Finite Group Databasebeta

← #15649361

Subgroups — #15649361

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#13082527C211yesmaximal, characteristic, complemented
2#13081479C212yesmaximal, complemented
3#13081261C212yesmaximal, complemented
4#13081034C212yesmaximal, complemented
5#13080995C214yesmaximal, complemented
6#13080544C212yesmaximal, complemented
7#13080466C214yesmaximal, complemented
8#13079942C212yesmaximal, complemented
9#13079928C211yesmaximal, characteristic, complemented
10#13079791C212yesmaximal, complemented
11#13079764C211yesmaximal, characteristic, complemented
12#13078676C212yesmaximal, complemented
13#13078616C211yesmaximal, characteristic, complemented
14#13078404C212yesmaximal, complemented
15C2×#10622621C211yesmaximal, characteristic, complemented
16#13077727C211yesmaximal, characteristic, complemented
17C11×#3475C211yesmaximal, characteristic, complemented
18C11×#556C2211yescharacteristic
19C11×#555C2211yescharacteristic
20C11×#554C2211yescharacteristic
21C11×#553—21no—
22C11×#552—21no—
23C11×#552C2212yes—
24C11×#551—22no—
25C11×#547C2211yescharacteristic
26C11×#546C2212yes—
27C11×#533C2211yescharacteristic
28C11×#529—22no—
29C11×#529C2212yes—
30C11×#525—21no—
31C4×C11×#41C2212yes—
32C4×C11×#41C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117—21no—
35#10623364—21no—
36#10623115—21no—
37#10623110C2212yescomplemented
38#10623096C2214yes—
39#10623094C2212yescomplemented
40#10623083—22no—
41#10623082—21no—
42#10623065—22no—
43#10623054—21no—
44#10623008C2211yescharacteristic
45#10623008C2212yescomplemented
46#10623001C2212yescomplemented
47C2×#66922C2211yescharacteristic
48#10622851C2214yes—
49#10622846C2214yes—
50#10622830C2212yes—
51C2×#66896C2212yes—
52#10622697C2212yescomplemented
53#10622696C2212yescomplemented
54#10622694C2212yescomplemented
55#10622691C2212yescomplemented
56#10622679C2214yescomplemented
57#10622677C2214yescomplemented
58#10622670C2214yes—
59#10622669C2214yes—
60#10622661C2214yes—
61#10622661C2214yescomplemented
62#10622658C2214yescomplemented
63#10622657C2214yes—
64#10622651C2214yes—
65#10622648C2214yes—
66#10622640C2212yescomplemented
67C4×#4325C2214yescomplemented
68Q8×C11⋊C8C2212yescomplemented
69#10622635C2214yescomplemented
70#10622634C2212yescomplemented
71#10622634C2212yescomplemented
72#10622633C2212yescomplemented
73#10622628C2211yescharacteristic
74#10622628C2211yescharacteristic
75C4×#4323C2212yes—
76C4×#4323C2212yes—
77C4×#4323C2214yes—
78D4×C11⋊C8C2214yes—
79D4×C11⋊C8C2212yescomplemented
80#10622622C2214yes—
81#10622621C2212yes—
82#10622621C2212yes—
83#10622621C2212yes—
84#10622621C2212yes—
85#10622620C2211yescharacteristic
86#10622620C2211yescharacteristic
87#10622616C2214yescomplemented
88#10622611C2214yescomplemented
89#10622580C2212yes—
90C2×#66872C2212yes—
91#10622538C2211yescharacteristic
92#10622538C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41D411yescharacteristic
96C2×C11×#41C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C2×#4339—21no—
100C2×#4339—22no—
101C22×Dic22—21no—
102C11×C4⋊Q8C2311yescharacteristic
103C11×C4⋊Q8C2311yescharacteristic
104C11×#126—22no—
105C11×#126—22no—
106C11×#126—22no—
107C11×#125—22no—
108C11×#125—21no—
109C11×#125C2312yes—
110C11×#124—22no—
111C11×#124C2312yes—
112C11×#123—22no—
113C11×#123—22no—
114C11×#123—22no—
115C11×#123—22no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2312yes—
121C11×C22⋊Q8C2312yes—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—22no—
125C11×#121C2312yes—
126C11×#120—22no—
127C4×Q8×C11—21no—
128C4×Q8×C11D411yescharacteristic
129C4×Q8×C11C2312yes—
130C4×Q8×C11C2312yes—
131C4×Q8×C11C2311yescharacteristic
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—22no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11D411yescharacteristic
138C4×D4×C11D412yes—
139C4×D4×C11C2311yescharacteristic
140C4×D4×C11C2311yescharacteristic
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2311yescharacteristic
143C4×D4×C11C2312yes—
144C4×D4×C11C2311yescharacteristic
145C4×D4×C11C2312yes—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117—22no—
150C11×#117—22no—
151C11×#117—22no—
152C11×#117D411yescharacteristic
153C11×#117D412yes—
154C11×#117C2312yes—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—22no—
160C2×C42×C11—22no—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#66999—22no—
164C2×#4325C2314yes—
165#66992—24no—
166#66991—22no—
167C2×#4323C2312yes—
168C2×#4323C2312yes—
169#66983—21no—
170#66983—22no—
171#66983C2312yes—
172#66983C2314yes—
173#66979C2314yes—
174C2×C4⋊Dic11—21no—
175C2×C4⋊Dic11C2312yes—
176#66977—22no—
177#66977—22no—
178C22×C11⋊C8C2312yes—
179C22×C11⋊C8C2314yes—
180#66951—24no—
181#66949—24no—
182#66945—22no—
183C4⋊C4×D11—22no—
184#66938—24no—
185#66936—24no—
186(C22⋊D11)⋊C4—24no—
187#66928—21no—
188#66928—22no—
189#66927C2311yescharacteristic
190C4×D44—21no—
191C4×D44—22no—
192C4×D44C2312yes—
193C4×D44C2314yes—
194#66923C2314yes—
195#66922—21no—
196#66922—21no—
197#66922C2312yes—
198#66922C2312yes—
199#66922C2311yescharacteristic
200C4×Dic22—22no—
201C4×Dic22—22no—
202#66899C2314yes—
203#66899C2314yes—
204#66899C2314yes—
205#66896C2314yes—
206#66896C2314yes—
207#66896C2312yes—
208#66896C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2314yes—
211#66873C2312yes—
212#66873C2312yes—
213#66873C2314yes—
214#66872C2314yes—
215#66872C2314yes—
216#66872C2314yes—
217#66871C2312yes—
218#66871C2312yes—
219#66871C2314yes—
220#66871C2314yes—
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
229C24×C11—21no—
230C11×#41—24no—
231C11×#41—24no—
232C11×#41—42no—
233C2×Q8×C11—21no—
234C2×Q8×C11C2×D411yescharacteristic
235C2×Q8×C11C2412yes—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—21no—
240C2×D4×C11—41no—
241C2×D4×C11C2×D411yescharacteristic
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2411yescharacteristic
244C2×D4×C11C2411yescharacteristic
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—22no—
252C22×C4×C11—44no—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2412yes—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—24no—
261C22×Dic11—22no—
262#4339—44no—
263#4339—84no—
264C2×D44—21no—
265C2×D44—21no—
266C2×D44C2412yes—
267C2×C4×D11—22no—
268C2×C4×D11—24no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—22no—
272C2×Dic22—82no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4C2×D411yescharacteristic
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D412yes—
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2412yes—
288C11×C4⋊C4C2411yescharacteristic
289C11×C4⋊C4C2411yescharacteristic
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C42×C11—22no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11C2×D412yes—
308C42×C11C2×D412yes—
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2411yescharacteristic
312C42×C11C2412yes—
313C42×C11C2411yescharacteristic
314C22⋊Dic11—24no—
315#4325—44no—
316#4323—24no—
317#4323—42no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—24no—
322C4⋊Dic11—21no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11C2414yes—
327C4⋊Dic11C2412yes—
328Dic11⋊C4—24no—
329Dic11⋊C4—24no—
330C4×Dic11—24no—
331C2×C11⋊C8—42no—
332C2×C11⋊C8—44no—
333C2×C11⋊C8C2412yes—
334C2×C11⋊C8C2412yes—
335C2×C11⋊C8C2414yes—
336#3511—111no—
337#3475D1111yescharacteristic, complemented
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—21no—
354C23×C11—21no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—81no—
358C23×C11C22×D412yes—
359C23×C11C22×D411yescharacteristic
360C22×D11—22no—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—22no—
364Q8×C11—81no—
365D4×C11—24no—
366D4×C11—22no—
367D4×C11—21no—
368D4×C11—21no—
369D4×C11—21no—
370D4×C11—42no—
371D4×C11—44no—
372D4×C11—82no—
373D4×C112−1+412yes—
374C2×C4×C11—24no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—44no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—82no—
392C2×C4×C11#13514yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C2511yescharacteristic
402C22⋊D11—44no—
403C22⋊D11—84no—
404C2×Dic11—22no—
405C2×Dic11—24no—
406C2×Dic11—82no—
407D44—22no—
408D44—22no—
409D44—42no—
410D44—42no—
411C4×D11—44no—
412C4×D11—84no—
413Dic22—44no—
414Dic22—42no—
415Dic22—82no—
416C11⋊C8—22no—
417C11⋊C8—22no—
418C11⋊C8—24no—
419#556—221no—
420#556C2×D1111yescharacteristic
421#555—112no—
422#555C2×D1111yescharacteristic
423#554—112no—
424#554C2×D1111yescharacteristic
425#553—21no—
426#553—114no—
427#552—21no—
428#552C2×D1112yes—
429#551—22no—
430#548—222no—
431#547—221no—
432#547C2×D1111yescharacteristic
433#546C2×D1112yes—
434#542—222no—
435#537—221no—
436#533—112no—
437#533C2×D1111yescharacteristic
438#532—111no—
439#532—112no—
440C2×C4⋊Q8—111no—
441#529—22no—
442#529C2×D1112yes—
443#525—21no—
444#520—221no—
445C4×#41C2×D1112yes—
446C4×#41C2×D1111yescharacteristic
447C2×C4×D4C2×D1111yescharacteristic
448C2×#117—21no—
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—22no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—84no—
508C22×C11C2×#13512yes—
509C22×C11C23×D411yescharacteristic
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C4×C11—21no—
514C4×C11—22no—
515C4×C11—21no—
516C4×C11—22no—
517C4×C11—21no—
518C4×C11—22no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11—41no—
522C4×C11—41no—
523C4×C11C2×#13512yes—
524C4×C11C2×#13512yes—
525C4×C11C2×2−1+411yescharacteristic
526C4×C11#58511yescharacteristic
527Dic11—44no—
528Dic11—42no—
529C2×#41—221no—
530C2×#41—222no—
531C2×#41C22⋊D1111yescharacteristic
532C2×#41C22×D1112yes—
533C22×Q8—221no—
534C22×D4C22×D1111yescharacteristic
535C23×C4—21no—
536C2×SD16—114no—
537C2×D8—112no—
538C2×D8—112no—
539C22×C8—112no—
540C22×C8—114no—
541C4⋊Q8—112no—
542C4⋊Q8—112no—
543C4⋊Q8—111no—
544C4⋊Q8—221no—
545C4⋊Q8—221no—
546C4⋊Q8C22×D1111yescharacteristic
547C4⋊Q8C22×D1111yescharacteristic
548#127—111no—
549#126—22no—
550#126—22no—
551#126—22no—
552#126—224no—
553#125—22no—
554#125—21no—
555#125—114no—
556#125C22×D1112yes—
557#124—22no—
558#124—224no—
559#124—221no—
560#124—222no—
561#124C22×D1112yes—
562#123—22no—
563#123—22no—
564#123—22no—
565#123—22no—
566#123—224no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—22no—
571C22⋊Q8—222no—
572C22⋊Q8—222no—
573C22⋊Q8—222no—
574C22⋊Q8—224no—
575C22⋊Q8C22×D1112yes—
576C22⋊Q8C22×D1112yes—
577#121—21no—
578#121—21no—
579#121—22no—
580#121—112no—
581#121—114no—
582#121—222no—
583#121—224no—
584#121—222no—
585#121—221no—
586#121C22×D1112yes—
587#120—22no—
588C4×Q8—21no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×Q8C22⋊D1111yescharacteristic
592C4×Q8C22×D1112yes—
593C4×Q8C22×D1112yes—
594C4×Q8C22×D1111yescharacteristic
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—114no—
601C4×D4—112no—
602C4×D4—224no—
603C4×D4—222no—
604C4×D4—221no—
605C4×D4C22⋊D1111yescharacteristic
606C4×D4C22⋊D1112yes—
607C4×D4C22×D1111yescharacteristic
608C4×D4C22×D1111yescharacteristic
609C4×D4C22×D1111yescharacteristic
610C4×D4C22×D1111yescharacteristic
611C4×D4C22×D1112yes—
612C4×D4C22×D1112yes—
613C4×D4C22×D1111yescharacteristic
614#117—21no—
615#117—21no—
616#117—21no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—114no—
621#117—222no—
622#117C22⋊D1111yescharacteristic
623#117C22⋊D1112yes—
624#117C22×D1112yes—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—221no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—22no—
633C2×C42—22no—
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—114no—
652#102—114no—
653#102—112no—
654#102—112no—
655#102—112no—
656#102—112no—
657#102—114no—
658C22⋊C8—112no—
659C22⋊C8—114no—
660C4×C8—112no—
661C4×C8—114no—
662C2×C11—22no—
663C2×C11—42no—
664C2×C11—42no—
665C2×C11—81no—
666C2×C11#348911yescharacteristic
667C2×C11C22×#13511yescharacteristic
668C2×C11#358511yescharacteristic
669D11—82no—
670C24—21no—
671#41—24no—
672#41—24no—
673#41—42no—
674#41—444no—
675#41—884no—
676C2×Q8—21no—
677C2×Q8—221no—
678C2×Q8—222no—
679C2×Q8—222no—
680C2×Q8—882no—
681C2×Q8C2×C22⋊D1111yescharacteristic
682C2×Q8C23×D1112yes—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—21no—
687C2×D4—41no—
688C2×D4—112no—
689C2×D4—222no—
690C2×D4—224no—
691C2×D4—221no—
692C2×D4—221no—
693C2×D4C2×C22⋊D1112yes—
694C2×D4C2×C22⋊D1111yescharacteristic
695C2×D4C23×D1111yescharacteristic
696C2×D4C23×D1111yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—44no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—224no—
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—21no—
723C4⋊C4—21no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—114no—
733C4⋊C4—112no—
734C4⋊C4—222no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4—224no—
738C4⋊C4—221no—
739C4⋊C4—224no—
740C4⋊C4C2×C22⋊D1111yescharacteristic
741C4⋊C4C2×C22⋊D1111yescharacteristic
742C4⋊C4C2×C22⋊D1112yes—
743C4⋊C4C2×C22⋊D1112yes—
744C4⋊C4C23×D1111yescharacteristic
745C4⋊C4C23×D1111yescharacteristic
746C4⋊C4C23×D1112yes—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—21no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4C2×C22⋊D1112yes—
764C22⋊C4C2×C22⋊D1112yes—
765C22⋊C4C2×C22⋊D1112yes—
766C42—22no—
767C42—22no—
768C42—22no—
769C42—224no—
770C42C2×C22⋊D1112yes—
771C42C2×C22⋊D1112yes—
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1112yes—
776C42C23×D1111yescharacteristic
777C11#6209811yescharacteristic, complemented, Sylow
778C23—21no—
779C23—21no—
780C23—42no—
781C23—42no—
782C23—81no—
783C23—222no—
784C23C22×C22⋊D1112yes—
785C23C22×C22⋊D1111yescharacteristic
786Q8—22no—
787Q8—22no—
788Q8—22no—
789Q8—81no—
790Q8—444no—
791Q8—442no—
792Q8—882no—
793D4—24no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—42no—
799D4—44no—
800D4—82no—
801D4—222no—
802D4—222no—
803D4—442no—
804D4—444no—
805D4—442no—
806D4—884no—
807D4#6704312yes—
808C2×C4—24no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—82no—
826C2×C4—222no—
827C2×C4—224no—
828C2×C4—444no—
829C2×C4—884no—
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—22no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—84no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22C2×#6700312yes—
860C22C23×C22⋊D1111yescharacteristic
861C4—21no—
862C4—22no—
863C4—21no—
864C4—22no—
865C4—21no—
866C4—22no—
867C4—42no—
868C4—42no—
869C4—41no—
870C4—41no—
871C4—444no—
872C4—442no—
873C4C2×#6700312yes—
874C4C2×#6700312yes—
875C4C2×#6704311yescharacteristic
876C4#1062345311yescharacteristic
877C2—22no—
878C2—42no—
879C2—42no—
880C2—81no—
881C2—882no—
882C2#1308229611yescharacteristic
883C2C22×#6700311yescharacteristic
884C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3475C2
socleC22×C11C23×D4
hypercenter#3475D11
hypocenterC11#62098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13082527C2semidirect
2. #13081479C2semidirect
3. #13081261C2semidirect
4. #13081034C2semidirect
5. #13080995C2semidirect
6. #13080544C2semidirect
7. #13080466C2semidirect
8. #13079942C2semidirect
9. #13079928C2semidirect
10. #13079791C2semidirect
11. #13079764C2semidirect
12. #13078676C2semidirect
13. #13078616C2semidirect
14. #13078404C2semidirect
15. C2×#10622621C2semidirect
16. #13077727C2semidirect
17. C11×#3475C2semidirect
37. #10623110C22semidirect
39. #10623094C22semidirect
45. #10623008C22semidirect
46. #10623001C22semidirect
52. #10622697C22semidirect
53. #10622696C22semidirect
54. #10622694C22semidirect
55. #10622691C22semidirect
56. #10622679C22semidirect
57. #10622677C22semidirect
61. #10622661C22semidirect
62. #10622658C22semidirect
66. #10622640C22semidirect
67. C4×#4325C22semidirect
68. Q8×C11⋊C8C22semidirect
69. #10622635C22semidirect
70. #10622634C22semidirect
71. #10622634C22semidirect
72. #10622633C22semidirect
79. D4×C11⋊C8C22semidirect
87. #10622616C22semidirect
88. #10622611C22semidirect
92. #10622538C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
337. #3475D11semidirect
777. C11#62098semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130814792
#130812612
#130810342
#130809952
#130805442
#130804662
#130799422
#130799282
#130797912
#130797642
#130786762
#130786162
#130784042
C2×#106226212
#130777272
C11×#34752
#6209811