Finite Group Databasebeta

← #15633664

Subgroups — #15633664

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081346C214yesmaximal, complemented
4#13081343C212yesmaximal, complemented
5#13081324C214yesmaximal, complemented
6#13081321C212yesmaximal, complemented
7#13081285C212yesmaximal, complemented
8#13081249C212yesmaximal, complemented
9#13078991C211yesmaximal, characteristic, complemented
10#13078988C212yesmaximal, complemented
11#13078413C211yesmaximal, characteristic, complemented
12#13078412C212yesmaximal, complemented
13#13078096C211yesmaximal, characteristic, complemented
14#13078094C212yesmaximal, complemented
15M16×Dic22C211yesmaximal, characteristic, complemented
16#13077429C212yesmaximal, complemented
17C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
18C22×#4339—21no—
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22#41×Dic11C2212yes—
23C2×#67002C2212yes—
24C2×#66993C2212yes—
25C2×#66983—21no—
26#10623101C2211yescharacteristic, complemented
27#10623100C2212yescomplemented
28Q8×Dic22C2211yescharacteristic, complemented
29#10623084—21no—
30#10623084—21no—
31#10623084—22no—
32#10623084C2214yes—
33#10623084C2212yes—
34#10623084C2212yes—
35#10623074—21no—
36#10623074C2211yescharacteristic, complemented
37#10623070—22no—
38#10623070C2212yescomplemented
39D4×Dic22—21no—
40D4×Dic22C2211yescharacteristic, complemented
41#10623048—22no—
42#10623048C2212yes—
43C2×#66946C2212yes—
44C2×#66937—22no—
45C2×#66927C2211yescharacteristic
46#10623001—21no—
47#10623001C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22C2211yescharacteristic
50C11×#442C2212yescomplemented
51C11×#440C2212yescomplemented
52C4×C11×SD16C2212yescomplemented
53C4×C11×D8C2212yescomplemented
54C11×#428C2211yescharacteristic
55C11×#418C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C4×C11×M16C2211yescharacteristic
58#10622828C2212yes—
59#10622776C2214yescomplemented
60#10622776C2214yescomplemented
61#10622763C2214yescomplemented
62#10622763C2214yescomplemented
63#10622744C2212yes—
64#10622744C2212yes—
65#10622731C2212yes—
66M16×Dic11C2212yes—
67#10622640C2212yescomplemented
68#10622640C2212yescomplemented
69#10622628C2212yescomplemented
70#10622628C2212yescomplemented
71#10622622C2214yescomplemented
72#10622621C2212yescomplemented
73#10622620C2212yescomplemented
74#10622614C2212yes—
75#10622577C2212yes—
76#10622537C2211yescharacteristic
77#10622504C2214yescomplemented
78#10622503C2214yescomplemented
79#10622484C2214yescomplemented
80#10622483C2214yescomplemented
81#10622430C2214yescomplemented
82#10622401C2214yescomplemented
83#10622398C2214yescomplemented
84#10622377C2214yescomplemented
85#10622377C2214yescomplemented
86#10622373C2214yescomplemented
87#10622373C2214yescomplemented
88#10622369C2214yescomplemented
89#10622326C2214yescomplemented
90#10622314C2214yescomplemented
91#10622307C2212yescomplemented
92#10622307C2212yescomplemented
93#10622292C2212yescomplemented
94C8×Dic22C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C22×C22⋊D11—22no—
99C22×C22⋊D11—22no—
100C2×#4339—22no—
101C2×#4339—24no—
102C2×#4339—22no—
103C2×#4339—48no—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44C2312yes—
107C22×C4×D11—22no—
108C22×Dic22—21no—
109C22×Dic22D411yescharacteristic
110C11×AGL(1,ℤ/8)—24no—
111C2×C11×SD16C2312yes—
112C2×C11×D8C2312yes—
113C2×C11×M16C2311yescharacteristic
114C2×C11×M16C2311yescharacteristic
115C4×Q8×C11C2311yescharacteristic
116C4×Q8×C11C2311yescharacteristic
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11C2311yescharacteristic
122C4×D4×C11C2311yescharacteristic
123C4×D4×C11C2312yes—
124C4×D4×C11C2312yes—
125C11×#117—21no—
126C11×#117C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4—21no—
129C2×C42×C11—21no—
130C2×C42×C11C2311yescharacteristic
131#67002—28no—
132Q8×Dic11C2312yes—
133Q8×Dic11C2312yes—
134C2×#4325C2314yes—
135#66993—22no—
136#66993—22no—
137#66993C2314yes—
138#66993C2314yes—
139D4×Dic11—22no—
140D4×Dic11—22no—
141D4×Dic11C2312yes—
142D4×Dic11C2312yes—
143C2×#4323C2314yes—
144#66983—22no—
145#66983—22no—
146#66983—24no—
147C2×(C2×D11)⋊C4—22no—
148#66979—22no—
149#66979C2312yes—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11D411yescharacteristic
152#66977—21no—
153#66977—21no—
154#66977—21no—
155#66977—21no—
156#66977—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4D412yes—
159C2×C4×Dic11—22no—
160C2×C4×Dic11C2312yes—
161C2×#4318C2312yes—
162#66946—22no—
163#66946—22no—
164#66946C2314yes—
165#66946C2314yes—
166#66943—22no—
167#66943—22no—
168#66943C2312yes—
169#66943C2312yes—
170#66941—22no—
171#66941—22no—
172#66941C2312yes—
173#66941C2312yes—
174#66937—24no—
175#66937—24no—
176#66937—24no—
177#66937—24no—
178#66931—22no—
179#66931—22no—
180#66931—22no—
181#66931—22no—
182#66931—22no—
183#66931—22no—
184#66927—21no—
185#66927—21no—
186#66927C2312yes—
187#66927C2312yes—
188#66923—22no—
189#66923C2312yes—
190#66922—21no—
191#66922—21no—
192#66922C2311yescharacteristic
193#66922C2311yescharacteristic
194C4×Dic22—21no—
195C4×Dic22—21no—
196C4×Dic22—21no—
197C4×Dic22—21no—
198C4×Dic22—22no—
199C4×Dic22—22no—
200C4×Dic22—22no—
201C4×Dic22D411yescharacteristic
202C4×Dic22D411yescharacteristic
203C4×Dic22D412yes—
204C4×Dic22C2311yescharacteristic
205C4×Dic22C2311yescharacteristic
206C4×Dic22C2312yes—
207C11×#107C2312yes—
208C11×#106C2312yes—
209C11×#103C2312yes—
210C11×#102C2312yes—
211C11×#102C2312yes—
212C11×#102C2312yes—
213C11×#97C2312yes—
214C4×C8×C11C2312yes—
215#66896C2314yes—
216#66896C2314yes—
217#66885C2314yes—
218#66885C2314yes—
219#66885C2314yes—
220#66885C2314yes—
221#66879C2314yes—
222Dic11⋊C8C2314yes—
223Dic11⋊C8C2314yes—
224C8×Dic11C2314yes—
225#66873C2314yes—
226#66873C2314yes—
227#66872C2314yes—
228#66871C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#61321—111nomaximal, Sylow
232C24×C11—21no—
233C23×D11—22no—
234C11×#41—22no—
235C11×#41#4114yescomplemented
236C2×Q8×C11C2411yescharacteristic
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11C2412yes—
242C2×D4×C11C2411yescharacteristic
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—21no—
249C22×C4×C11—44no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—48no—
258C2×C22⋊D11—84no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263#4339—416no—
264#4339—48no—
265#4339—48no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—22no—
270C2×D44—22no—
271C2×D44—24no—
272C2×D44—24no—
273C2×D44—44no—
274C2×D44—82no—
275C2×D44C2414yes—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—48no—
279C2×Dic22—24no—
280C2×Dic22—22no—
281C2×Dic22—22no—
282C2×Dic22—21no—
283C2×Dic22—21no—
284C2×Dic22—44no—
285C2×Dic22C2×D411yescharacteristic
286C2×Dic22C2×D412yes—
287C2×Dic22C2×D411yescharacteristic
288C11×SD16—24no—
289C11×D8—24no—
290C11×M16—22no—
291C11×M16—22no—
292C2×C8×C11C2412yes—
293C2×C8×C11C2412yes—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2411yescharacteristic
299C11×C4⋊C4C2411yescharacteristic
300C11×C22⋊C4—21no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C42×C11—21no—
306C42×C11—21no—
307C42×C11—21no—
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2411yescharacteristic
311C42×C11C2411yescharacteristic
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314C22⋊Dic11—22no—
315#4325—28no—
316#4323—28no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2×D411yescharacteristic
326C4⋊Dic11C2×D411yescharacteristic
327C4⋊Dic11C2×D412yes—
328C4⋊Dic11C2412yes—
329C4⋊Dic11C2412yes—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4C2×D412yes—
337Dic11⋊C4C2×D412yes—
338Dic11⋊C4C2×D412yes—
339Dic11⋊C4C2×D412yes—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11C2×D412yes—
344C4×Dic11C2×D412yes—
345C4×Dic11C2412yes—
346C4×Dic11C2412yes—
347#4318—24no—
348C2×C11⋊C8C2414yes—
349Q8×#41—111no—
350C2×#550—111no—
351#3368—114no—
352#3368—112no—
353#3366—114no—
354#3366—112no—
355#3362—112no—
356#3358—112no—
357#3138—112no—
358#3138—111no—
359#3077—112no—
360#3077—111no—
361#3038—112no—
362#3038—111no—
363Q8×M16—111no—
364C4×AGL(1,ℤ/8)—112no—
365C4×AGL(1,ℤ/8)D1111yescharacteristic, complemented
366C23×C11—21no—
367C23×C11—22no—
368C23×C11—42no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11C22×D411yescharacteristic
372C22×D11—24no—
373C22×D11—44no—
374C22×D11—44no—
375C22×D11—44no—
376Q8×C11—21no—
377Q8×C11C2×#4112yescomplemented
378D4×C11—24no—
379D4×C11—22no—
380D4×C11—21no—
381D4×C11—22no—
382D4×C11—42no—
383D4×C11C2×#4112yescomplemented
384C2×C4×C11—21no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—22no—
390C2×C4×C11—41no—
391C2×C4×C11—44no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—44no—
395C2×C4×C11—81no—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C2×#4112yes—
402C2×C4×C112−1+412yes—
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—48no—
405C22⋊D11—48no—
406C22⋊D11—84no—
407C22⋊D11—84no—
408C2×Dic11—24no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—42no—
412C2×Dic11—44no—
413C2×Dic11—82no—
414C2×Dic11C22×D412yes—
415C2×Dic11C22×D412yes—
416C2×Dic11C22×D412yes—
417C2×Dic11C22×D412yes—
418D44—24no—
419D44—24no—
420D44—44no—
421D44—44no—
422D44—44no—
423D44—82no—
424D44—82no—
425C4×D11—48no—
426C4×D11—48no—
427Dic22—22no—
428Dic22—24no—
429Dic22—42no—
430Dic22—44no—
431Dic22—82no—
432Dic22—81no—
433Dic22AGL(1,ℤ/8)14yescomplemented
434C8×C11—22no—
435C8×C11—22no—
436C11⋊C8—24no—
437C22×#41—221no—
438C2×AGL(1,ℤ/8)—112no—
439C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
440Q82—111no—
441#557—112no—
442#557—111no—
443#554—112no—
444#554—111no—
445#554—222no—
446#554—221no—
447#550—112no—
448#550—114no—
449#550—112no—
450#550—221no—
451#550—221no—
452#550—222no—
453D4×Q8—111no—
454D4×Q8—221no—
455#533—112no—
456#533—111no—
457#533—221no—
458#533—222no—
459C2×#127—112no—
460C2×#127—111no—
461C2×#121—222no—
462C2×#121—221no—
463C4×#41—112no—
464C4×#41C2×D1111yescharacteristic
465C2×C4×Q8—111no—
466C2×C4×Q8—221no—
467C2×C4×D4—112no—
468C2×C4×D4C2×D1111yescharacteristic
469#490—114no—
470#490—114no—
471#490—114no—
472#486—114no—
473#486—114no—
474#486—112no—
475#486—112no—
476#478—114no—
477#478—114no—
478#478—114no—
479#476—112no—
480#476—114no—
481#474—112no—
482#474—114no—
483#460—114no—
484#460—114no—
485#460—112no—
486#460—112no—
487#459—114no—
488#459—114no—
489#459—112no—
490#459—112no—
491#446—114no—
492#446—112no—
493C8×Q8—112no—
494#442—114no—
495#442C2×D1112yescomplemented
496#440—114no—
497#440C2×D1112yescomplemented
498C4×SD16—114no—
499C4×SD16C2×D1112yescomplemented
500C4×D8—114no—
501C4×D8C2×D1112yescomplemented
502#428—112no—
503#428C2×D1111yescharacteristic
504#423—112no—
505#423—111no—
506#418—112no—
507#418—112no—
508#418—112no—
509#418—112no—
510#418C2×D1111yescharacteristic
511#417C2×D1111yescharacteristic
512C4×M16—112no—
513C4×M16C2×D1111yescharacteristic
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—84no—
523C22×C11#54812yes—
524C22×C11C23×D411yescharacteristic
525C2×D11—44no—
526C2×D11—44no—
527C2×D11—44no—
528C2×D11—88no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—21no—
533C4×C11—41no—
534C4×C11—42no—
535C4×C11—41no—
536C4×C11#54812yes—
537C4×C11C2×AGL(1,ℤ/8)12yes—
538C4×C11C22×#4111yescharacteristic
539C4×C11C2×2−1+411yescharacteristic
540Dic11—22no—
541Dic11—22no—
542Dic11—22no—
543Dic11—42no—
544Dic11—42no—
545Dic11C2×AGL(1,ℤ/8)14yes—
546C2×#41—222no—
547C2×#41—224no—
548C2×#41—222no—
549C2×#41—448no—
550C2×#41C22×D1111yescharacteristic
551C22×Q8—111no—
552C22×Q8—221no—
553C22×D4—112no—
554C22×D4—222no—
555C22×D4—222no—
556C22×D4—221no—
557C22×D4—221no—
558C22×D4C22×D1111yescharacteristic
559C23×C4—21no—
560C23×C4—222no—
561AGL(1,ℤ/8)—24no—
562AGL(1,ℤ/8)—228no—
563C2×SD16—114no—
564C2×SD16C22×D1112yes—
565C2×D8—114no—
566C2×D8C22×D1112yes—
567C2×M16—112no—
568C2×M16C22×D1111yescharacteristic
569C2×M16C22×D1111yescharacteristic
570C4⋊Q8—112no—
571C4⋊Q8—112no—
572C4⋊Q8—111no—
573C4⋊Q8—111no—
574C4⋊Q8—221no—
575C4⋊Q8—221no—
576C4⋊Q8—222no—
577C4⋊Q8—222no—
578#127—114no—
579#127—114no—
580#127—112no—
581#127—112no—
582#127—222no—
583#127—222no—
584#127—221no—
585#127—221no—
586#125—112no—
587#125—112no—
588#125—112no—
589#125—222no—
590#125—222no—
591#125—222no—
592C22⋊Q8—222no—
593C22⋊Q8—222no—
594C22⋊Q8—222no—
595C22⋊Q8—222no—
596C22⋊Q8—222no—
597C22⋊Q8—222no—
598C22⋊Q8—221no—
599C22⋊Q8—222no—
600C22⋊Q8—221no—
601C22⋊Q8—221no—
602C22⋊Q8—221no—
603#121—224no—
604#121—224no—
605#121—224no—
606#121—224no—
607#121—222no—
608#121—224no—
609#121—222no—
610C4×Q8—111no—
611C4×Q8—112no—
612C4×Q8—111no—
613C4×Q8—111no—
614C4×Q8—112no—
615C4×Q8—111no—
616C4×Q8—112no—
617C4×Q8—112no—
618C4×Q8—222no—
619C4×Q8—222no—
620C4×Q8—222no—
621C4×Q8—221no—
622C4×Q8—221no—
623C4×Q8—221no—
624C4×Q8—221no—
625C4×Q8C22×D1111yescharacteristic
626C4×Q8C22×D1111yescharacteristic
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—112no—
632C4×D4—112no—
633C4×D4—114no—
634C4×D4—114no—
635C4×D4—222no—
636C4×D4—222no—
637C4×D4—222no—
638C4×D4—222no—
639C4×D4C22×D1112yes—
640C4×D4C22×D1112yes—
641C4×D4C22×D1111yescharacteristic
642C4×D4C22×D1111yescharacteristic
643#117—21no—
644#117—112no—
645#117—222no—
646#117C22×D1111yescharacteristic
647C2×C4⋊C4—112no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—221no—
651C2×C4⋊C4C22×D1111yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—222no—
654C2×C42—21no—
655C2×C42—112no—
656C2×C42—222no—
657C2×C42C22×D1111yescharacteristic
658#107—114no—
659#107C22×D1112yes—
660#106—114no—
661#106C22×D1112yes—
662C4⋊C8—114no—
663C4⋊C8—114no—
664C4⋊C8—112no—
665C4⋊C8—112no—
666#103C22×D1112yes—
667#102—114no—
668#102—114no—
669#102—114no—
670#102—114no—
671#102—114no—
672#102—114no—
673#102—114no—
674#102—114no—
675#102C22×D1112yes—
676#102C22×D1112yes—
677#102C22×D1112yes—
678#97—114no—
679#97C22×D1112yes—
680C4×C8—114no—
681C4×C8C22×D1112yes—
682C2×C11—22no—
683C2×C11—42no—
684C2×C11—82no—
685C2×C11C2×#54811yescharacteristic
686C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
687C2×C11#358511yescharacteristic
688D11—84no—
689C24—21no—
690C24—222no—
691#41—22no—
692#41—448no—
693#41—4416no—
694#41—448no—
695#41#433914yescomplemented
696C2×Q8—111no—
697C2×Q8—112no—
698C2×Q8—111no—
699C2×Q8—222no—
700C2×Q8—222no—
701C2×Q8—224no—
702C2×Q8—221no—
703C2×Q8—221no—
704C2×Q8—444no—
705C2×Q8C23×D1111yescharacteristic
706C2×D4—21no—
707C2×D4—22no—
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—114no—
711C2×D4—224no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—224no—
715C2×D4—224no—
716C2×D4—222no—
717C2×D4—222no—
718C2×D4—222no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—224no—
722C2×D4—444no—
723C2×D4—448no—
724C2×D4—882no—
725C2×D4—884no—
726C2×D4C23×D1112yes—
727C2×D4C23×D1111yescharacteristic
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—44no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—224no—
738C22×C4—224no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—448no—
742C22×C4D4×D1111yescharacteristic
743C22×C4D4×D1111yescharacteristic
744C22×C4C23×D1111yescharacteristic
745SD16—24no—
746SD16—228no—
747D8—24no—
748D8—228no—
749M16—22no—
750M16—22no—
751M16—224no—
752C2×C8—114no—
753C2×C8C23×D1112yes—
754C2×C8C23×D1112yes—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—112no—
759C4⋊C4—111no—
760C4⋊C4—112no—
761C4⋊C4—112no—
762C4⋊C4—112no—
763C4⋊C4—112no—
764C4⋊C4—111no—
765C4⋊C4—112no—
766C4⋊C4—112no—
767C4⋊C4—222no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4—222no—
774C4⋊C4—222no—
775C4⋊C4—222no—
776C4⋊C4—221no—
777C4⋊C4—222no—
778C4⋊C4—221no—
779C4⋊C4C23×D1111yescharacteristic
780C4⋊C4C23×D1111yescharacteristic
781C4⋊C4C23×D1112yes—
782C22⋊C4—21no—
783C22⋊C4—22no—
784C22⋊C4—22no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—224no—
788C22⋊C4—224no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C42—21no—
793C42—21no—
794C42—21no—
795C42—112no—
796C42—112no—
797C42—112no—
798C42—112no—
799C42—222no—
800C42—222no—
801C42—222no—
802C42D4×D1111yescharacteristic
803C42D4×D1111yescharacteristic
804C42C23×D1111yescharacteristic
805C42C23×D1111yescharacteristic
806C11#6132111yescharacteristic, complemented, Sylow
807C23—21no—
808C23—22no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—224no—
813C23—444no—
814C23—444no—
815C23—444no—
816C23C2×D4×D1111yescharacteristic
817Q8—21no—
818Q8—114no—
819Q8—224no—
820Q8—222no—
821Q8—444no—
822Q8—442no—
823Q8—881no—
824Q8—882no—
825Q8C2×#433912yescomplemented
826D4—24no—
827D4—22no—
828D4—21no—
829D4—22no—
830D4—42no—
831D4—224no—
832D4—224no—
833D4—444no—
834D4—448no—
835D4—448no—
836D4—444no—
837D4—444no—
838D4—882no—
839D4—882no—
840D4—884no—
841D4—884no—
842D4C2×#433912yescomplemented
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—41no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—42no—
854C2×C4—81no—
855C2×C4—112no—
856C2×C4—112no—
857C2×C4—112no—
858C2×C4—112no—
859C2×C4—224no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—448no—
863C2×C4—448no—
864C2×C4—444no—
865C2×C4—442no—
866C2×C4—882no—
867C2×C4C2×#433912yes—
868C2×C4C2×D4×D1111yescharacteristic
869C2×C4C2×D4×D1111yescharacteristic
870C2×C4C2×D4×D1111yescharacteristic
871C2×C4C2×D4×D1111yescharacteristic
872C2×C4C2×D4×D1111yescharacteristic
873C2×C4#6704312yes—
874C2×C4C24×D1111yescharacteristic
875C8—22no—
876C8—22no—
877C8—224no—
878C22—21no—
879C22—21no—
880C22—22no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—84no—
887C22—444no—
888C22—444no—
889C22—444no—
890C22—888no—
891C22#1062308312yes—
892C22C22×D4×D1111yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—114no—
901C4—222no—
902C4—222no—
903C4—222no—
904C4—442no—
905C4—442no—
906C4#1062308312yes—
907C4D11×AGL(1,ℤ/8)12yes—
908C4C22×#433911yescharacteristic
909C4C2×#6704311yescharacteristic
910C2—22no—
911C2—42no—
912C2—82no—
913C2—884no—
914C2C2×#1062308311yescharacteristic
915C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
916C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#61321
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×Dic22C2semidirect
2. C2×#10623084C2semidirect
3. #13081346C2semidirect
4. #13081343C2semidirect
5. #13081324C2semidirect
6. #13081321C2semidirect
7. #13081285C2semidirect
8. #13081249C2semidirect
9. #13078991C2semidirect
10. #13078988C2semidirect
11. #13078413C2semidirect
12. #13078412C2semidirect
13. #13078096C2semidirect
14. #13078094C2semidirect
15. M16×Dic22C2semidirect
16. #13077429C2semidirect
17. C4×C11×AGL(1,ℤ/8)C2semidirect
26. #10623101C22semidirect
27. #10623100C22semidirect
28. Q8×Dic22C22semidirect
36. #10623074C22semidirect
38. #10623070C22semidirect
40. D4×Dic22C22semidirect
50. C11×#442C22semidirect
51. C11×#440C22semidirect
52. C4×C11×SD16C22semidirect
53. C4×C11×D8C22semidirect
59. #10622776C22semidirect
60. #10622776C22semidirect
61. #10622763C22semidirect
62. #10622763C22semidirect
67. #10622640C22semidirect
68. #10622640C22semidirect
69. #10622628C22semidirect
70. #10622628C22semidirect
71. #10622622C22semidirect
72. #10622621C22semidirect
73. #10622620C22semidirect
77. #10622504C22semidirect
78. #10622503C22semidirect
79. #10622484C22semidirect
80. #10622483C22semidirect
81. #10622430C22semidirect
82. #10622401C22semidirect
83. #10622398C22semidirect
84. #10622377C22semidirect
85. #10622377C22semidirect
86. #10622373C22semidirect
87. #10622373C22semidirect
88. #10622369C22semidirect
89. #10622326C22semidirect
90. #10622314C22semidirect
91. #10622307C22semidirect
92. #10622307C22semidirect
93. #10622292C22semidirect
94. C8×Dic22C22semidirect
235. C11×#41#41semidirect
365. C4×AGL(1,ℤ/8)D11semidirect
377. Q8×C11C2×#41semidirect
383. D4×C11C2×#41semidirect
433. Dic22AGL(1,ℤ/8)semidirect
495. #442C2×D11semidirect
497. #440C2×D11semidirect
499. C4×SD16C2×D11semidirect
501. C4×D8C2×D11semidirect
695. #41#4339semidirect
806. C11#61321semidirect
825. Q8C2×#4339semidirect
842. D4C2×#4339semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
C2×#106230842
#130813462
#130813432
#130813242
#130813212
#130812852
#130812492
#130789912
#130789882
#130784132
#130784122
#130780962
#130780942
M16×Dic222
#130774292
C4×C11×AGL(1,ℤ/8)2
#6132111