Finite Group Databasebeta

← #15622607

Subgroups — #15622607

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082368C211yesmaximal, characteristic
2#13078916C214yesmaximal, complemented
3#13078845C214yesmaximal, complemented
4#13078787C212yesmaximal, complemented
5#13078746C212yesmaximal, complemented
6#13078696C212yesmaximal, complemented
7#13078655C212yesmaximal, complemented
8#13078564C211yesmaximal, characteristic, complemented
9#13078529C211yesmaximal, characteristic
10#13078458C212yesmaximal, complemented
11#13078146C212yesmaximal, complemented
12#13077850C211yesmaximal, characteristic
13C2×#10622841C211yesmaximal, characteristic, complemented
14#13077482C212yesmaximal, complemented
15#13077459C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C2×C11×#519C211yesmaximal, characteristic, complemented
18C23×Q8×C11C2211yescharacteristic
19C11×#519—21no—
20C11×#519—22no—
21C11×#519—21no—
22C11×#519C2214yes—
23C11×#519C2212yes—
24C11×#519C2212yes—
25C2×C4×Q8×C11—21no—
26C2×C4×Q8×C11—21no—
27C2×C4×Q8×C11C2212yes—
28C2×C4×Q8×C11C2212yes—
29C2×C11×#117—22no—
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×#4326C2212yes—
33C2×#66995C2212yes—
34#10623322C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36#10623065C2212yes—
37#10623064—21no—
38#10623062—22no—
39#10623060—21no—
40#10623057C2211yescharacteristic
41#10623054C2211yescharacteristic
42#10623050C2211yescharacteristic
43#10623049C2212yes—
44#10623047C2211yescharacteristic
45#10623044—21no—
46#10623042—21no—
47#10623026—22no—
48#10623010C2212yes—
49#10623001C2212yes—
50#10622841C2212yes—
51#10622841C2214yes—
52#10622841C2212yes—
53#10622841C2212yes—
54#10622841C2212yes—
55#10622840C2212yes—
56#10622840C2212yes—
57#10622838C2212yes—
58C2×#66899C2212yes—
59#10622820C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61#10622644C2214yescomplemented
62#10622644C2214yescomplemented
63#10622643C2214yescomplemented
64#10622643C2214yescomplemented
65#10622643C2214yescomplemented
66C4×#4326C2214yescomplemented
67C4×#4326C2214yescomplemented
68C4×#4326C2214yescomplemented
69#10622641C2214yescomplemented
70#10622641C2214yescomplemented
71#10622639C2214yescomplemented
72C4×#4325C2214yescomplemented
73#10622635C2214yescomplemented
74#10622635C2214yescomplemented
75#10622634C2214yescomplemented
76#10622633C2214yescomplemented
77#10622617C2212yes—
78#10622616C2212yes—
79#10622615C2212yes—
80#10622613C2214yes—
81#10622612C2212yes—
82#10622611C2212yes—
83#10622610C2212yes—
84#10622609C2212yes—
85#10622609C2214yes—
86#10622608C2212yes—
87#10622584C2211yescharacteristic
88#10622584C2212yes—
89#10622583C2211yescharacteristic
90#10622583C2212yes—
91#10622581C2211yescharacteristic
92#10622580C2211yescharacteristic
93#10622539C2212yes—
94#10622538C2212yes—
95C22×Q8×C11—28no—
96C22×Q8×C11—21no—
97C22×Q8×C11—21no—
98C22×Q8×C11—21no—
99C22×Q8×C11C2312yes—
100C22×Q8×C11C2312yes—
101C22×Q8×C11C2312yes—
102C23×C4×C11—21no—
103C23×C4×C11C2311yescharacteristic
104C2×#4339C2311yescharacteristic
105C22×Dic22C2311yescharacteristic
106C4×Q8×C11—22no—
107C4×Q8×C11—22no—
108C4×Q8×C11—22no—
109C4×Q8×C11—24no—
110C4×Q8×C11—24no—
111C4×Q8×C11—22no—
112C4×Q8×C11—22no—
113C4×Q8×C11—22no—
114C4×Q8×C11—22no—
115C4×Q8×C11—22no—
116C4×Q8×C11C2314yes—
117C4×Q8×C11C2314yes—
118C4×Q8×C11C2314yes—
119C4×Q8×C11C2314yes—
120C11×#117—21no—
121C11×#117—21no—
122C11×#117—24no—
123C11×#117—24no—
124C11×#117—24no—
125C11×#117—24no—
126C11×#117D411yescharacteristic
127C11×#117D412yes—
128C11×#117D411yescharacteristic
129C11×#117C2312yes—
130C11×#117C2312yes—
131C11×#117C2311yescharacteristic
132C11×#117C2312yes—
133C11×#117C2311yescharacteristic
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4D411yescharacteristic
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4D412yes—
142C2×C42×C11—22no—
143C2×C42×C11—22no—
144C2×C42×C11—21no—
145C2×C42×C11C2312yes—
146#67006—21no—
147C2×C22⋊Dic11—21no—
148C2×#4326—28no—
149C2×#4326C2314yes—
150C2×#4326C2314yes—
151C2×#4326C2314yes—
152#66995—28no—
153C2×#4325C2314yes—
154#66983C2311yescharacteristic
155#66983C2311yescharacteristic
156#66982—22no—
157#66982—21no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11—21no—
160C4×C22⋊D11—21no—
161#66979—22no—
162#66979C2311yescharacteristic
163C2×C4⋊Dic11C2311yescharacteristic
164#66977—22no—
165#66977—21no—
166#66977—21no—
167#66977C2311yescharacteristic
168#66977C2312yes—
169#66977C2311yescharacteristic
170#66977C2312yes—
171C2×Dic11⋊C4—21no—
172C2×#4318C2312yes—
173C22×C11⋊C8C2312yes—
174#66951—22no—
175#66950—21no—
176#66950—21no—
177#66949—22no—
178#66945—21no—
179C4⋊C4×D11—21no—
180#66943—21no—
181#66942—22no—
182#66942—22no—
183#66941—21no—
184#66940—21no—
185#66940—21no—
186#66939—22no—
187#66938—22no—
188#66936—22no—
189(C22⋊D11)⋊C4—22no—
190#66932—22no—
191#66932—22no—
192#66931—22no—
193#66930—22no—
194#66929—22no—
195#66928C2312yes—
196C4×D44C2312yes—
197#66925—22no—
198#66923—22no—
199#66923C2312yes—
200#66922C2312yes—
201#66922C2312yes—
202C4×Dic22—22no—
203C4×Dic22C2312yes—
204C4×Dic22C2312yes—
205C4×Dic22C2312yes—
206#66899C2314yes—
207#66899C2314yes—
208#66899C2314yes—
209#66899C2314yes—
210C22⋊(C11⋊C8)C2311yescharacteristic
211C22⋊(C11⋊C8)C2312yes—
212C22⋊(C11⋊C8)C2311yescharacteristic
213C22⋊(C11⋊C8)C2312yes—
214C22⋊(C11⋊C8)C2312yes—
215#66874C2312yes—
216#66874C2314yes—
217#66874C2312yes—
218#66874C2314yes—
219#66873C2312yes—
220#66873C2312yes—
221#66872C2312yes—
222#66872C2314yes—
223#66872C2312yes—
224#66871C2312yes—
225#66871C2314yes—
226#66871C2312yes—
227C4⋊(C11⋊C8)C2314yes—
228C4⋊(C11⋊C8)C2314yes—
229#66867C2314yes—
230C4×C11⋊C8C2314yes—
231#60583—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C2×Q8×C11—28no—
234C2×Q8×C11—28no—
235C2×Q8×C11—28no—
236C2×Q8×C11—28no—
237C2×Q8×C11—28no—
238C2×Q8×C11—22no—
239C2×Q8×C11—22no—
240C2×Q8×C11—22no—
241C2×Q8×C11—24no—
242C2×Q8×C11#4118yes—
243C2×Q8×C11C2414yes—
244C22×C4×C11—28no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—24no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C2×C22⋊D11—21no—
260C2×C22⋊D11—21no—
261C2×C22⋊D11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264#4339—24no—
265C2×D44C2411yescharacteristic
266C2×C4×D11—21no—
267C2×C4×D11—22no—
268C2×Dic22—21no—
269C2×Dic22—22no—
270C2×Dic22—24no—
271C2×Dic22C2411yescharacteristic
272C2×Dic22C2412yes—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—24no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4C2×D411yescharacteristic
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D411yescharacteristic
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2412yes—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4C2×D412yes—
290C11×C22⋊C4C2×D412yes—
291C11×C22⋊C4C2×D412yes—
292C11×C22⋊C4C2×D412yes—
293C42×C11—24no—
294C42×C11—24no—
295C42×C11—24no—
296C42×C11—24no—
297C42×C11—22no—
298C42×C11—22no—
299C42×C11C2×D412yes—
300C42×C11C2×D412yes—
301C42×C11C2412yes—
302C42×C11C2412yes—
303C22⋊Dic11—21no—
304C22⋊Dic11—21no—
305C22⋊Dic11—22no—
306C22⋊Dic11—21no—
307C22⋊Dic11—22no—
308#4326—28no—
309#4326—28no—
310#4326—28no—
311#4325—28no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—21no—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—22no—
320C4⋊Dic11—21no—
321C4⋊Dic11C2411yescharacteristic
322C4⋊Dic11C2411yescharacteristic
323C4⋊Dic11C2412yes—
324Dic11⋊C4—21no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—21no—
332Dic11⋊C4—22no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—21no—
337#4318—24no—
338C2×C11⋊C8—24no—
339C2×C11⋊C8C2412yes—
340C2×C11⋊C8C2414yes—
341C2×C11⋊C8C2412yes—
342#3495—111no—
343C2×#519D1111yescharacteristic, complemented
344#3127—114no—
345#3121—114no—
346#3117—112no—
347#3113—112no—
348#3108—112no—
349#3104—112no—
350#3095—111no—
351#3091—111no—
352#3082—112no—
353#3044—112no—
354#3004—111no—
355C2×#451—111no—
356#2950—112no—
357#2947—112no—
358#2924—111no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—41no—
362C23×C11C22×D411yescharacteristic
363C23×C11C22×D411yescharacteristic
364C23×C11C22×D411yescharacteristic
365C22×D11—21no—
366Q8×C11—28no—
367Q8×C11—28no—
368Q8×C11—28no—
369Q8×C11—24no—
370Q8×C11C2×#4118yes—
371C2×C4×C11—28no—
372C2×C4×C11—28no—
373C2×C4×C11—28no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—42no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C2×#4114yes—
394C2×C4×C11C2511yescharacteristic
395C22⋊D11—42no—
396C22⋊D11—42no—
397C22⋊D11—81no—
398C2×Dic11—21no—
399C2×Dic11—21no—
400C2×Dic11—21no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—42no—
404C2×Dic11—81no—
405D44—22no—
406C4×D11—42no—
407C4×D11—82no—
408Dic22—24no—
409Dic22—22no—
410Dic22—42no—
411Dic22—82no—
412C11⋊C8—22no—
413C11⋊C8—22no—
414C11⋊C8—24no—
415C23×Q8C2×D1111yescharacteristic
416C2×#137—112no—
417C22×Q16—112no—
418#556—221no—
419#554—221no—
420#552—221no—
421#552—222no—
422#552—221no—
423#551—222no—
424#544—111no—
425#542—112no—
426#541—112no—
427#536—111no—
428#533—112no—
429#529—112no—
430#525—111no—
431C2×C22⋊Q8—111no—
432#520—111no—
433#519—22no—
434#519—21no—
435#519—21no—
436#519—111no—
437#519C2×D1112yes—
438#519C2×D1114yes—
439#519C2×D1112yes—
440C2×C4×Q8—21no—
441C2×C4×Q8—21no—
442C2×C4×Q8C2×D1112yes—
443C2×C4×Q8C2×D1112yes—
444C2×#117—22no—
445C2×#117C2×D1111yescharacteristic
446C2×#117C2×D1111yescharacteristic
447#485—112no—
448#485—114no—
449#484—111no—
450#484—112no—
451#483—111no—
452#483—112no—
453#482—112no—
454#481—111no—
455#480—111no—
456#479—114no—
457#479—114no—
458#477—114no—
459#475—114no—
460#464—114no—
461#464—114no—
462#462—114no—
463#462—114no—
464#451—112no—
465#451—112no—
466#451—112no—
467#451—114no—
468#451—112no—
469#448—112no—
470#448—112no—
471#441—114no—
472#441—114no—
473#441—114no—
474#440—114no—
475C4×Q16—114no—
476C4×Q16—114no—
477C4×Q16—114no—
478C4×SD16—114no—
479#433—114no—
480#432—112no—
481#431—112no—
482#428—112no—
483#427—112no—
484#424—112no—
485#419—112no—
486#419—112no—
487#416—112no—
488C2×#103—112no—
489#407—111no—
490C2×C22⋊C8—111no—
491#405—112no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—44no—
500C22×C11#52512yes—
501C22×C11#57812yes—
502C22×C11C23×D411yescharacteristic
503C2×D11—41no—
504C2×D11—41no—
505C2×D11—41no—
506C4×C11—22no—
507C4×C11—22no—
508C4×C11—28no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—22no—
512C4×C11—22no—
513C4×C11—42no—
514C4×C11—42no—
515C4×C11#52512yes—
516C4×C11C22×#4112yes—
517Dic11—41no—
518Dic11—42no—
519Dic11—42no—
520Dic11—41no—
521Dic11—41no—
522C2×#41—111no—
523C22×Q8—28no—
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8—111no—
528C22×Q8C22×D1112yes—
529C22×Q8C22×D1112yes—
530C22×Q8C22×D1112yes—
531C23×C4—21no—
532C23×C4C22×D1111yescharacteristic
533#137—228no—
534C2×Q16—114no—
535C2×Q16—114no—
536C2×Q16—114no—
537C2×Q16—228no—
538C2×SD16—114no—
539C2×M16—112no—
540C22×C8—112no—
541C4⋊Q8—112no—
542C4⋊Q8—112no—
543C4⋊Q8—221no—
544#126—222no—
545#126—222no—
546#126—222no—
547#126—222no—
548#125—112no—
549#125—222no—
550#125—222no—
551#125—221no—
552#125—222no—
553#124—112no—
554#124—222no—
555#123—221no—
556#123—222no—
557#123—222no—
558#123—222no—
559C22⋊Q8—112no—
560C22⋊Q8—112no—
561C22⋊Q8—111no—
562C22⋊Q8—111no—
563C22⋊Q8—221no—
564C22⋊Q8—221no—
565C22⋊Q8—222no—
566C22⋊Q8—221no—
567C22⋊Q8—221no—
568C22⋊Q8—222no—
569C22⋊Q8—222no—
570#121—111no—
571#121—111no—
572#120—221no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—24no—
577C4×Q8—22no—
578C4×Q8—24no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—112no—
584C4×Q8—112no—
585C4×Q8—112no—
586C4×Q8—221no—
587C4×Q8—221no—
588C4×Q8—222no—
589C4×Q8C22×D1114yes—
590C4×Q8C22×D1114yes—
591C4×Q8C22×D1114yes—
592C4×Q8C22×D1114yes—
593C4×D4—112no—
594C4×D4—221no—
595C4×D4—221no—
596C4×D4—222no—
597C4×D4—222no—
598#117—21no—
599#117—21no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—111no—
605#117—222no—
606#117—221no—
607#117—222no—
608#117—222no—
609#117C22⋊D1111yescharacteristic
610#117C22⋊D1112yes—
611#117C22⋊D1111yescharacteristic
612#117C22×D1112yes—
613#117C22×D1112yes—
614#117C22×D1111yescharacteristic
615#117C22×D1111yescharacteristic
616#117C22×D1112yes—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C4⋊C4C22⋊D1111yescharacteristic
623C2×C4⋊C4C22⋊D1111yescharacteristic
624C2×C4⋊C4C22×D1111yescharacteristic
625C2×C4⋊C4C22×D1111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4C22⋊D1112yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—21no—
632C2×C42C22×D1112yes—
633#107—112no—
634#107—112no—
635#107—114no—
636#106—112no—
637#106—112no—
638#106—114no—
639C4⋊C8—114no—
640C4⋊C8—114no—
641#103—114no—
642#103—114no—
643#103—114no—
644#103—114no—
645#103—112no—
646#103—112no—
647#103—114no—
648#103—114no—
649#102—112no—
650#102—112no—
651C22⋊C8—111no—
652C22⋊C8—111no—
653C22⋊C8—112no—
654C22⋊C8—112no—
655C22⋊C8—112no—
656#97—114no—
657C4×C8—114no—
658C2×C11—22no—
659C2×C11—22no—
660C2×C11—41no—
661C2×C11C2×#52511yescharacteristic
662C2×C11C2×#57811yescharacteristic
663C2×C11#358611yescharacteristic
664D11—81no—
665C24C2×C22⋊D1111yescharacteristic
666#41—224no—
667C2×Q8—28no—
668C2×Q8—28no—
669C2×Q8—28no—
670C2×Q8—28no—
671C2×Q8—28no—
672C2×Q8—24no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—112no—
677C2×Q8—111no—
678C2×Q8—221no—
679C2×Q8—222no—
680C2×Q8—224no—
681C2×Q8#433918yes—
682C2×Q8C23×D1114yes—
683C2×D4—111no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—221no—
687C22×C4—28no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—222no—
698C22×C4C2×C22⋊D1112yes—
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C2×C22⋊D1111yescharacteristic
701C22×C4C2×C22⋊D1111yescharacteristic
702C22×C4C2×C22⋊D1112yes—
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705C22×C4C23×D1111yescharacteristic
706Q16—228no—
707Q16—228no—
708Q16—228no—
709SD16—228no—
710M16—224no—
711C2×C8—112no—
712C2×C8—114no—
713C2×C8—112no—
714C2×C8—224no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—112no—
722C4⋊C4—111no—
723C4⋊C4—111no—
724C4⋊C4—221no—
725C4⋊C4—222no—
726C4⋊C4—222no—
727C4⋊C4—222no—
728C4⋊C4—222no—
729C4⋊C4—222no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4—221no—
734C4⋊C4—221no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4C2×C22⋊D1111yescharacteristic
738C4⋊C4C2×C22⋊D1111yescharacteristic
739C4⋊C4C2×C22⋊D1112yes—
740C4⋊C4C2×C22⋊D1111yescharacteristic
741C4⋊C4C2×C22⋊D1111yescharacteristic
742C4⋊C4C2×C22⋊D1112yes—
743C4⋊C4C23×D1112yes—
744C4⋊C4C23×D1112yes—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—222no—
748C22⋊C4—222no—
749C22⋊C4—221no—
750C22⋊C4—221no—
751C22⋊C4—221no—
752C22⋊C4—221no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—221no—
756C22⋊C4—222no—
757C22⋊C4C2×C22⋊D1112yes—
758C22⋊C4C2×C22⋊D1112yes—
759C22⋊C4C2×C22⋊D1112yes—
760C22⋊C4C2×C22⋊D1112yes—
761C42—24no—
762C42—24no—
763C42—24no—
764C42—24no—
765C42—22no—
766C42—22no—
767C42—221no—
768C42—222no—
769C42—222no—
770C42—222no—
771C42C2×C22⋊D1112yes—
772C42C2×C22⋊D1112yes—
773C42C23×D1112yes—
774C42C23×D1112yes—
775C11#6058311yescharacteristic, complemented, Sylow
776C23—22no—
777C23—22no—
778C23—41no—
779C23—221no—
780C23C22×C22⋊D1111yescharacteristic
781C23C22×C22⋊D1111yescharacteristic
782C23C22×C22⋊D1111yescharacteristic
783Q8—28no—
784Q8—28no—
785Q8—28no—
786Q8—24no—
787Q8—224no—
788Q8—222no—
789Q8—442no—
790Q8—882no—
791Q8C2×#433918yes—
792D4—222no—
793D4—442no—
794D4—442no—
795D4—881no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—221no—
812C2×C4—221no—
813C2×C4—222no—
814C2×C4—221no—
815C2×C4—222no—
816C2×C4—442no—
817C2×C4—442no—
818C2×C4—882no—
819C2×C4—881no—
820C2×C4C2×#433914yes—
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1112yes—
823C2×C4C22×C22⋊D1112yes—
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1111yescharacteristic
826C2×C4C22×C22⋊D1111yescharacteristic
827C2×C4C22×C22⋊D1111yescharacteristic
828C2×C4C24×D1111yescharacteristic
829C8—222no—
830C8—222no—
831C8—224no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—44no—
840C22—441no—
841C22—441no—
842C22—441no—
843C22#1062332212yes—
844C22#1062336912yes—
845C22C23×C22⋊D1111yescharacteristic
846C4—28no—
847C4—21no—
848C4—21no—
849C4—22no—
850C4—22no—
851C4—22no—
852C4—22no—
853C4—42no—
854C4—42no—
855C4—441no—
856C4—442no—
857C4—442no—
858C4—441no—
859C4—441no—
860C4#1062332212yes—
861C4C22×#433912yes—
862C2—22no—
863C2—22no—
864C2—41no—
865C2—881no—
866C2C2×#1062332211yescharacteristic
867C2C2×#1062336911yescharacteristic
868C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#519C2
socleC22×C11C23×D4
prime radical#10623322C22
hypercenterC2×#519D11
hypocenterC11#60583
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #13078916C2semidirect
3. #13078845C2semidirect
4. #13078787C2semidirect
5. #13078746C2semidirect
6. #13078696C2semidirect
7. #13078655C2semidirect
8. #13078564C2semidirect
10. #13078458C2semidirect
11. #13078146C2semidirect
13. C2×#10622841C2semidirect
14. #13077482C2semidirect
15. #13077459C2semidirect
16. #13077274C2semidirect
17. C2×C11×#519C2semidirect
61. #10622644C22semidirect
62. #10622644C22semidirect
63. #10622643C22semidirect
64. #10622643C22semidirect
65. #10622643C22semidirect
66. C4×#4326C22semidirect
67. C4×#4326C22semidirect
68. C4×#4326C22semidirect
69. #10622641C22semidirect
70. #10622641C22semidirect
71. #10622639C22semidirect
72. C4×#4325C22semidirect
73. #10622635C22semidirect
74. #10622635C22semidirect
75. #10622634C22semidirect
76. #10622633C22semidirect
343. C2×#519D11semidirect
775. C11#60583semidirect

Maximal subgroups

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

subgroupindex
#130823682
#130789162
#130788452
#130787872
#130787462
#130786962
#130786552
#130785642
#130785292
#130784582
#130781462
#130778502
C2×#106228412
#130774822
#130774592
#130772742
C2×C11×#5192
#6058311