Finite Group Databasebeta

← #15623443

Subgroups — #15623443

Order 2816.

1798 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082019C211yesmaximal, characteristic
2C2×#10623220C211yesmaximal, characteristic
3#13079166C212yesmaximal, complemented
4#13079165C211yesmaximal, characteristic, complemented
5#13079163C211yesmaximal, characteristic, complemented
6#13079162C211yesmaximal, characteristic, complemented
7#13079160C212yesmaximal, complemented
8#13079153C214yesmaximal, complemented
9#13079151C214yesmaximal, complemented
10#13079145C214yesmaximal, complemented
11#13079143C214yesmaximal, complemented
12#13077203C212yesmaximal
13D11×#428C212yesmaximal
14#13077033C211yesmaximal, characteristic
15C11×#3166C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×M16×D11C2212yes—
19#10623260C2212yes—
20#10623260C2212yes—
21#10623220—22no—
22#10623220—22no—
23#10623220C2214yes—
24#10623220C2212yes—
25#10623220C2214yes—
26#10623220C2212yes—
27#10623165—21no—
28#10623165—21no—
29#10623154—21no—
30#10623154—21no—
31#10623109—22no—
32#10623109—22no—
33D11×#117C2212yes—
34#10623048C2212yes—
35C2×#66950—21no—
36C2×#66949—21no—
37C2×#66945C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66942—21no—
41C2×#66941—21no—
42C2×#66941C2211yescharacteristic
43C2×#66925C2211yescharacteristic
44#10623001C2211yescharacteristic
45C2×#66922C2211yescharacteristic
46C11×#501C2212yescomplemented
47C11×#501C2212yescomplemented
48C11×#499C2214yescomplemented
49C11×#428C2212yes—
50C11×#428C2212yes—
51C4×C11×M16C2211yescharacteristic
52#10622734C2212yes—
53#10622734C2212yes—
54M16×Dic11C2212yes—
55#10622692C2212yescomplemented
56#10622691C2212yescomplemented
57#10622678C2212yescomplemented
58#10622678C2214yescomplemented
59#10622678C2212yescomplemented
60#10622677C2214yescomplemented
61#10622608C2212yes—
62#10622608C2212yes—
63#10622577C2212yes—
64#10622577C2212yes—
65C4×#4318C2211yescharacteristic
66#10622494C2214yes—
67#10622494C2214yes—
68#10622493C2214yes—
69D11×#107C2214yes—
70#10622491C2214yescomplemented
71#10622489C2214yescomplemented
72#10622489C2214yescomplemented
73#10622487C2214yescomplemented
74#10622474C2214yes—
75#10622474C2214yes—
76#10622473C2214yes—
77D11×#106C2214yes—
78#10622471C2214yescomplemented
79#10622469C2214yescomplemented
80#10622469C2214yescomplemented
81#10622468C2214yescomplemented
82#10622321C2214yes—
83#10622315C2214yescomplemented
84#10622302C2214yes—
85#10622295C2212yescomplemented
86#10622293C2212yescomplemented
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22—21no—
90C22×Dic22—21no—
91C2×C11×M16C2312yes—
92C11×C4⋊Q8C2311yescharacteristic
93C11×C4⋊Q8C2311yescharacteristic
94C11×#125—21no—
95C11×#125—21no—
96C11×#125C2312yes—
97C11×#125C2312yes—
98C11×#125C2312yes—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8—21no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C11×#117C2312yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109#66999—22no—
110#66999—22no—
111#66997—22no—
112#66997—22no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4D411yescharacteristic
115C2×(C2×D11)⋊C4D411yescharacteristic
116#66979C2312yes—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121#66977—21no—
122#66977—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4D411yescharacteristic
127C2×Dic11⋊C4D411yescharacteristic
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C2×#4318C2312yes—
131M16×D11Q8116yescomplemented
132C2×#4313C2314yes—
133C2×C8×D11C2314yes—
134#66950—24no—
135#66950—24no—
136#66950—22no—
137#66950—22no—
138#66949—22no—
139#66949—22no—
140#66949—24no—
141#66949—24no—
142#66949—22no—
143#66949—22no—
144#66945—22no—
145#66945C2312yes—
146#66945C2314yes—
147#66945C2312yes—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2312yes—
150C4⋊C4×D11C2314yes—
151C4⋊C4×D11C2312yes—
152#66943—22no—
153#66943C2312yes—
154#66943C2314yes—
155#66943C2312yes—
156#66942—22no—
157#66942—22no—
158#66942—24no—
159#66942—24no—
160#66942—22no—
161#66942—22no—
162#66941—24no—
163#66941—24no—
164#66941—22no—
165#66941—22no—
166#66941—22no—
167#66941C2312yes—
168#66941C2314yes—
169#66941C2312yes—
170C22⋊C4×D11—22no—
171#66931—22no—
172#66931—22no—
173#66930—22no—
174#66925—22no—
175#66925D412yes—
176#66925D412yes—
177#66925C2312yes—
178#66925C2312yes—
179C42×D11—22no—
180#66923C2312yes—
181#66922—21no—
182#66922—21no—
183#66922C2312yes—
184#66922C2312yes—
185#66922C2311yescharacteristic
186#66922C2311yescharacteristic
187C4×Dic22—21no—
188C4×Dic22—21no—
189C4×Dic22—22no—
190C4×Dic22—22no—
191C11×#107C2314yes—
192C11×#107C2314yes—
193C11×#106C2314yes—
194C11×#106C2314yes—
195C11×#97C2312yes—
196C4×C8×C11C2312yes—
197#66882C2314yes—
198#66882C2314yes—
199#66881C2314yes—
200#66881C2314yes—
201#66879C2314yes—
202C8×Dic11C2314yes—
203#66872C2314yes—
204#66872C2314yes—
205#66872C2314yes—
206#66872C2314yes—
207#66871C2314yes—
208#66871C2314yes—
209#66871C2314yes—
210#66871C2314yes—
211#66867C2312yes—
212C4×C11⋊C8C2312yes—
213#60664—111nomaximal, Sylow
214C23×D11C2×D411yescharacteristic
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2411yescharacteristic
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—24no—
230C2×C4×D11—82no—
231C2×C4×D11C2×D412yes—
232C2×C4×D11C2×Q818yes—
233C2×C4×D11C2412yes—
234C2×Dic22—22no—
235C2×Dic22—22no—
236C2×Dic22—24no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—82no—
242C2×Dic22—82no—
243C11×M16C2×Q818yes—
244C2×C8×C11C2414yes—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—22no—
260C42×C11—22no—
261C42×C11C2×D411yescharacteristic
262C42×C11C2×D411yescharacteristic
263C42×C11C2411yescharacteristic
264C42×C11C2411yescharacteristic
265C22⋊Dic11—22no—
266(C2×D11)⋊C4—22no—
267(C2×D11)⋊C4—22no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4C2×D412yes—
270(C2×D11)⋊C4C2×D412yes—
271(C2×D11)⋊C4C2×D412yes—
272(C2×D11)⋊C4C2×D412yes—
273C4⋊Dic11—22no—
274C4⋊Dic11—22no—
275C4⋊Dic11—24no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—22no—
281C4⋊Dic11—22no—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286Dic11⋊C4—22no—
287Dic11⋊C4—22no—
288Dic11⋊C4—22no—
289Dic11⋊C4—22no—
290Dic11⋊C4—22no—
291Dic11⋊C4—22no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295Dic11⋊C4—22no—
296Dic11⋊C4—22no—
297Dic11⋊C4C2×D412yes—
298Dic11⋊C4C2×D412yes—
299Dic11⋊C4C2×D412yes—
300Dic11⋊C4C2×D412yes—
301C4×Dic11—22no—
302C4×Dic11—22no—
303C4×Dic11—24no—
304C4×Dic11—22no—
305C4×Dic11C2×D412yes—
306C4×Dic11C2412yes—
307#4318C2×Q818yes—
308C2×C11⋊C8C2414yes—
309#4313C2×Q8116yescomplemented
310C8×D11C2×Q8116yescomplemented
311#3458—111no—
312C2×#544—111no—
313#3166—112no—
314#3166—111no—
315#3166D1111yescharacteristic, complemented
316#3165—112no—
317#3165—111no—
318#3165—111no—
319#3164—114no—
320#3164—114no—
321#3163—114no—
322#3163—114no—
323#2911—112no—
324C2×#428—112no—
325#2873—111no—
326C23×C11C22×D411yescharacteristic
327C22×D11—41no—
328C22×D11—41no—
329C22×D11C4⋊Q814yes—
330C22×D11C22×D412yes—
331Q8×C11—81no—
332Q8×C11—81no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×Q814yes—
347C2×C4×C11C2511yescharacteristic
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11C4⋊Q814yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C4×D11—82no—
361C4×D11—82no—
362C4×D11—84no—
363C4×D11C4⋊Q818yes—
364C4×D11C22×Q814yes—
365C4×D11C22×Q814yes—
366Dic22—82no—
367Dic22—82no—
368Dic22—84no—
369Dic22—81no—
370Dic22—81no—
371Dic22—82no—
372Dic22—82no—
373C8×C11C22×Q818yes—
374C11⋊C8C22×Q818yes—
375C22×M16—112no—
376#544—112no—
377#544—112no—
378#544—112no—
379#544—114no—
380#544—114no—
381#544—112no—
382#544—221no—
383#544—221no—
384#544—222no—
385#544—222no—
386#543—221no—
387#543—221no—
388#533—112no—
389#533—111no—
390#533—222no—
391#533—222no—
392#533C2×D1111yescharacteristic
393C2×C4⋊Q8—111no—
394C2×C4⋊Q8—111no—
395C2×C4⋊Q8—221no—
396C2×#125—111no—
397C2×#125—221no—
398C2×#125C2×D1111yescharacteristic
399C2×C22⋊Q8—221no—
400C2×C22⋊Q8—221no—
401C2×#117—111no—
402C2×#117—112no—
403C2×#117—111no—
404C22×C4⋊C4—111no—
405#501—112no—
406#501—114no—
407#501—112no—
408#501—114no—
409#501—114no—
410#501—114no—
411#501—114no—
412#501—114no—
413#501C2×D1112yescomplemented
414#501C2×D1112yescomplemented
415#500—112no—
416#500—114no—
417#500—112no—
418#499—114no—
419#499—114no—
420#499—114no—
421#499C2×D1114yescomplemented
422#498—112no—
423#498—114no—
424#498—112no—
425#428—112no—
426#428—112no—
427#428—112no—
428#428—112no—
429#428—112no—
430#428—112no—
431#428—114no—
432#428—114no—
433#428—114no—
434#428—114no—
435#428C2×D1112yes—
436#428C2×D1112yes—
437#427—114no—
438#427—114no—
439C2×#107—114no—
440C2×#106—114no—
441#405—114no—
442#405—114no—
443C4×M16—112no—
444C4×M16—111no—
445C4×M16C2×D1111yescharacteristic
446C22×C11—21no—
447C22×C11—21no—
448C22×C11C2×C4⋊Q812yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—44no—
453C2×D11C2×C4⋊Q814yes—
454C4×C11—21no—
455C4×C11—21no—
456C4×C11—21no—
457C4×C11—21no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11C2×C4⋊Q812yes—
463C4×C11C23×Q812yes—
464Dic11—22no—
465Dic11—22no—
466Dic11—42no—
467Dic11—42no—
468Dic11—42no—
469Dic11—42no—
470Dic11C2×C4⋊Q814yes—
471C22×Q8—221no—
472C22×Q8—221no—
473C23×C4—111no—
474C23×C4—221no—
475C2×M16—112no—
476C2×M16—1116no—
477C2×M16—114no—
478C2×M16C22×D1112yes—
479C22×C8—114no—
480C4⋊Q8—114no—
481C4⋊Q8—112no—
482C4⋊Q8—112no—
483C4⋊Q8—112no—
484C4⋊Q8—112no—
485C4⋊Q8—111no—
486C4⋊Q8—111no—
487C4⋊Q8—222no—
488C4⋊Q8—224no—
489C4⋊Q8—224no—
490C4⋊Q8—222no—
491C4⋊Q8—222no—
492C4⋊Q8—222no—
493C4⋊Q8—222no—
494C4⋊Q8—221no—
495C4⋊Q8—221no—
496C4⋊Q8C22×D1111yescharacteristic
497C4⋊Q8C22×D1111yescharacteristic
498#125—21no—
499#125—21no—
500#125—114no—
501#125—112no—
502#125—112no—
503#125—112no—
504#125—222no—
505#125—224no—
506#125—224no—
507#125—222no—
508#125—222no—
509#125—222no—
510#125—222no—
511#125C22×D1112yes—
512#125C22×D1112yes—
513#125C22×D1112yes—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—222no—
517C22⋊Q8—222no—
518C22⋊Q8—224no—
519C22⋊Q8—224no—
520C22⋊Q8—224no—
521C22⋊Q8—224no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526C22⋊Q8—222no—
527C22⋊Q8—222no—
528C22⋊Q8—222no—
529C22⋊Q8—222no—
530C22⋊Q8—221no—
531C22⋊Q8—221no—
532C4×Q8—21no—
533C4×Q8—21no—
534C4×Q8—222no—
535C4×Q8—222no—
536C4×Q8—221no—
537C4×Q8—221no—
538#117—112no—
539#117—112no—
540#117—112no—
541#117—112no—
542#117—112no—
543#117—112no—
544#117—114no—
545#117—112no—
546#117—222no—
547#117—222no—
548#117—222no—
549#117C22×D1112yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—112no—
558C2×C4⋊C4—112no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4C22×D1111yescharacteristic
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C22⋊C4—111no—
568C2×C22⋊C4—111no—
569C2×C22⋊C4—222no—
570C2×C22⋊C4—221no—
571C2×C42—111no—
572C2×C42—222no—
573C2×C42—221no—
574C2×C42C22×D1111yescharacteristic
575#107—114no—
576#107—114no—
577#107—114no—
578#107—114no—
579#107—114no—
580#107—114no—
581#107C22×D1114yes—
582#107C22×D1114yes—
583#106—114no—
584#106—114no—
585#106—114no—
586#106—114no—
587#106—114no—
588#106—114no—
589#106C22×D1114yes—
590#106C22×D1114yes—
591#97—114no—
592#97—112no—
593#97C22×D1112yes—
594C4×C8—114no—
595C4×C8—112no—
596C4×C8C22×D1112yes—
597C2×C11—22no—
598C2×C11C22×C4⋊Q811yescharacteristic
599C2×C11#358511yescharacteristic
600C2×C11#358611yescharacteristic
601D11—24no—
602C24—111no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—222no—
606C2×Q8—222no—
607C2×Q8—224no—
608C2×Q8—221no—
609C2×Q8—221no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8—882no—
613C2×Q8—882no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—111no—
617C22×C4—112no—
618C22×C4—118no—
619C22×C4—112no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—224no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—882no—
628C22×C4D4×D1111yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4C23×D1111yescharacteristic
631M16—118no—
632M16—1116no—
633M16Q8×D1118yes—
634C2×C8—114no—
635C2×C8—1116no—
636C2×C8C23×D1114yes—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—112no—
648C4⋊C4—112no—
649C4⋊C4—112no—
650C4⋊C4—112no—
651C4⋊C4—112no—
652C4⋊C4—112no—
653C4⋊C4—112no—
654C4⋊C4—112no—
655C4⋊C4—224no—
656C4⋊C4—222no—
657C4⋊C4—222no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—222no—
662C4⋊C4—222no—
663C4⋊C4—222no—
664C4⋊C4—222no—
665C4⋊C4—222no—
666C4⋊C4—222no—
667C4⋊C4—221no—
668C4⋊C4—221no—
669C4⋊C4—222no—
670C4⋊C4—222no—
671C4⋊C4—222no—
672C4⋊C4—222no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4C23×D1112yes—
676C4⋊C4C23×D1112yes—
677C4⋊C4C23×D1112yes—
678C4⋊C4C23×D1112yes—
679C22⋊C4—22no—
680C22⋊C4—112no—
681C22⋊C4—112no—
682C22⋊C4—112no—
683C22⋊C4—112no—
684C22⋊C4—222no—
685C22⋊C4—222no—
686C22⋊C4—224no—
687C22⋊C4—222no—
688C42—22no—
689C42—112no—
690C42—112no—
691C42—222no—
692C42—222no—
693C42—224no—
694C42—222no—
695C42D4×D1111yescharacteristic
696C42D4×D1111yescharacteristic
697C42C23×D1111yescharacteristic
698C42C23×D1111yescharacteristic
699C11#6066411yescharacteristic, complemented, Sylow
700C23—112no—
701C23—114no—
702C23—441no—
703C23—441no—
704C23C2×D4×D1111yescharacteristic
705Q8—81no—
706Q8—81no—
707Q8—882no—
708Q8—882no—
709Q8—881no—
710Q8—881no—
711Q8—884no—
712Q8—882no—
713Q8—882no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—114no—
723C2×C4—112no—
724C2×C4—118no—
725C2×C4—114no—
726C2×C4—114no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—884no—
738C2×C4—882no—
739C2×C4—882no—
740C2×C4C2×D4×D1111yescharacteristic
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4C2×D4×D1111yescharacteristic
743C2×C4C2×D4×D1111yescharacteristic
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4C2×Q8×D1114yes—
746C2×C4C24×D1111yescharacteristic
747C8—118no—
748C8C2×Q8×D1118yes—
749C22—21no—
750C22—21no—
751C22—114no—
752C22—222no—
753C22—222no—
754C22—444no—
755C22D11×C4⋊Q812yes—
756C22C22×D4×D1111yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—114no—
766C4—222no—
767C4—222no—
768C4—442no—
769C4—442no—
770C4—442no—
771C4—442no—
772C4D11×C4⋊Q812yes—
773C4C22×Q8×D1112yes—
774C2—22no—
775C2—224no—
776C2C2×D11×C4⋊Q811yescharacteristic
777C2#1308339311yescharacteristic
778C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3166C2
socleC22×C11C23×D4
prime radicalC23×D11C2×D4
hypercenter#3166D11
hypocenterC11#60664
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
3. #13079166C2semidirect
4. #13079165C2semidirect
5. #13079163C2semidirect
6. #13079162C2semidirect
7. #13079160C2semidirect
8. #13079153C2semidirect
9. #13079151C2semidirect
10. #13079145C2semidirect
11. #13079143C2semidirect
15. C11×#3166C2semidirect
46. C11×#501C22semidirect
47. C11×#501C22semidirect
48. C11×#499C22semidirect
55. #10622692C22semidirect
56. #10622691C22semidirect
57. #10622678C22semidirect
58. #10622678C22semidirect
59. #10622678C22semidirect
60. #10622677C22semidirect
70. #10622491C22semidirect
71. #10622489C22semidirect
72. #10622489C22semidirect
73. #10622487C22semidirect
78. #10622471C22semidirect
79. #10622469C22semidirect
80. #10622469C22semidirect
81. #10622468C22semidirect
83. #10622315C22semidirect
85. #10622295C22semidirect
86. #10622293C22semidirect
131. M16×D11Q8semidirect
309. #4313C2×Q8semidirect
310. C8×D11C2×Q8semidirect
315. #3166D11semidirect
413. #501C2×D11semidirect
414. #501C2×D11semidirect
421. #499C2×D11semidirect
699. C11#60664semidirect

Maximal subgroups

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

subgroupindex
#130820192
C2×#106232202
#130791662
#130791652
#130791632
#130791622
#130791602
#130791532
#130791512
#130791452
#130791432
#130772032
D11×#4282
#130770332
C11×#31662
#6066411