Finite Group Databasebeta

← #14721629

Subgroups — #14721629

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082459C211yesmaximal, characteristic
2#13077655C211yesmaximal, characteristic, complemented
3#13071520C211yesmaximal, characteristic, complemented
4#13067178C211yesmaximal, characteristic, complemented
5#13067174C211yesmaximal, characteristic, complemented
6#13067158C211yesmaximal, characteristic, complemented
7#13067157C211yesmaximal, characteristic, complemented
8#13067156C211yesmaximal, characteristic, complemented
9#13067121C211yesmaximal, characteristic, complemented
10#13067120C211yesmaximal, characteristic, complemented
11#13067119C211yesmaximal, characteristic, complemented
12#13067117C211yesmaximal, characteristic, complemented
13#13067113C211yesmaximal, characteristic, complemented
14#13067109C211yesmaximal, characteristic, complemented
15C11×#1513C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17#10623365C411yescharacteristic, complemented
18#10623355C411yescharacteristic, complemented
19#10623322C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21#10623195—21no—
22#10623192—21no—
23#10623172C411yescharacteristic, complemented
24#10623162C411yescharacteristic, complemented
25#10623158C2211yescharacteristic
26#10623153C2211yescharacteristic
27#10623147C411yescharacteristic, complemented
28#10623137C2211yescharacteristic
29#10623130C411yescharacteristic, complemented
30#10623127C2211yescharacteristic
31#10623124—21no—
32#10623123—21no—
33#10623091—21no—
34#10623090—21no—
35#10623077—21no—
36#10623071—21no—
37#10623064C411yescharacteristic, complemented
38#10623063C411yescharacteristic, complemented
39C2×(C22⋊D11)⋊C4—21no—
40C11×#407C2211yescharacteristic
41C11×#380C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43#10622820C2211yescharacteristic
44#10622741—21no—
45#10622741—21no—
46#10622602—21no—
47#10622585—21no—
48#10622559—21no—
49#10622342—21no—
50#10622342—21no—
51#10622339C2211yescharacteristic
52#10622339C2211yescharacteristic
53#10622331C2211yescharacteristic
54#10622331C2211yescharacteristic
55#10622280C2211yescharacteristic
56D11×#95C2211yescharacteristic
57#10622263C2211yescharacteristic
58#10622262C2211yescharacteristic
59C11×#328C2211yescharacteristic
60C11×#328C2211yescharacteristic
61C11×#327C2211yescharacteristic
62C11×#327C2211yescharacteristic
63#10622176C2211yescharacteristic
64#10622176C2211yescharacteristic
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622108C2211yescharacteristic
68#10622108C2211yescharacteristic
69#10622105C2211yescharacteristic
70#10622105C2211yescharacteristic
71#10622090C2211yescharacteristic
72#10622090C2211yescharacteristic
73#10622089C2211yescharacteristic
74#10622089C2211yescharacteristic
75C2×C11×#41C2×C411yescharacteristic, complemented
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C2×#4343C2×C411yescharacteristic, complemented
80C2×#4341—21no—
81C2×#4341C2×C411yescharacteristic, complemented
82C2×#4339C2×C411yescharacteristic, complemented
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C2×C11×M16—21no—
86C11×#123—21no—
87C11×C22⋊Q8C2×C411yescharacteristic, complemented
88C11×C22⋊Q8C2311yescharacteristic
89C11×#121C2×C411yescharacteristic, complemented
90C11×#121C2311yescharacteristic
91C11×#120—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C11×#117C2×C411yescharacteristic, complemented
95C2×C11×C4⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97#67006—21no—
98C2×C22⋊Dic11D411yescharacteristic
99#66999C2×C411yescharacteristic, complemented
100Q8×Dic11C2×C411yescharacteristic, complemented
101#66997C2×C411yescharacteristic, complemented
102#66993—21no—
103#66993—21no—
104#66993C2×C411yescharacteristic, complemented
105#66992—21no—
106#66992—21no—
107#66992—21no—
108#66992—21no—
109#66991—21no—
110#66991C2×C411yescharacteristic, complemented
111#66990—21no—
112#66989—21no—
113#66988—21no—
114D4×Dic11—21no—
115D4×Dic11C2×C411yescharacteristic, complemented
116#66983—21no—
117#66983C2×C411yescharacteristic, complemented
118#66983C2311yescharacteristic
119#66982—21no—
120#66982—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11—21no—
123C4×C22⋊D11—21no—
124C4×C22⋊D11C2×C411yescharacteristic
125C4×C22⋊D11C2×C411yescharacteristic
126C4×C22⋊D11C2×C411yescharacteristic
127C4×C22⋊D11C2×C411yescharacteristic
128C4×C22⋊D11D411yescharacteristic
129C4×C22⋊D11D411yescharacteristic
130C4×C22⋊D11D411yescharacteristic
131C4×C22⋊D11D411yescharacteristic
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4D411yescharacteristic
134#66979C2×C411yescharacteristic, complemented
135#66977C2×C411yescharacteristic, complemented
136#66977C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11C2311yescharacteristic
144C2×#4318—21no—
145C2×#4313—21no—
146C2×#4313—21no—
147#66951—21no—
148#66950C2×C411yescharacteristic, complemented
149#66948C2×C411yescharacteristic, complemented
150#66947—21no—
151#66947—21no—
152#66946—21no—
153#66946C2×C411yescharacteristic, complemented
154#66945C2×C411yescharacteristic, complemented
155#66945C2×C411yescharacteristic, complemented
156C4⋊C4×D11—21no—
157#66942—21no—
158#66941C2×C411yescharacteristic, complemented
159#66941C2×C411yescharacteristic, complemented
160#66940—21no—
161#66940—21no—
162#66940C2×C411yescharacteristic, complemented
163#66938—21no—
164#66938—21no—
165#66938—21no—
166#66938—21no—
167#66938—21no—
168#66937—21no—
169#66937—21no—
170#66937—21no—
171#66936—21no—
172#66936—21no—
173#66935—21no—
174(C22⋊D11)⋊C4—21no—
175(C22⋊D11)⋊C4—21no—
176(C22⋊D11)⋊C4—21no—
177(C22⋊D11)⋊C4—21no—
178(C22⋊D11)⋊C4—44no—
179#66932—21no—
180#66932—21no—
181#66931—21no—
182#66930—21no—
183#66930—21no—
184#66929—21no—
185#66928—21no—
186#66925—21no—
187C4×Dic22—21no—
188C11×C22⋊C8—21no—
189C11×C22⋊C8C2311yescharacteristic
190C11×C22⋊C8C2311yescharacteristic
191C11×#95C2311yescharacteristic
192C11×#95C2311yescharacteristic
193C11⋊#95—21no—
194C11⋊#95—21no—
195C11⋊#95—21no—
196C11⋊#95C2311yescharacteristic
197C11⋊#95C2311yescharacteristic
198C22⋊(C11⋊C8)—21no—
199C22⋊(C11⋊C8)C2311yescharacteristic
200C22⋊(C11⋊C8)C2311yescharacteristic
201(C2×D11)⋊C8—21no—
202(C2×D11)⋊C8—21no—
203Dic11⋊C8—21no—
204Dic11⋊C8—21no—
205C8×Dic11—21no—
206C8×Dic11—21no—
207#17630—111nomaximal, Sylow
208C24×C11C2×D411yescharacteristic
209C23×D11C2×D411yescharacteristic
210C11×#41—81no—
211C2×Q8×C11C22×C411yescharacteristic
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11C22×C411yescharacteristic
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—81no—
220C22×C4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—21no—
227C2×C22⋊D11—21no—
228C2×C22⋊D11—22no—
229C2×C22⋊D11—22no—
230C2×C22⋊D11—21no—
231C2×C22⋊D11—21no—
232C2×C22⋊D11—21no—
233C2×C22⋊D11—21no—
234C2×C22⋊D11—21no—
235C2×C22⋊D11C22⋊C411yescharacteristic
236C2×C22⋊D11C22⋊C411yescharacteristic
237C2×C22⋊D11C22⋊C411yescharacteristic
238C2×C22⋊D11C22⋊C411yescharacteristic
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—42no—
244C22×Dic11—42no—
245C22×Dic11—81no—
246C22×Dic11C2×D411yescharacteristic
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249#4343—81no—
250#4341—42no—
251#4341—42no—
252#4341—81no—
253#4339—81no—
254C2×D44—21no—
255C2×D44—21no—
256C2×D44C22×C411yescharacteristic
257C2×C4×D11—21no—
258C2×C4×D11—21no—
259C2×C4×D11—21no—
260C2×C4×D11—42no—
261C2×C4×D11—42no—
262C2×C4×D11—81no—
263C2×C4×D11—81no—
264C2×C4×D11C22×C411yescharacteristic
265C2×C4×D11C22×C411yescharacteristic
266C2×C4×D11C2×D411yescharacteristic
267C2×C4×D11C2×D411yescharacteristic
268C2×Dic22—21no—
269C2×Dic22—21no—
270C2×Dic22C22×C411yescharacteristic
271C11×M16—81no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—81no—
277C11×C4⋊C4C22×C411yescharacteristic
278C11×C4⋊C4C22×C411yescharacteristic
279C11×C22⋊C4—21no—
280C11×C22⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—21no—
283C11×C22⋊C4—21no—
284C11×C22⋊C4—42no—
285C42×C11—21no—
286C22⋊Dic11—21no—
287C22⋊Dic11—21no—
288C22⋊Dic11—21no—
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291C22⋊Dic11C22⋊C411yescharacteristic
292C22⋊Dic11C22⋊C411yescharacteristic
293C22⋊Dic11C22⋊C411yescharacteristic
294C22⋊Dic11C22⋊C411yescharacteristic
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—21no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—42no—
304(C2×D11)⋊C4C22⋊C411yescharacteristic
305(C2×D11)⋊C4C22⋊C411yescharacteristic
306(C2×D11)⋊C4C22⋊C411yescharacteristic
307(C2×D11)⋊C4C22⋊C411yescharacteristic
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11C22×C411yescharacteristic
311C4⋊Dic11C22×C411yescharacteristic
312Dic11⋊C4—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—42no—
321Dic11⋊C4—42no—
322Dic11⋊C4—81no—
323Dic11⋊C4C22⋊C411yescharacteristic
324Dic11⋊C4C22⋊C411yescharacteristic
325Dic11⋊C4C22⋊C411yescharacteristic
326Dic11⋊C4C22⋊C411yescharacteristic
327C4×Dic11—21no—
328C4×Dic11—21no—
329C4×Dic11—21no—
330C4×Dic11—21no—
331C4×Dic11—21no—
332C4×Dic11—42no—
333C4×Dic11C22×C411yescharacteristic
334C4×Dic11C22×C411yescharacteristic
335C4×Dic11C2×D411yescharacteristic
336C4×Dic11C2×D411yescharacteristic
337#4318—81no—
338C2×C11⋊C8—21no—
339C2×C11⋊C8—21no—
340#4313—81no—
341#4313—81no—
342#3506—111no—
343#2975—111no—
344#2349—111no—
345#1518—111no—
346#1517—111no—
347#1513—111no—
348#1513—111no—
349#1513—111no—
350#1513D1111yescharacteristic, complemented
351#1504—111no—
352#1504—111no—
353#1504—111no—
354#1504—111no—
355#1503—111no—
356#1502—111no—
357C23×C11—21no—
358C23×C11—21no—
359C23×C11—21no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11C2×C22⋊C411yescharacteristic
363C23×C11C2×C22⋊C411yescharacteristic
364C23×C11C22×D411yescharacteristic
365C22×D11—21no—
366C22×D11—21no—
367C22×D11—21no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11C2×C22⋊C411yescharacteristic
371C22×D11C2×C22⋊C411yescharacteristic
372Q8×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—81no—
377D4×C11—81no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—81no—
394C2×C4×C11C2×C22⋊C411yescharacteristic
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C23×C411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C22⋊D11—22no—
399C22⋊D11—22no—
400C22⋊D11—22no—
401C22⋊D11—22no—
402C22⋊D11—41no—
403C22⋊D11—41no—
404C22⋊D11—42no—
405C22⋊D11—81no—
406C22⋊D11—81no—
407C22⋊D11—81no—
408C22⋊D11—81no—
409C22⋊D11—81no—
410C2×Dic11—22no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—21no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—42no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—81no—
423C2×Dic11—84no—
424C2×Dic11C2×C22⋊C411yescharacteristic
425C2×Dic11C2×C22⋊C411yescharacteristic
426C2×Dic11C2×C22⋊C411yescharacteristic
427C2×Dic11C2×C22⋊C411yescharacteristic
428C2×Dic11C2×C22⋊C411yescharacteristic
429C2×Dic11C2×C22⋊C411yescharacteristic
430C2×Dic11AGL(1,ℤ/8)12yes—
431C2×Dic11#13712yes—
432D44—41no—
433D44—81no—
434D44—81no—
435C4×D11—41no—
436C4×D11—41no—
437C4×D11—41no—
438C4×D11—41no—
439C4×D11—42no—
440C4×D11—81no—
441C4×D11—81no—
442C4×D11—84no—
443Dic22—42no—
444Dic22—41no—
445Dic22—81no—
446C8×C11—41no—
447C8×C11—41no—
448C11⋊C8—41no—
449C11⋊C8—41no—
450#559—221no—
451#559—221no—
452#556—111no—
453#556—111no—
454#555—111no—
455#555—111no—
456#553—221no—
457#553—221no—
458#550—111no—
459#550—111no—
460#547—111no—
461#547—111no—
462#538—221no—
463#538—221no—
464#535—221no—
465#533—111no—
466#532—111no—
467#525—111no—
468#525—111no—
469#525—111no—
470#525C2×D1111yescharacteristic
471#520—221no—
472C2×C4×D4—111no—
473C2×C4×D4—221no—
474#436—221no—
475#436—221no—
476#436—221no—
477#436—221no—
478#431—111no—
479#431—111no—
480#407—111no—
481#407—111no—
482#407—111no—
483#407C2×D1111yescharacteristic
484#389—221no—
485#385—221no—
486#385—221no—
487#382—111no—
488#380—111no—
489#380C2×D1111yescharacteristic
490C4×C4⋊C4—111no—
491C2×#95—111no—
492C2×#95—111no—
493#328—111no—
494#328—111no—
495#328—111no—
496#328—111no—
497#328—111no—
498#328—111no—
499#328C2×D1111yescharacteristic
500#328C2×D1111yescharacteristic
501#327—111no—
502#327—111no—
503#327—111no—
504#327—111no—
505#327—111no—
506#327—111no—
507#327C2×D1111yescharacteristic
508#327C2×D1111yescharacteristic
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11C22×C22⋊C411yescharacteristic
523C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
524C22×C11C2×#13711yescharacteristic
525C2×D11—21no—
526C2×D11—21no—
527C2×D11—21no—
528C2×D11—21no—
529C2×D11—21no—
530C2×D11—21no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—41no—
534C2×D11—41no—
535C2×D11—41no—
536C4×C11—21no—
537C4×C11—21no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—41no—
541C4×C11—41no—
542C4×C11—41no—
543C4×C11—81no—
544C4×C11—81no—
545Dic11—21no—
546Dic11—21no—
547Dic11—21no—
548Dic11—21no—
549Dic11—42no—
550Dic11—41no—
551Dic11—41no—
552Dic11—41no—
553Dic11—81no—
554Dic11#41712yes—
555Dic11#41712yes—
556C2×#41—111no—
557C2×#41—111no—
558C2×#41—111no—
559C2×#41—221no—
560C2×#41C4×D1111yescharacteristic, complemented
561C22×D4—111no—
562C23×C4—111no—
563C23×C4—221no—
564C23×C4—221no—
565C23×C4C22×D1111yescharacteristic
566C2×M16—21no—
567C2×M16—221no—
568C2×M16—221no—
569C2×M16—221no—
570C4⋊Q8—111no—
571C4⋊Q8—111no—
572C4⋊Q8—111no—
573#127—111no—
574#127—221no—
575#127—221no—
576#126—221no—
577#126—221no—
578#126—221no—
579#126—221no—
580#125—221no—
581#124—221no—
582#124—221no—
583#124—221no—
584#124—221no—
585#124—221no—
586#124—221no—
587#124—221no—
588#123—21no—
589#123—221no—
590#123—221no—
591#123—221no—
592#123—221no—
593#123—221no—
594#123—221no—
595#123—221no—
596C22⋊Q8—111no—
597C22⋊Q8—111no—
598C22⋊Q8—111no—
599C22⋊Q8—111no—
600C22⋊Q8—221no—
601C22⋊Q8C4×D1111yescharacteristic, complemented
602C22⋊Q8C22×D1111yescharacteristic
603#121—111no—
604#121—111no—
605#121—111no—
606#121—111no—
607#121—221no—
608#121—221no—
609#121—221no—
610#121—221no—
611#121—221no—
612#121—221no—
613#121—221no—
614#121—221no—
615#121—221no—
616#121C4×D1111yescharacteristic, complemented
617#121C22×D1111yescharacteristic
618#120—21no—
619#120—221no—
620#120—221no—
621#120—221no—
622C4×Q8—111no—
623C4×Q8—111no—
624C4×Q8—221no—
625C4×Q8—221no—
626C4×Q8—221no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—111no—
630C4×D4—111no—
631C4×D4—111no—
632C4×D4—111no—
633C4×D4—111no—
634C4×D4—111no—
635C4×D4—111no—
636C4×D4—111no—
637C4×D4—111no—
638C4×D4—111no—
639C4×D4—221no—
640C4×D4—221no—
641C4×D4—221no—
642C4×D4—221no—
643C4×D4—221no—
644C4×D4—221no—
645C4×D4—221no—
646C4×D4—221no—
647C4×D4—221no—
648C4×D4—444no—
649#117—111no—
650#117—111no—
651#117—111no—
652#117—221no—
653#117—221no—
654#117—221no—
655#117C4×D1111yescharacteristic, complemented
656C2×C4⋊C4—21no—
657C2×C4⋊C4—111no—
658C2×C4⋊C4—221no—
659C2×C4⋊C4—221no—
660C2×C4⋊C4—221no—
661C2×C4⋊C4—221no—
662C2×C4⋊C4—221no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—111no—
665C2×C22⋊C4—111no—
666C2×C22⋊C4—221no—
667C2×C42—111no—
668C2×C42—221no—
669C4⋊C8—221no—
670C4⋊C8—221no—
671C22⋊C8—21no—
672C22⋊C8—111no—
673C22⋊C8—111no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8C22×D1111yescharacteristic
678C22⋊C8C22×D1111yescharacteristic
679C4×C8—221no—
680C4×C8—221no—
681#95—111no—
682#95—111no—
683#95—221no—
684#95—221no—
685#95—221no—
686#95C22×D1111yescharacteristic
687#95C22×D1111yescharacteristic
688C2×C11—21no—
689C2×C11—21no—
690C2×C11—41no—
691C2×C11—41no—
692C2×C11—81no—
693C2×C11#288311yescharacteristic
694C2×C11C2×#41711yescharacteristic
695C2×C11#290111yescharacteristic
696D11—41no—
697D11—41no—
698D11—81no—
699C24—111no—
700C24D4×D1111yescharacteristic
701#41—81no—
702#41—442no—
703#41—442no—
704#41—881no—
705#41—881no—
706#41—881no—
707C2×Q8—111no—
708C2×Q8—221no—
709C2×Q8—221no—
710C2×Q8C2×C4×D1111yescharacteristic
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—111no—
715C2×D4—111no—
716C2×D4—111no—
717C2×D4—111no—
718C2×D4—111no—
719C2×D4—221no—
720C2×D4—221no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—221no—
724C2×D4—221no—
725C2×D4—221no—
726C2×D4—221no—
727C2×D4—221no—
728C2×D4—221no—
729C2×D4—221no—
730C2×D4C2×C4×D1111yescharacteristic
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—81no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—442no—
750C22×C4—442no—
751C22×C4—442no—
752C22×C4—442no—
753C22×C4—881no—
754C22×C4—881no—
755C22×C4—881no—
756C22×C4C2×C4×D1111yescharacteristic
757C22×C4C2×C4×D1111yescharacteristic
758C22×C4D4×D1111yescharacteristic
759C22×C4D4×D1111yescharacteristic
760C22×C4D4×D1111yescharacteristic
761C22×C4C23×D1111yescharacteristic
762M16—81no—
763M16—881no—
764M16—881no—
765M16—881no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—221no—
769C2×C8—221no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—81no—
773C4⋊C4—111no—
774C4⋊C4—111no—
775C4⋊C4—111no—
776C4⋊C4—111no—
777C4⋊C4—111no—
778C4⋊C4—111no—
779C4⋊C4—221no—
780C4⋊C4—221no—
781C4⋊C4—221no—
782C4⋊C4—221no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4—221no—
786C4⋊C4—221no—
787C4⋊C4—221no—
788C4⋊C4—221no—
789C4⋊C4—442no—
790C4⋊C4—442no—
791C4⋊C4—881no—
792C4⋊C4C2×C4×D1111yescharacteristic
793C4⋊C4C2×C4×D1111yescharacteristic
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—42no—
800C22⋊C4—111no—
801C22⋊C4—111no—
802C22⋊C4—111no—
803C22⋊C4—111no—
804C22⋊C4—111no—
805C22⋊C4—111no—
806C22⋊C4—111no—
807C22⋊C4—111no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—221no—
813C22⋊C4—221no—
814C22⋊C4—221no—
815C22⋊C4—221no—
816C22⋊C4—221no—
817C22⋊C4—221no—
818C22⋊C4—221no—
819C22⋊C4—221no—
820C22⋊C4—221no—
821C22⋊C4—442no—
822C42—21no—
823C42—111no—
824C42—111no—
825C42—111no—
826C42—111no—
827C42—221no—
828C42—221no—
829C42—221no—
830C42—221no—
831C42—221no—
832C42—442no—
833C11#1763011yescharacteristic, complemented, Sylow
834C23—21no—
835C23—21no—
836C23—21no—
837C23—41no—
838C23—41no—
839C23—111no—
840C23—111no—
841C23—221no—
842C23—221no—
843C23—221no—
844C23—441no—
845C23—441no—
846C23C22⋊C4×D1111yescharacteristic
847C23C22⋊C4×D1111yescharacteristic
848C23C2×D4×D1111yescharacteristic
849Q8—41no—
850Q8—441no—
851Q8—442no—
852Q8—881no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—222no—
859D4—222no—
860D4—222no—
861D4—222no—
862D4—441no—
863D4—442no—
864D4—441no—
865D4—441no—
866D4—881no—
867D4—881no—
868D4—881no—
869D4—881no—
870D4—881no—
871D4—881no—
872D4—881no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—81no—
889C2×C4—111no—
890C2×C4—111no—
891C2×C4—112no—
892C2×C4—112no—
893C2×C4—111no—
894C2×C4—111no—
895C2×C4—111no—
896C2×C4—111no—
897C2×C4—222no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—442no—
906C2×C4—442no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—881no—
915C2×C4—881no—
916C2×C4—884no—
917C2×C4—881no—
918C2×C4—884no—
919C2×C4C22⋊C4×D1111yescharacteristic
920C2×C4C22⋊C4×D1111yescharacteristic
921C2×C4C22×C4×D1111yescharacteristic
922C2×C4C2×D4×D1111yescharacteristic
923C8—41no—
924C8—41no—
925C8—441no—
926C8—441no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—42no—
936C22—42no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—221no—
941C22—221no—
942C22—221no—
943C22—221no—
944C22—221no—
945C22—221no—
946C22—442no—
947C22—442no—
948C22—441no—
949C22—441no—
950C22—441no—
951C22C2×C22⋊C4×D1111yescharacteristic
952C22D11×AGL(1,ℤ/8)11yescharacteristic
953C22D11×#13711yescharacteristic
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—81no—
962C4—81no—
963C4—112no—
964C4—112no—
965C4—221no—
966C4—221no—
967C4—221no—
968C4—221no—
969C4—442no—
970C4—441no—
971C4—441no—
972C4—441no—
973C4—881no—
974C2—21no—
975C2—21no—
976C2—41no—
977C2—41no—
978C2—81no—
979C2—441no—
980C2—441no—
981C2—881no—
982C2#1307707411yescharacteristic
983C2D11×#41711yescharacteristic
984C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1513C2
socleC22×C11C22×C22⋊C4
prime radical#13082459C2
cosocleC22×C4×C11C24
hypercenter#1513D11
hypocenterC11#17630
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #13077655C2semidirect
3. #13071520C2semidirect
4. #13067178C2semidirect
5. #13067174C2semidirect
6. #13067158C2semidirect
7. #13067157C2semidirect
8. #13067156C2semidirect
9. #13067121C2semidirect
10. #13067120C2semidirect
11. #13067119C2semidirect
12. #13067117C2semidirect
13. #13067113C2semidirect
14. #13067109C2semidirect
15. C11×#1513C2semidirect
17. #10623365C4semidirect
18. #10623355C4semidirect
23. #10623172C4semidirect
24. #10623162C4semidirect
27. #10623147C4semidirect
29. #10623130C4semidirect
37. #10623064C4semidirect
38. #10623063C4semidirect
75. C2×C11×#41C2×C4semidirect
79. C2×#4343C2×C4semidirect
81. C2×#4341C2×C4semidirect
82. C2×#4339C2×C4semidirect
87. C11×C22⋊Q8C2×C4semidirect
89. C11×#121C2×C4semidirect
94. C11×#117C2×C4semidirect
99. #66999C2×C4semidirect
100. Q8×Dic11C2×C4semidirect
101. #66997C2×C4semidirect
104. #66993C2×C4semidirect
110. #66991C2×C4semidirect
115. D4×Dic11C2×C4semidirect
117. #66983C2×C4semidirect
134. #66979C2×C4semidirect
135. #66977C2×C4semidirect
148. #66950C2×C4semidirect
149. #66948C2×C4semidirect
153. #66946C2×C4semidirect
154. #66945C2×C4semidirect
155. #66945C2×C4semidirect
158. #66941C2×C4semidirect
159. #66941C2×C4semidirect
162. #66940C2×C4semidirect
350. #1513D11semidirect
560. C2×#41C4×D11semidirect
601. C22⋊Q8C4×D11semidirect
616. #121C4×D11semidirect
655. #117C4×D11semidirect
833. C11#17630semidirect

Maximal subgroups

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

subgroupindex
#130824592
#130776552
#130715202
#130671782
#130671742
#130671582
#130671572
#130671562
#130671212
#130671202
#130671192
#130671172
#130671132
#130671092
C11×#15132
#1763011