Finite Group Databasebeta

← #15622504

Subgroups — #15622504

Order 2816.

2274 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082345C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13078855C214yesmaximal, complemented
4#13078795C214yesmaximal, complemented
5#13078751C212yesmaximal, complemented
6#13078704C212yesmaximal, complemented
7#13078660C212yesmaximal, complemented
8#13078613C212yesmaximal, complemented
9#13078529C211yesmaximal, characteristic, complemented
10#13078445C212yesmaximal, complemented
11#13078118C212yesmaximal, complemented
12#13077846C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14#13077464C212yesmaximal, complemented
15#13077446C212yesmaximal, complemented
16#13077276C211yesmaximal, characteristic, complemented
17C11×#3094C211yesmaximal, characteristic, complemented
18C23×D44C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21#10623337—22no—
22#10623336C2211yescharacteristic, complemented
23#10623329C2211yescharacteristic, complemented
24C22×#4323C2212yes—
25#10623322C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C2×#66961C2212yes—
28#10623150C2212yescomplemented
29#10623149—21no—
30#10623147—21no—
31#10623145—21no—
32#10623142—21no—
33#10623134C2212yescomplemented
34#10623131C2212yescomplemented
35#10623127C2212yescomplemented
36#10623052—21no—
37#10623052—21no—
38#10623052—22no—
39#10623052C2212yes—
40#10623052C2212yes—
41#10623052C2214yescomplemented
42#10623035C2211yescharacteristic, complemented
43C2×#66946C2212yescomplemented
44C2×#66946C2212yescomplemented
45#10623031C2211yescharacteristic, complemented
46#10623026—22no—
47C2×C22⋊C4×D11—22no—
48C2×C4×D44—21no—
49C2×C4×D44—21no—
50C11×#482C2214yescomplemented
51C11×#481C2212yescomplemented
52C11×#480C2212yescomplemented
53C11×#428C2212yescomplemented
54C11×#418C2212yescomplemented
55C11×#407C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic
57#10622744C2212yes—
58#10622735C2212yescomplemented
59#10622732C2212yescomplemented
60#10622649C2214yes—
61#10622649C2212yes—
62#10622649C2212yes—
63#10622616C2212yescomplemented
64#10622615C2212yescomplemented
65#10622611C2212yescomplemented
66#10622609C2212yescomplemented
67#10622584C2211yescharacteristic, complemented
68#10622583C2211yescharacteristic, complemented
69#10622581C2211yescharacteristic, complemented
70#10622580C2211yescharacteristic, complemented
71C2×#66873C2212yes—
72#10622504C2214yescomplemented
73#10622503C2214yescomplemented
74#10622502C2214yescomplemented
75#10622485C2214yescomplemented
76#10622484C2214yescomplemented
77#10622483C2214yescomplemented
78#10622482C2214yescomplemented
79#10622465C2214yescomplemented
80#10622400C2214yescomplemented
81#10622400C2214yescomplemented
82#10622399C2214yescomplemented
83#10622399C2214yescomplemented
84#10622398C2214yescomplemented
85#10622398C2214yescomplemented
86#10622369C2214yescomplemented
87#10622369C2214yescomplemented
88#10622345C2212yescomplemented
89#10622345C2212yescomplemented
90#10622344C2212yescomplemented
91#10622344C2212yescomplemented
92#10622333C2214yescomplemented
93#10622332C2212yescomplemented
94#10622331C2212yescomplemented
95C24×D11—21no—
96C22×D4×C11—21no—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C2×#4341—22no—
100C2×#4339C2311yescharacteristic
101C22×D44—21no—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—28no—
105C22×D44C2312yes—
106C22×D44C2312yes—
107C22×D44C2312yes—
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C2×C11×M16C2312yes—
111C11×#121—21no—
112C11×#121—21no—
113C11×#121C2312yes—
114C11×#121C2312yes—
115C11×#117—21no—
116C11×#117—21no—
117C11×#117C2312yes—
118C11×#117C2312yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C42×C11—21no—
125#67006—21no—
126#67006—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11D412yes—
129#66993C2312yescomplemented
130#66992—22no—
131#66992—22no—
132#66991—22no—
133#66991—21no—
134#66991—21no—
135#66989—22no—
136#66989C2312yescomplemented
137#66988—22no—
138#66988—22no—
139D4×Dic11—22no—
140D4×Dic11—21no—
141D4×Dic11—21no—
142D4×Dic11C2312yescomplemented
143D4×Dic11C2312yescomplemented
144C2×#4323—28no—
145C2×#4323C2314yes—
146C2×#4323C2314yes—
147#66983C2311yescharacteristic
148#66983C2311yescharacteristic
149#66982—21no—
150C4×C22⋊D11—21no—
151C4×C22⋊D11—21no—
152C4×C22⋊D11—22no—
153C2×(C2×D11)⋊C4—22no—
154C2×(C2×D11)⋊C4—22no—
155#66979D412yes—
156#66979D411yescharacteristic
157#66979D411yescharacteristic
158#66979C2311yescharacteristic
159#66979C2311yescharacteristic
160#66979C2311yescharacteristic
161#66979C2312yes—
162C2×C4⋊Dic11D411yescharacteristic
163C2×C4⋊Dic11D411yescharacteristic
164#66977—22no—
165#66977C2311yescharacteristic
166#66977C2311yescharacteristic
167C2×C4×Dic11C2312yes—
168C22×C11⋊C8C2312yes—
169#66961—28no—
170C2×D88C2314yes—
171C2×#4314C2314yes—
172#66946—22no—
173#66946—22no—
174#66946—22no—
175#66946—22no—
176#66946C2314yes—
177#66946C2314yes—
178#66946C2314yes—
179#66946C2314yes—
180#66946C2312yescomplemented
181#66945—21no—
182C4⋊C4×D11—21no—
183#66943—21no—
184#66943C2312yescomplemented
185#66941—21no—
186#66941C2312yescomplemented
187#66940C2312yescomplemented
188#66939—22no—
189#66938—22no—
190#66936—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—24no—
193C22⋊C4×D11—24no—
194C22⋊C4×D11—24no—
195C22⋊C4×D11—24no—
196#66932—22no—
197#66932—22no—
198#66931—22no—
199#66930—22no—
200C4×D44—22no—
201C4×D44—22no—
202C4×D44—22no—
203C4×D44—22no—
204C4×D44—24no—
205C4×D44—24no—
206C11×#107C2314yescomplemented
207C11×#106C2314yescomplemented
208C11×#102C2314yescomplemented
209C11×#102C2314yescomplemented
210C11×C22⋊C8C2312yes—
211C11×C22⋊C8C2312yes—
212C22⋊(C11⋊C8)C2311yescharacteristic
213C22⋊(C11⋊C8)C2311yescharacteristic
214C22⋊(C11⋊C8)C2312yes—
215#66885C2314yes—
216#66885C2314yes—
217#66879C2314yescomplemented
218Dic11⋊C8C2314yescomplemented
219Dic11⋊C8C2314yescomplemented
220C8×Dic11C2314yescomplemented
221#66874C2312yescomplemented
222#66874C2312yescomplemented
223#66873C2314yes—
224#66873C2314yes—
225#66873C2312yescomplemented
226#66873C2312yescomplemented
227#66872C2312yescomplemented
228#66872C2312yescomplemented
229#66871C2312yescomplemented
230#66871C2312yescomplemented
231#60578—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11C2×D411yescharacteristic
234C23×D11—22no—
235C23×D11—28no—
236C23×D11—22no—
237C23×D11—22no—
238C23×D11—82no—
239C23×D11—82no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—24no—
244C2×D4×C11—82no—
245C2×D4×C11C2412yes—
246C22×C4×C11—24no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C2×C22⋊D11—22no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—21no—
259C2×C22⋊D11—21no—
260C2×C22⋊D11—21no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265#4341—84no—
266#4339—24no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—28no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—24no—
276C2×D44#4118yescomplemented
277C2×D44C2411yescharacteristic
278C2×D44C2414yes—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—21no—
285C2×C4×D11—84no—
286C2×C4×D11—84no—
287C2×Dic22—22no—
288C2×Dic22C2411yescharacteristic
289C11×M16—24no—
290C2×C8×C11C2414yes—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2412yes—
296C11×C4⋊C4C2412yes—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C42×C11—22no—
302C42×C11—22no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—22no—
306C22⋊Dic11—22no—
307C22⋊Dic11—21no—
308C22⋊Dic11—21no—
309C22⋊Dic11—21no—
310C22⋊Dic11C2×D412yes—
311C22⋊Dic11C2×D412yes—
312C22⋊Dic11C2×D412yes—
313C22⋊Dic11C2×D412yes—
314#4323—28no—
315#4323—28no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—21no—
322(C2×D11)⋊C4—21no—
323C4⋊Dic11—22no—
324C4⋊Dic11C2×D412yes—
325C4⋊Dic11C2×D412yes—
326C4⋊Dic11C2×D411yescharacteristic
327C4⋊Dic11C2×D411yescharacteristic
328C4⋊Dic11C2×D411yescharacteristic
329C4⋊Dic11C2×D411yescharacteristic
330C4⋊Dic11C2411yescharacteristic
331C4⋊Dic11C2411yescharacteristic
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—21no—
336Dic11⋊C4—21no—
337C4×Dic11—22no—
338C4×Dic11—21no—
339C4×Dic11C2×D412yes—
340C4×Dic11C2×D412yes—
341C4×Dic11C2412yes—
342C4×Dic11C2412yes—
343C2×C11⋊C8—24no—
344C2×C11⋊C8C2412yes—
345C2×C11⋊C8C2412yes—
346D88—28no—
347#4314—28no—
348#3494—111no—
349C2×#518—111no—
350#3122—114no—
351#3118—114no—
352#3114—112no—
353#3109—112no—
354#3105—112no—
355#3100—112no—
356#3094D1111yescharacteristic, complemented
357#3091—111no—
358#3081—112no—
359#3041—112no—
360#3003—111no—
361C2×#447—111no—
362#2948—112no—
363#2946—112no—
364#2924—111no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—41no—
369C23×C11—42no—
370C23×C11—81no—
371C23×C11—81no—
372C23×C11C22×D411yescharacteristic
373C23×C11C22×D411yescharacteristic
374C23×C11C22×D411yescharacteristic
375C22×D11—28no—
376C22×D11—24no—
377C22×D11—28no—
378C22×D11—28no—
379C22×D11—21no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—82no—
383C22×D11—82no—
384C22×D11—82no—
385C22×D11—82no—
386C22×D11—816no—
387D4×C11—24no—
388D4×C11—44no—
389D4×C11—42no—
390D4×C11—82no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—42no—
400C2×C4×C11—42no—
401C2×C4×C11—81no—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C2×#4114yes—
406C2×C4×C11C2511yescharacteristic
407C22⋊D11—42no—
408C22⋊D11—42no—
409C22⋊D11—82no—
410C22⋊D11—82no—
411C22⋊D11—81no—
412C2×Dic11—24no—
413C2×Dic11—21no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—42no—
417C2×Dic11—82no—
418C2×Dic11—82no—
419C2×Dic11C22×D412yes—
420C2×Dic11C22×D412yes—
421C2×Dic11C22×D412yes—
422C2×Dic11C22×D412yes—
423D44—28no—
424D44—28no—
425D44—28no—
426D44—24no—
427D44—22no—
428D44C2×#4118yes—
429C4×D11—42no—
430C4×D11—84no—
431C4×D11—84no—
432C4×D11—84no—
433C4×D11—84no—
434C4×D11—82no—
435Dic22—22no—
436Dic22—82no—
437C8×C11—24no—
438C11⋊C8—22no—
439C11⋊C8—22no—
440C23×D4—111no—
441C2×AGL(1,ℤ/8)—112no—
442C22×D8—112no—
443#555—221no—
444#553—221no—
445#553—221no—
446#551—222no—
447#547—221no—
448#546—222no—
449#544—111no—
450#542—112no—
451#540—112no—
452#535—111no—
453#532—112no—
454#529—112no—
455#525—111no—
456C2×#121C2×D1111yescharacteristic
457#520—111no—
458#518—111no—
459#518—112no—
460#518—114no—
461#518—112no—
462#518—222no—
463#518—221no—
464#518—221no—
465C2×C4×D4—112no—
466C2×C4×D4—112no—
467C2×C4×D4—221no—
468C2×C4×D4—221no—
469C2×#117—111no—
470C2×#117C2×D1111yescharacteristic
471C22×C22⋊C4—222no—
472#485—112no—
473#484—111no—
474#483—111no—
475#482—112no—
476#482C2×D1114yescomplemented
477#481—111no—
478#481C2×D1112yescomplemented
479#480—111no—
480#480C2×D1112yescomplemented
481#478—114no—
482#478—114no—
483#476—114no—
484#474—114no—
485#463—114no—
486#463—114no—
487#459—114no—
488#459—114no—
489#450—112no—
490#450—112no—
491#447—112no—
492#447—112no—
493#447—114no—
494#447—112no—
495#447—112no—
496#442—114no—
497#442—114no—
498#442—114no—
499#440—114no—
500C4×SD16—114no—
501C4×D8—114no—
502C4×D8—114no—
503C4×D8—114no—
504#433—114no—
505#432—112no—
506#431—112no—
507#428C2×D1112yescomplemented
508#427—112no—
509#424—112no—
510#418—112no—
511#418C2×D1112yescomplemented
512#416—112no—
513C2×#102—112no—
514#407C2×D1111yescharacteristic
515C2×C22⋊C8—111no—
516#405—112no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—44no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—162no—
529C22×C11#52512yes—
530C22×C11#57612yes—
531C22×C11C23×D411yescharacteristic
532C2×D11—28no—
533C2×D11—416no—
534C2×D11—44no—
535C2×D11—44no—
536C2×D11—41no—
537C2×D11—41no—
538C2×D11—41no—
539C2×D11—88no—
540C2×D11—88no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11#52512yes—
547C4×C11C22×#4112yes—
548Dic11—22no—
549Dic11—22no—
550Dic11—22no—
551Dic11—22no—
552Dic11—41no—
553Dic11—41no—
554Dic11—41no—
555C25—221no—
556C2×#41—111no—
557C2×#41—222no—
558C22×D4—21no—
559C22×D4—112no—
560C22×D4—112no—
561C22×D4—112no—
562C22×D4—228no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4C22×D1111yescharacteristic
567C23×C4—222no—
568C23×C4—222no—
569C23×C4C22×D1111yescharacteristic
570AGL(1,ℤ/8)—228no—
571C2×SD16—114no—
572C2×D8—114no—
573C2×D8—114no—
574C2×D8—114no—
575C2×D8—228no—
576C2×M16C22×D1112yes—
577C22×C8—112no—
578C4⋊Q8—112no—
579C4⋊Q8—221no—
580#127—112no—
581#126—222no—
582#126—222no—
583#125—112no—
584#125—221no—
585#124—112no—
586#124—222no—
587#124—222no—
588#123—222no—
589#123—222no—
590#123—222no—
591#123—222no—
592#123—221no—
593C22⋊Q8—111no—
594C22⋊Q8—111no—
595C22⋊Q8—222no—
596C22⋊Q8—222no—
597#121—21no—
598#121—21no—
599#121—111no—
600#121—111no—
601#121—222no—
602#121—222no—
603#121—221no—
604#121—221no—
605#121—222no—
606#121C22×D1112yes—
607#121C22×D1112yes—
608#120—222no—
609#120—221no—
610C4×Q8—112no—
611C4×D4—112no—
612C4×D4—112no—
613C4×D4—114no—
614C4×D4—114no—
615C4×D4—114no—
616C4×D4—114no—
617C4×D4—112no—
618C4×D4—222no—
619C4×D4—222no—
620C4×D4—222no—
621C4×D4—222no—
622C4×D4—224no—
623C4×D4—224no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4—222no—
629C4×D4—222no—
630C4×D4—221no—
631C4×D4—221no—
632C4×D4—222no—
633C4×D4—221no—
634C4×D4—221no—
635#117—21no—
636#117—21no—
637#117—112no—
638#117—111no—
639#117—111no—
640#117—111no—
641#117—111no—
642#117—112no—
643#117—111no—
644#117—222no—
645#117—221no—
646#117C22×D1112yes—
647#117C22×D1112yes—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—221no—
651C2×C4⋊C4C22×D1111yescharacteristic
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—224no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C42—21no—
665C2×C42—112no—
666#107—112no—
667#107—112no—
668#107C22×D1114yescomplemented
669#106—112no—
670#106—112no—
671#106C22×D1114yescomplemented
672C4⋊C8—114no—
673C4⋊C8—114no—
674#103—112no—
675#103—112no—
676#102—114no—
677#102—114no—
678#102—114no—
679#102—114no—
680#102—112no—
681#102—112no—
682#102C22×D1114yescomplemented
683#102C22×D1114yescomplemented
684C22⋊C8—111no—
685C22⋊C8—111no—
686C22⋊C8—112no—
687C22⋊C8C22×D1112yes—
688C22⋊C8C22×D1112yes—
689#97—114no—
690C4×C8—114no—
691C2×C11—22no—
692C2×C11—22no—
693C2×C11—41no—
694C2×C11—82no—
695C2×C11C2×#52511yescharacteristic
696C2×C11C2×#57611yescharacteristic
697C2×C11#358511yescharacteristic
698D11—48no—
699D11—81no—
700C24—21no—
701C24—228no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—882no—
706C24—882no—
707C24D4×D1111yescharacteristic
708#41—224no—
709#41—884no—
710C2×Q8—111no—
711C2×Q8—222no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—21no—
715C2×D4—24no—
716C2×D4—82no—
717C2×D4—118no—
718C2×D4—114no—
719C2×D4—111no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—222no—
726C2×D4—222no—
727C2×D4—221no—
728C2×D4—221no—
729C2×D4—221no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—224no—
734C2×D4C23×D1112yes—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—224no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—224no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—221no—
749C22×C4—884no—
750C22×C4—884no—
751C22×C4D4×D1111yescharacteristic
752C22×C4D4×D1111yescharacteristic
753C22×C4D4×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757SD16—228no—
758D8—228no—
759D8—228no—
760D8—228no—
761M16—24no—
762C2×C8—112no—
763C2×C8—112no—
764C2×C8—224no—
765C2×C8C23×D1114yes—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—111no—
770C4⋊C4—111no—
771C4⋊C4—111no—
772C4⋊C4—111no—
773C4⋊C4—112no—
774C4⋊C4—112no—
775C4⋊C4—111no—
776C4⋊C4—111no—
777C4⋊C4—222no—
778C4⋊C4—222no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—221no—
782C4⋊C4—221no—
783C4⋊C4C23×D1112yes—
784C4⋊C4C23×D1112yes—
785C4⋊C4C23×D1112yes—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—112no—
791C22⋊C4—112no—
792C22⋊C4—112no—
793C22⋊C4—112no—
794C22⋊C4—224no—
795C22⋊C4—224no—
796C22⋊C4—224no—
797C22⋊C4—224no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C22⋊C4—222no—
802C22⋊C4—222no—
803C22⋊C4—221no—
804C22⋊C4—221no—
805C22⋊C4—221no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C42—22no—
809C42—22no—
810C42—112no—
811C42—112no—
812C42—112no—
813C42—112no—
814C42—222no—
815C42—221no—
816C11#6057811yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—22no—
820C23—41no—
821C23—42no—
822C23—81no—
823C23—81no—
824C23—228no—
825C23—228no—
826C23—224no—
827C23—228no—
828C23—221no—
829C23—444no—
830C23—444no—
831C23—882no—
832C23—882no—
833C23—882no—
834C23—882no—
835C23—8816no—
836C23C2×D4×D1111yescharacteristic
837C23C2×D4×D1111yescharacteristic
838C23C2×D4×D1111yescharacteristic
839Q8—222no—
840Q8—882no—
841D4—24no—
842D4—44no—
843D4—42no—
844D4—82no—
845D4—118no—
846D4—228no—
847D4—228no—
848D4—228no—
849D4—224no—
850D4—222no—
851D4—442no—
852D4—442no—
853D4—882no—
854D4—882no—
855D4—881no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—81no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—224no—
872C2×C4—221no—
873C2×C4—221no—
874C2×C4—221no—
875C2×C4—442no—
876C2×C4—442no—
877C2×C4—884no—
878C2×C4—884no—
879C2×C4—884no—
880C2×C4—884no—
881C2×C4—882no—
882C2×C4—882no—
883C2×C4—882no—
884C2×C4C2×D4×D1111yescharacteristic
885C2×C4C2×D4×D1111yescharacteristic
886C2×C4C2×D4×D1111yescharacteristic
887C2×C4#41×D1114yes—
888C2×C4C24×D1111yescharacteristic
889C8—24no—
890C8—222no—
891C8—222no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—44no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—162no—
904C22—228no—
905C22—4416no—
906C22—444no—
907C22—444no—
908C22—441no—
909C22—441no—
910C22—441no—
911C22—888no—
912C22—888no—
913C22#1062318712yes—
914C22#1062330512yes—
915C22C22×D4×D1111yescharacteristic
916C4—21no—
917C4—21no—
918C4—42no—
919C4—42no—
920C4—42no—
921C4—222no—
922C4—222no—
923C4—222no—
924C4—222no—
925C4—441no—
926C4—441no—
927C4—441no—
928C4#1062318712yes—
929C4C2×#41×D1112yes—
930C2—22no—
931C2—22no—
932C2—41no—
933C2—82no—
934C2—448no—
935C2—881no—
936C2C2×#1062318711yescharacteristic
937C2C2×#1062330511yescharacteristic
938C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3094C2
socleC22×C11C23×D4
hypercenter#3094D11
hypocenterC11#60578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #13082345C2semidirect
2. C2×#10623052C2semidirect
3. #13078855C2semidirect
4. #13078795C2semidirect
5. #13078751C2semidirect
6. #13078704C2semidirect
7. #13078660C2semidirect
8. #13078613C2semidirect
9. #13078529C2semidirect
10. #13078445C2semidirect
11. #13078118C2semidirect
12. #13077846C2semidirect
13. C2×#10622649C2semidirect
14. #13077464C2semidirect
15. #13077446C2semidirect
16. #13077276C2semidirect
17. C11×#3094C2semidirect
22. #10623336C22semidirect
23. #10623329C22semidirect
28. #10623150C22semidirect
33. #10623134C22semidirect
34. #10623131C22semidirect
35. #10623127C22semidirect
41. #10623052C22semidirect
42. #10623035C22semidirect
43. C2×#66946C22semidirect
44. C2×#66946C22semidirect
45. #10623031C22semidirect
50. C11×#482C22semidirect
51. C11×#481C22semidirect
52. C11×#480C22semidirect
53. C11×#428C22semidirect
54. C11×#418C22semidirect
58. #10622735C22semidirect
59. #10622732C22semidirect
63. #10622616C22semidirect
64. #10622615C22semidirect
65. #10622611C22semidirect
66. #10622609C22semidirect
67. #10622584C22semidirect
68. #10622583C22semidirect
69. #10622581C22semidirect
70. #10622580C22semidirect
72. #10622504C22semidirect
73. #10622503C22semidirect
74. #10622502C22semidirect
75. #10622485C22semidirect
76. #10622484C22semidirect
77. #10622483C22semidirect
78. #10622482C22semidirect
79. #10622465C22semidirect
80. #10622400C22semidirect
81. #10622400C22semidirect
82. #10622399C22semidirect
83. #10622399C22semidirect
84. #10622398C22semidirect
85. #10622398C22semidirect
86. #10622369C22semidirect
87. #10622369C22semidirect
88. #10622345C22semidirect
89. #10622345C22semidirect
90. #10622344C22semidirect
91. #10622344C22semidirect
92. #10622333C22semidirect
93. #10622332C22semidirect
94. #10622331C22semidirect
129. #66993C23semidirect
136. #66989C23semidirect
142. D4×Dic11C23semidirect
143. D4×Dic11C23semidirect
180. #66946C23semidirect
184. #66943C23semidirect
186. #66941C23semidirect
187. #66940C23semidirect
206. C11×#107C23semidirect
207. C11×#106C23semidirect
208. C11×#102C23semidirect
209. C11×#102C23semidirect
217. #66879C23semidirect
218. Dic11⋊C8C23semidirect
219. Dic11⋊C8C23semidirect
220. C8×Dic11C23semidirect
221. #66874C23semidirect
222. #66874C23semidirect
225. #66873C23semidirect
226. #66873C23semidirect
227. #66872C23semidirect
228. #66872C23semidirect
229. #66871C23semidirect
230. #66871C23semidirect
276. C2×D44#41semidirect
356. #3094D11semidirect
476. #482C2×D11semidirect
478. #481C2×D11semidirect
480. #480C2×D11semidirect
507. #428C2×D11semidirect
511. #418C2×D11semidirect
668. #107C22×D11semidirect
671. #106C22×D11semidirect
682. #102C22×D11semidirect
683. #102C22×D11semidirect
816. C11#60578semidirect

Maximal subgroups

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

subgroupindex
#130823452
C2×#106230522
#130788552
#130787952
#130787512
#130787042
#130786602
#130786132
#130785292
#130784452
#130781182
#130778462
C2×#106226492
#130774642
#130774462
#130772762
C11×#30942
#6057811