Finite Group Databasebeta

← #15622521

Subgroups — #15622521

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#13082362C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13078864C214yesmaximal, complemented
4#13078803C214yesmaximal, complemented
5#13078757C212yesmaximal, complemented
6#13078712C212yesmaximal, complemented
7#13078666C212yesmaximal, complemented
8#13078621C212yesmaximal, complemented
9#13078529C211yesmaximal, characteristic, complemented
10#13078445C212yesmaximal, complemented
11#13078127C212yesmaximal, complemented
12#13077846C211yesmaximal, characteristic
13C2×#10622659C211yesmaximal, characteristic, complemented
14#13077471C212yesmaximal, complemented
15#13077446C212yesmaximal, complemented
16#13077276C211yesmaximal, characteristic, complemented
17C11×#3095C211yesmaximal, characteristic, complemented
18C23×D44C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21#10623347C2211yescharacteristic, complemented
22#10623343C2211yescharacteristic, complemented
23C22×#4325C2212yes—
24#10623322C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C2×#66961C2212yes—
27#10623174C2212yescomplemented
28#10623173—21no—
29#10623172—21no—
30#10623170—21no—
31#10623166—21no—
32#10623156C2212yescomplemented
33#10623155C2212yescomplemented
34#10623153C2212yescomplemented
35#10623052—22no—
36#10623052—21no—
37#10623052—21no—
38#10623052C2214yes—
39#10623052C2212yes—
40#10623052C2212yes—
41#10623044—22no—
42#10623035C2211yescharacteristic, complemented
43C2×#66946C2212yes—
44C2×#66946C2212yes—
45#10623031C2211yescharacteristic, complemented
46#10623026—22no—
47C2×C22⋊C4×D11—22no—
48C2×C4×D44—21no—
49C2×C4×D44—21no—
50C11×#485C2214yescomplemented
51C11×#484C2212yescomplemented
52C11×#483C2212yescomplemented
53C11×#428C2212yescomplemented
54C11×#419C2212yescomplemented
55C11×#407C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic
57#10622744C2212yes—
58#10622735C2212yescomplemented
59#10622732C2212yescomplemented
60#10622659C2214yes—
61#10622659C2212yes—
62#10622659C2212yes—
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#10622432C2214yescomplemented
81#10622432C2214yescomplemented
82#10622431C2214yescomplemented
83#10622431C2214yescomplemented
84#10622430C2214yescomplemented
85#10622430C2214yescomplemented
86#10622401C2214yescomplemented
87#10622401C2214yescomplemented
88#10622345C2212yes—
89#10622345C2212yes—
90#10622344C2212yes—
91#10622344C2212yes—
92#10622333C2214yescomplemented
93#10622332C2212yescomplemented
94#10622331C2212yescomplemented
95C24×D11—21no—
96C22×Q8×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C2×#4339C2311yescharacteristic
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—28no—
103C22×D44C2312yes—
104C22×D44C2312yes—
105C22×D44C2312yes—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C2×C11×M16C2312yes—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8C2312yes—
112C11×C22⋊Q8C2312yes—
113C11×#117—21no—
114C11×#117—21no—
115C11×#117C2312yes—
116C11×#117C2312yes—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C42×C11—21no—
124#67006—21no—
125C2×C22⋊Dic11D412yes—
126#67000C2312yescomplemented
127#66999—21no—
128#66999—21no—
129Q8×Dic11—21no—
130Q8×Dic11—21no—
131Q8×Dic11C2312yescomplemented
132Q8×Dic11C2312yescomplemented
133#66997C2312yescomplemented
134C2×#4325—28no—
135C2×#4325C2314yes—
136C2×#4325C2314yes—
137#66983C2311yescharacteristic
138#66983C2311yescharacteristic
139#66982—21no—
140#66982—22no—
141C4×C22⋊D11—21no—
142C4×C22⋊D11—21no—
143C4×C22⋊D11—22no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—22no—
146#66979—22no—
147#66979D412yes—
148#66979D411yescharacteristic
149#66979D411yescharacteristic
150#66979C2311yescharacteristic
151#66979C2311yescharacteristic
152#66979C2311yescharacteristic
153#66979C2312yes—
154C2×C4⋊Dic11D411yescharacteristic
155C2×C4⋊Dic11D411yescharacteristic
156#66977—22no—
157#66977C2311yescharacteristic
158#66977C2311yescharacteristic
159C2×C4×Dic11C2312yes—
160C22×C11⋊C8C2312yes—
161#66961—28no—
162C2×D88C2314yes—
163C2×#4314C2314yes—
164#66951—22no—
165#66951—22no—
166#66950—22no—
167#66946—22no—
168#66946—22no—
169#66946—22no—
170#66946—22no—
171#66946C2314yes—
172#66946C2314yes—
173#66946C2314yes—
174#66946C2314yes—
175#66946C2312yescomplemented
176#66945—21no—
177#66945—22no—
178C4⋊C4×D11—21no—
179#66943—21no—
180#66943—22no—
181#66943C2312yescomplemented
182#66942—22no—
183#66942—22no—
184#66941—21no—
185#66941C2312yescomplemented
186#66940—22no—
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—24no—
202C4×D44—24no—
203C4×D44—22no—
204C4×D44—22no—
205C4×D44—22no—
206C11×#107C2314yescomplemented
207C11×#106C2314yescomplemented
208C11×#103C2314yescomplemented
209C11×#103C2314yescomplemented
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#60579—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—22no—
234C23×D11—28no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—82no—
238C23×D11—82no—
239C2×Q8×C11—21no—
240C2×Q8×C11—24no—
241C2×Q8×C11C2412yes—
242C22×C4×C11—24no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—21no—
254C2×C22⋊D11—21no—
255C2×C22⋊D11—21no—
256C22×Dic11C2×D412yes—
257C22×Dic11C2×D412yes—
258#4339—24no—
259C2×D44—28no—
260C2×D44—28no—
261C2×D44—28no—
262C2×D44—28no—
263C2×D44—28no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44—22no—
267C2×D44—24no—
268C2×D44#4118yes—
269C2×D44C2411yescharacteristic
270C2×D44C2414yes—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—24no—
275C2×C4×D11—22no—
276C2×C4×D11—21no—
277C2×C4×D11—84no—
278C2×C4×D11—84no—
279C2×Dic22—22no—
280C2×Dic22C2411yescharacteristic
281C11×M16—24no—
282C2×C8×C11C2414yes—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2412yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C42×C11—22no—
296C42×C11—22no—
297C22⋊Dic11—21no—
298C22⋊Dic11—21no—
299C22⋊Dic11—21no—
300C22⋊Dic11C2×D412yes—
301C22⋊Dic11C2×D412yes—
302C22⋊Dic11C2×D412yes—
303C22⋊Dic11C2×D412yes—
304#4325—28no—
305#4325—28no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—21no—
314(C2×D11)⋊C4—21no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11C2×D411yescharacteristic
319C4⋊Dic11C2×D412yes—
320C4⋊Dic11C2×D412yes—
321C4⋊Dic11C2×D411yescharacteristic
322C4⋊Dic11C2×D411yescharacteristic
323C4⋊Dic11C2×D411yescharacteristic
324C4⋊Dic11C2411yescharacteristic
325C4⋊Dic11C2411yescharacteristic
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—21no—
332Dic11⋊C4—21no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—21no—
337C4×Dic11C2×D412yes—
338C4×Dic11C2×D412yes—
339C4×Dic11C2412yes—
340C4×Dic11C2412yes—
341C2×C11⋊C8—24no—
342C2×C11⋊C8C2412yes—
343C2×C11⋊C8C2412yes—
344D88—28no—
345#4314—28no—
346#3495—111no—
347C2×#518—111no—
348#3123—114no—
349#3118—114no—
350#3114—112no—
351#3110—112no—
352#3105—112no—
353#3101—112no—
354#3095D1111yescharacteristic, complemented
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—22no—
364C23×C11—22no—
365C23×C11—41no—
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—28no—
370C22×D11—24no—
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—21no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—82no—
377C22×D11—82no—
378C22×D11—82no—
379C22×D11—82no—
380C22×D11—816no—
381Q8×C11—24no—
382Q8×C11—42no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—81no—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C2×#4114yes—
400C2×C4×C11C2511yescharacteristic
401C22⋊D11—42no—
402C22⋊D11—42no—
403C22⋊D11—81no—
404C2×Dic11—24no—
405C2×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—42no—
409C2×Dic11C22×D412yes—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412C2×Dic11C22×D412yes—
413D44—28no—
414D44—28no—
415D44—28no—
416D44—24no—
417D44—22no—
418D44C2×#4118yes—
419C4×D11—42no—
420C4×D11—82no—
421C4×D11—84no—
422C4×D11—84no—
423C4×D11—84no—
424C4×D11—84no—
425Dic22—22no—
426Dic22—82no—
427C8×C11—24no—
428C11⋊C8—22no—
429C11⋊C8—22no—
430C23×D4—111no—
431C2×AGL(1,ℤ/8)—112no—
432C22×SD16—112no—
433#556—221no—
434#554—221no—
435#552—222no—
436#552—221no—
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⋊Q8C2×D1111yescharacteristic
447#520—111no—
448#519—111no—
449#518—112no—
450#518—114no—
451#518—112no—
452#518—222no—
453#518—221no—
454#518—221no—
455C2×C4×D4—112no—
456C2×C4×D4—112no—
457C2×C4×D4—221no—
458C2×C4×D4—221no—
459C2×#117—111no—
460C2×#117C2×D1111yescharacteristic
461C22×C22⋊C4—222no—
462#485—112no—
463#485C2×D1114yescomplemented
464#484—111no—
465#484C2×D1112yescomplemented
466#483—111no—
467#483C2×D1112yescomplemented
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—114no—
482#450—112no—
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#428C2×D1112yescomplemented
498#427—112no—
499#424—112no—
500#419C2×D1112yescomplemented
501#418—112no—
502#416—112no—
503C2×#102—112no—
504#407C2×D1111yescharacteristic
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—21no—
514C22×C11—44no—
515C22×C11#52512yes—
516C22×C11#57712yes—
517C22×C11C23×D411yescharacteristic
518C2×D11—28no—
519C2×D11—416no—
520C2×D11—44no—
521C2×D11—44no—
522C2×D11—41no—
523C2×D11—41no—
524C2×D11—41no—
525C2×D11—88no—
526C2×D11—88no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11#52512yes—
534C4×C11C22×#4112yes—
535Dic11—22no—
536Dic11—22no—
537Dic11—22no—
538Dic11—22no—
539Dic11—41no—
540Dic11—41no—
541Dic11—41no—
542C25—221no—
543C2×#41—111no—
544C22×Q8C22×D1111yescharacteristic
545C22×D4—112no—
546C22×D4—112no—
547C22×D4—112no—
548C22×D4—228no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C23×C4—222no—
553C23×C4—222no—
554C23×C4C22×D1111yescharacteristic
555AGL(1,ℤ/8)—228no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—114no—
559C2×SD16—228no—
560C2×D8—114no—
561C2×M16C22×D1112yes—
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—222no—
574#125—221no—
575#124—112no—
576#124—222no—
577#123—222no—
578#123—222no—
579#123—222no—
580#123—221no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—111no—
584C22⋊Q8—111no—
585C22⋊Q8—222no—
586C22⋊Q8—222no—
587C22⋊Q8—222no—
588C22⋊Q8—221no—
589C22⋊Q8—221no—
590C22⋊Q8C22×D1112yes—
591C22⋊Q8C22×D1112yes—
592#121—111no—
593#121—111no—
594#120—221no—
595C4×Q8—112no—
596C4×Q8—112no—
597C4×Q8—112no—
598C4×Q8—222no—
599C4×Q8—221no—
600C4×Q8—221no—
601C4×D4—114no—
602C4×D4—114no—
603C4×D4—114no—
604C4×D4—114no—
605C4×D4—112no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—224no—
610C4×D4—222no—
611C4×D4—224no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4—222no—
615C4×D4—222no—
616C4×D4—222no—
617C4×D4—222no—
618C4×D4—221no—
619C4×D4—221no—
620#117—21no—
621#117—21no—
622#117—111no—
623#117—112no—
624#117—111no—
625#117—111no—
626#117—111no—
627#117—112no—
628#117—111no—
629#117—222no—
630#117—222no—
631#117—222no—
632#117—221no—
633#117C22×D1112yes—
634#117C22×D1112yes—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1111yescharacteristic
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—224no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—224no—
648C2×C22⋊C4—224no—
649C2×C22⋊C4—222no—
650C2×C22⋊C4—222no—
651C2×C42—21no—
652C2×C42—112no—
653#107—112no—
654#107—112no—
655#107C22×D1114yescomplemented
656#106—112no—
657#106—112no—
658#106C22×D1114yescomplemented
659C4⋊C8—114no—
660C4⋊C8—114no—
661#103—112no—
662#103—112no—
663#103C22×D1114yescomplemented
664#103C22×D1114yescomplemented
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⋊C8C22×D1112yes—
675C22⋊C8C22×D1112yes—
676#97—114no—
677C4×C8—114no—
678C2×C11—22no—
679C2×C11—22no—
680C2×C11—41no—
681C2×C11C2×#52511yescharacteristic
682C2×C11C2×#57711yescharacteristic
683C2×C11#358511yescharacteristic
684D11—48no—
685D11—81no—
686C24—228no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—882no—
691C24—882no—
692C24D4×D1111yescharacteristic
693#41—224no—
694C2×Q8—21no—
695C2×Q8—24no—
696C2×Q8—111no—
697C2×Q8—222no—
698C2×Q8C23×D1112yes—
699C2×D4—118no—
700C2×D4—114no—
701C2×D4—111no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—221no—
708C2×D4—221no—
709C2×D4—221no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—224no—
714C22×C4—24no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—224no—
722C22×C4—224no—
723C22×C4—224no—
724C22×C4—224no—
725C22×C4—222no—
726C22×C4—221no—
727C22×C4—884no—
728C22×C4—884no—
729C22×C4D4×D1111yescharacteristic
730C22×C4D4×D1111yescharacteristic
731C22×C4D4×D1111yescharacteristic
732C22×C4C23×D1111yescharacteristic
733C22×C4C23×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735SD16—228no—
736SD16—228no—
737SD16—228no—
738D8—228no—
739M16—24no—
740C2×C8—112no—
741C2×C8—112no—
742C2×C8—224no—
743C2×C8C23×D1114yes—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—111no—
750C4⋊C4—111no—
751C4⋊C4—112no—
752C4⋊C4—111no—
753C4⋊C4—111no—
754C4⋊C4—112no—
755C4⋊C4—111no—
756C4⋊C4—111no—
757C4⋊C4—222no—
758C4⋊C4—222no—
759C4⋊C4—222no—
760C4⋊C4—222no—
761C4⋊C4—222no—
762C4⋊C4—222no—
763C4⋊C4—222no—
764C4⋊C4—222no—
765C4⋊C4—221no—
766C4⋊C4—221no—
767C4⋊C4C23×D1112yes—
768C4⋊C4C23×D1112yes—
769C4⋊C4C23×D1112yes—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—112no—
775C22⋊C4—112no—
776C22⋊C4—112no—
777C22⋊C4—112no—
778C22⋊C4—224no—
779C22⋊C4—224no—
780C22⋊C4—224no—
781C22⋊C4—224no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—221no—
786C22⋊C4—221no—
787C22⋊C4—221no—
788C22⋊C4—221no—
789C22⋊C4—221no—
790C42—22no—
791C42—22no—
792C42—112no—
793C42—112no—
794C42—112no—
795C42—112no—
796C42—222no—
797C42—222no—
798C42—222no—
799C42—221no—
800C11#6057911yescharacteristic, complemented, Sylow
801C23—22no—
802C23—22no—
803C23—41no—
804C23—228no—
805C23—228no—
806C23—224no—
807C23—228no—
808C23—221no—
809C23—444no—
810C23—444no—
811C23—882no—
812C23—882no—
813C23—882no—
814C23—882no—
815C23—8816no—
816C23C2×D4×D1111yescharacteristic
817C23C2×D4×D1111yescharacteristic
818C23C2×D4×D1111yescharacteristic
819Q8—24no—
820Q8—42no—
821Q8—222no—
822Q8—882no—
823D4—118no—
824D4—228no—
825D4—228no—
826D4—228no—
827D4—224no—
828D4—222no—
829D4—442no—
830D4—442no—
831D4—881no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—81no—
845C2×C4—112no—
846C2×C4—112no—
847C2×C4—112no—
848C2×C4—112no—
849C2×C4—224no—
850C2×C4—221no—
851C2×C4—221no—
852C2×C4—221no—
853C2×C4—442no—
854C2×C4—442no—
855C2×C4—884no—
856C2×C4—884no—
857C2×C4—884no—
858C2×C4—884no—
859C2×C4—882no—
860C2×C4C2×D4×D1111yescharacteristic
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4C2×D4×D1111yescharacteristic
863C2×C4#41×D1114yes—
864C2×C4C24×D1111yescharacteristic
865C8—24no—
866C8—222no—
867C8—222no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—228no—
877C22—4416no—
878C22—444no—
879C22—444no—
880C22—441no—
881C22—441no—
882C22—441no—
883C22—888no—
884C22—888no—
885C22#1062318712yes—
886C22#1062330912yes—
887C22C22×D4×D1111yescharacteristic
888C4—21no—
889C4—21no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—222no—
895C4—222no—
896C4—222no—
897C4—222no—
898C4—441no—
899C4—441no—
900C4—441no—
901C4#1062318712yes—
902C4C2×#41×D1112yes—
903C2—22no—
904C2—22no—
905C2—41no—
906C2—448no—
907C2—881no—
908C2C2×#1062318711yescharacteristic
909C2C2×#1062330911yescharacteristic
910C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3095C2
socleC22×C11C23×D4
prime radical#13077846C2
hypercenter#3095D11
hypocenterC11#60579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. #13082362C2semidirect
2. C2×#10623052C2semidirect
3. #13078864C2semidirect
4. #13078803C2semidirect
5. #13078757C2semidirect
6. #13078712C2semidirect
7. #13078666C2semidirect
8. #13078621C2semidirect
9. #13078529C2semidirect
10. #13078445C2semidirect
11. #13078127C2semidirect
13. C2×#10622659C2semidirect
14. #13077471C2semidirect
15. #13077446C2semidirect
16. #13077276C2semidirect
17. C11×#3095C2semidirect
21. #10623347C22semidirect
22. #10623343C22semidirect
27. #10623174C22semidirect
32. #10623156C22semidirect
33. #10623155C22semidirect
34. #10623153C22semidirect
42. #10623035C22semidirect
45. #10623031C22semidirect
50. C11×#485C22semidirect
51. C11×#484C22semidirect
52. C11×#483C22semidirect
53. C11×#428C22semidirect
54. C11×#419C22semidirect
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. #10622432C22semidirect
81. #10622432C22semidirect
82. #10622431C22semidirect
83. #10622431C22semidirect
84. #10622430C22semidirect
85. #10622430C22semidirect
86. #10622401C22semidirect
87. #10622401C22semidirect
92. #10622333C22semidirect
93. #10622332C22semidirect
94. #10622331C22semidirect
126. #67000C23semidirect
131. Q8×Dic11C23semidirect
132. Q8×Dic11C23semidirect
133. #66997C23semidirect
175. #66946C23semidirect
181. #66943C23semidirect
185. #66941C23semidirect
187. #66940C23semidirect
206. C11×#107C23semidirect
207. C11×#106C23semidirect
208. C11×#103C23semidirect
209. C11×#103C23semidirect
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
354. #3095D11semidirect
463. #485C2×D11semidirect
465. #484C2×D11semidirect
467. #483C2×D11semidirect
497. #428C2×D11semidirect
500. #419C2×D11semidirect
655. #107C22×D11semidirect
658. #106C22×D11semidirect
663. #103C22×D11semidirect
664. #103C22×D11semidirect
800. C11#60579semidirect

Maximal subgroups

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

subgroupindex
#130823622
C2×#106230522
#130788642
#130788032
#130787572
#130787122
#130786662
#130786212
#130785292
#130784452
#130781272
#130778462
C2×#106226592
#130774712
#130774462
#130772762
C11×#30952
#6057911