Finite Group Databasebeta

← #14721554

Subgroups — #14721554

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082444C211yesmaximal, characteristic
2#13077643C211yesmaximal, characteristic, complemented
3#13071520C211yesmaximal, characteristic, complemented
4#13067186C211yesmaximal, characteristic, complemented
5#13067182C211yesmaximal, characteristic, complemented
6#13067157C211yesmaximal, characteristic, complemented
7#13067153C211yesmaximal, characteristic, complemented
8#13067151C211yesmaximal, characteristic, complemented
9#13067140C211yesmaximal, characteristic, complemented
10#13067138C211yesmaximal, characteristic, complemented
11#13067121C211yesmaximal, characteristic, complemented
12#13067120C211yesmaximal, characteristic, complemented
13D11×#328C211yesmaximal, characteristic, complemented
14D11×#327C211yesmaximal, characteristic, complemented
15C11×#1513C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17#10623362C411yescharacteristic, complemented
18#10623360C411yescharacteristic, complemented
19#10623322C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21#10623192—21no—
22#10623190—21no—
23#10623170C411yescharacteristic, complemented
24#10623164C411yescharacteristic, complemented
25D11×C22⋊Q8C2211yescharacteristic
26#10623155C2211yescharacteristic
27#10623145C411yescharacteristic, complemented
28#10623143C411yescharacteristic, complemented
29D11×#121C2211yescharacteristic
30#10623131C2211yescharacteristic
31#10623124—21no—
32#10623120—21no—
33#10623095—21no—
34#10623089—21no—
35#10623087—21no—
36#10623076—21no—
37#10623061C411yescharacteristic, complemented
38#10623060C411yescharacteristic, complemented
39C2×(C22⋊D11)⋊C4—21no—
40C11×#407C2211yescharacteristic, complemented
41C11×#380C2211yescharacteristic, complemented
42C2×C11⋊#95C2211yescharacteristic, complemented
43#10622820C2211yescharacteristic, complemented
44#10622740—21no—
45#10622740—21no—
46#10622602—21no—
47#10622585—21no—
48#10622559—21no—
49#10622341—21no—
50#10622341—21no—
51D11×C22⋊C8C2211yescharacteristic
52D11×C22⋊C8C2211yescharacteristic
53#10622332C2211yescharacteristic, complemented
54#10622332C2211yescharacteristic, complemented
55#10622280C2211yescharacteristic
56D11×#95C2211yescharacteristic
57#10622263C2211yescharacteristic, complemented
58#10622262C2211yescharacteristic, complemented
59C11×#328C2211yescharacteristic, complemented
60C11×#328C2211yescharacteristic, complemented
61C11×#327C2211yescharacteristic
62C11×#327C2211yescharacteristic
63#10622176C2211yescharacteristic, complemented
64#10622176C2211yescharacteristic, complemented
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622108C2211yescharacteristic
68#10622108C2211yescharacteristic
69#10622105C2211yescharacteristic, complemented
70#10622105C2211yescharacteristic, complemented
71#10622090C2211yescharacteristic, complemented
72#10622090C2211yescharacteristic, complemented
73#10622089C2211yescharacteristic
74#10622089C2211yescharacteristic
75C2×C11×#41C2×C411yescharacteristic, complemented
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C2×Q8×D11C2×C411yescharacteristic, complemented
80C2×D4×D11—21no—
81C2×D4×D11C2×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#67000C2×C411yescharacteristic, complemented
100#66999C2×C411yescharacteristic, complemented
101Q8×Dic11C2×C411yescharacteristic, complemented
102#66992—21no—
103#66992—21no—
104#66991—21no—
105#66991—21no—
106#66991—21no—
107#66991C2×C411yescharacteristic, complemented
108#66990—21no—
109#66990—21no—
110#66989—21no—
111#66989C2×C411yescharacteristic, complemented
112#66988—21no—
113#66988—21no—
114D4×Dic11—21no—
115D4×Dic11C2×C411yescharacteristic, complemented
116#66983C2×C411yescharacteristic, complemented
117#66983C2311yescharacteristic
118#66982—21no—
119#66982—21no—
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11—21no—
123C4×C22⋊D11C2×C411yescharacteristic
124C4×C22⋊D11C2×C411yescharacteristic
125C4×C22⋊D11C2×C411yescharacteristic
126C4×C22⋊D11C2×C411yescharacteristic
127C4×C22⋊D11D411yescharacteristic
128C4×C22⋊D11D411yescharacteristic
129C4×C22⋊D11D411yescharacteristic
130C4×C22⋊D11D411yescharacteristic
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4D411yescharacteristic
134#66979C2×C411yescharacteristic, complemented
135#66977—21no—
136#66977C2×C411yescharacteristic, complemented
137#66977C2311yescharacteristic
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×C8×D11—21no—
146C2×C8×D11—21no—
147#66951—21no—
148#66950C2×C411yescharacteristic, complemented
149#66949—21no—
150#66949—21no—
151#66948C2×C411yescharacteristic, complemented
152#66946—21no—
153#66946C2×C411yescharacteristic, complemented
154#66945—21no—
155#66945—21no—
156C4⋊C4×D11—21no—
157C4⋊C4×D11C2×C411yescharacteristic, complemented
158C4⋊C4×D11C2×C411yescharacteristic, complemented
159#66943C2×C411yescharacteristic, complemented
160#66943C2×C411yescharacteristic, complemented
161#66942—21no—
162#66940C2×C411yescharacteristic, complemented
163#66939—21no—
164#66938—21no—
165#66937—21no—
166#66937—21no—
167#66937—21no—
168#66936—21no—
169#66936—21no—
170#66936—21no—
171#66936—21no—
172(C22⋊D11)⋊C4—21no—
173(C22⋊D11)⋊C4—21no—
174(C22⋊D11)⋊C4—44no—
175C22⋊C4×D11—21no—
176C22⋊C4×D11—21no—
177C22⋊C4×D11—21no—
178#66932—21no—
179#66932—21no—
180#66932—21no—
181#66932—21no—
182#66931—21no—
183#66930—21no—
184#66929—21no—
185C4×D44—21no—
186#66925—21no—
187#66923—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—
203#66879—21no—
204#66879—21no—
205Dic11⋊C8—21no—
206Dic11⋊C8—21no—
207#17622—111nomaximal, Sylow
208C24×C11C2×D411yescharacteristic
209C23×D11—21no—
210C23×D11C2×D411yescharacteristic
211C11×#41—81no—
212C2×Q8×C11C22×C411yescharacteristic
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11C22×C411yescharacteristic
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—81no—
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C22×C411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2411yescharacteristic
227C2×C22⋊D11—21no—
228C2×C22⋊D11—21no—
229C2×C22⋊D11—21no—
230C2×C22⋊D11—21no—
231C2×C22⋊D11—21no—
232C2×C22⋊D11—22no—
233C2×C22⋊D11—22no—
234C2×C22⋊D11C22⋊C411yescharacteristic
235C2×C22⋊D11C22⋊C411yescharacteristic
236C2×C22⋊D11C22⋊C411yescharacteristic
237C2×C22⋊D11C22⋊C411yescharacteristic
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11—81no—
244C22×Dic11C2×D411yescharacteristic
245C22×Dic11C2×D411yescharacteristic
246C22×Dic11C2×D411yescharacteristic
247Q8×D11—81no—
248D4×D11—42no—
249D4×D11—42no—
250D4×D11—81no—
251#4339—81no—
252C2×D44—21no—
253C2×D44C22×C411yescharacteristic
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—21no—
259C2×C4×D11—42no—
260C2×C4×D11—42no—
261C2×C4×D11—81no—
262C2×C4×D11—81no—
263C2×C4×D11C22×C411yescharacteristic
264C2×C4×D11C22×C411yescharacteristic
265C2×C4×D11C2×D411yescharacteristic
266C2×C4×D11C2×D411yescharacteristic
267C2×Dic22—21no—
268C2×Dic22C22×C411yescharacteristic
269C11×M16—81no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—81no—
275C11×C4⋊C4C22×C411yescharacteristic
276C11×C4⋊C4C22×C411yescharacteristic
277C11×C22⋊C4—21no—
278C11×C22⋊C4—21no—
279C11×C22⋊C4—21no—
280C11×C22⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—42no—
283C42×C11—21no—
284C22⋊Dic11—21no—
285C22⋊Dic11—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⋊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—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—42no—
323Dic11⋊C4—42no—
324Dic11⋊C4—81no—
325Dic11⋊C4C22⋊C411yescharacteristic
326Dic11⋊C4C22⋊C411yescharacteristic
327Dic11⋊C4C22⋊C411yescharacteristic
328Dic11⋊C4C22⋊C411yescharacteristic
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—
340C8×D11—81no—
341C8×D11—81no—
342#3505—111no—
343#2973—111no—
344#2349—111no—
345#1520—111no—
346#1519—111no—
347#1513—111no—
348#1513D1111yescharacteristic, complemented
349#1512—111no—
350#1512—111no—
351#1509—111no—
352#1509—111no—
353#1504—111no—
354#1504—111no—
355C2×#328—111no—
356C2×#327—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—41no—
367C22×D11—41no—
368C22×D11—42no—
369C22×D11—81no—
370C22×D11—81no—
371C22×D11C2×C22⋊C411yescharacteristic
372C22×D11C2×C22⋊C411yescharacteristic
373C22×D11AGL(1,ℤ/8)12yes—
374C22×D11#13712yes—
375Q8×C11—41no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—81no—
380D4×C11—81no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
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—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—81no—
397C2×C4×C11C2×C22⋊C411yescharacteristic
398C2×C4×C11C2×C22⋊C411yescharacteristic
399C2×C4×C11C23×C411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C22⋊D11—22no—
402C22⋊D11—22no—
403C22⋊D11—22no—
404C22⋊D11—22no—
405C22⋊D11—41no—
406C22⋊D11—41no—
407C22⋊D11—42no—
408C22⋊D11—81no—
409C22⋊D11—81no—
410C22⋊D11—81no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—22no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—81no—
425C2×Dic11—84no—
426C2×Dic11C2×C22⋊C411yescharacteristic
427C2×Dic11C2×C22⋊C411yescharacteristic
428C2×Dic11C2×C22⋊C411yescharacteristic
429C2×Dic11C2×C22⋊C411yescharacteristic
430C2×Dic11C2×C22⋊C411yescharacteristic
431C2×Dic11C2×C22⋊C411yescharacteristic
432D44—41no—
433D44—42no—
434C4×D11—41no—
435C4×D11—41no—
436C4×D11—41no—
437C4×D11—41no—
438C4×D11—42no—
439C4×D11—81no—
440C4×D11—81no—
441C4×D11—81no—
442C4×D11—81no—
443C4×D11—84no—
444Dic22—41no—
445Dic22—81no—
446C8×C11—41no—
447C8×C11—41no—
448C11⋊C8—41no—
449C11⋊C8—41no—
450#553—111no—
451#553—111no—
452#553—221no—
453#553—221no—
454#552—111no—
455#552—111no—
456#551—221no—
457#551—221no—
458#548—111no—
459#548—111no—
460#546—111no—
461#546—111no—
462#539—221no—
463#538—221no—
464#534—221no—
465#529—111no—
466#529—111no—
467#525—111no—
468#525C2×D1111yescharacteristic
469C2×C22⋊Q8—111no—
470C2×#121—111no—
471#518—221no—
472C2×C4×D4—111no—
473C2×C4×D4—221no—
474#435—221no—
475#435—221no—
476#435—221no—
477#435—221no—
478#432—111no—
479#432—111no—
480#407—111no—
481#407C2×D1111yescharacteristic, complemented
482C2×C22⋊C8—111no—
483C2×C22⋊C8—111no—
484#389—221no—
485#385—221no—
486#385—221no—
487#382—111no—
488#380—111no—
489#380C2×D1111yescharacteristic, complemented
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, complemented
500#328C2×D1111yescharacteristic, complemented
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—42no—
530C2×D11—42no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—41no—
534C2×D11—162no—
535C2×D11#41712yes—
536C2×D11#41712yes—
537C4×C11—21no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—21no—
541C4×C11—41no—
542C4×C11—41no—
543C4×C11—41no—
544C4×C11—81no—
545C4×C11—81no—
546Dic11—21no—
547Dic11—21no—
548Dic11—21no—
549Dic11—21no—
550Dic11—21no—
551Dic11—21no—
552Dic11—42no—
553Dic11—41no—
554Dic11—41no—
555Dic11—41no—
556Dic11—81no—
557C2×#41—111no—
558C2×#41C4×D1111yescharacteristic, complemented
559C22×Q8—111no—
560C22×D4—111no—
561C22×D4—111no—
562C22×D4—221no—
563C23×C4—111no—
564C23×C4—221no—
565C23×C4—221no—
566C23×C4C22×D1111yescharacteristic
567C2×M16—21no—
568C2×M16—221no—
569C22×C8—221no—
570C22×C8—221no—
571#126—221no—
572#126—221no—
573#126—221no—
574#126—221no—
575#126—221no—
576#126—221no—
577#125—111no—
578#125—111no—
579#125—221no—
580#125—221no—
581#124—111no—
582#124—111no—
583#124—221no—
584#124—221no—
585#123—21no—
586#123—221no—
587#123—221no—
588#123—221no—
589#123—221no—
590#123—221no—
591#123—221no—
592#123—221no—
593#123—221no—
594#123—221no—
595C22⋊Q8—111no—
596C22⋊Q8—111no—
597C22⋊Q8—111no—
598C22⋊Q8—111no—
599C22⋊Q8—221no—
600C22⋊Q8—221no—
601C22⋊Q8—221no—
602C22⋊Q8—221no—
603C22⋊Q8C4×D1111yescharacteristic, complemented
604C22⋊Q8C22×D1111yescharacteristic
605#121—111no—
606#121—111no—
607#121—111no—
608#121—111no—
609#121—221no—
610#121—221no—
611#121—221no—
612#121—221no—
613#121—221no—
614#121—221no—
615#121—221no—
616#121—221no—
617#121C4×D1111yescharacteristic, complemented
618#121C22×D1111yescharacteristic
619#120—21no—
620#120—221no—
621#120—221no—
622#120—221no—
623C4×Q8—111no—
624C4×Q8—111no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—111no—
628C4×D4—111no—
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—221no—
638C4×D4—221no—
639C4×D4—221no—
640C4×D4—221no—
641C4×D4—221no—
642C4×D4—221no—
643C4×D4—221no—
644C4×D4—221no—
645C4×D4—444no—
646#117—111no—
647#117—221no—
648#117—221no—
649#117—221no—
650#117—221no—
651#117C4×D1111yescharacteristic, complemented
652C2×C4⋊C4—21no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—221no—
657C2×C4⋊C4—221no—
658C2×C4⋊C4—221no—
659C2×C4⋊C4—221no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—111no—
662C2×C22⋊C4—111no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C22⋊C4—221no—
666C2×C22⋊C4—221no—
667C2×C22⋊C4—221no—
668C2×C42—111no—
669C2×C42—221no—
670C4⋊C8—221no—
671C4⋊C8—221no—
672C22⋊C8—21no—
673C22⋊C8—111no—
674C22⋊C8—111no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8—221no—
678C22⋊C8C22×D1111yescharacteristic
679C22⋊C8C22×D1111yescharacteristic
680#97—221no—
681#97—221no—
682#95—111no—
683#95—111no—
684#95—221no—
685#95—221no—
686#95—221no—
687#95C22×D1111yescharacteristic
688#95C22×D1111yescharacteristic
689C2×C11—21no—
690C2×C11—21no—
691C2×C11—41no—
692C2×C11—41no—
693C2×C11—81no—
694C2×C11#288311yescharacteristic
695C2×C11C2×#41711yescharacteristic
696C2×C11#290111yescharacteristic
697D11—22no—
698D11—22no—
699D11—81no—
700C24—111no—
701C24—221no—
702C24D4×D1111yescharacteristic
703#41—81no—
704#41—881no—
705C2×Q8—111no—
706C2×Q8—221no—
707C2×Q8—881no—
708C2×Q8C2×C4×D1111yescharacteristic
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—111no—
713C2×D4—111no—
714C2×D4—111no—
715C2×D4—111no—
716C2×D4—111no—
717C2×D4—221no—
718C2×D4—221no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—221no—
722C2×D4—221no—
723C2×D4—221no—
724C2×D4—221no—
725C2×D4—442no—
726C2×D4—442no—
727C2×D4—881no—
728C2×D4C2×C4×D1111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—81no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—442no—
749C22×C4—442no—
750C22×C4—442no—
751C22×C4—442no—
752C22×C4—881no—
753C22×C4—881no—
754C22×C4—881no—
755C22×C4C2×C4×D1111yescharacteristic
756C22×C4C2×C4×D1111yescharacteristic
757C22×C4D4×D1111yescharacteristic
758C22×C4D4×D1111yescharacteristic
759C22×C4D4×D1111yescharacteristic
760C22×C4C23×D1111yescharacteristic
761M16—81no—
762M16—881no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—221no—
766C2×C8—221no—
767C2×C8—881no—
768C2×C8—881no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—81no—
772C4⋊C4—111no—
773C4⋊C4—111no—
774C4⋊C4—111no—
775C4⋊C4—111no—
776C4⋊C4—111no—
777C4⋊C4—111no—
778C4⋊C4—221no—
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—221no—
790C4⋊C4—442no—
791C4⋊C4—442no—
792C4⋊C4—881no—
793C4⋊C4C2×C4×D1111yescharacteristic
794C4⋊C4C2×C4×D1111yescharacteristic
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—42no—
801C22⋊C4—111no—
802C22⋊C4—111no—
803C22⋊C4—111no—
804C22⋊C4—111no—
805C22⋊C4—111no—
806C22⋊C4—111no—
807C22⋊C4—111no—
808C22⋊C4—111no—
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—221no—
822C22⋊C4—221no—
823C22⋊C4—221no—
824C22⋊C4—442no—
825C42—21no—
826C42—111no—
827C42—111no—
828C42—111no—
829C42—111no—
830C42—221no—
831C42—221no—
832C42—221no—
833C42—442no—
834C11#1762211yescharacteristic, complemented, Sylow
835C23—21no—
836C23—21no—
837C23—21no—
838C23—41no—
839C23—41no—
840C23—111no—
841C23—111no—
842C23—112no—
843C23—112no—
844C23—221no—
845C23—441no—
846C23—441no—
847C23—442no—
848C23—881no—
849C23—881no—
850C23C22⋊C4×D1111yescharacteristic
851C23C22⋊C4×D1111yescharacteristic
852C23C2×D4×D1111yescharacteristic
853Q8—41no—
854Q8—441no—
855Q8—881no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—81no—
860D4—81no—
861D4—222no—
862D4—222no—
863D4—222no—
864D4—222no—
865D4—441no—
866D4—442no—
867D4—442no—
868D4—441no—
869D4—441no—
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—111no—
892C2×C4—111no—
893C2×C4—111no—
894C2×C4—111no—
895C2×C4—221no—
896C2×C4—221no—
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—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—881no—
914C2×C4—881no—
915C2×C4—881no—
916C2×C4—881no—
917C2×C4—884no—
918C2×C4—881no—
919C2×C4—884no—
920C2×C4C22⋊C4×D1111yescharacteristic
921C2×C4C22⋊C4×D1111yescharacteristic
922C2×C4C22×C4×D1111yescharacteristic
923C2×C4C2×D4×D1111yescharacteristic
924C8—41no—
925C8—41no—
926C8—441no—
927C8—441no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—112no—
942C22—112no—
943C22—221no—
944C22—221no—
945C22—221no—
946C22—221no—
947C22—442no—
948C22—442no—
949C22—441no—
950C22—441no—
951C22—441no—
952C22—1762no—
953C22C2×C22⋊C4×D1111yescharacteristic
954C22D11×AGL(1,ℤ/8)11yescharacteristic
955C22D11×#13711yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—41no—
961C4—41no—
962C4—41no—
963C4—81no—
964C4—81no—
965C4—221no—
966C4—221no—
967C4—221no—
968C4—221no—
969C4—221no—
970C4—221no—
971C4—442no—
972C4—441no—
973C4—441no—
974C4—441no—
975C4—881no—
976C2—21no—
977C2—21no—
978C2—41no—
979C2—41no—
980C2—81no—
981C2—222no—
982C2—222no—
983C2—881no—
984C2#1307707411yescharacteristic
985C2D11×#41711yescharacteristic
986C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1513C2
socleC22×C11C22×C22⋊C4
prime radical#13082444C2
cosocleC22×C4×C11C24
hypercenter#1513D11
hypocenterC11#17622
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. #13077643C2semidirect
3. #13071520C2semidirect
4. #13067186C2semidirect
5. #13067182C2semidirect
6. #13067157C2semidirect
7. #13067153C2semidirect
8. #13067151C2semidirect
9. #13067140C2semidirect
10. #13067138C2semidirect
11. #13067121C2semidirect
12. #13067120C2semidirect
13. D11×#328C2semidirect
14. D11×#327C2semidirect
15. C11×#1513C2semidirect
17. #10623362C4semidirect
18. #10623360C4semidirect
23. #10623170C4semidirect
24. #10623164C4semidirect
27. #10623145C4semidirect
28. #10623143C4semidirect
37. #10623061C4semidirect
38. #10623060C4semidirect
40. C11×#407C22semidirect
41. C11×#380C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622820C22semidirect
53. #10622332C22semidirect
54. #10622332C22semidirect
57. #10622263C22semidirect
58. #10622262C22semidirect
59. C11×#328C22semidirect
60. C11×#328C22semidirect
63. #10622176C22semidirect
64. #10622176C22semidirect
69. #10622105C22semidirect
70. #10622105C22semidirect
71. #10622090C22semidirect
72. #10622090C22semidirect
75. C2×C11×#41C2×C4semidirect
79. C2×Q8×D11C2×C4semidirect
81. C2×D4×D11C2×C4semidirect
82. C2×#4339C2×C4semidirect
87. C11×C22⋊Q8C2×C4semidirect
89. C11×#121C2×C4semidirect
94. C11×#117C2×C4semidirect
99. #67000C2×C4semidirect
100. #66999C2×C4semidirect
101. Q8×Dic11C2×C4semidirect
107. #66991C2×C4semidirect
111. #66989C2×C4semidirect
115. D4×Dic11C2×C4semidirect
116. #66983C2×C4semidirect
134. #66979C2×C4semidirect
136. #66977C2×C4semidirect
148. #66950C2×C4semidirect
151. #66948C2×C4semidirect
153. #66946C2×C4semidirect
157. C4⋊C4×D11C2×C4semidirect
158. C4⋊C4×D11C2×C4semidirect
159. #66943C2×C4semidirect
160. #66943C2×C4semidirect
162. #66940C2×C4semidirect
348. #1513D11semidirect
481. #407C2×D11semidirect
489. #380C2×D11semidirect
499. #328C2×D11semidirect
500. #328C2×D11semidirect
558. C2×#41C4×D11semidirect
603. C22⋊Q8C4×D11semidirect
617. #121C4×D11semidirect
651. #117C4×D11semidirect
834. C11#17622semidirect

Maximal subgroups

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

subgroupindex
#130824442
#130776432
#130715202
#130671862
#130671822
#130671572
#130671532
#130671512
#130671402
#130671382
#130671212
#130671202
D11×#3282
D11×#3272
C11×#15132
#1762211