Finite Group Databasebeta

← #14720933

Subgroups — #14720933

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4#13067134C212yesmaximal, complemented
5#13067130C212yesmaximal, complemented
6#13067119C212yesmaximal, complemented
7#13067117C212yesmaximal, complemented
8#13067108C211yesmaximal, characteristic, complemented
9#13067107C211yesmaximal, characteristic, complemented
10#13067105C211yesmaximal, characteristic, complemented
11C11×#1501C211yesmaximal, characteristic, complemented
12C2×#41×D11C411yescharacteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C11×#525C2211yescharacteristic
15#10623359C411yescharacteristic, complemented
16#10623322C2211yescharacteristic
17C22×#4313—21no—
18#10623187—21no—
19D11×#123—21no—
20#10623158C411yescharacteristic, complemented
21#10623158C2211yescharacteristic
22D11×C22⋊Q8C411yescharacteristic, complemented
23D11×C22⋊Q8C2211yescharacteristic
24#10623137C411yescharacteristic, complemented
25#10623137C2211yescharacteristic
26D11×#121C411yescharacteristic, complemented
27D11×#121C2211yescharacteristic
28D11×#120—21no—
29#10623117—21no—
30#10623078—21no—
31#10623078—21no—
32C4×D4×D11—21no—
33C4×D4×D11—21no—
34#10623055C411yescharacteristic, complemented
35D11×#117C411yescharacteristic, complemented
36C2×C22⋊C4×D11—21no—
37C2×C42×D11—21no—
38C2×C11×C22⋊C8C2211yescharacteristic, complemented
39C4×C11×C22⋊C4C2211yescharacteristic, complemented
40C4×C22⋊Dic11C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
42C2×(C2×D11)⋊C8—21no—
43C22⋊C4×Dic11—21no—
44C4×(C2×D11)⋊C4—21no—
45#10622339—21no—
46#10622339—21no—
47#10622339C2212yes—
48#10622339C2212yescomplemented
49#10622279C2212yes—
50D11×#95C2212yescomplemented
51C11×#328C2212yescomplemented
52C11×#327C2212yescomplemented
53#10622176C2212yescomplemented
54#10622175C2212yescomplemented
55#10622108C2212yescomplemented
56#10622105C2212yescomplemented
57#10622090C2212yescomplemented
58#10622089C2212yescomplemented
59C24×D11D411yescharacteristic
60C2×C11×#41C2×C411yescharacteristic, complemented
61C23×C4×C11C2311yescharacteristic
62C23×Dic11D411yescharacteristic
63#41×D11—44no—
64C2×#4343C2×C411yescharacteristic
65C2×Q8×D11C2×C411yescharacteristic, complemented
66C2×#4341—21no—
67C2×#4341C2×C411yescharacteristic
68C2×D4×D11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C2×D4×D11C2×C411yescharacteristic, complemented
72C2×#4339—21no—
73C2×#4339C2×C411yescharacteristic, complemented
74C22×C4×D11—22no—
75C22×C4×D11—21no—
76C22×C4×D11—44no—
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11D411yescharacteristic
82C22×C4×D11D411yescharacteristic
83C22×C4×D11D411yescharacteristic
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11D411yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C8×C11—21no—
90C11×#123—21no—
91C11×C22⋊Q8C2×C411yescharacteristic, complemented
92C11×C22⋊Q8C2311yescharacteristic
93C11×#121C2×C411yescharacteristic, complemented
94C11×#121C2311yescharacteristic
95C11×#120—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C11×#117C2×C411yescharacteristic, complemented
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101#67006—21no—
102C2×C22⋊Dic11—21no—
103#66999C2×C411yescharacteristic
104#66999C2×C411yescharacteristic, complemented
105#66992—21no—
106#66992—21no—
107#66991C2×C411yescharacteristic
108#66991C2×C411yescharacteristic, complemented
109#66990—21no—
110#66990—21no—
111#66990—21no—
112#66988—21no—
113D4×Dic11—21no—
114D4×Dic11—21no—
115#66983C2×C411yescharacteristic, complemented
116#66983C2311yescharacteristic
117#66982—21no—
118C4×C22⋊D11—21no—
119C4×C22⋊D11—21no—
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C2×(C2×D11)⋊C4—22no—
123#66979C2×C411yescharacteristic, complemented
124#66977C2×C411yescharacteristic, complemented
125#66977C2311yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—22no—
128C22×C11⋊C8—21no—
129C2×#4313—22no—
130C2×#4313—22no—
131C2×#4313—44no—
132#66950C2×C411yescharacteristic
133#66950C2×C411yescharacteristic, complemented
134#66949—21no—
135#66949—21no—
136#66948C2×C411yescharacteristic
137#66948C2×C411yescharacteristic, complemented
138#66947—21no—
139#66947—21no—
140#66946—21no—
141#66946—21no—
142#66945C2×C411yescharacteristic
143#66945C2×C411yescharacteristic
144C4⋊C4×D11—21no—
145C4⋊C4×D11—21no—
146C4⋊C4×D11C2×C411yescharacteristic, complemented
147C4⋊C4×D11C2×C411yescharacteristic, complemented
148#66939—21no—
149#66937—21no—
150#66937—21no—
151#66936—21no—
152#66936—21no—
153#66935—21no—
154#66935—21no—
155#66935—21no—
156(C22⋊D11)⋊C4—21no—
157(C22⋊D11)⋊C4—21no—
158(C22⋊D11)⋊C4—21no—
159(C22⋊D11)⋊C4—21no—
160C22⋊C4×D11—28no—
161C22⋊C4×D11—21no—
162C22⋊C4×D11—21no—
163C22⋊C4×D11—21no—
164C22⋊C4×D11—21no—
165C22⋊C4×D11—21no—
166#66931—21no—
167#66931—21no—
168#66930—21no—
169C4×D44—21no—
170C4×D44—21no—
171#66925—21no—
172C42×D11—21no—
173C42×D11—44no—
174C11×C22⋊C8—21no—
175C11×C22⋊C8C2312yes—
176C11×#95C2312yes—
177C11⋊#95—22no—
178C11⋊#95C2312yes—
179C22⋊(C11⋊C8)—21no—
180C22⋊(C11⋊C8)C2312yes—
181(C2×D11)⋊C8—22no—
182(C2×D11)⋊C8—22no—
183#17542—111nomaximal, Sylow
184C24×C11C2×D411yescharacteristic
185C23×D11—24no—
186C23×D11—21no—
187C23×D11—42no—
188C23×D11—42no—
189C23×D11C22⋊C411yescharacteristic
190C23×D11C22⋊C411yescharacteristic
191C23×D11C22⋊C411yescharacteristic
192C23×D11C22⋊C411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C23×D11C2×D411yescharacteristic
195C11×#41—42no—
196C2×Q8×C11C22×C411yescharacteristic
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11C22×C411yescharacteristic
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—42no—
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—21no—
211C2×C22⋊D11—21no—
212C2×C22⋊D11—21no—
213C2×C22⋊D11—21no—
214C2×C22⋊D11—21no—
215C2×C22⋊D11—21no—
216C2×C22⋊D11—21no—
217C22×Dic11—21no—
218C22×Dic11—22no—
219C22×Dic11—42no—
220C22×Dic11C22⋊C411yescharacteristic
221C22×Dic11C22⋊C411yescharacteristic
222C22×Dic11C22⋊C411yescharacteristic
223C22×Dic11C22⋊C411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226#4343—42no—
227Q8×D11—42no—
228#4341—42no—
229#4341—44no—
230D4×D11—44no—
231D4×D11—44no—
232D4×D11—42no—
233D4×D11—44no—
234#4339—42no—
235#4339—44no—
236C2×D44—21no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44C22×C411yescharacteristic
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—28no—
244C2×C4×D11—21no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—42no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11—42no—
258C2×C4×D11—42no—
259C2×C4×D11—42no—
260C2×C4×D11—44no—
261C2×C4×D11C22⋊C411yescharacteristic
262C2×C4×D11C22⋊C411yescharacteristic
263C2×C4×D11C22⋊C411yescharacteristic
264C2×C4×D11C22⋊C411yescharacteristic
265C2×C4×D11C22⋊C411yescharacteristic
266C2×C4×D11C22⋊C411yescharacteristic
267C2×C4×D11C22⋊C411yescharacteristic
268C2×C4×D11C22⋊C411yescharacteristic
269C2×C4×D11C22×C411yescharacteristic
270C2×C4×D11C22×C411yescharacteristic
271C2×C4×D11C22×C411yescharacteristic
272C2×C4×D11C22×C411yescharacteristic
273C2×C4×D11C2×D411yescharacteristic
274C2×C4×D11C2×D411yescharacteristic
275C2×C4×D11C2×D411yescharacteristic
276C2×C4×D11C2×D411yescharacteristic
277C2×Dic22—21no—
278C2×Dic22C22×C411yescharacteristic
279C2×C8×C11—22no—
280C2×C8×C11—42no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4C22×C411yescharacteristic
284C11×C4⋊C4C22×C411yescharacteristic
285C11×C22⋊C4—24no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C42×C11—21no—
292C42×C11—42no—
293C22⋊Dic11—24no—
294C22⋊Dic11—21no—
295C22⋊Dic11—21no—
296C22⋊Dic11—21no—
297C22⋊Dic11—21no—
298C22⋊Dic11—21no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—21no—
309(C2×D11)⋊C4—21no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11C22×C411yescharacteristic
313C4⋊Dic11C22×C411yescharacteristic
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320C4×Dic11—21no—
321C4×Dic11—21no—
322C4×Dic11—21no—
323C4×Dic11—42no—
324C4×Dic11—44no—
325C2×C11⋊C8—22no—
326C2×C11⋊C8—42no—
327#4313—44no—
328#4313—44no—
329C2×#525—111no—
330C2×#407—111no—
331C2×C4×C22⋊C4—111no—
332#1508—112no—
333#1507—112no—
334#1504—112no—
335#1504—112no—
336#1501—111no—
337#1501—111no—
338#1501—111no—
339#1501D1111yescharacteristic, complemented
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—21no—
343C23×C11—41no—
344C23×C11C2×C22⋊C411yescharacteristic
345C23×C11C2×C22⋊C411yescharacteristic
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—21no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—416no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11#10414yes—
370C22×D11C2×C22⋊C411yescharacteristic
371C22×D11C2×C22⋊C411yescharacteristic
372C22×D11C2×C22⋊C411yescharacteristic
373C22×D11C2×C22⋊C411yescharacteristic
374Q8×C11—41no—
375D4×C11—41no—
376D4×C11—42no—
377D4×C11—42no—
378D4×C11—42no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—24no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11C2×C22⋊C411yescharacteristic
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C23×C411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C22⋊D11—42no—
397C22⋊D11—42no—
398C22⋊D11—42no—
399C22⋊D11—42no—
400C22⋊D11—42no—
401C22⋊D11—42no—
402C22⋊D11—42no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—24no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11C2×C22⋊C411yescharacteristic
417C2×Dic11C2×C22⋊C411yescharacteristic
418C2×Dic11C2×C22⋊C411yescharacteristic
419C2×Dic11C2×C22⋊C411yescharacteristic
420D44—41no—
421D44—42no—
422D44—42no—
423D44—42no—
424C4×D11—22no—
425C4×D11—22no—
426C4×D11—22no—
427C4×D11—22no—
428C4×D11—22no—
429C4×D11—22no—
430C4×D11—22no—
431C4×D11—22no—
432C4×D11—22no—
433C4×D11—41no—
434C4×D11—41no—
435C4×D11—41no—
436C4×D11—41no—
437C4×D11—41no—
438C4×D11—41no—
439C4×D11—42no—
440C4×D11—416no—
441C4×D11—42no—
442C4×D11—42no—
443C4×D11—42no—
444C4×D11—42no—
445C4×D11#9914yes—
446Dic22—42no—
447Dic22—41no—
448C8×C11—42no—
449C11⋊C8—42no—
450C22×#41—111no—
451C24×C4—111no—
452C22×M16—221no—
453#525—111no—
454#525—111no—
455#525—111no—
456#525—111no—
457#525—111no—
458#525—111no—
459#525—111no—
460#525—221no—
461#525—221no—
462#525—221no—
463#525—221no—
464#525C2×D1111yescharacteristic
465C2×#123—221no—
466C2×C22⋊Q8—111no—
467C2×C22⋊Q8—111no—
468C2×#121—111no—
469C2×#121—111no—
470C2×#120—221no—
471C2×C4×D4—221no—
472C2×C4×D4—221no—
473C2×#117—111no—
474C22×C22⋊C4—221no—
475C22×C42—221no—
476#407—112no—
477#407—112no—
478#407—221no—
479#407—221no—
480C2×C22⋊C8—111no—
481C2×C22⋊C8—221no—
482C2×C22⋊C8C2×D1111yescharacteristic, complemented
483C4×C22⋊C4—111no—
484C4×C22⋊C4—112no—
485C4×C22⋊C4—221no—
486C4×C22⋊C4—221no—
487C4×C22⋊C4C2×D1111yescharacteristic, complemented
488C2×#95—112no—
489#328—112no—
490#328—112no—
491#328—112no—
492#328C2×D1112yescomplemented
493#327—112no—
494#327—112no—
495#327—112no—
496#327C2×D1112yescomplemented
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—44no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11C2×#10412yes—
509C22×C11C22×C22⋊C411yescharacteristic
510C22×C11#57512yes—
511C2×D11—28no—
512C2×D11—21no—
513C2×D11—21no—
514C2×D11—21no—
515C2×D11—21no—
516C2×D11—21no—
517C2×D11—21no—
518C2×D11—21no—
519C2×D11—21no—
520C2×D11—21no—
521C2×D11—44no—
522C2×D11—44no—
523C2×D11—44no—
524C2×D11—44no—
525C2×D11—44no—
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—41no—
529C2×D11—84no—
530C2×D11C2×#9912yes—
531C2×D11C2×#10412yes—
532C2×D11C2×#10412yes—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—44no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11—41no—
540C4×C11C2×#9912yes—
541Dic11—21no—
542Dic11—21no—
543Dic11—21no—
544Dic11—44no—
545Dic11—41no—
546Dic11—41no—
547Dic11—41no—
548Dic11C2×#9912yes—
549C25—111no—
550C2×#41—111no—
551C2×#41—111no—
552C2×#41—111no—
553C2×#41—221no—
554C2×#41—221no—
555C2×#41—444no—
556C2×#41C4×D1111yescharacteristic, complemented
557C22×Q8—111no—
558C22×D4—111no—
559C22×D4—221no—
560C22×D4—221no—
561C22×D4—221no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—221no—
576C23×C4—222no—
577C23×C4—444no—
578C23×C4C22×D1111yescharacteristic
579C2×M16—222no—
580C2×M16—222no—
581C2×M16—444no—
582C22×C8—21no—
583C22×C8—221no—
584#123—21no—
585#123—221no—
586#123—221no—
587#123—221no—
588#123—221no—
589#123—221no—
590#123—221no—
591#123—221no—
592C22⋊Q8—111no—
593C22⋊Q8—111no—
594C22⋊Q8—111no—
595C22⋊Q8—111no—
596C22⋊Q8—111no—
597C22⋊Q8—111no—
598C22⋊Q8—221no—
599C22⋊Q8—221no—
600C22⋊Q8—221no—
601C22⋊Q8—221no—
602C22⋊Q8C4×D1111yescharacteristic, complemented
603C22⋊Q8C22×D1111yescharacteristic
604#121—111no—
605#121—111no—
606#121—111no—
607#121—111no—
608#121—111no—
609#121—111no—
610#121—221no—
611#121—221no—
612#121—221no—
613#121—221no—
614#121C4×D1111yescharacteristic, complemented
615#121C22×D1111yescharacteristic
616#120—21no—
617#120—221no—
618#120—221no—
619#120—221no—
620#120—221no—
621#120—221no—
622#120—221no—
623#120—221no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—221no—
627C4×D4—221no—
628C4×D4—221no—
629C4×D4—221no—
630C4×D4—221no—
631C4×D4—221no—
632C4×D4—221no—
633C4×D4—221no—
634C4×D4—221no—
635C4×D4—221no—
636C4×D4—221no—
637C4×D4—221no—
638C4×D4—221no—
639C4×D4—221no—
640#117—111no—
641#117—111no—
642#117—111no—
643#117—221no—
644#117—221no—
645#117C4×D1111yescharacteristic, complemented
646C2×C4⋊C4—111no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—221no—
649C2×C4⋊C4—221no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C22⋊C4—228no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—221no—
659C2×C42—21no—
660C2×C42—221no—
661C2×C42—222no—
662C2×C42—221no—
663C2×C42—444no—
664C22⋊C8—21no—
665C22⋊C8—112no—
666C22⋊C8—222no—
667C22⋊C8—222no—
668C22⋊C8—221no—
669C22⋊C8C22×D1112yes—
670#95—112no—
671#95—222no—
672#95C22×D1112yes—
673C2×C11—22no—
674C2×C11—22no—
675C2×C11—41no—
676C2×C11—81no—
677C2×C11C22×#9911yescharacteristic
678C2×C11#289611yescharacteristic
679C2×C11C22×#10411yescharacteristic
680D11—22no—
681D11—22no—
682D11—22no—
683D11—41no—
684D11—81no—
685C24—111no—
686C24—111no—
687C24—111no—
688C24—111no—
689C24—111no—
690C24—111no—
691C24—224no—
692C24—221no—
693C24—442no—
694C24—442no—
695C24D4×D1111yescharacteristic
696#41—42no—
697#41—442no—
698#41—444no—
699#41—444no—
700#41—442no—
701#41—442no—
702C2×Q8—111no—
703C2×Q8—221no—
704C2×Q8—442no—
705C2×Q8C2×C4×D1111yescharacteristic
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—111no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—221no—
714C2×D4—221no—
715C2×D4—221no—
716C2×D4—221no—
717C2×D4—221no—
718C2×D4—221no—
719C2×D4—221no—
720C2×D4—442no—
721C2×D4—444no—
722C2×D4—444no—
723C2×D4—444no—
724C2×D4C2×C4×D1111yescharacteristic
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—111no—
743C22×C4—111no—
744C22×C4—111no—
745C22×C4—111no—
746C22×C4—111no—
747C22×C4—111no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—224no—
751C22×C4—224no—
752C22×C4—224no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—228no—
758C22×C4—221no—
759C22×C4—222no—
760C22×C4—221no—
761C22×C4—442no—
762C22×C4—442no—
763C22×C4—442no—
764C22×C4—442no—
765C22×C4—442no—
766C22×C4—442no—
767C22×C4—442no—
768C22×C4—442no—
769C22×C4—442no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—442no—
774C22×C4C2×C4×D1111yescharacteristic
775C22×C4C2×C4×D1111yescharacteristic
776C22×C4D4×D1111yescharacteristic
777C22×C4D4×D1111yescharacteristic
778C22×C4D4×D1111yescharacteristic
779C22×C4C23×D1111yescharacteristic
780M16—444no—
781M16—444no—
782C2×C8—22no—
783C2×C8—42no—
784C2×C8—222no—
785C2×C8—442no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—111no—
789C4⋊C4—111no—
790C4⋊C4—221no—
791C4⋊C4—221no—
792C4⋊C4—221no—
793C4⋊C4—221no—
794C4⋊C4—221no—
795C4⋊C4—221no—
796C4⋊C4—221no—
797C4⋊C4—221no—
798C4⋊C4C2×C4×D1111yescharacteristic
799C4⋊C4C2×C4×D1111yescharacteristic
800C22⋊C4—24no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—221no—
813C22⋊C4—221no—
814C22⋊C4—228no—
815C22⋊C4—221no—
816C22⋊C4—221no—
817C22⋊C4—224no—
818C22⋊C4—221no—
819C22⋊C4—221no—
820C22⋊C4—221no—
821C22⋊C4—221no—
822C22⋊C4—221no—
823C42—21no—
824C42—42no—
825C42—221no—
826C42—221no—
827C42—221no—
828C42—442no—
829C42—444no—
830C11#1754211yescharacteristic, complemented, Sylow
831C23—22no—
832C23—22no—
833C23—21no—
834C23—41no—
835C23—111no—
836C23—111no—
837C23—111no—
838C23—114no—
839C23—111no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—221no—
851C23—441no—
852C23—441no—
853C23—441no—
854C23—441no—
855C23—441no—
856C23—441no—
857C23—441no—
858C23—442no—
859C23—4416no—
860C23—442no—
861C23—442no—
862C23C22⋊C4×D1111yescharacteristic
863C23C22⋊C4×D1111yescharacteristic
864C23C2×D4×D1111yescharacteristic
865Q8—41no—
866Q8—441no—
867Q8—442no—
868D4—41no—
869D4—42no—
870D4—42no—
871D4—42no—
872D4—441no—
873D4—442no—
874D4—442no—
875D4—442no—
876D4—442no—
877D4—442no—
878D4—442no—
879D4—442no—
880D4—442no—
881D4—442no—
882D4—442no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—111no—
897C2×C4—114no—
898C2×C4—111no—
899C2×C4—111no—
900C2×C4—111no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—224no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—442no—
924C2×C4—442no—
925C2×C4—442no—
926C2×C4—4416no—
927C2×C4—442no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—442no—
932C2×C4—442no—
933C2×C4—442no—
934C2×C4—442no—
935C2×C4C22⋊C4×D1111yescharacteristic
936C2×C4C22⋊C4×D1111yescharacteristic
937C2×C4C22×C4×D1111yescharacteristic
938C2×C4C2×D4×D1111yescharacteristic
939C8—42no—
940C8—442no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—44no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—112no—
953C22—112no—
954C22—112no—
955C22—228no—
956C22—221no—
957C22—221no—
958C22—221no—
959C22—221no—
960C22—221no—
961C22—221no—
962C22—221no—
963C22—221no—
964C22—221no—
965C22—444no—
966C22—444no—
967C22—444no—
968C22—444no—
969C22—444no—
970C22—441no—
971C22—441no—
972C22—441no—
973C22—884no—
974C22D11×#10412yes—
975C22C2×C22⋊C4×D1111yescharacteristic
976C22#1062329912yes—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—44no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—112no—
985C4—221no—
986C4—221no—
987C4—221no—
988C4—444no—
989C4—441no—
990C4—441no—
991C4—441no—
992C4D11×#9912yes—
993C2—22no—
994C2—22no—
995C2—41no—
996C2—81no—
997C2—222no—
998C2—222no—
999C2—222no—
1000C2—441no—
1001C2—881no—
1002C2C2×D11×#9911yescharacteristic
1003C2#1307713111yescharacteristic
1004C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1501C2
socleC22×C11C22×C22⋊C4
prime radicalD11×#525C2
cosocleC22×C4×C11C24
hypercenter#1501D11
hypocenterC11#17542
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. C2×#10622339C2semidirect
3. C4×C22⋊C4×D11C2semidirect
4. #13067134C2semidirect
5. #13067130C2semidirect
6. #13067119C2semidirect
7. #13067117C2semidirect
8. #13067108C2semidirect
9. #13067107C2semidirect
10. #13067105C2semidirect
11. C11×#1501C2semidirect
12. C2×#41×D11C4semidirect
15. #10623359C4semidirect
20. #10623158C4semidirect
22. D11×C22⋊Q8C4semidirect
24. #10623137C4semidirect
26. D11×#121C4semidirect
34. #10623055C4semidirect
35. D11×#117C4semidirect
38. C2×C11×C22⋊C8C22semidirect
39. C4×C11×C22⋊C4C22semidirect
40. C4×C22⋊Dic11C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
48. #10622339C22semidirect
50. D11×#95C22semidirect
51. C11×#328C22semidirect
52. C11×#327C22semidirect
53. #10622176C22semidirect
54. #10622175C22semidirect
55. #10622108C22semidirect
56. #10622105C22semidirect
57. #10622090C22semidirect
58. #10622089C22semidirect
60. C2×C11×#41C2×C4semidirect
65. C2×Q8×D11C2×C4semidirect
71. C2×D4×D11C2×C4semidirect
73. C2×#4339C2×C4semidirect
91. C11×C22⋊Q8C2×C4semidirect
93. C11×#121C2×C4semidirect
98. C11×#117C2×C4semidirect
104. #66999C2×C4semidirect
108. #66991C2×C4semidirect
115. #66983C2×C4semidirect
123. #66979C2×C4semidirect
124. #66977C2×C4semidirect
133. #66950C2×C4semidirect
137. #66948C2×C4semidirect
146. C4⋊C4×D11C2×C4semidirect
147. C4⋊C4×D11C2×C4semidirect
339. #1501D11semidirect
482. C2×C22⋊C8C2×D11semidirect
487. C4×C22⋊C4C2×D11semidirect
492. #328C2×D11semidirect
496. #327C2×D11semidirect
556. C2×#41C4×D11semidirect
602. C22⋊Q8C4×D11semidirect
614. #121C4×D11semidirect
645. #117C4×D11semidirect
830. C11#17542semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
C2×#106223392
C4×C22⋊C4×D112
#130671342
#130671302
#130671192
#130671172
#130671082
#130671072
#130671052
C11×#15012
#1754211