C22×D11#137semidirect
625. C22×C4⋊C4C2×D11semidirect
631. #484C2×D11semidirect
634. #483C2×D11semidirect
636. #481C2×D11semidirect
638. #480C2×D11semidirect
660. #428C2×D11semidirect
664. #417C2×D11semidirect
669. #407C2×D11semidirect
880. #107C22×D11semidirect
882. #106C22×D11semidirect
888. #103C22×D11semidirect
890. #102C22×D11semidirect
1078. C11#60751semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
C22×#669502
#130794512
#130794452
#130794392
#130794242
#130794022
#130793962
#130793902
#130793752
#130785662
#130785392
#130782492
#130782472
#130778772
#130778532
#130778492
D11×#4072
C11×#30922
#6075111