Finite Group Databasebeta

← #15625278

Subgroups — #15625278

Order 2816.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2#13079653C214yesmaximal, complemented
3#13079643C212yesmaximal, complemented
4#13079634C212yesmaximal, complemented
5#13079592C214yesmaximal, complemented
6#13079581C214yesmaximal, complemented
7#13079084C212yesmaximal, complemented
8#13079016C212yesmaximal, complemented
9#13078084C212yesmaximal, complemented
10#13078076C212yesmaximal, complemented
11#13077876C212yesmaximal, complemented
12#13077868C212yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C2×C11×#532C211yesmaximal, characteristic, complemented
15C22×C11×#41C2212yes—
16C11×#532—21no—
17C11×#532—21no—
18C11×#532—21no—
19C11×#532—21no—
20C11×#532C2212yes—
21C11×#532C2212yes—
22C11×#532C2212yescomplemented
23C11×#532C2212yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic, complemented
25C2×C11×#127C2211yescharacteristic, complemented
26C2×C11×#124C2212yescomplemented
27C2×C11×#121—21no—
28C2×C11×#121—21no—
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11—21no—
31C22×C42×C11C2211yescharacteristic
32C2×#67004C2214yescomplemented
33C2×#67002C2214yescomplemented
34C2×#66983C2211yescharacteristic
35C2×#66982—21no—
36C2×C4×C22⋊D11—21no—
37C2×#66977C2211yescharacteristic
38#10623010—21no—
39#10623010—21no—
40#10623010—21no—
41#10623010—21no—
42#10623010C2212yes—
43#10623010C2212yes—
44#10623010C2212yescomplemented
45#10623010C2212yescomplemented
46C2×#66929—21no—
47C2×#66928C2211yescharacteristic, complemented
48C2×C4×D44C2211yescharacteristic, complemented
49C2×#66925—21no—
50C2×#66923C2211yescharacteristic, complemented
51C2×C4×Dic22C2211yescharacteristic, complemented
52#10622852C2218yescomplemented
53#10622851C2218yescomplemented
54#10622845C2214yescomplemented
55#10622845C2214yescomplemented
56#10622841C2214yescomplemented
57#10622840C2214yes—
58#10622831C2214yescomplemented
59#10622830C2214yes—
60#10622820C2212yes—
61#10622703C2214yescomplemented
62#10622699C2214yescomplemented
63#10622696C2214yescomplemented
64#10622695C2214yescomplemented
65#10622688C2214yescomplemented
66#10622687C2214yescomplemented
67#10622685C2214yescomplemented
68#10622684C2214yescomplemented
69#10622672C2218yescomplemented
70#10622670C2218yescomplemented
71#10622669C2218yescomplemented
72#10622667C2218yescomplemented
73#10622539C2212yescomplemented
74#10622539C2212yescomplemented
75#10622538C2212yescomplemented
76#10622538C2212yescomplemented
77#10622537C2212yescomplemented
78C4×#4318C2212yescomplemented
79C2×C11×#41—22no—
80C2×C11×#41—22no—
81C2×C11×#41—48no—
82C2×C11×#41C2314yes—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2312yes—
85C22×D4×C11—22no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11C2312yes—
89C23×C4×C11—22no—
90C23×C4×C11D411yescharacteristic
91C23×C4×C11D411yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×Dic22C2311yescharacteristic
97C11×C4⋊Q8—21no—
98C11×C4⋊Q8—21no—
99C11×C4⋊Q8C2312yes—
100C11×C4⋊Q8C2312yes—
101C11×#127—21no—
102C11×#127—21no—
103C11×#127C2312yes—
104C11×#127C2312yes—
105C11×#124—22no—
106C11×#124—22no—
107C11×#124C2314yes—
108C11×#124C2314yes—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—22no—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C22⋊C4—22no—
128C2×C11×C22⋊C4—22no—
129C2×C42×C11D411yescharacteristic
130C2×C42×C11D411yescharacteristic
131C2×C42×C11D411yescharacteristic
132C2×C42×C11D411yescharacteristic
133C2×C42×C11D411yescharacteristic
134C2×C42×C11D411yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C2×C22⋊Dic11—21no—
142#67004—48no—
143#67002—48no—
144C2×#4326C2318yes—
145C2×#4325C2318yes—
146C2×#4324C2318yes—
147C2×#4323C2318yes—
148#66983—21no—
149#66983—21no—
150#66983C2312yes—
151#66983C2312yes—
152#66982—22no—
153#66982—22no—
154#66982—22no—
155#66982—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11—22no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166#66977—21no—
167#66977—21no—
168#66977C2312yes—
169#66977C2312yes—
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4—21no—
173C2×Dic11⋊C4—21no—
174C2×C4×Dic11—21no—
175C2×#4318C2314yes—
176#66929—22no—
177#66929—22no—
178#66929—22no—
179#66929—22no—
180#66928—21no—
181#66928—21no—
182#66928C2312yes—
183#66928C2312yes—
184C4×D44—21no—
185C4×D44—21no—
186C4×D44C2312yes—
187C4×D44C2312yes—
188#66925—22no—
189#66925—22no—
190#66925—22no—
191#66925—22no—
192#66923—21no—
193#66923—21no—
194#66923C2312yes—
195#66923C2312yes—
196C4×Dic22—21no—
197C4×Dic22—21no—
198C4×Dic22C2312yes—
199C4×Dic22C2312yes—
200#66899C2318yes—
201#66899C2318yes—
202#66896C2318yes—
203#66896C2318yes—
204C22⋊(C11⋊C8)C2314yes—
205C22⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207C4⋊(C11⋊C8)C2314yes—
208#66867C2314yes—
209C4×C11⋊C8C2314yes—
210#60805—111nomaximal, Sylow
211C24×C11—22no—
212C24×C11C2×D411yescharacteristic
213C23×D11—21no—
214C11×#41—28no—
215C11×#41—28no—
216C11×#41—44no—
217C11×#41—44no—
218C11×#41—48no—
219C11×#41—48no—
220C2×Q8×C11—22no—
221C2×Q8×C11—44no—
222C2×Q8×C11C2414yes—
223C2×D4×C11—24no—
224C2×D4×C11—24no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—22no—
230C2×D4×C11—44no—
231C2×D4×C11—44no—
232C2×D4×C11—44no—
233C2×D4×C11—48no—
234C2×D4×C11C2414yes—
235C22×C4×C11—24no—
236C22×C4×C11—22no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11—48no—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—44no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C2×D44—21no—
267C2×D44—24no—
268C2×D44C2412yes—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—44no—
272C2×Dic22—21no—
273C2×Dic22—24no—
274C2×Dic22C2412yes—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299C22⋊Dic11—22no—
300C22⋊Dic11—22no—
301#4326—48no—
302#4325—48no—
303#4324—48no—
304#4323—48no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11C2412yes—
316C4⋊Dic11C2412yes—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325C4×Dic11—22no—
326C4×Dic11—22no—
327#4318—28no—
328C2×C11⋊C8C2418yes—
329C2×#532D1111yescharacteristic, complemented
330C2×#529—111no—
331#3219—114no—
332#3218—112no—
333#3217—112no—
334#3212—114no—
335#3211—114no—
336#3153—112no—
337#3142—112no—
338#3037—112no—
339#3036—112no—
340#3007—112no—
341#3006—112no—
342#2920—111no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—24no—
346C23×C11—41no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C22×D11—22no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357Q8×C11—24no—
358Q8×C11—24no—
359Q8×C11—44no—
360D4×C11—24no—
361D4×C11—24no—
362D4×C11—44no—
363D4×C11—44no—
364D4×C11—44no—
365D4×C11—44no—
366D4×C11—48no—
367D4×C11—48no—
368D4×C11—44no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—24no—
380C2×C4×C11—41no—
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—48no—
388C2×C4×C11—44no—
389C2×C4×C11—48no—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11H(5,𝔽2)14yes—
402C2×C4×C11C2511yescharacteristic
403C22⋊D11—44no—
404C22⋊D11—44no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—42no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411D44—24no—
412D44—42no—
413C4×D11—44no—
414C4×D11—44no—
415Dic22—24no—
416Dic22—42no—
417C11⋊C8—28no—
418C22×#41C2×D1112yes—
419C2×#137—114no—
420C2×AGL(1,ℤ/8)—114no—
421#532—21no—
422#532—21no—
423#532—21no—
424#532—21no—
425#532C2×D1112yes—
426#532C2×D1112yes—
427#532C2×D1112yescomplemented
428#532C2×D1112yescomplemented
429C2×C4⋊Q8C2×D1111yescharacteristic, complemented
430C2×#127C2×D1111yescharacteristic, complemented
431#529—112no—
432#529—112no—
433#529—112no—
434#529—112no—
435#529—221no—
436#529—221no—
437#529—221no—
438#529—221no—
439C2×#126—221no—
440C2×#125—111no—
441C2×#124—111no—
442C2×#124C2×D1112yescomplemented
443C2×#123—221no—
444C2×C22⋊Q8—111no—
445C2×#121—21no—
446C2×#121—21no—
447C2×#121—111no—
448C2×C4×Q8—111no—
449C2×C4×D4—21no—
450C2×C4×D4—21no—
451C2×C4×D4—111no—
452C2×C4×D4—221no—
453C2×#117—221no—
454C22×C42C2×D1111yescharacteristic
455#497—114no—
456#496—114no—
457#495—118no—
458#491—114no—
459#490—114no—
460#488—118no—
461#464—118no—
462#463—118no—
463#462—114no—
464#461—114no—
465#460—114no—
466#459—114no—
467#452—118no—
468#451—114no—
469#450—114no—
470#449—118no—
471#448—114no—
472#447—114no—
473#432—112no—
474#432—112no—
475#431—112no—
476#431—112no—
477#423—112no—
478#417—114no—
479#417—114no—
480#407—112no—
481C4×M16—112no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—44no—
490C22×C11—44no—
491C22×C11—44no—
492C22×C11—44no—
493C22×C11—88no—
494C22×C11#53512yes—
495C22×C11#57512yes—
496C22×C11C23×D411yescharacteristic
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—84no—
501C4×C11—21no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—44no—
511C4×C11#53512yes—
512C4×C11#57512yes—
513C4×C11C2×H(5,𝔽2)12yes—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—48no—
520C2×#41C22×D1114yes—
521C2×#41C22×D1114yes—
522C22×Q8—111no—
523C22×Q8C22×D1112yes—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—111no—
528C22×D4—221no—
529C22×D4C22×D1112yes—
530C23×C4—22no—
531C23×C4—221no—
532C23×C4C22⋊D1111yescharacteristic
533C23×C4C22⋊D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535#137—448no—
536AGL(1,ℤ/8)—448no—
537C2×Q16—118no—
538C2×SD16—118no—
539C2×SD16—118no—
540C2×D8—118no—
541C2×M16—114no—
542C4⋊Q8—21no—
543C4⋊Q8—21no—
544C4⋊Q8C22×D1112yes—
545C4⋊Q8C22×D1112yes—
546#127—21no—
547#127—21no—
548#127C22×D1112yes—
549#127C22×D1112yes—
550#126—222no—
551#126—222no—
552#126—222no—
553#126—222no—
554#125—112no—
555#125—112no—
556#125—221no—
557#125—221no—
558#124—22no—
559#124—22no—
560#124—112no—
561#124—112no—
562#124—221no—
563#124—221no—
564#124C22×D1114yes—
565#124C22×D1114yes—
566#123—222no—
567#123—222no—
568#123—222no—
569#123—222no—
570C22⋊Q8—112no—
571C22⋊Q8—112no—
572C22⋊Q8—221no—
573C22⋊Q8—221no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—112no—
583#121—112no—
584#121—221no—
585#121—221no—
586C4×Q8—112no—
587C4×Q8—112no—
588C4×Q8—221no—
589C4×Q8—221no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—112no—
599C4×D4—112no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—221no—
605C4×D4—221no—
606#117—222no—
607#117—222no—
608#117—222no—
609#117—222no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—111no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4—221no—
617C2×C4⋊C4—221no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—221no—
621C2×C22⋊C4—221no—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—221no—
624C2×C22⋊C4—221no—
625C2×C42—221no—
626C2×C42C22⋊D1111yescharacteristic
627C2×C42C22⋊D1111yescharacteristic
628C2×C42C22⋊D1111yescharacteristic
629C2×C42C22⋊D1111yescharacteristic
630C2×C42C22⋊D1111yescharacteristic
631C2×C42C22⋊D1111yescharacteristic
632C2×C42C22×D1111yescharacteristic
633C2×C42C22×D1111yescharacteristic
634C2×C42C22×D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C4⋊C8—114no—
639C4⋊C8—114no—
640#103—118no—
641#103—118no—
642#102—118no—
643#102—118no—
644C22⋊C8—114no—
645C22⋊C8—114no—
646#97—114no—
647C4×C8—114no—
648C2×C11—22no—
649C2×C11—22no—
650C2×C11—41no—
651C2×C11—84no—
652C2×C11C2×#53511yescharacteristic
653C2×C11C2×#57511yescharacteristic
654C2×C11C2×#57511yescharacteristic
655D11—82no—
656C24—22no—
657C24—221no—
658C24C2×C22⋊D1111yescharacteristic
659#41—28no—
660#41—28no—
661#41—44no—
662#41—44no—
663#41—48no—
664#41—48no—
665C2×Q8—22no—
666C2×Q8—44no—
667C2×Q8—112no—
668C2×Q8—221no—
669C2×Q8—224no—
670C2×Q8C23×D1114yes—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—48no—
682C2×D4—112no—
683C2×D4—222no—
684C2×D4—222no—
685C2×D4—224no—
686C2×D4—221no—
687C2×D4—444no—
688C2×D4C23×D1114yes—
689C22×C4—24no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—48no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—444no—
702C22×C4C2×C22⋊D1111yescharacteristic
703C22×C4C2×C22⋊D1111yescharacteristic
704C22×C4C2×C22⋊D1111yescharacteristic
705C22×C4C2×C22⋊D1111yescharacteristic
706C22×C4C2×C22⋊D1111yescharacteristic
707C22×C4C2×C22⋊D1111yescharacteristic
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720Q16—448no—
721SD16—448no—
722SD16—448no—
723D8—448no—
724M16—228no—
725C2×C8—118no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—112no—
731C4⋊C4—112no—
732C4⋊C4—221no—
733C4⋊C4—221no—
734C4⋊C4—222no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—222no—
747C22⋊C4—222no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C42—222no—
757C42—222no—
758C42C2×C22⋊D1111yescharacteristic
759C42C2×C22⋊D1111yescharacteristic
760C42C2×C22⋊D1111yescharacteristic
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1111yescharacteristic
764C42C2×C22⋊D1111yescharacteristic
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C2×C22⋊D1111yescharacteristic
769C42C2×C22⋊D1111yescharacteristic
770C42C23×D1111yescharacteristic
771C42C23×D1111yescharacteristic
772C42C23×D1111yescharacteristic
773C42C23×D1111yescharacteristic
774C11#6080511yescharacteristic, complemented, Sylow
775C23—22no—
776C23—22no—
777C23—24no—
778C23—41no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—222no—
783C23—442no—
784C23—442no—
785C23—442no—
786C23C22×C22⋊D1111yescharacteristic
787C23C22×C22⋊D1111yescharacteristic
788C23C22×C22⋊D1111yescharacteristic
789Q8—24no—
790Q8—24no—
791Q8—44no—
792Q8—224no—
793Q8—442no—
794D4—24no—
795D4—24no—
796D4—44no—
797D4—44no—
798D4—44no—
799D4—44no—
800D4—48no—
801D4—48no—
802D4—44no—
803D4—224no—
804D4—444no—
805D4—444no—
806D4—442no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—48no—
826C2×C4—44no—
827C2×C4—48no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—444no—
832C2×C4—442no—
833C2×C4—442no—
834C2×C4—442no—
835C2×C4—444no—
836C2×C4#6703714yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C24×D1111yescharacteristic
849C8—228no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—88no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—884no—
866C22#1062333612yes—
867C22#1062335312yes—
868C22C23×C22⋊D1111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—44no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4#1062333612yes—
883C4#1062335312yes—
884C4C2×#6703712yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—84no—
889C2—882no—
890C2C2×#1062333611yescharacteristic
891C2C2×#1062335311yescharacteristic
892C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#532C2
socleC22×C11C23×D4
hypercenterC2×#532D11
hypocenterC11#60805
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13079653C2semidirect
3. #13079643C2semidirect
4. #13079634C2semidirect
5. #13079592C2semidirect
6. #13079581C2semidirect
7. #13079084C2semidirect
8. #13079016C2semidirect
9. #13078084C2semidirect
10. #13078076C2semidirect
11. #13077876C2semidirect
12. #13077868C2semidirect
13. #13077249C2semidirect
14. C2×C11×#532C2semidirect
22. C11×#532C22semidirect
23. C11×#532C22semidirect
24. C2×C11×C4⋊Q8C22semidirect
25. C2×C11×#127C22semidirect
26. C2×C11×#124C22semidirect
32. C2×#67004C22semidirect
33. C2×#67002C22semidirect
44. #10623010C22semidirect
45. #10623010C22semidirect
47. C2×#66928C22semidirect
48. C2×C4×D44C22semidirect
50. C2×#66923C22semidirect
51. C2×C4×Dic22C22semidirect
52. #10622852C22semidirect
53. #10622851C22semidirect
54. #10622845C22semidirect
55. #10622845C22semidirect
56. #10622841C22semidirect
58. #10622831C22semidirect
61. #10622703C22semidirect
62. #10622699C22semidirect
63. #10622696C22semidirect
64. #10622695C22semidirect
65. #10622688C22semidirect
66. #10622687C22semidirect
67. #10622685C22semidirect
68. #10622684C22semidirect
69. #10622672C22semidirect
70. #10622670C22semidirect
71. #10622669C22semidirect
72. #10622667C22semidirect
73. #10622539C22semidirect
74. #10622539C22semidirect
75. #10622538C22semidirect
76. #10622538C22semidirect
77. #10622537C22semidirect
78. C4×#4318C22semidirect
329. C2×#532D11semidirect
427. #532C2×D11semidirect
428. #532C2×D11semidirect
429. C2×C4⋊Q8C2×D11semidirect
430. C2×#127C2×D11semidirect
442. C2×#124C2×D11semidirect
774. C11#60805semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130796532
#130796432
#130796342
#130795922
#130795812
#130790842
#130790162
#130780842
#130780762
#130778762
#130778682
#130772492
C2×C11×#5322
#6080511