Finite Group Databasebeta

← #15622527

Subgroups — #15622527

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082368C211yesmaximal, characteristic, complemented
2#13078868C214yesmaximal, complemented
3#13078800C214yesmaximal, complemented
4#13078754C212yesmaximal, complemented
5#13078715C212yesmaximal, complemented
6#13078663C212yesmaximal, complemented
7#13078624C212yesmaximal, complemented
8#13078564C211yesmaximal, characteristic, complemented
9#13078529C211yesmaximal, characteristic, complemented
10#13078447C212yesmaximal, complemented
11#13078128C212yesmaximal, complemented
12#13077843C211yesmaximal, characteristic
13C2×#10622831C211yesmaximal, characteristic, complemented
14#13077473C212yesmaximal, complemented
15#13077448C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C2×C11×#518C211yesmaximal, characteristic, complemented
18C23×D4×C11C2211yescharacteristic
19C11×#518—21no—
20C11×#518—22no—
21C11×#518—21no—
22C11×#518C2214yes—
23C11×#518C2212yes—
24C11×#518C2212yes—
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2212yes—
29C2×C11×#117C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C22⋊C4—22no—
32C22×#4324C2212yes—
33C2×#66985C2212yes—
34#10623322C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36#10623065C2212yescomplemented
37#10623064—21no—
38#10623062—22no—
39#10623060—21no—
40#10623057C2211yescharacteristic, complemented
41#10623054C2211yescharacteristic, complemented
42#10623050C2211yescharacteristic, complemented
43#10623049C2212yescomplemented
44#10623047C2211yescharacteristic, complemented
45#10623044—21no—
46#10623042—21no—
47#10623026—22no—
48#10623010C2212yescomplemented
49#10623001C2212yescomplemented
50#10622831C2214yes—
51#10622831C2212yes—
52#10622831C2212yes—
53#10622831C2212yes—
54#10622831C2212yes—
55#10622830C2212yes—
56#10622830C2212yes—
57#10622828C2212yes—
58C2×#66896C2212yes—
59#10622820C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61#10622632C2214yescomplemented
62#10622632C2214yescomplemented
63#10622631C2214yescomplemented
64#10622631C2214yescomplemented
65#10622631C2214yescomplemented
66C4×#4324C2214yescomplemented
67C4×#4324C2214yescomplemented
68C4×#4324C2214yescomplemented
69#10622629C2214yescomplemented
70#10622629C2214yescomplemented
71#10622627C2214yescomplemented
72C4×#4323C2214yescomplemented
73#10622622C2214yescomplemented
74#10622622C2214yescomplemented
75#10622621C2214yescomplemented
76#10622620C2214yescomplemented
77#10622617C2212yescomplemented
78#10622616C2212yescomplemented
79#10622615C2212yescomplemented
80#10622613C2214yescomplemented
81#10622612C2212yescomplemented
82#10622611C2212yescomplemented
83#10622610C2212yescomplemented
84#10622609C2212yescomplemented
85#10622609C2214yescomplemented
86#10622608C2212yescomplemented
87#10622584C2211yescharacteristic, complemented
88#10622584C2212yescomplemented
89#10622583C2211yescharacteristic, complemented
90#10622583C2212yescomplemented
91#10622581C2211yescharacteristic, complemented
92#10622580C2211yescharacteristic, complemented
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95C25×C11—21no—
96C22×D4×C11—28no—
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11C2312yes—
101C22×D4×C11C2312yes—
102C22×D4×C11C2312yes—
103C23×C4×C11—22no—
104C23×C4×C11—22no—
105C23×C4×C11C2311yescharacteristic
106C2×#4339C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C4×D4×C11—22no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C4×D4×C11—24no—
112C4×D4×C11—24no—
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11C2314yes—
119C4×D4×C11C2314yes—
120C4×D4×C11C2314yes—
121C4×D4×C11C2314yes—
122C11×#117—21no—
123C11×#117—21no—
124C11×#117D411yescharacteristic
125C11×#117D412yes—
126C11×#117D411yescharacteristic
127C11×#117C2312yes—
128C11×#117C2312yes—
129C11×#117C2311yescharacteristic
130C11×#117C2312yes—
131C11×#117C2311yescharacteristic
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C4⋊C4D411yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—22no—
138C2×C11×C22⋊C4—22no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—24no—
143C2×C11×C22⋊C4D412yes—
144C2×C42×C11—21no—
145C2×C42×C11C2312yes—
146#67006—21no—
147C2×C22⋊Dic11—21no—
148C2×#4324—28no—
149C2×#4324C2314yes—
150C2×#4324C2314yes—
151C2×#4324C2314yes—
152#66985—28no—
153C2×#4323C2314yes—
154#66983C2311yescharacteristic
155#66983C2311yescharacteristic
156#66982—22no—
157#66982—21no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11—21no—
160C4×C22⋊D11—21no—
161#66979—22no—
162#66979C2311yescharacteristic
163C2×C4⋊Dic11C2311yescharacteristic
164#66977—22no—
165#66977—21no—
166#66977—21no—
167#66977C2311yescharacteristic
168#66977C2312yes—
169#66977C2311yescharacteristic
170#66977C2312yes—
171C2×Dic11⋊C4—21no—
172C2×#4318C2312yes—
173C22×C11⋊C8C2312yes—
174#66951—22no—
175#66950—21no—
176#66950—21no—
177#66949—22no—
178#66945—21no—
179C4⋊C4×D11—21no—
180#66943—21no—
181#66942—22no—
182#66942—22no—
183#66941—21no—
184#66940—21no—
185#66940—21no—
186#66939—22no—
187#66938—22no—
188#66936—22no—
189(C22⋊D11)⋊C4—22no—
190#66932—22no—
191#66932—22no—
192#66931—22no—
193#66930—22no—
194#66929—22no—
195#66928C2312yescomplemented
196C4×D44C2312yescomplemented
197#66925—22no—
198#66923—22no—
199#66923C2312yescomplemented
200#66922C2312yescomplemented
201#66922C2312yescomplemented
202C4×Dic22—22no—
203C4×Dic22C2312yescomplemented
204C4×Dic22C2312yescomplemented
205C4×Dic22C2312yescomplemented
206#66896C2314yes—
207#66896C2314yes—
208#66896C2314yes—
209#66896C2314yes—
210C22⋊(C11⋊C8)C2311yescharacteristic
211C22⋊(C11⋊C8)C2312yes—
212C22⋊(C11⋊C8)C2311yescharacteristic
213C22⋊(C11⋊C8)C2312yes—
214C22⋊(C11⋊C8)C2312yes—
215#66874C2312yescomplemented
216#66874C2314yescomplemented
217#66874C2312yescomplemented
218#66874C2314yescomplemented
219#66873C2312yescomplemented
220#66873C2312yescomplemented
221#66872C2312yescomplemented
222#66872C2314yescomplemented
223#66872C2312yescomplemented
224#66871C2312yescomplemented
225#66871C2314yescomplemented
226#66871C2312yescomplemented
227C4⋊(C11⋊C8)C2314yescomplemented
228C4⋊(C11⋊C8)C2314yescomplemented
229#66867C2314yescomplemented
230C4×C11⋊C8C2314yescomplemented
231#60579—111nomaximal, Sylow
232C24×C11—28no—
233C24×C11—22no—
234C24×C11—22no—
235C24×C11—22no—
236C24×C11—82no—
237C24×C11—82no—
238C24×C11C2×D411yescharacteristic
239C2×D4×C11—28no—
240C2×D4×C11—28no—
241C2×D4×C11—28no—
242C2×D4×C11—28no—
243C2×D4×C11—28no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—24no—
248C2×D4×C11#4118yes—
249C2×D4×C11C2414yes—
250C22×C4×C11—24no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—24no—
254C22×C4×C11—24no—
255C22×C4×C11—24no—
256C22×C4×C11—24no—
257C22×C4×C11—84no—
258C22×C4×C11—84no—
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C2×C22⋊D11—21no—
268C2×C22⋊D11—21no—
269C2×C22⋊D11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272#4339—24no—
273C2×D44C2411yescharacteristic
274C2×C4×D11—21no—
275C2×C4×D11—22no—
276C2×Dic22—21no—
277C2×Dic22—22no—
278C2×Dic22—24no—
279C2×Dic22C2411yescharacteristic
280C2×Dic22C2412yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4C2×D411yescharacteristic
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2412yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4C2×D412yes—
298C11×C22⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C42×C11—22no—
302C42×C11—22no—
303C42×C11C2×D412yes—
304C42×C11C2×D412yes—
305C42×C11C2412yes—
306C42×C11C2412yes—
307C22⋊Dic11—21no—
308C22⋊Dic11—21no—
309C22⋊Dic11—22no—
310C22⋊Dic11—21no—
311C22⋊Dic11—22no—
312#4324—28no—
313#4324—28no—
314#4324—28no—
315#4323—28no—
316(C2×D11)⋊C4—21no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—21no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2411yescharacteristic
326C4⋊Dic11C2411yescharacteristic
327C4⋊Dic11C2412yes—
328Dic11⋊C4—21no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—21no—
336Dic11⋊C4—22no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339C4×Dic11—22no—
340C4×Dic11—21no—
341#4318—24no—
342C2×C11⋊C8—24no—
343C2×C11⋊C8C2412yes—
344C2×C11⋊C8C2414yes—
345C2×C11⋊C8C2412yes—
346#3495—111no—
347C2×#518D1111yescharacteristic, complemented
348#3123—114no—
349#3118—114no—
350#3114—112no—
351#3110—112no—
352#3105—112no—
353#3101—112no—
354#3095—111no—
355#3091—111no—
356#3081—112no—
357#3042—112no—
358#3003—111no—
359C2×#450—111no—
360#2949—112no—
361#2946—112no—
362#2924—111no—
363C23×C11—28no—
364C23×C11—28no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—24no—
368C23×C11—28no—
369C23×C11—41no—
370C23×C11—44no—
371C23×C11—44no—
372C23×C11—82no—
373C23×C11—82no—
374C23×C11—82no—
375C23×C11—82no—
376C23×C11—816no—
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C22×D11—21no—
381D4×C11—28no—
382D4×C11—28no—
383D4×C11—28no—
384D4×C11—24no—
385D4×C11C2×#4118yes—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—42no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11—84no—
398C2×C4×C11—84no—
399C2×C4×C11—84no—
400C2×C4×C11—84no—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2×#4114yes—
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—42no—
411C22⋊D11—42no—
412C22⋊D11—81no—
413C2×Dic11—21no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—42no—
419C2×Dic11—81no—
420D44—22no—
421C4×D11—42no—
422C4×D11—82no—
423Dic22—24no—
424Dic22—22no—
425Dic22—42no—
426Dic22—82no—
427C11⋊C8—22no—
428C11⋊C8—22no—
429C11⋊C8—24no—
430C23×D4C2×D1111yescharacteristic
431C2×AGL(1,ℤ/8)—112no—
432C22×SD16—112no—
433#556—221no—
434#554—221no—
435#552—221no—
436#552—222no—
437#552—221no—
438#551—222no—
439#544—111no—
440#542—112no—
441#541—112no—
442#536—111no—
443#533—112no—
444#529—112no—
445#525—111no—
446C2×C22⋊Q8—111no—
447#520—111no—
448#519—111no—
449#518—22no—
450#518—21no—
451#518—21no—
452#518C2×D1112yes—
453#518C2×D1114yes—
454#518C2×D1112yes—
455C2×C4×D4—21no—
456C2×C4×D4—21no—
457C2×C4×D4C2×D1112yes—
458C2×C4×D4C2×D1112yes—
459C2×#117C2×D1111yescharacteristic
460C2×#117C2×D1111yescharacteristic
461C22×C22⋊C4—22no—
462#485—112no—
463#485—114no—
464#484—111no—
465#484—112no—
466#483—111no—
467#483—112no—
468#482—112no—
469#481—111no—
470#480—111no—
471#478—114no—
472#478—114no—
473#476—114no—
474#474—114no—
475#463—114no—
476#463—114no—
477#461—114no—
478#461—114no—
479#450—112no—
480#450—112no—
481#450—112no—
482#450—114no—
483#450—112no—
484#447—112no—
485#447—112no—
486#442—114no—
487#440—114no—
488#440—114no—
489#440—114no—
490C4×SD16—114no—
491C4×SD16—114no—
492C4×SD16—114no—
493C4×D8—114no—
494#433—114no—
495#432—112no—
496#431—112no—
497#428—112no—
498#427—112no—
499#424—112no—
500#419—112no—
501#418—112no—
502#416—112no—
503C2×#102—112no—
504#407—111no—
505C2×C22⋊C8—111no—
506#405—112no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—28no—
514C22×C11—21no—
515C22×C11—44no—
516C22×C11—416no—
517C22×C11—44no—
518C22×C11—44no—
519C22×C11—88no—
520C22×C11—88no—
521C22×C11#52512yes—
522C22×C11#57712yes—
523C22×C11C23×D411yescharacteristic
524C2×D11—41no—
525C2×D11—41no—
526C2×D11—41no—
527C4×C11—22no—
528C4×C11—22no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11#52512yes—
536C4×C11C22×#4112yes—
537Dic11—41no—
538Dic11—42no—
539Dic11—42no—
540Dic11—41no—
541Dic11—41no—
542C25—21no—
543C2×#41—111no—
544C22×Q8—111no—
545C22×D4—28no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4C22×D1112yes—
550C22×D4C22×D1112yes—
551C22×D4C22×D1112yes—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4C22×D1111yescharacteristic
555AGL(1,ℤ/8)—228no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—114no—
559C2×SD16—228no—
560C2×D8—114no—
561C2×M16—112no—
562C22×C8—112no—
563C4⋊Q8—112no—
564C4⋊Q8—112no—
565C4⋊Q8—221no—
566#126—222no—
567#126—222no—
568#126—222no—
569#126—222no—
570#125—112no—
571#125—222no—
572#125—222no—
573#125—221no—
574#125—222no—
575#124—112no—
576#124—222no—
577#123—221no—
578#123—222no—
579#123—222no—
580#123—222no—
581C22⋊Q8—112no—
582C22⋊Q8—112no—
583C22⋊Q8—111no—
584C22⋊Q8—111no—
585C22⋊Q8—221no—
586C22⋊Q8—221no—
587C22⋊Q8—222no—
588C22⋊Q8—221no—
589C22⋊Q8—221no—
590C22⋊Q8—222no—
591C22⋊Q8—222no—
592#121—111no—
593#121—111no—
594#120—221no—
595C4×Q8—112no—
596C4×Q8—112no—
597C4×Q8—112no—
598C4×Q8—221no—
599C4×Q8—221no—
600C4×Q8—222no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—24no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—112no—
612C4×D4—221no—
613C4×D4—221no—
614C4×D4—222no—
615C4×D4—222no—
616C4×D4C22×D1114yes—
617C4×D4C22×D1114yes—
618C4×D4C22×D1114yes—
619C4×D4C22×D1114yes—
620#117—21no—
621#117—21no—
622#117—111no—
623#117—222no—
624#117—221no—
625#117—222no—
626#117—222no—
627#117C22⋊D1111yescharacteristic
628#117C22⋊D1112yes—
629#117C22⋊D1111yescharacteristic
630#117C22×D1112yes—
631#117C22×D1112yes—
632#117C22×D1111yescharacteristic
633#117C22×D1111yescharacteristic
634#117C22×D1112yes—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4—221no—
638C2×C4⋊C4C22⋊D1111yescharacteristic
639C2×C4⋊C4C22⋊D1111yescharacteristic
640C2×C4⋊C4C22×D1111yescharacteristic
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—24no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4C22⋊D1112yes—
651C2×C42—21no—
652C2×C42C22×D1112yes—
653#107—112no—
654#107—112no—
655#107—114no—
656#106—112no—
657#106—112no—
658#106—114no—
659C4⋊C8—114no—
660C4⋊C8—114no—
661#103—112no—
662#103—112no—
663#103—114no—
664#103—114no—
665#102—114no—
666#102—114no—
667#102—114no—
668#102—114no—
669#102—112no—
670#102—112no—
671C22⋊C8—111no—
672C22⋊C8—111no—
673C22⋊C8—112no—
674C22⋊C8—112no—
675C22⋊C8—112no—
676#97—114no—
677C4×C8—114no—
678C2×C11—22no—
679C2×C11—22no—
680C2×C11—41no—
681C2×C11—48no—
682C2×C11C2×#52511yescharacteristic
683C2×C11C2×#57711yescharacteristic
684C2×C11#358511yescharacteristic
685D11—81no—
686C24—28no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—82no—
691C24—82no—
692C24C2×C22⋊D1111yescharacteristic
693#41—224no—
694C2×Q8—112no—
695C2×Q8—111no—
696C2×Q8—221no—
697C2×Q8—222no—
698C2×Q8—224no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—111no—
709C2×D4—221no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4#433918yes—
713C2×D4C23×D1114yes—
714C22×C4—24no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—84no—
722C22×C4—84no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—222no—
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1112yes—
729C22×C4C2×C22⋊D1111yescharacteristic
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1112yes—
732C22×C4C23×D1111yescharacteristic
733C22×C4C23×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735SD16—228no—
736SD16—228no—
737SD16—228no—
738D8—228no—
739M16—224no—
740C2×C8—112no—
741C2×C8—114no—
742C2×C8—112no—
743C2×C8—224no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—112no—
747C4⋊C4—111no—
748C4⋊C4—111no—
749C4⋊C4—221no—
750C4⋊C4—222no—
751C4⋊C4—222no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C4⋊C4—222no—
755C4⋊C4—222no—
756C4⋊C4—222no—
757C4⋊C4—222no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—222no—
761C4⋊C4—222no—
762C4⋊C4C2×C22⋊D1111yescharacteristic
763C4⋊C4C2×C22⋊D1111yescharacteristic
764C4⋊C4C2×C22⋊D1112yes—
765C4⋊C4C2×C22⋊D1111yescharacteristic
766C4⋊C4C2×C22⋊D1111yescharacteristic
767C4⋊C4C2×C22⋊D1112yes—
768C4⋊C4C23×D1112yes—
769C4⋊C4C23×D1112yes—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—222no—
777C22⋊C4—222no—
778C22⋊C4—221no—
779C22⋊C4—221no—
780C22⋊C4—221no—
781C22⋊C4—221no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—221no—
785C22⋊C4—222no—
786C22⋊C4C2×C22⋊D1112yes—
787C22⋊C4C2×C22⋊D1112yes—
788C22⋊C4C2×C22⋊D1112yes—
789C22⋊C4C2×C22⋊D1112yes—
790C42—22no—
791C42—22no—
792C42—221no—
793C42—222no—
794C42—222no—
795C42—222no—
796C42C2×C22⋊D1112yes—
797C42C2×C22⋊D1112yes—
798C42C23×D1112yes—
799C42C23×D1112yes—
800C11#6057911yescharacteristic, complemented, Sylow
801C23—28no—
802C23—28no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—28no—
807C23—41no—
808C23—44no—
809C23—44no—
810C23—82no—
811C23—82no—
812C23—82no—
813C23—82no—
814C23—816no—
815C23—221no—
816C23C22×C22⋊D1111yescharacteristic
817C23C22×C22⋊D1111yescharacteristic
818C23C22×C22⋊D1111yescharacteristic
819Q8—224no—
820Q8—222no—
821Q8—442no—
822Q8—882no—
823D4—28no—
824D4—28no—
825D4—28no—
826D4—24no—
827D4—222no—
828D4—442no—
829D4—442no—
830D4—881no—
831D4C2×#433918yes—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—84no—
844C2×C4—84no—
845C2×C4—84no—
846C2×C4—84no—
847C2×C4—221no—
848C2×C4—221no—
849C2×C4—222no—
850C2×C4—221no—
851C2×C4—222no—
852C2×C4—442no—
853C2×C4—442no—
854C2×C4—882no—
855C2×C4—881no—
856C2×C4C2×#433914yes—
857C2×C4C22×C22⋊D1111yescharacteristic
858C2×C4C22×C22⋊D1112yes—
859C2×C4C22×C22⋊D1112yes—
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1112yes—
862C2×C4C22×C22⋊D1112yes—
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C24×D1111yescharacteristic
865C8—222no—
866C8—222no—
867C8—224no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—28no—
874C22—21no—
875C22—21no—
876C22—44no—
877C22—416no—
878C22—44no—
879C22—44no—
880C22—88no—
881C22—88no—
882C22—441no—
883C22—441no—
884C22—441no—
885C22#1062332212yes—
886C22#1062336712yes—
887C22C23×C22⋊D1111yescharacteristic
888C4—21no—
889C4—21no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—441no—
897C4—442no—
898C4—442no—
899C4—441no—
900C4—441no—
901C4#1062332212yes—
902C4C22×#433912yes—
903C2—22no—
904C2—22no—
905C2—41no—
906C2—48no—
907C2—881no—
908C2C2×#1062332211yescharacteristic
909C2C2×#1062336711yescharacteristic
910C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#518C2
socleC22×C11C23×D4
prime radical#13077843C2
hypercenterC2×#518D11
hypocenterC11#60579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. #13082368C2semidirect
2. #13078868C2semidirect
3. #13078800C2semidirect
4. #13078754C2semidirect
5. #13078715C2semidirect
6. #13078663C2semidirect
7. #13078624C2semidirect
8. #13078564C2semidirect
9. #13078529C2semidirect
10. #13078447C2semidirect
11. #13078128C2semidirect
13. C2×#10622831C2semidirect
14. #13077473C2semidirect
15. #13077448C2semidirect
16. #13077274C2semidirect
17. C2×C11×#518C2semidirect
36. #10623065C22semidirect
40. #10623057C22semidirect
41. #10623054C22semidirect
42. #10623050C22semidirect
43. #10623049C22semidirect
44. #10623047C22semidirect
48. #10623010C22semidirect
49. #10623001C22semidirect
61. #10622632C22semidirect
62. #10622632C22semidirect
63. #10622631C22semidirect
64. #10622631C22semidirect
65. #10622631C22semidirect
66. C4×#4324C22semidirect
67. C4×#4324C22semidirect
68. C4×#4324C22semidirect
69. #10622629C22semidirect
70. #10622629C22semidirect
71. #10622627C22semidirect
72. C4×#4323C22semidirect
73. #10622622C22semidirect
74. #10622622C22semidirect
75. #10622621C22semidirect
76. #10622620C22semidirect
77. #10622617C22semidirect
78. #10622616C22semidirect
79. #10622615C22semidirect
80. #10622613C22semidirect
81. #10622612C22semidirect
82. #10622611C22semidirect
83. #10622610C22semidirect
84. #10622609C22semidirect
85. #10622609C22semidirect
86. #10622608C22semidirect
87. #10622584C22semidirect
88. #10622584C22semidirect
89. #10622583C22semidirect
90. #10622583C22semidirect
91. #10622581C22semidirect
92. #10622580C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
195. #66928C23semidirect
196. C4×D44C23semidirect
199. #66923C23semidirect
200. #66922C23semidirect
201. #66922C23semidirect
203. C4×Dic22C23semidirect
204. C4×Dic22C23semidirect
205. C4×Dic22C23semidirect
215. #66874C23semidirect
216. #66874C23semidirect
217. #66874C23semidirect
218. #66874C23semidirect
219. #66873C23semidirect
220. #66873C23semidirect
221. #66872C23semidirect
222. #66872C23semidirect
223. #66872C23semidirect
224. #66871C23semidirect
225. #66871C23semidirect
226. #66871C23semidirect
227. C4⋊(C11⋊C8)C23semidirect
228. C4⋊(C11⋊C8)C23semidirect
229. #66867C23semidirect
230. C4×C11⋊C8C23semidirect
347. C2×#518D11semidirect
800. C11#60579semidirect

Maximal subgroups

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

subgroupindex
#130823682
#130788682
#130788002
#130787542
#130787152
#130786632
#130786242
#130785642
#130785292
#130784472
#130781282
#130778432
C2×#106228312
#130774732
#130774482
#130772742
C2×C11×#5182
#6057911