Finite Group Databasebeta

← #15649351

Subgroups — #15649351

Order 2816.

1794 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic, complemented
2#13081479C212yesmaximal, complemented
3#13081265C212yesmaximal, complemented
4#13081034C212yesmaximal, complemented
5#13080989C214yesmaximal, complemented
6#13080538C212yesmaximal, complemented
7#13080460C214yesmaximal, complemented
8#13079936C212yesmaximal, complemented
9#13079932C211yesmaximal, characteristic, complemented
10#13079795C212yesmaximal, complemented
11#13079767C211yesmaximal, characteristic, complemented
12#13078670C212yesmaximal, complemented
13#13078612C211yesmaximal, characteristic, complemented
14#13078398C212yesmaximal, complemented
15C2×#10622697C211yesmaximal, characteristic, complemented
16#13077727C211yesmaximal, characteristic, complemented
17C11×#3511C211yesmaximal, characteristic, complemented
18C11×#556—21no—
19C11×#555C2212yescomplemented
20C11×#554C2212yescomplemented
21C11×#553C2214yes—
22C11×#548—22no—
23C11×#547—21no—
24C11×#542—22no—
25C11×#537—21no—
26C11×#533C2212yescomplemented
27C11×#532C2211yescharacteristic
28C11×#532C2212yescomplemented
29C2×C11×C4⋊Q8C2211yescharacteristic
30C11×#520—21no—
31C4×C11×#41C2211yescharacteristic
32#10623359—21no—
33#10623115C2211yescharacteristic
34#10623112—21no—
35#10623110C2211yescharacteristic
36#10623094C2211yescharacteristic
37#10623089—21no—
38#10623087—22no—
39#10623082C2211yescharacteristic
40#10623081C2212yes—
41#10623072C2212yes—
42#10623059—22no—
43D11×#117—21no—
44#10623010C2212yes—
45C4×#4339C2212yes—
46C2×C4×D44C2211yescharacteristic
47#10623001C2211yescharacteristic
48#10622707C2212yescomplemented
49#10622706C2212yescomplemented
50#10622704C2212yescomplemented
51#10622704C2212yescomplemented
52#10622700C2211yescharacteristic
53#10622700C2211yescharacteristic
54#10622697C2212yes—
55#10622697C2212yes—
56#10622697C2212yes—
57#10622697C2212yes—
58#10622691C2212yescomplemented
59#10622688C2212yescomplemented
60#10622685C2211yescharacteristic
61#10622685C2211yescharacteristic
62#10622681C2214yes—
63#10622679C2214yes—
64#10622677C2214yescomplemented
65#10622676C2214yescomplemented
66#10622654C2214yes—
67#10622654C2214yescomplemented
68#10622651C2214yes—
69#10622650C2214yes—
70#10622649C2212yes—
71#10622648C2214yescomplemented
72#10622646C2212yes—
73Q8×C11⋊C8C2212yescomplemented
74#10622632C2212yescomplemented
75C4×#4324C2214yescomplemented
76#10622629C2214yes—
77C4×#4323C2212yes—
78C4×#4323C2212yes—
79C4×#4323C2214yes—
80D4×C11⋊C8C2214yes—
81D4×C11⋊C8C2212yescomplemented
82#10622622C2214yescomplemented
83#10622621C2212yescomplemented
84#10622616C2214yes—
85#10622615C2214yes—
86#10622611C2214yescomplemented
87#10622609C2214yescomplemented
88#10622583C2214yes—
89C2×#66873C2212yes—
90C2×#66872C2212yes—
91#10622538C2211yescharacteristic
92#10622538C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41—21no—
96C2×C11×#41—22no—
97C2×C11×#41D411yescharacteristic
98C22×Q8×C11—21no—
99C2×#4339C2312yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8C2312yes—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2311yescharacteristic
107C11×#127C2311yescharacteristic
108C11×#126—24no—
109C11×#125C2314yes—
110C11×#124—24no—
111C11×#124—21no—
112C11×#124—22no—
113C11×#123—24no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—24no—
118C11×#121—22no—
119C11×#121—24no—
120C11×#121—21no—
121C11×#121—22no—
122C11×#121C2312yes—
123C11×#121C2314yes—
124C4×Q8×C11—22no—
125C4×Q8×C11—22no—
126C4×Q8×C11D411yescharacteristic
127C4×Q8×C11C2311yescharacteristic
128C4×D4×C11—24no—
129C4×D4×C11—22no—
130C4×D4×C11—21no—
131C4×D4×C11D412yes—
132C4×D4×C11D411yescharacteristic
133C4×D4×C11C2312yes—
134C4×D4×C11C2314yes—
135C4×D4×C11C2312yes—
136C4×D4×C11C2311yescharacteristic
137C11×#117—22no—
138C11×#117D411yescharacteristic
139C11×#117D412yes—
140C11×#117C2314yes—
141C2×C11×C4⋊C4—21no—
142C2×C11×C4⋊C4—22no—
143C2×C11×C4⋊C4C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2312yes—
146#66999—21no—
147#66999—21no—
148#66991—21no—
149#66991—21no—
150#66990—22no—
151#66988—22no—
152C2×#4324C2314yes—
153C2×#4323C2312yes—
154C2×#4323C2312yes—
155#66983C2312yes—
156#66982—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11—22no—
160C2×(C2×D11)⋊C4—21no—
161#66979—21no—
162#66979C2312yes—
163C2×C4⋊Dic11C2311yescharacteristic
164#66977—21no—
165#66977C2312yes—
166#66977C2312yes—
167C22×C11⋊C8C2312yes—
168C22×C11⋊C8C2314yes—
169#66951—22no—
170#66949—22no—
171#66947—22no—
172#66945—21no—
173#66945—21no—
174C4⋊C4×D11—21no—
175C4⋊C4×D11—21no—
176#66942—22no—
177#66938—22no—
178#66937—22no—
179#66936—22no—
180C22⋊C4×D11—22no—
181#66932—22no—
182#66930—22no—
183#66929—22no—
184#66928C2312yes—
185C4×D44—21no—
186C4×D44—21no—
187C4×D44C2311yescharacteristic
188C4×D44C2311yescharacteristic
189C4×D44C2311yescharacteristic
190C4×D44C2311yescharacteristic
191C4×D44C2312yes—
192#66925—22no—
193#66925—22no—
194C42×D11—22no—
195#66923—21no—
196#66923C2312yes—
197#66922C2311yescharacteristic
198#66922C2311yescharacteristic
199C4×Dic22—21no—
200C4×Dic22C2312yes—
201C4×Dic22C2312yes—
202#66896C2314yes—
203#66896C2312yes—
204#66896C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2314yes—
207#66874C2314yes—
208#66874C2314yes—
209#66874C2314yes—
210#66873C2314yes—
211#66873C2314yes—
212#66873C2312yes—
213#66873C2312yes—
214#66872C2314yes—
215#66872C2314yes—
216#66872C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2312yes—
220#66871C2312yes—
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2311yescharacteristic
224C4⋊(C11⋊C8)C2314yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4×C11⋊C8C2312yes—
227C4×C11⋊C8C2314yes—
228#62098—111nomaximal, Sylow
229C23×D11—21no—
230C11×#41—24no—
231C11×#41—44no—
232C11×#41—84no—
233C2×Q8×C11—21no—
234C2×Q8×C11—22no—
235C2×Q8×C11—22no—
236C2×Q8×C11—82no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×D4×C11—22no—
239C2×D4×C11—24no—
240C2×D4×C11—21no—
241C2×D4×C11—21no—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D411yescharacteristic
244C2×D4×C11C2412yes—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—24no—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C22×Dic11—21no—
257#4339—24no—
258#4339—42no—
259C2×D44—22no—
260C2×D44—21no—
261C2×D44—41no—
262C2×D44C2411yescharacteristic
263C2×D44C2411yescharacteristic
264C2×C4×D11—21no—
265C2×C4×D11—22no—
266C2×C4×D11—21no—
267C2×C4×D11—21no—
268C2×C4×D11—21no—
269C2×C4×D11—22no—
270C2×C4×D11—44no—
271C2×Dic22—21no—
272C2×Dic22C2412yes—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—24no—
279C11×C4⋊C4C2×D412yes—
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D411yescharacteristic
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2414yes—
284C11×C4⋊C4C2412yes—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4C2×D412yes—
291C11×C22⋊C4C2×D412yes—
292C11×C22⋊C4C2×D412yes—
293C42×C11—24no—
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D412yes—
297C42×C11C2×D412yes—
298C42×C11C2412yes—
299C42×C11C2411yescharacteristic
300C42×C11C2411yescharacteristic
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303C22⋊Dic11—22no—
304#4324—44no—
305#4323—24no—
306#4323—42no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—21no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—21no—
314(C2×D11)⋊C4—22no—
315C4⋊Dic11—21no—
316C4⋊Dic11—21no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11C2412yes—
320C4⋊Dic11C2411yescharacteristic
321C4⋊Dic11C2411yescharacteristic
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331C2×C11⋊C8—42no—
332C2×C11⋊C8—44no—
333C2×C11⋊C8C2412yes—
334C2×C11⋊C8C2412yes—
335C2×C11⋊C8C2414yes—
336#3511D1111yescharacteristic, complemented
337#3475—111no—
338#3380—112no—
339#3360—112no—
340#3341—112no—
341#3337—114no—
342#3303—112no—
343#3297—114no—
344#3247—112no—
345#3246—111no—
346#3233—112no—
347#3230—111no—
348#3106—112no—
349#3100—111no—
350#3076—112no—
351C2×#476—111no—
352#2988—111no—
353C23×C11—22no—
354C23×C11C22×D412yes—
355C23×C11C22×D411yescharacteristic
356C22×D11—21no—
357C22×D11—21no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—81no—
361Q8×C11—22no—
362Q8×C11—44no—
363Q8×C11—42no—
364Q8×C11—82no—
365D4×C11—24no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—42no—
370D4×C11—44no—
371D4×C11—42no—
372D4×C11—84no—
373C2×C4×C11—24no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—24no—
380C2×C4×C11—41no—
381C2×C4×C11—42no—
382C2×C4×C11—44no—
383C2×C4×C11—84no—
384C2×C4×C11—82no—
385C2×C4×C11#13514yes—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C2511yescharacteristic
395C22⋊D11—44no—
396C22⋊D11—82no—
397C2×Dic11—21no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—21no—
401C2×Dic11—42no—
402D44—21no—
403D44—21no—
404D44—21no—
405D44—42no—
406D442−1+412yes—
407C4×D11—44no—
408C4×D11—42no—
409C4×D11—42no—
410C4×D11—42no—
411C4×D11—42no—
412C4×D11—82no—
413Dic22—22no—
414Dic22—22no—
415Dic22—81no—
416C11⋊C8—22no—
417C11⋊C8—22no—
418C11⋊C8—24no—
419#556—21no—
420#556—111no—
421#555—111no—
422#555C2×D1112yescomplemented
423#554—111no—
424#554C2×D1112yescomplemented
425#553—221no—
426#553C2×D1114yes—
427#552—112no—
428#552—221no—
429#551—222no—
430#548—22no—
431#547—21no—
432#547—111no—
433#546—112no—
434#542—22no—
435#537—21no—
436#533—111no—
437#533C2×D1112yescomplemented
438#532C2×D1111yescharacteristic
439#532C2×D1112yescomplemented
440C2×C4⋊Q8C2×D1111yescharacteristic
441#529—112no—
442#529—222no—
443#525—221no—
444#520—21no—
445C4×#41—112no—
446C4×#41C2×D1111yescharacteristic
447C2×C4×D4—111no—
448C2×#117—221no—
449#500—112no—
450#499—114no—
451#488—114no—
452#487—112no—
453#485—114no—
454#484—114no—
455#482—114no—
456#482—114no—
457#480—112no—
458#479—114no—
459#478—114no—
460#478—114no—
461#477—112no—
462#477—112no—
463#476—112no—
464#476—112no—
465#476—112no—
466#476—112no—
467#476—112no—
468#475—112no—
469#474—111no—
470#474—111no—
471#466—114no—
472#465—114no—
473#465—114no—
474#463—114no—
475#461—112no—
476#460—112no—
477#459—111no—
478#459—111no—
479#449—114no—
480#447—112no—
481C8×Q8—112no—
482C4×SD16—114no—
483C4×D8—112no—
484C4×D8—112no—
485C4×D8—114no—
486C8×D4—114no—
487C8×D4—112no—
488#431—111no—
489#431—112no—
490#427—114no—
491C2×#106—112no—
492C2×C4⋊C8—112no—
493C2×C4⋊C8—111no—
494#416—114no—
495C2×#102—112no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11C2×#13512yes—
505C22×C11C23×D411yescharacteristic
506C2×D11—22no—
507C2×D11—41no—
508C2×D11—41no—
509C2×D11—41no—
510C2×D11—41no—
511C2×D11—41no—
512C2×D11—84no—
513C4×C11—21no—
514C4×C11—22no—
515C4×C11—21no—
516C4×C11—22no—
517C4×C11—21no—
518C4×C11—22no—
519C4×C11—44no—
520C4×C11—42no—
521C4×C11C2×#13512yes—
522C4×C11C2×#13512yes—
523C4×C11C2×2−1+411yescharacteristic
524C4×C11#58511yescharacteristic
525Dic11—42no—
526Dic11—42no—
527Dic11—41no—
528Dic11—41no—
529C2×#41—21no—
530C2×#41—22no—
531C2×#41—112no—
532C2×#41C22⋊D1111yescharacteristic
533C22×Q8—21no—
534C22×D4—111no—
535C23×C4—221no—
536C2×SD16—114no—
537C2×D8—112no—
538C2×D8—112no—
539C22×C8—112no—
540C22×C8—114no—
541C4⋊Q8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—111no—
544C4⋊Q8—111no—
545C4⋊Q8C22×D1112yes—
546C4⋊Q8C22×D1112yes—
547C4⋊Q8C22×D1111yescharacteristic
548#127C22×D1111yescharacteristic
549#126—24no—
550#126—222no—
551#126—222no—
552#126—222no—
553#125—112no—
554#125—222no—
555#125—221no—
556#125C22×D1114yes—
557#124—24no—
558#124—21no—
559#124—22no—
560#124—112no—
561#124—222no—
562#123—24no—
563#123—222no—
564#123—222no—
565#123—222no—
566#123—222no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—24no—
571C22⋊Q8—112no—
572C22⋊Q8—112no—
573C22⋊Q8—221no—
574C22⋊Q8—221no—
575C22⋊Q8—221no—
576C22⋊Q8—222no—
577#121—22no—
578#121—24no—
579#121—21no—
580#121—22no—
581#121—112no—
582#121—221no—
583#121—221no—
584#121—222no—
585#121C22×D1112yes—
586#121C22×D1114yes—
587#120—222no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—112no—
591C4×Q8—112no—
592C4×Q8—221no—
593C4×Q8C22⋊D1111yescharacteristic
594C4×Q8C22×D1111yescharacteristic
595C4×D4—24no—
596C4×D4—22no—
597C4×D4—21no—
598C4×D4—111no—
599C4×D4—111no—
600C4×D4—111no—
601C4×D4—111no—
602C4×D4—112no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4C22⋊D1111yescharacteristic
609C4×D4C22⋊D1112yes—
610C4×D4C22×D1112yes—
611C4×D4C22×D1114yes—
612C4×D4C22×D1112yes—
613C4×D4C22×D1111yescharacteristic
614#117—22no—
615#117—112no—
616#117—221no—
617#117—221no—
618#117—221no—
619#117—222no—
620#117—222no—
621#117—222no—
622#117C22⋊D1111yescharacteristic
623#117C22⋊D1112yes—
624#117C22×D1114yes—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—221no—
629C2×C4⋊C4—221no—
630C2×C4⋊C4C22×D1112yes—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—222no—
633C2×C42—222no—
634C2×C42C22×D1111yescharacteristic
635C2×C42C22×D1112yes—
636#107—112no—
637#107—114no—
638#107—112no—
639#107—114no—
640#106—114no—
641#106—114no—
642#106—114no—
643C4⋊C8—111no—
644C4⋊C8—112no—
645C4⋊C8—112no—
646C4⋊C8—114no—
647C4⋊C8—111no—
648#103—114no—
649#103—114no—
650#103—114no—
651#102—112no—
652#102—112no—
653#102—114no—
654#102—114no—
655#102—114no—
656#102—112no—
657#102—112no—
658C22⋊C8—112no—
659C22⋊C8—114no—
660C4×C8—112no—
661C4×C8—114no—
662C2×C11—22no—
663C2×C11—42no—
664C2×C11—82no—
665C2×C11#348911yescharacteristic
666C2×C11C22×#13511yescharacteristic
667C2×C11#358511yescharacteristic
668D11—42no—
669D11—81no—
670C24—221no—
671#41—24no—
672#41—44no—
673#41—84no—
674#41—224no—
675#41—442no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—82no—
680C2×Q8—112no—
681C2×Q8—221no—
682C2×Q8C2×C22⋊D1111yescharacteristic
683C2×D4—22no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—111no—
688C2×D4—111no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—222no—
692C2×D4—221no—
693C2×D4—441no—
694C2×D4C2×C22⋊D1112yes—
695C2×D4C2×C22⋊D1111yescharacteristic
696C2×D4C23×D1112yes—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—222no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—222no—
707C22×C4—444no—
708C22×C4C2×C22⋊D1112yes—
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C2×C22⋊D1112yes—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C23×D1111yescharacteristic
713C22×C4C23×D1112yes—
714SD16—444no—
715D8—224no—
716D8—442no—
717C2×C8—112no—
718C2×C8—114no—
719C2×C8—112no—
720C2×C8—444no—
721C2×C8—442no—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—24no—
728C4⋊C4—111no—
729C4⋊C4—111no—
730C4⋊C4—112no—
731C4⋊C4—221no—
732C4⋊C4—221no—
733C4⋊C4—221no—
734C4⋊C4—222no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—221no—
741C4⋊C4C2×C22⋊D1111yescharacteristic
742C4⋊C4C2×C22⋊D1111yescharacteristic
743C4⋊C4C2×C22⋊D1112yes—
744C4⋊C4C2×C22⋊D1112yes—
745C4⋊C4C23×D1114yes—
746C4⋊C4C23×D1112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—221no—
756C22⋊C4—222no—
757C22⋊C4—222no—
758C22⋊C4—221no—
759C22⋊C4—221no—
760C22⋊C4—221no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4C2×C22⋊D1112yes—
764C22⋊C4C2×C22⋊D1112yes—
765C22⋊C4C2×C22⋊D1112yes—
766C42—24no—
767C42—222no—
768C42—222no—
769C42—222no—
770C42C2×C22⋊D1112yes—
771C42C2×C22⋊D1112yes—
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1112yes—
776C42C23×D1111yescharacteristic
777C11#6209811yescharacteristic, complemented, Sylow
778C23—22no—
779C23—221no—
780C23—221no—
781C23—442no—
782C23—442no—
783C23—881no—
784C23C22×C22⋊D1112yes—
785C23C22×C22⋊D1111yescharacteristic
786Q8—22no—
787Q8—44no—
788Q8—42no—
789Q8—82no—
790Q8—222no—
791Q8—222no—
792Q8—881no—
793D4—24no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—42no—
798D4—44no—
799D4—42no—
800D4—84no—
801D4—112no—
802D4—221no—
803D4—221no—
804D4—221no—
805D4—442no—
806D4—444no—
807D4—882no—
808C2×C4—24no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—84no—
819C2×C4—82no—
820C2×C4—221no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—221no—
824C2×C4—444no—
825C2×C4—442no—
826C2×C4—442no—
827C2×C4—442no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—882no—
831C2×C4#6700314yes—
832C2×C4C22×C22⋊D1112yes—
833C2×C4C22×C22⋊D1112yes—
834C2×C4C22×C22⋊D1111yescharacteristic
835C2×C4C22×C22⋊D1111yescharacteristic
836C2×C4C22×C22⋊D1111yescharacteristic
837C2×C4C22×C22⋊D1112yes—
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C24×D1111yescharacteristic
841C8—222no—
842C8—222no—
843C8—224no—
844C22—21no—
845C22—21no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—222no—
853C22—441no—
854C22—441no—
855C22—441no—
856C22—441no—
857C22—441no—
858C22—884no—
859C22C2×#6700312yes—
860C22C23×C22⋊D1111yescharacteristic
861C4—21no—
862C4—22no—
863C4—21no—
864C4—22no—
865C4—21no—
866C4—22no—
867C4—44no—
868C4—42no—
869C4—442no—
870C4—442no—
871C4—441no—
872C4—441no—
873C4C2×#6700312yes—
874C4C2×#6700312yes—
875C4D11×2−1+411yescharacteristic
876C4#1062345711yescharacteristic
877C2—22no—
878C2—42no—
879C2—82no—
880C2—442no—
881C2—881no—
882C2#1308228911yescharacteristic
883C2C22×#6700311yescharacteristic
884C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3511C2
socleC22×C11C23×D4
hypercenter#3511D11
hypocenterC11#62098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13082180C2semidirect
2. #13081479C2semidirect
3. #13081265C2semidirect
4. #13081034C2semidirect
5. #13080989C2semidirect
6. #13080538C2semidirect
7. #13080460C2semidirect
8. #13079936C2semidirect
9. #13079932C2semidirect
10. #13079795C2semidirect
11. #13079767C2semidirect
12. #13078670C2semidirect
13. #13078612C2semidirect
14. #13078398C2semidirect
15. C2×#10622697C2semidirect
16. #13077727C2semidirect
17. C11×#3511C2semidirect
19. C11×#555C22semidirect
20. C11×#554C22semidirect
26. C11×#533C22semidirect
28. C11×#532C22semidirect
48. #10622707C22semidirect
49. #10622706C22semidirect
50. #10622704C22semidirect
51. #10622704C22semidirect
58. #10622691C22semidirect
59. #10622688C22semidirect
64. #10622677C22semidirect
65. #10622676C22semidirect
67. #10622654C22semidirect
71. #10622648C22semidirect
73. Q8×C11⋊C8C22semidirect
74. #10622632C22semidirect
75. C4×#4324C22semidirect
81. D4×C11⋊C8C22semidirect
82. #10622622C22semidirect
83. #10622621C22semidirect
86. #10622611C22semidirect
87. #10622609C22semidirect
92. #10622538C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
336. #3511D11semidirect
422. #555C2×D11semidirect
424. #554C2×D11semidirect
437. #533C2×D11semidirect
439. #532C2×D11semidirect
777. C11#62098semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130814792
#130812652
#130810342
#130809892
#130805382
#130804602
#130799362
#130799322
#130797952
#130797672
#130786702
#130786122
#130783982
C2×#106226972
#130777272
C11×#35112
#6209811