Finite Group Databasebeta

← #14720971

Subgroups — #14720971

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082642C211yesmaximal, characteristic
2#13077652C211yesmaximal, characteristic, complemented
3#13070975C211yesmaximal, characteristic, complemented
4#13067138C211yesmaximal, characteristic, complemented
5#13067130C211yesmaximal, characteristic, complemented
6#13067122C211yesmaximal, characteristic, complemented
7#13067121C211yesmaximal, characteristic, complemented
8#13067117C211yesmaximal, characteristic, complemented
9#13067109C211yesmaximal, characteristic, complemented
10#13067105C211yesmaximal, characteristic, complemented
11#13067104C211yesmaximal, characteristic, complemented
12#13067099C211yesmaximal, characteristic, complemented
13C2×#10622175C211yesmaximal, characteristic, complemented
14D11×#327C211yesmaximal, characteristic, complemented
15C11×#1507C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17#10623337—21no—
18#10623337C411yescharacteristic, complemented
19D4×C22⋊D11—21no—
20D4×C22⋊D11C411yescharacteristic, complemented
21#10623322C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23#10623147C411yescharacteristic, complemented
24#10623146—21no—
25#10623145C411yescharacteristic, complemented
26#10623144—21no—
27#10623143C411yescharacteristic, complemented
28#10623141—21no—
29#10623137C2211yescharacteristic
30D11×#121C2211yescharacteristic
31#10623132—21no—
32#10623131C2211yescharacteristic
33#10623130C411yescharacteristic, complemented
34#10623127C2211yescharacteristic
35#10623045C411yescharacteristic, complemented
36#10623042C411yescharacteristic, complemented
37#10623025—21no—
38#10623017—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C11×#407C2211yescharacteristic, complemented
41C4×C11×C22⋊C4C2211yescharacteristic, complemented
42C2×C11⋊#95C2211yescharacteristic, complemented
43C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
44#10622741—21no—
45#10622740—21no—
46C22⋊C4×Dic11—21no—
47C4×(C2×D11)⋊C4—21no—
48C4×Dic11⋊C4—21no—
49#10622343—21no—
50#10622339C2211yescharacteristic, complemented
51(C22⋊D11)⋊C8—21no—
52D11×C22⋊C8C2211yescharacteristic, complemented
53#10622332C2211yescharacteristic, complemented
54#10622331C2211yescharacteristic, complemented
55#10622279C2211yescharacteristic, complemented
56D11×#95C2211yescharacteristic, complemented
57#10622262C2211yescharacteristic, complemented
58#10622261C2211yescharacteristic, complemented
59C11×#327C2211yescharacteristic
60C11×#327C2211yescharacteristic
61C11×#327C2211yescharacteristic, complemented
62C11×#327C2211yescharacteristic, complemented
63#10622175C2211yescharacteristic
64#10622175C2211yescharacteristic
65#10622175C2211yescharacteristic, complemented
66#10622175C2211yescharacteristic, complemented
67#10622108C2211yescharacteristic, complemented
68#10622108C2211yescharacteristic, complemented
69#10622105C2211yescharacteristic, complemented
70#10622105C2211yescharacteristic, complemented
71#10622090C2211yescharacteristic, complemented
72#10622090C2211yescharacteristic, complemented
73#10622089C2211yescharacteristic, complemented
74#10622089C2211yescharacteristic, complemented
75C22×D4×C11—21no—
76C22×D4×C11C2×C411yescharacteristic, complemented
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×C22⋊D11D411yescharacteristic
80C23×Dic11—21no—
81C2×#4341—21no—
82C2×#4341C2×C411yescharacteristic, complemented
83C2×D4×D11—21no—
84C2×D4×D11C2×C411yescharacteristic, complemented
85C2×#4339C2×C411yescharacteristic, complemented
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C2×C11×M16—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121C2×C411yescharacteristic, complemented
92C11×#121C2×C411yescharacteristic, complemented
93C11×#121C2311yescharacteristic
94C11×#121C2311yescharacteristic
95C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99#67006—21no—
100#67006—21no—
101#67006—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104#66993—21no—
105#66993C2×C411yescharacteristic, complemented
106#66992—21no—
107#66992—21no—
108#66992—21no—
109#66992—21no—
110#66992—21no—
111#66992—21no—
112#66991—21no—
113#66991—21no—
114#66991C2×C411yescharacteristic, complemented
115#66991C2×C411yescharacteristic, complemented
116#66990—21no—
117#66990—21no—
118#66990—21no—
119#66989—21no—
120#66989C2×C411yescharacteristic, complemented
121#66988—21no—
122#66988—21no—
123#66988—21no—
124D4×Dic11—21no—
125D4×Dic11—21no—
126D4×Dic11C2×C411yescharacteristic, complemented
127D4×Dic11C2×C411yescharacteristic, complemented
128#66983—21no—
129#66983C2×C411yescharacteristic, complemented
130#66983C2311yescharacteristic
131#66982—21no—
132C4×C22⋊D11—21no—
133C4×C22⋊D11—21no—
134C4×C22⋊D11—21no—
135C4×C22⋊D11—21no—
136C4×C22⋊D11C2×C411yescharacteristic
137C4×C22⋊D11C2×C411yescharacteristic
138C4×C22⋊D11C2×C411yescharacteristic
139C4×C22⋊D11C2×C411yescharacteristic
140C4×C22⋊D11D411yescharacteristic
141C4×C22⋊D11D411yescharacteristic
142C4×C22⋊D11D411yescharacteristic
143C4×C22⋊D11D411yescharacteristic
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4D411yescharacteristic
146#66979C2×C411yescharacteristic, complemented
147#66977—21no—
148#66977C2×C411yescharacteristic, complemented
149#66977C2311yescharacteristic
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4D411yescharacteristic
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11—21no—
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8—21no—
157C2×#4313—21no—
158C2×C8×D11—21no—
159#66951—21no—
160#66950C2×C411yescharacteristic, complemented
161#66949—21no—
162#66948C2×C411yescharacteristic, complemented
163#66947—21no—
164#66946C2×C411yescharacteristic, complemented
165#66945C2×C411yescharacteristic, complemented
166C4⋊C4×D11C2×C411yescharacteristic, complemented
167#66943C2×C411yescharacteristic, complemented
168#66942—21no—
169#66941C2×C411yescharacteristic, complemented
170#66940C2×C411yescharacteristic, complemented
171#66938—21no—
172#66938—21no—
173#66937—21no—
174#66937—21no—
175#66936—21no—
176#66936—21no—
177(C22⋊D11)⋊C4—28no—
178(C22⋊D11)⋊C4—21no—
179(C22⋊D11)⋊C4—21no—
180(C22⋊D11)⋊C4—21no—
181(C22⋊D11)⋊C4—21no—
182C22⋊C4×D11—21no—
183C22⋊C4×D11—21no—
184#66932—21no—
185#66932—21no—
186#66930—21no—
187#66930—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—
204Dic11⋊C8—21no—
205Dic11⋊C8—21no—
206C8×Dic11—21no—
207#17547—111nomaximal, Sylow
208C24×C11—21no—
209C24×C11C2×D411yescharacteristic
210C23×D11—21no—
211C23×D11C2×D411yescharacteristic
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—81no—
218C2×D4×C11—81no—
219C2×D4×C11—81no—
220C2×D4×C11C22×C411yescharacteristic
221C2×D4×C11C22×C411yescharacteristic
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—81no—
226C22×C4×C11C22×C411yescharacteristic
227C22×C4×C11C22×C411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C2×C22⋊D11—24no—
233C2×C22⋊D11—21no—
234C2×C22⋊D11—21no—
235C2×C22⋊D11—21no—
236C2×C22⋊D11—21no—
237C2×C22⋊D11—21no—
238C2×C22⋊D11—21no—
239C2×C22⋊D11—21no—
240C2×C22⋊D11—21no—
241C2×C22⋊D11—21no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11C22⋊C411yescharacteristic
244C2×C22⋊D11C22⋊C411yescharacteristic
245C2×C22⋊D11C22⋊C411yescharacteristic
246C2×C22⋊D11C22⋊C411yescharacteristic
247C22×Dic11—24no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—81no—
254C22×Dic11—81no—
255C22×Dic11C2×D411yescharacteristic
256C22×Dic11C2×D411yescharacteristic
257C22×Dic11C2×D411yescharacteristic
258#4341—81no—
259#4341—81no—
260#4341—81no—
261D4×D11—81no—
262D4×D11—81no—
263D4×D11—81no—
264#4339—81no—
265C2×D44—21no—
266C2×D44C22×C411yescharacteristic
267C2×C4×D11—24no—
268C2×C4×D11—21no—
269C2×C4×D11—21no—
270C2×C4×D11—21no—
271C2×C4×D11—81no—
272C2×C4×D11—81no—
273C2×C4×D11—81no—
274C2×C4×D11C22×C411yescharacteristic
275C2×C4×D11C22×C411yescharacteristic
276C2×C4×D11C2×D411yescharacteristic
277C2×C4×D11C2×D411yescharacteristic
278C2×Dic22—21no—
279C2×Dic22C22×C411yescharacteristic
280C11×M16—81no—
281C2×C8×C11—21no—
282C2×C8×C11—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C22×C411yescharacteristic
285C11×C4⋊C4C22×C411yescharacteristic
286C11×C22⋊C4—24no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C42×C11—81no—
292C22⋊Dic11—21no—
293C22⋊Dic11—21no—
294C22⋊Dic11—21no—
295C22⋊Dic11—21no—
296C22⋊Dic11—21no—
297C22⋊Dic11—21no—
298C22⋊Dic11—21no—
299C22⋊Dic11—21no—
300C22⋊Dic11—21no—
301C22⋊Dic11C22⋊C411yescharacteristic
302C22⋊Dic11C22⋊C411yescharacteristic
303C22⋊Dic11C22⋊C411yescharacteristic
304C22⋊Dic11C22⋊C411yescharacteristic
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—21no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—21no—
312(C2×D11)⋊C4C22⋊C411yescharacteristic
313(C2×D11)⋊C4C22⋊C411yescharacteristic
314(C2×D11)⋊C4C22⋊C411yescharacteristic
315(C2×D11)⋊C4C22⋊C411yescharacteristic
316C4⋊Dic11—21no—
317C4⋊Dic11—21no—
318C4⋊Dic11C22×C411yescharacteristic
319C4⋊Dic11C22×C411yescharacteristic
320Dic11⋊C4—24no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325Dic11⋊C4—21no—
326Dic11⋊C4—21no—
327Dic11⋊C4C22⋊C411yescharacteristic
328Dic11⋊C4C22⋊C411yescharacteristic
329Dic11⋊C4C22⋊C411yescharacteristic
330Dic11⋊C4C22⋊C411yescharacteristic
331C4×Dic11—24no—
332C4×Dic11—21no—
333C4×Dic11—21no—
334C4×Dic11—21no—
335C4×Dic11—81no—
336C4×Dic11—81no—
337C4×Dic11C22×C411yescharacteristic
338C4×Dic11C22×C411yescharacteristic
339C4×Dic11C2×D411yescharacteristic
340C4×Dic11C2×D411yescharacteristic
341C2×C11⋊C8—21no—
342C2×C11⋊C8—21no—
343C2×C11⋊C8—81no—
344#4313—81no—
345C8×D11—81no—
346#3519—111no—
347#2974—111no—
348#2275—111no—
349#1509—111no—
350#1507—111no—
351#1507D1111yescharacteristic, complemented
352#1505—111no—
353#1504—111no—
354#1504—111no—
355#1502—111no—
356#1501—111no—
357#1501—111no—
358#1500—111no—
359C2×#327—111no—
360C2×#327—111no—
361C23×C11—21no—
362C23×C11—21no—
363C23×C11—22no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11—41no—
367C23×C11—42no—
368C23×C11—81no—
369C23×C11—81no—
370C23×C11C2×C22⋊C411yescharacteristic
371C23×C11C2×C22⋊C411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C22×D11—21no—
374C22×D11—21no—
375C22×D11—22no—
376C22×D11—21no—
377C22×D11—41no—
378C22×D11—42no—
379C22×D11—81no—
380C22×D11—81no—
381C22×D11C2×C22⋊C411yescharacteristic
382C22×D11C2×C22⋊C411yescharacteristic
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—41no—
387D4×C11—41no—
388D4×C11—41no—
389D4×C11—81no—
390D4×C11—81no—
391D4×C11—81no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—81no—
407C2×C4×C11C2×C22⋊C411yescharacteristic
408C2×C4×C11C2×C22⋊C411yescharacteristic
409C2×C4×C11C23×C411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C22⋊D11—22no—
412C22⋊D11—22no—
413C22⋊D11—22no—
414C22⋊D11—41no—
415C22⋊D11—41no—
416C22⋊D11—42no—
417C22⋊D11—42no—
418C22⋊D11—42no—
419C22⋊D11—81no—
420C22⋊D11—81no—
421C22⋊D11—81no—
422C22⋊D11—81no—
423C22⋊D11—81no—
424C22⋊D11#10414yes—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—42no—
439C2×Dic11—81no—
440C2×Dic11—81no—
441C2×Dic11—84no—
442C2×Dic11C2×C22⋊C411yescharacteristic
443C2×Dic11C2×C22⋊C411yescharacteristic
444C2×Dic11C2×C22⋊C411yescharacteristic
445C2×Dic11C2×C22⋊C411yescharacteristic
446C2×Dic11C2×C22⋊C411yescharacteristic
447C2×Dic11C2×C22⋊C411yescharacteristic
448D44—41no—
449D44—81no—
450C4×D11—41no—
451C4×D11—41no—
452C4×D11—41no—
453C4×D11—41no—
454C4×D11—81no—
455C4×D11—81no—
456C4×D11—81no—
457C4×D11—84no—
458Dic22—41no—
459Dic22—81no—
460C8×C11—41no—
461C8×C11—41no—
462C11⋊C8—41no—
463C11⋊C8—41no—
464#555—111no—
465#554—111no—
466#553—111no—
467#553—111no—
468#553—221no—
469#550—111no—
470#546—111no—
471#546—111no—
472#546—221no—
473#546—221no—
474D42—111no—
475D42—221no—
476#540—221no—
477#538—221no—
478#538—221no—
479#532—111no—
480#529—111no—
481#525—111no—
482#525—111no—
483C2×#121—111no—
484C2×#121C2×D1111yescharacteristic
485#518—221no—
486C2×C4×D4—111no—
487C2×C4×D4—221no—
488#436—221no—
489#435—221no—
490#435—221no—
491C8×D4—221no—
492#432—111no—
493#431—111no—
494#407—111no—
495#407C2×D1111yescharacteristic, complemented
496C2×C22⋊C8—111no—
497C2×C22⋊C8—111no—
498C4×C4⋊C4—111no—
499C4×C4⋊C4—221no—
500C4×C22⋊C4—111no—
501C4×C22⋊C4—221no—
502C4×C22⋊C4—221no—
503C4×C22⋊C4C2×D1111yescharacteristic, complemented
504#376—111no—
505C2×#95—111no—
506C2×#95—111no—
507#328—111no—
508#328—111no—
509#328—111no—
510#328—111no—
511#327—111no—
512#327—111no—
513#327—111no—
514#327—111no—
515#327—111no—
516#327—111no—
517#327—111no—
518#327—111no—
519#327C2×D1111yescharacteristic
520#327C2×D1111yescharacteristic
521#327C2×D1111yescharacteristic, complemented
522#327C2×D1111yescharacteristic, complemented
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11—41no—
535C22×C11—41no—
536C22×C11—41no—
537C22×C11—41no—
538C22×C11—162no—
539C22×C11C2×#10412yes—
540C22×C11C22×C22⋊C411yescharacteristic
541C22×C11#57611yescharacteristic
542C22×C11#57711yescharacteristic
543C2×D11—21no—
544C2×D11—21no—
545C2×D11—21no—
546C2×D11—21no—
547C2×D11—21no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—41no—
551C2×D11—41no—
552C2×D11—41no—
553C2×D11—162no—
554C2×D11C2×#10412yes—
555C4×C11—21no—
556C4×C11—21no—
557C4×C11—21no—
558C4×C11—21no—
559C4×C11—42no—
560C4×C11—42no—
561C4×C11—41no—
562C4×C11—41no—
563Dic11—21no—
564Dic11—21no—
565Dic11—21no—
566Dic11—21no—
567Dic11—21no—
568Dic11—42no—
569Dic11—42no—
570Dic11—41no—
571Dic11—41no—
572Dic11—41no—
573Dic11C2×#10412yes—
574C2×#41—111no—
575C2×#41—111no—
576C2×#41—221no—
577C22×D4—21no—
578C22×D4—111no—
579C22×D4—111no—
580C22×D4—221no—
581C22×D4—221no—
582C22×D4C4×D1111yescharacteristic, complemented
583C23×C4—111no—
584C23×C4—221no—
585C23×C4—221no—
586C23×C4C22×D1111yescharacteristic
587C2×M16—21no—
588C2×M16—221no—
589C22×C8—221no—
590C22×C8—221no—
591C4⋊Q8—111no—
592#127—111no—
593#127—221no—
594#126—221no—
595#126—221no—
596#126—221no—
597#125—111no—
598#125—221no—
599#124—111no—
600#124—221no—
601#124—221no—
602#124—221no—
603#123—221no—
604#123—221no—
605#123—221no—
606#123—221no—
607#123—221no—
608#123—221no—
609#123—221no—
610C22⋊Q8—111no—
611C22⋊Q8—111no—
612C22⋊Q8—111no—
613C22⋊Q8—221no—
614C22⋊Q8—221no—
615#121—21no—
616#121—21no—
617#121—111no—
618#121—111no—
619#121—111no—
620#121—111no—
621#121—111no—
622#121—221no—
623#121—221no—
624#121—221no—
625#121—221no—
626#121—221no—
627#121—221no—
628#121—221no—
629#121—221no—
630#121—221no—
631#121—221no—
632#121—221no—
633#121C4×D1111yescharacteristic, complemented
634#121C4×D1111yescharacteristic, complemented
635#121C22×D1111yescharacteristic
636#121C22×D1111yescharacteristic
637#120—221no—
638#120—221no—
639#120—221no—
640#120—221no—
641#120—221no—
642#120—221no—
643C4×Q8—111no—
644C4×D4—111no—
645C4×D4—111no—
646C4×D4—111no—
647C4×D4—111no—
648C4×D4—111no—
649C4×D4—111no—
650C4×D4—111no—
651C4×D4—111no—
652C4×D4—111no—
653C4×D4—111no—
654C4×D4—111no—
655C4×D4—221no—
656C4×D4—221no—
657C4×D4—221no—
658C4×D4—221no—
659C4×D4—228no—
660C4×D4—221no—
661C4×D4—221no—
662C4×D4—221no—
663C4×D4—221no—
664C4×D4—221no—
665C4×D4—221no—
666#117—111no—
667#117—111no—
668#117—221no—
669#117—221no—
670C2×C4⋊C4—111no—
671C2×C4⋊C4—111no—
672C2×C4⋊C4—221no—
673C2×C4⋊C4C4×D1111yescharacteristic, complemented
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—111no—
678C2×C22⋊C4—221no—
679C2×C22⋊C4—221no—
680C2×C22⋊C4—221no—
681C2×C22⋊C4—221no—
682C2×C42—21no—
683C2×C42—111no—
684C2×C42—221no—
685C2×C42—221no—
686C2×C42—221no—
687C4⋊C8—221no—
688C4⋊C8—221no—
689C22⋊C8—21no—
690C22⋊C8—111no—
691C22⋊C8—111no—
692C22⋊C8—221no—
693C22⋊C8—221no—
694C22⋊C8—221no—
695C22⋊C8C22×D1111yescharacteristic
696C22⋊C8C22×D1111yescharacteristic
697#97—221no—
698C4×C8—221no—
699#95—111no—
700#95—111no—
701#95—221no—
702#95—221no—
703#95—221no—
704#95C22×D1111yescharacteristic
705#95C22×D1111yescharacteristic
706C2×C11—21no—
707C2×C11—21no—
708C2×C11—22no—
709C2×C11—41no—
710C2×C11—81no—
711C2×C11—81no—
712C2×C11#288311yescharacteristic
713C2×C11#289711yescharacteristic
714C2×C11C22×#10411yescharacteristic
715D11—22no—
716D11—41no—
717D11—81no—
718C24—21no—
719C24—111no—
720C24—221no—
721C24D4×D1111yescharacteristic
722#41—881no—
723#41—881no—
724#41—881no—
725#41—881no—
726C2×Q8—111no—
727C2×Q8—221no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—111no—
737C2×D4—111no—
738C2×D4—111no—
739C2×D4—111no—
740C2×D4—111no—
741C2×D4—221no—
742C2×D4—221no—
743C2×D4—221no—
744C2×D4—221no—
745C2×D4—224no—
746C2×D4—221no—
747C2×D4—221no—
748C2×D4—221no—
749C2×D4—221no—
750C2×D4—221no—
751C2×D4—221no—
752C2×D4—444no—
753C2×D4—881no—
754C2×D4—881no—
755C2×D4—881no—
756C2×D4C2×C4×D1111yescharacteristic
757C2×D4C2×C4×D1111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—81no—
762C22×C4—111no—
763C22×C4—111no—
764C22×C4—111no—
765C22×C4—111no—
766C22×C4—111no—
767C22×C4—111no—
768C22×C4—111no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—224no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—224no—
778C22×C4—221no—
779C22×C4—881no—
780C22×C4—881no—
781C22×C4—881no—
782C22×C4—881no—
783C22×C4—881no—
784C22×C4C2×C4×D1111yescharacteristic
785C22×C4C2×C4×D1111yescharacteristic
786C22×C4D4×D1111yescharacteristic
787C22×C4D4×D1111yescharacteristic
788C22×C4D4×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790M16—81no—
791M16—881no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—221no—
795C2×C8—221no—
796C2×C8—881no—
797C2×C8—881no—
798C4⋊C4—21no—
799C4⋊C4—111no—
800C4⋊C4—111no—
801C4⋊C4—111no—
802C4⋊C4—111no—
803C4⋊C4—111no—
804C4⋊C4—111no—
805C4⋊C4—221no—
806C4⋊C4—221no—
807C4⋊C4—221no—
808C4⋊C4—221no—
809C4⋊C4—221no—
810C4⋊C4—221no—
811C4⋊C4—224no—
812C4⋊C4—221no—
813C4⋊C4—221no—
814C4⋊C4C2×C4×D1111yescharacteristic
815C4⋊C4C2×C4×D1111yescharacteristic
816C22⋊C4—24no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—111no—
822C22⋊C4—111no—
823C22⋊C4—111no—
824C22⋊C4—111no—
825C22⋊C4—111no—
826C22⋊C4—111no—
827C22⋊C4—111no—
828C22⋊C4—111no—
829C22⋊C4—221no—
830C22⋊C4—221no—
831C22⋊C4—221no—
832C22⋊C4—221no—
833C22⋊C4—224no—
834C22⋊C4—221no—
835C22⋊C4—221no—
836C22⋊C4—221no—
837C22⋊C4—221no—
838C22⋊C4—221no—
839C22⋊C4—221no—
840C22⋊C4—221no—
841C22⋊C4—221no—
842C22⋊C4—221no—
843C22⋊C4—221no—
844C22⋊C4—221no—
845C42—81no—
846C42—111no—
847C42—111no—
848C42—111no—
849C42—111no—
850C42—221no—
851C42—221no—
852C42—224no—
853C42—221no—
854C42—881no—
855C42—881no—
856C11#1754711yescharacteristic, complemented, Sylow
857C23—21no—
858C23—21no—
859C23—22no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—111no—
867C23—111no—
868C23—222no—
869C23—221no—
870C23—221no—
871C23—221no—
872C23—441no—
873C23—442no—
874C23—881no—
875C23—881no—
876C23C22⋊C4×D1111yescharacteristic
877C23C22⋊C4×D1111yescharacteristic
878C23C2×D4×D1111yescharacteristic
879Q8—441no—
880Q8—881no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—114no—
891D4—222no—
892D4—222no—
893D4—222no—
894D4—441no—
895D4—442no—
896D4—442no—
897D4—441no—
898D4—441no—
899D4—442no—
900D4—881no—
901D4—881no—
902D4—881no—
903D4—881no—
904D4—881no—
905D4—881no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—111no—
922C2×C4—111no—
923C2×C4—111no—
924C2×C4—111no—
925C2×C4—111no—
926C2×C4—111no—
927C2×C4—222no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—221no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—442no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—881no—
946C2×C4—881no—
947C2×C4—881no—
948C2×C4—884no—
949C2×C4—881no—
950C2×C4—881no—
951C2×C4—884no—
952C2×C4C22⋊C4×D1111yescharacteristic
953C2×C4C22⋊C4×D1111yescharacteristic
954C2×C4C22×C4×D1111yescharacteristic
955C2×C4C2×D4×D1111yescharacteristic
956C8—41no—
957C8—41no—
958C8—441no—
959C8—441no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—112no—
976C22—162no—
977C22—221no—
978C22—221no—
979C22—221no—
980C22—221no—
981C22—221no—
982C22—442no—
983C22—442no—
984C22—441no—
985C22—441no—
986C22—441no—
987C22—1762no—
988C22D11×#10412yes—
989C22C2×C22⋊C4×D1111yescharacteristic
990C22#1062330511yescharacteristic
991C22#1062330611yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—112no—
1001C4—221no—
1002C4—221no—
1003C4—221no—
1004C4—221no—
1005C4—221no—
1006C4—442no—
1007C4—442no—
1008C4—441no—
1009C4—441no—
1010C4—441no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—222no—
1018C2—441no—
1019C2—881no—
1020C2#1307707411yescharacteristic
1021C2#1307714111yescharacteristic
1022C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1507C2
socleC22×C11C22×C22⋊C4
prime radical#13082642C2
cosocleC22×C4×C11C24
hypercenter#1507D11
hypocenterC11#17547
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #13077652C2semidirect
3. #13070975C2semidirect
4. #13067138C2semidirect
5. #13067130C2semidirect
6. #13067122C2semidirect
7. #13067121C2semidirect
8. #13067117C2semidirect
9. #13067109C2semidirect
10. #13067105C2semidirect
11. #13067104C2semidirect
12. #13067099C2semidirect
13. C2×#10622175C2semidirect
14. D11×#327C2semidirect
15. C11×#1507C2semidirect
18. #10623337C4semidirect
20. D4×C22⋊D11C4semidirect
23. #10623147C4semidirect
25. #10623145C4semidirect
27. #10623143C4semidirect
33. #10623130C4semidirect
35. #10623045C4semidirect
36. #10623042C4semidirect
40. C11×#407C22semidirect
41. C4×C11×C22⋊C4C22semidirect
42. C2×C11⋊#95C22semidirect
43. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622339C22semidirect
52. D11×C22⋊C8C22semidirect
53. #10622332C22semidirect
54. #10622331C22semidirect
55. #10622279C22semidirect
56. D11×#95C22semidirect
57. #10622262C22semidirect
58. #10622261C22semidirect
61. C11×#327C22semidirect
62. C11×#327C22semidirect
65. #10622175C22semidirect
66. #10622175C22semidirect
67. #10622108C22semidirect
68. #10622108C22semidirect
69. #10622105C22semidirect
70. #10622105C22semidirect
71. #10622090C22semidirect
72. #10622090C22semidirect
73. #10622089C22semidirect
74. #10622089C22semidirect
76. C22×D4×C11C2×C4semidirect
82. C2×#4341C2×C4semidirect
84. C2×D4×D11C2×C4semidirect
85. C2×#4339C2×C4semidirect
91. C11×#121C2×C4semidirect
92. C11×#121C2×C4semidirect
95. C2×C11×C4⋊C4C2×C4semidirect
105. #66993C2×C4semidirect
114. #66991C2×C4semidirect
115. #66991C2×C4semidirect
120. #66989C2×C4semidirect
126. D4×Dic11C2×C4semidirect
127. D4×Dic11C2×C4semidirect
129. #66983C2×C4semidirect
146. #66979C2×C4semidirect
148. #66977C2×C4semidirect
160. #66950C2×C4semidirect
162. #66948C2×C4semidirect
164. #66946C2×C4semidirect
165. #66945C2×C4semidirect
166. C4⋊C4×D11C2×C4semidirect
167. #66943C2×C4semidirect
169. #66941C2×C4semidirect
170. #66940C2×C4semidirect
351. #1507D11semidirect
495. #407C2×D11semidirect
503. C4×C22⋊C4C2×D11semidirect
521. #327C2×D11semidirect
522. #327C2×D11semidirect
582. C22×D4C4×D11semidirect
633. #121C4×D11semidirect
634. #121C4×D11semidirect
673. C2×C4⋊C4C4×D11semidirect
856. C11#17547semidirect

Maximal subgroups

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

subgroupindex
#130826422
#130776522
#130709752
#130671382
#130671302
#130671222
#130671212
#130671172
#130671092
#130671052
#130671042
#130670992
C2×#106221752
D11×#3272
C11×#15072
#1754711