Finite Group Databasebeta

← #15626520

Subgroups — #15626520

Order 2816.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082032C211yesmaximal, characteristic
2#13079914C214yesmaximal, complemented
3#13079869C214yesmaximal, complemented
4#13079837C212yesmaximal, complemented
5#13079814C212yesmaximal, complemented
6#13079795C212yesmaximal, complemented
7#13079744C212yesmaximal, complemented
8#13079142C212yesmaximal, complemented
9#13078975C212yesmaximal, complemented
10#13078605C212yesmaximal, complemented
11#13078574C212yesmaximal, complemented
12#13078425C211yesmaximal, characteristic, complemented
13#13078409C211yesmaximal, characteristic, complemented
14#13078398C211yesmaximal, characteristic, complemented
15C2×#10622697C211yesmaximal, characteristic, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3503C211yesmaximal, characteristic, complemented
18Q82×C11—21no—
19C11×#557—21no—
20C11×#554—22no—
21C11×#554—21no—
22D4×Q8×C11—22no—
23D4×Q8×C11—21no—
24C11×#544C2212yes—
25C11×#544C2214yescomplemented
26C11×#533C2211yescharacteristic
27C11×#533C2212yescomplemented
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×C4⋊Q8C2212yescomplemented
30C11×#520C2212yes—
31C4×C11×#41C2211yescharacteristic
32#10623364C2211yescharacteristic
33#10623361C2211yescharacteristic
34#10623113—21no—
35#10623111—21no—
36#10623093—21no—
37#10623091—22no—
38#10623079—21no—
39#10623078—22no—
40#10623066C2212yes—
41#10623065C2212yes—
42#10623056C2211yescharacteristic
43#10623050C2211yescharacteristic
44#10623010C2212yes—
45#10623008C2212yes—
46C4×#4339C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48#10622847C2212yes—
49#10622707C2212yescomplemented
50#10622707C2211yescharacteristic, complemented
51#10622704C2211yescharacteristic, complemented
52#10622704C2212yescomplemented
53#10622702C2214yes—
54#10622701C2214yes—
55#10622700C2212yes—
56#10622700C2211yescharacteristic, complemented
57#10622700C2212yescomplemented
58#10622697C2212yes—
59#10622697C2212yes—
60#10622697C2214yes—
61#10622697C2212yes—
62#10622697C2212yescomplemented
63#10622697C2211yescharacteristic, complemented
64#10622693C2214yescomplemented
65#10622692C2214yescomplemented
66#10622681C2214yes—
67#10622680C2214yes—
68#10622679C2214yes—
69#10622679C2212yescomplemented
70#10622678C2214yescomplemented
71#10622677C2214yescomplemented
72#10622676C2212yescomplemented
73#10622616C2214yes—
74#10622616C2214yes—
75#10622616C2214yescomplemented
76#10622615C2212yes—
77#10622614C2212yes—
78#10622613C2214yescomplemented
79#10622611C2212yes—
80#10622610C2212yes—
81#10622609C2214yescomplemented
82#10622608C2212yes—
83#10622584C2214yescomplemented
84#10622581C2214yes—
85#10622581C2214yescomplemented
86#10622580C2214yes—
87#10622579C2212yes—
88C2×#66873C2212yes—
89#10622577C2212yes—
90C2×#66872C2212yes—
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11—21no—
97C22×Q8×C11—22no—
98C2×#4339—22no—
99C2×#4339C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C11×C4⋊Q8—22no—
103C11×C4⋊Q8—24no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8—21no—
106C11×C4⋊Q8—22no—
107C11×C4⋊Q8—22no—
108C11×C4⋊Q8C2312yes—
109C11×C4⋊Q8C2312yes—
110C11×C4⋊Q8C2311yescharacteristic
111C11×C4⋊Q8C2314yes—
112C11×C4⋊Q8C2311yescharacteristic
113C11×#125—22no—
114C11×#125—24no—
115C11×#125C2312yes—
116C11×#125C2314yes—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8—24no—
122C11×C22⋊Q8—24no—
123C11×C22⋊Q8—24no—
124C4×Q8×C11—22no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—22no—
128C4×Q8×C11—22no—
129C4×Q8×C11D411yescharacteristic
130C4×Q8×C11D411yescharacteristic
131C4×D4×C11—24no—
132C4×D4×C11—22no—
133C4×D4×C11D412yes—
134C4×D4×C11D411yescharacteristic
135C4×D4×C11D412yes—
136C4×D4×C11D411yescharacteristic
137C11×#117C2312yes—
138C11×#117C2314yes—
139C11×#117C2311yescharacteristic
140C11×#117C2312yes—
141C2×C11×C4⋊C4—21no—
142C2×C11×C4⋊C4—22no—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2314yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147#67000—21no—
148#66999—21no—
149#66993—21no—
150#66992—22no—
151#66991—21no—
152#66990—22no—
153#66983—22no—
154#66983C2312yes—
155#66983C2312yes—
156#66983C2312yes—
157#66982—22no—
158C4×C22⋊D11—21no—
159C4×C22⋊D11—21no—
160C4×C22⋊D11—22no—
161C2×(C2×D11)⋊C4—21no—
162#66979C2311yescharacteristic
163C2×C4⋊Dic11C2311yescharacteristic
164#66977C2312yes—
165C2×#4318C2312yes—
166C22×C11⋊C8C2312yes—
167#66951—22no—
168#66949—22no—
169#66948—21no—
170#66948—21no—
171#66947—22no—
172#66947—22no—
173#66943—21no—
174#66941—21no—
175#66938—22no—
176#66937—22no—
177#66937—22no—
178#66936—22no—
179#66935—22no—
180#66931—22no—
181#66929—22no—
182#66928—22no—
183#66928C2312yes—
184#66927C2312yes—
185C4×D44—21no—
186C4×D44—21no—
187C4×D44—22no—
188C4×D44C2312yes—
189C4×D44C2312yes—
190C4×D44C2311yescharacteristic
191C4×D44C2311yescharacteristic
192#66925—21no—
193#66925—22no—
194C42×D11—21no—
195#66923C2312yes—
196#66922C2312yes—
197C4×Dic22C2311yescharacteristic
198C4×Dic22C2311yescharacteristic
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2314yes—
202#66874C2312yes—
203#66874C2312yes—
204#66873C2314yes—
205#66873C2314yes—
206#66873C2314yes—
207#66873C2314yes—
208#66873C2312yes—
209#66873C2314yes—
210#66873C2312yes—
211#66872C2314yes—
212#66872C2314yes—
213#66872C2314yes—
214#66872C2312yes—
215#66872C2314yes—
216#66872C2312yes—
217#66871C2314yes—
218#66871C2312yes—
219#66871C2314yes—
220#66871C2312yes—
221C4⋊(C11⋊C8)C2311yescharacteristic
222C4⋊(C11⋊C8)C2311yescharacteristic
223C4⋊(C11⋊C8)C2312yes—
224C4⋊(C11⋊C8)C2312yes—
225C4⋊(C11⋊C8)C2312yes—
226#66867C2314yes—
227C4×C11⋊C8C2314yes—
228#60892—111nomaximal, Sylow
229C23×D11—21no—
230C11×#41—22no—
231C11×#41—22no—
232C2×Q8×C11—21no—
233C2×Q8×C11—21no—
234C2×Q8×C11—22no—
235C2×Q8×C11—22no—
236C2×Q8×C11—24no—
237C2×Q8×C11—82no—
238C2×Q8×C11—84no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×D4×C11C2×D412yes—
241C2×D4×C11C2×D411yescharacteristic
242C22×C4×C11—24no—
243C22×C4×C11—22no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—21no—
251C2×C22⋊D11—22no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254C22×Dic11—21no—
255#4339—22no—
256#4339—22no—
257#4339—84no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44C2411yescharacteristic
264C2×D44C2412yes—
265C2×C4×D11—21no—
266C2×C4×D11—21no—
267C2×C4×D11—22no—
268C2×C4×D11—21no—
269C2×C4×D11—22no—
270C2×C4×D11—82no—
271C2×Dic22—22no—
272C2×Dic22C2411yescharacteristic
273C11×C4⋊C4—22no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—24no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—24no—
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2414yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4C2×D412yes—
294C11×C22⋊C4C2×D412yes—
295C11×C22⋊C4C2×D412yes—
296C42×C11—24no—
297C42×C11—22no—
298C42×C11C2×D411yescharacteristic
299C42×C11C2×D412yes—
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D412yes—
302C42×C11C2412yes—
303C42×C11C2411yescharacteristic
304C42×C11C2411yescharacteristic
305C22⋊Dic11—21no—
306C22⋊Dic11—22no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—21no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—21no—
318C4⋊Dic11C2411yescharacteristic
319C4⋊Dic11C2411yescharacteristic
320C4⋊Dic11C2412yes—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326C4×Dic11—21no—
327C4×Dic11—21no—
328C4×Dic11—21no—
329#4318—24no—
330C2×C11⋊C8—24no—
331C2×C11⋊C8C2412yes—
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2412yes—
334#3503D1111yescharacteristic, complemented
335#3460—111no—
336#3244—114no—
337#3241—114no—
338#3238—112no—
339#3235—112no—
340#3233—112no—
341#3227—112no—
342#3163—112no—
343#3136—112no—
344#3099—112no—
345#3096—112no—
346#3079—111no—
347#3077—111no—
348#3076—111no—
349C2×#476—111no—
350#2925—111no—
351C23×C11C22×D412yes—
352C23×C11C22×D411yescharacteristic
353C22×D11—22no—
354C22×D11—21no—
355C22×D11—42no—
356C22×D11—81no—
357C22×D11—81no—
358Q8×C11—22no—
359Q8×C11—42no—
360Q8×C11—44no—
361Q8×C11—42no—
362Q8×C11—82no—
363Q8×C11—84no—
364D4×C11—24no—
365D4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—24no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—24no—
372C2×C4×C11—22no—
373C2×C4×C11—41no—
374C2×C4×C11—42no—
375C2×C4×C11—82no—
376C2×C4×C11—84no—
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C112−1+412yes—
386C2×C4×C112−1+412yes—
387C2×C4×C11C2511yescharacteristic
388C22⋊D11—42no—
389C22⋊D11—82no—
390C22⋊D11—82no—
391C22⋊D11—82no—
392C2×Dic11—21no—
393C2×Dic11—21no—
394C2×Dic11—21no—
395C2×Dic11—22no—
396C2×Dic11—81no—
397D44—22no—
398D44—22no—
399D44—21no—
400D44—21no—
401D44—42no—
402D44—82no—
403D44—82no—
404C4×D11—42no—
405C4×D11—44no—
406C4×D11—42no—
407C4×D11—81no—
408C4×D11—82no—
409Dic22—21no—
410Dic22—21no—
411Dic22—82no—
412C11⋊C8—22no—
413C11⋊C8—22no—
414C11⋊C8—24no—
415Q82—21no—
416#557—21no—
417#554—22no—
418#554—21no—
419D4×Q8—22no—
420D4×Q8—21no—
421#544—111no—
422#544C2×D1112yes—
423#544C2×D1114yescomplemented
424#542—112no—
425#542—221no—
426#540—112no—
427#540—221no—
428#538—222no—
429#537—111no—
430#535—111no—
431#535—111no—
432#533C2×D1111yescharacteristic
433#533C2×D1112yescomplemented
434#532—112no—
435#532—221no—
436C2×C4⋊Q8C2×D1111yescharacteristic
437C2×C4⋊Q8C2×D1112yescomplemented
438#529—112no—
439#529—221no—
440#525—222no—
441#520C2×D1112yes—
442C4×#41—111no—
443C4×#41C2×D1111yescharacteristic
444C2×C4×D4—111no—
445#501—114no—
446#501—114no—
447#499—114no—
448#498—114no—
449#490—114no—
450#489—114no—
451#488—114no—
452#486—114no—
453#485—114no—
454#483—114no—
455#482—114no—
456#482—114no—
457#482—114no—
458#481—114no—
459#481—114no—
460#480—114no—
461#479—112no—
462#478—112no—
463#478—114no—
464#477—111no—
465#477—112no—
466#476—111no—
467#476—112no—
468#476—112no—
469#476—112no—
470#476—112no—
471#476—114no—
472#475—111no—
473#475—112no—
474#474—111no—
475#474—112no—
476#474—112no—
477#433—114no—
478#432—112no—
479#431—112no—
480#428—112no—
481#428—112no—
482#427—112no—
483C2×#106—112no—
484#423—111no—
485C2×C4⋊C8—111no—
486#418—112no—
487#417—112no—
488#416—112no—
489C2×#102—112no—
490#408—112no—
491#405—112no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11#53612yes—
498C22×C11C23×D411yescharacteristic
499C2×D11—42no—
500C2×D11—41no—
501C2×D11—42no—
502C2×D11—41no—
503C2×D11—42no—
504C2×D11—41no—
505C2×D11—84no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—22no—
509C4×C11—22no—
510C4×C11—22no—
511C4×C11—21no—
512C4×C11—44no—
513C4×C11—42no—
514C4×C11—42no—
515C4×C11#53612yes—
516C4×C11#57712yes—
517C4×C11C2×2−1+411yescharacteristic
518C4×C11C2×2−1+411yescharacteristic
519Dic11—41no—
520Dic11—41no—
521Dic11—41no—
522Dic11—42no—
523C2×#41—111no—
524C2×#41—222no—
525C2×#41C22×D1111yescharacteristic
526C22×Q8—21no—
527C22×Q8—22no—
528C22×D4—111no—
529C23×C4—221no—
530C2×M16—112no—
531C22×C8—112no—
532C4⋊Q8—22no—
533C4⋊Q8—24no—
534C4⋊Q8—21no—
535C4⋊Q8—21no—
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—112no—
539C4⋊Q8—221no—
540C4⋊Q8C22×D1112yes—
541C4⋊Q8C22×D1112yes—
542C4⋊Q8C22×D1111yescharacteristic
543C4⋊Q8C22×D1114yes—
544C4⋊Q8C22×D1111yescharacteristic
545#127—112no—
546#127—221no—
547#126—222no—
548#126—222no—
549#125—22no—
550#125—24no—
551#125—112no—
552#125—221no—
553#125C22×D1112yes—
554#125C22×D1114yes—
555#124—112no—
556#124—221no—
557#124—222no—
558#124—222no—
559#123—222no—
560#123—222no—
561#123—222no—
562#123—222no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—24no—
568C22⋊Q8—24no—
569C22⋊Q8—24no—
570C22⋊Q8—112no—
571C22⋊Q8—221no—
572C22⋊Q8—222no—
573C22⋊Q8—222no—
574#121—112no—
575#121—112no—
576#121—112no—
577#121—222no—
578#121—221no—
579#121—222no—
580#121—221no—
581#121—221no—
582#121—222no—
583#121—222no—
584#120—222no—
585#120—222no—
586C4×Q8—22no—
587C4×Q8—21no—
588C4×Q8—21no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—111no—
592C4×Q8—111no—
593C4×Q8C22⋊D1111yescharacteristic
594C4×Q8C22⋊D1111yescharacteristic
595C4×D4—24no—
596C4×D4—22no—
597C4×D4—112no—
598C4×D4—112no—
599C4×D4—111no—
600C4×D4—111no—
601C4×D4—221no—
602C4×D4—221no—
603C4×D4—222no—
604C4×D4—221no—
605C4×D4—221no—
606C4×D4—222no—
607C4×D4C22⋊D1112yes—
608C4×D4C22⋊D1111yescharacteristic
609C4×D4C22⋊D1112yes—
610C4×D4C22⋊D1111yescharacteristic
611#117—111no—
612#117—221no—
613#117—222no—
614#117C22×D1112yes—
615#117C22×D1114yes—
616#117C22×D1111yescharacteristic
617#117C22×D1112yes—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4C22×D1112yes—
622C2×C4⋊C4C22×D1114yes—
623C2×C22⋊C4—221no—
624C2×C42—221no—
625C2×C42C22×D1111yescharacteristic
626C2×C42C22×D1112yes—
627#107—112no—
628#107—112no—
629#107—114no—
630#107—114no—
631#106—114no—
632#106—114no—
633#106—112no—
634#106—112no—
635#106—114no—
636#106—114no—
637C4⋊C8—111no—
638C4⋊C8—111no—
639C4⋊C8—112no—
640C4⋊C8—112no—
641C4⋊C8—112no—
642#103—112no—
643#103—112no—
644#103—114no—
645#102—114no—
646#102—114no—
647#102—112no—
648#102—112no—
649#102—114no—
650#102—114no—
651#102—114no—
652C22⋊C8—114no—
653C22⋊C8—114no—
654#97—114no—
655C4×C8—114no—
656C2×C11—22no—
657C2×C11—42no—
658C2×C11C2×#53611yescharacteristic
659C2×C11C2×#57711yescharacteristic
660C2×C11#358511yescharacteristic
661D11—81no—
662D11—82no—
663C24—221no—
664#41—22no—
665#41—22no—
666#41—222no—
667#41—222no—
668#41—884no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—24no—
674C2×Q8—82no—
675C2×Q8—84no—
676C2×Q8—111no—
677C2×Q8—222no—
678C2×Q8C2×C22⋊D1111yescharacteristic
679C2×D4—112no—
680C2×D4—111no—
681C2×D4—221no—
682C2×D4—222no—
683C2×D4—222no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—221no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4C2×C22⋊D1112yes—
691C2×D4C2×C22⋊D1111yescharacteristic
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—222no—
698C22×C4—221no—
699C22×C4—222no—
700C22×C4—882no—
701C22×C4C2×C22⋊D1111yescharacteristic
702C22×C4C2×C22⋊D1112yes—
703C22×C4C2×C22⋊D1111yescharacteristic
704C22×C4C2×C22⋊D1112yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1111yescharacteristic
707M16—224no—
708C2×C8—112no—
709C2×C8—114no—
710C2×C8—112no—
711C2×C8—224no—
712C4⋊C4—22no—
713C4⋊C4—21no—
714C4⋊C4—22no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—22no—
718C4⋊C4—21no—
719C4⋊C4—22no—
720C4⋊C4—24no—
721C4⋊C4—22no—
722C4⋊C4—24no—
723C4⋊C4—112no—
724C4⋊C4—111no—
725C4⋊C4—111no—
726C4⋊C4—221no—
727C4⋊C4—221no—
728C4⋊C4—221no—
729C4⋊C4—222no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4C2×C22⋊D1111yescharacteristic
734C4⋊C4C2×C22⋊D1111yescharacteristic
735C4⋊C4C2×C22⋊D1112yes—
736C4⋊C4C2×C22⋊D1112yes—
737C4⋊C4C23×D1114yes—
738C4⋊C4C23×D1112yes—
739C4⋊C4C23×D1112yes—
740C22⋊C4—24no—
741C22⋊C4—22no—
742C22⋊C4—221no—
743C22⋊C4—222no—
744C22⋊C4—222no—
745C22⋊C4—222no—
746C22⋊C4—221no—
747C22⋊C4—221no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C22⋊C4C2×C22⋊D1112yes—
754C22⋊C4C2×C22⋊D1112yes—
755C22⋊C4C2×C22⋊D1112yes—
756C42—24no—
757C42—22no—
758C42—221no—
759C42—221no—
760C42—221no—
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1112yes—
763C42C2×C22⋊D1111yescharacteristic
764C42C2×C22⋊D1112yes—
765C42C23×D1112yes—
766C42C23×D1111yescharacteristic
767C42C23×D1111yescharacteristic
768C11#6089211yescharacteristic, complemented, Sylow
769C23—222no—
770C23—221no—
771C23—442no—
772C23—881no—
773C23—881no—
774C23C22×C22⋊D1112yes—
775C23C22×C22⋊D1111yescharacteristic
776Q8—22no—
777Q8—42no—
778Q8—44no—
779Q8—42no—
780Q8—82no—
781Q8—84no—
782Q8—221no—
783Q8—221no—
784Q8—882no—
785D4—24no—
786D4—22no—
787D4—222no—
788D4—222no—
789D4—221no—
790D4—221no—
791D4—442no—
792D4—442no—
793D4—882no—
794D4—882no—
795D4—882no—
796D4—882no—
797D4—882no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—82no—
808C2×C4—84no—
809C2×C4—221no—
810C2×C4—221no—
811C2×C4—221no—
812C2×C4—222no—
813C2×C4—442no—
814C2×C4—444no—
815C2×C4—442no—
816C2×C4—882no—
817C2×C4—881no—
818C2×C4—881no—
819C2×C4#6704012yes—
820C2×C4#6704012yes—
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1111yescharacteristic
823C2×C4C22×C22⋊D1111yescharacteristic
824C2×C4C22×C22⋊D1111yescharacteristic
825C2×C4C22×C22⋊D1112yes—
826C2×C4C22×C22⋊D1112yes—
827C2×C4C22×C22⋊D1111yescharacteristic
828C2×C4C22×C22⋊D1111yescharacteristic
829C2×C4C24×D1111yescharacteristic
830C8—222no—
831C8—222no—
832C8—224no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—441no—
839C22—442no—
840C22—441no—
841C22—442no—
842C22—442no—
843C22—441no—
844C22—884no—
845C22#1062334712yes—
846C22C23×C22⋊D1111yescharacteristic
847C4—21no—
848C4—21no—
849C4—22no—
850C4—22no—
851C4—21no—
852C4—22no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—441no—
857C4—441no—
858C4—442no—
859C4—441no—
860C4#1062334712yes—
861C4#1062336812yes—
862C4C2×#6704011yescharacteristic
863C4C2×#6704011yescharacteristic
864C2—22no—
865C2—42no—
866C2—882no—
867C2—881no—
868C2C2×#1062334711yescharacteristic
869C2C2×#1062336811yescharacteristic
870C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3503C2
socleC22×C11C23×D4
prime radical#13082032C2
hypercenter#3503D11
hypocenterC11#60892
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3503

Complements

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

NH ≅ G/Ntype
2. #13079914C2semidirect
3. #13079869C2semidirect
4. #13079837C2semidirect
5. #13079814C2semidirect
6. #13079795C2semidirect
7. #13079744C2semidirect
8. #13079142C2semidirect
9. #13078975C2semidirect
10. #13078605C2semidirect
11. #13078574C2semidirect
12. #13078425C2semidirect
13. #13078409C2semidirect
14. #13078398C2semidirect
15. C2×#10622697C2semidirect
16. #13077282C2semidirect
17. C11×#3503C2semidirect
25. C11×#544C22semidirect
27. C11×#533C22semidirect
29. C2×C11×C4⋊Q8C22semidirect
49. #10622707C22semidirect
50. #10622707C22semidirect
51. #10622704C22semidirect
52. #10622704C22semidirect
56. #10622700C22semidirect
57. #10622700C22semidirect
62. #10622697C22semidirect
63. #10622697C22semidirect
64. #10622693C22semidirect
65. #10622692C22semidirect
69. #10622679C22semidirect
70. #10622678C22semidirect
71. #10622677C22semidirect
72. #10622676C22semidirect
75. #10622616C22semidirect
78. #10622613C22semidirect
81. #10622609C22semidirect
83. #10622584C22semidirect
85. #10622581C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
334. #3503D11semidirect
423. #544C2×D11semidirect
433. #533C2×D11semidirect
437. C2×C4⋊Q8C2×D11semidirect
768. C11#60892semidirect

Maximal subgroups

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

subgroupindex
#130820322
#130799142
#130798692
#130798372
#130798142
#130797952
#130797442
#130791422
#130789752
#130786052
#130785742
#130784252
#130784092
#130783982
C2×#106226972
#130772822
C11×#35032
#6089211