Finite Group Databasebeta

← #15638514

Subgroups — #15638514

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2#13080518C214yesmaximal, complemented
3#13080503C214yesmaximal, complemented
4#13080353C214yesmaximal, complemented
5#13080324C214yesmaximal, complemented
6#13079581C212yesmaximal, complemented
7#13079397C212yesmaximal, complemented
8#13079373C211yesmaximal, characteristic, complemented
9#13079364C211yesmaximal, characteristic, complemented
10#13078696C212yesmaximal, complemented
11#13077834C212yesmaximal, complemented
12C2×#10622841C211yesmaximal, characteristic, complemented
13C2×#10622840C211yesmaximal, characteristic, complemented
14#13077640C211yesmaximal, characteristic, complemented
15C2×C11×#548C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C11×#548—22no—
19C11×#548—22no—
20C11×#548C2214yes—
21C11×#548C2214yescomplemented
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic, complemented
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic, complemented
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×#67003C2214yescomplemented
32C22×#4326C2212yescomplemented
33C22×#4325C2212yescomplemented
34#10623335—21no—
35#10623322C2212yes—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623096C2212yescomplemented
39#10623087—22no—
40#10623083C2212yescomplemented
41#10623081C2212yescomplemented
42#10623072C2212yescomplemented
43#10623071—22no—
44#10623046—21no—
45#10623025—21no—
46#10623017—21no—
47#10623010C2212yes—
48#10622852C2214yescomplemented
49#10622851C2214yescomplemented
50#10622846C2214yescomplemented
51#10622841C2214yescomplemented
52#10622841C2212yescomplemented
53#10622841C2212yescomplemented
54#10622840C2212yes—
55#10622840C2212yes—
56#10622840C2214yescomplemented
57C2×#66899C2212yescomplemented
58C2×#66899C2212yescomplemented
59#10622831C2212yescomplemented
60#10622830C2212yes—
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2212yescomplemented
64#10622672C2214yescomplemented
65#10622670C2214yescomplemented
66#10622669C2214yescomplemented
67#10622667C2214yescomplemented
68#10622664C2214yescomplemented
69#10622661C2214yescomplemented
70#10622660C2214yescomplemented
71#10622658C2214yescomplemented
72#10622654C2214yescomplemented
73#10622653C2212yescomplemented
74#10622651C2214yescomplemented
75#10622649C2212yescomplemented
76#10622647C2212yescomplemented
77#10622646C2212yescomplemented
78C4×#4326C2214yescomplemented
79#10622641C2214yescomplemented
80C4×#4325C2214yescomplemented
81#10622635C2214yescomplemented
82D4×C11⋊C8C2214yescomplemented
83D4×C11⋊C8C2214yescomplemented
84#10622584C2212yescomplemented
85#10622580C2212yes—
86#10622538C2212yescomplemented
87C2×C11×#41—22no—
88C2×C11×#41—44no—
89C2×C11×#41C2314yes—
90C22×Q8×C11—21no—
91C22×Q8×C11—21no—
92C22×Q8×C11—21no—
93C22×Q8×C11—44no—
94C22×Q8×C11C2311yescharacteristic
95C22×Q8×C11C2312yes—
96C22×Q8×C11C2312yes—
97C22×Q8×C11C2311yescharacteristic
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11D411yescharacteristic
101C22×D4×C11C2311yescharacteristic
102C23×C4×C11—21no—
103C23×C4×C11—21no—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—21no—
107C2×#4339C2312yes—
108C22×D44C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C11×#124—24no—
111C11×#124—24no—
112C11×#124—22no—
113C11×#124C2314yes—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8C2314yes—
118C11×#121—24no—
119C11×#121—24no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121C2312yes—
123C11×#121C2312yes—
124C4×Q8×C11—22no—
125C4×Q8×C11C2314yes—
126C4×D4×C11—24no—
127C4×D4×C11—24no—
128C4×D4×C11D412yes—
129C4×D4×C11D412yes—
130C4×D4×C11C2312yes—
131C4×D4×C11C2312yes—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4D411yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C11×C22⋊C4D411yescharacteristic
142C2×C42×C11—21no—
143C2×C42×C11C2311yescharacteristic
144#67006—22no—
145C2×C22⋊Dic11—21no—
146#67003—48no—
147C2×#4326—44no—
148C2×#4326C2314yes—
149C2×#4326C2314yes—
150C2×#4325—44no—
151C2×#4325C2314yes—
152C2×#4325C2314yes—
153#66992—22no—
154#66992—22no—
155#66990—22no—
156#66988—22no—
157C2×#4324C2314yes—
158C2×#4323C2314yes—
159#66983—21no—
160#66983—21no—
161#66983C2312yes—
162#66983C2312yes—
163#66983C2312yes—
164#66982—22no—
165#66982—22no—
166C4×C22⋊D11—22no—
167C4×C22⋊D11—22no—
168C4×C22⋊D11—22no—
169C2×(C2×D11)⋊C4—21no—
170#66979C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173#66977—21no—
174#66977—21no—
175#66977C2312yes—
176#66977C2312yes—
177#66977C2312yes—
178C2×Dic11⋊C4—21no—
179C22×C11⋊C8C2312yes—
180C22×C11⋊C8C2312yes—
181C22×C11⋊C8C2314yes—
182#66951—22no—
183#66949—22no—
184#66947—22no—
185#66942—22no—
186#66938—22no—
187#66937—22no—
188#66936—22no—
189(C22⋊D11)⋊C4—22no—
190(C22⋊D11)⋊C4—22no—
191C22⋊C4×D11—22no—
192#66932—22no—
193#66930—22no—
194#66929—22no—
195#66928C2312yes—
196C4×D44C2312yes—
197#66925—22no—
198#66923C2312yes—
199C4×Dic22C2312yes—
200#66899C2314yes—
201#66899C2314yes—
202#66899C2314yes—
203#66899C2314yes—
204#66896C2314yes—
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2314yes—
211#66874C2314yes—
212#66873C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216C4×C11⋊C8C2314yes—
217#61564—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C11×#41—28no—
223C11×#41—44no—
224C11×#41—48no—
225C2×Q8×C11—24no—
226C2×Q8×C11—21no—
227C2×Q8×C11—22no—
228C2×Q8×C11—22no—
229C2×Q8×C11—21no—
230C2×Q8×C11—24no—
231C2×Q8×C11—24no—
232C2×Q8×C11—42no—
233C2×Q8×C11—42no—
234C2×Q8×C11—42no—
235C2×Q8×C11—44no—
236C2×Q8×C11—44no—
237C2×Q8×C11—44no—
238C2×Q8×C11C2412yes—
239C2×Q8×C11C2412yes—
240C2×D4×C11—24no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—24no—
244C2×D4×C11—21no—
245C2×D4×C11—42no—
246C2×D4×C11—44no—
247C2×D4×C11—44no—
248C2×D4×C11C2×D412yes—
249C2×D4×C11C2×D412yes—
250C2×D4×C11C2412yes—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—24no—
257C22×C4×C11—42no—
258C22×C4×C11—42no—
259C22×C4×C11—44no—
260C22×C4×C11—44no—
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2412yes—
271C22×C4×C11C2411yescharacteristic
272C2×C22⋊D11—22no—
273C2×C22⋊D11—22no—
274C2×C22⋊D11—22no—
275C2×C22⋊D11—22no—
276C2×C22⋊D11—44no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280#4339—44no—
281C2×D44—21no—
282C2×D44—42no—
283C2×D44C2412yes—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×Dic22—21no—
287C2×Dic22—42no—
288C2×Dic22C2412yes—
289C11×C4⋊C4—24no—
290C11×C4⋊C4—24no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2412yes—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C42×C11—24no—
305C42×C11C2×D412yes—
306C42×C11C2412yes—
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311#4326—28no—
312#4326—44no—
313#4325—28no—
314#4325—44no—
315#4324—44no—
316#4323—44no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C2×C11⋊C8—42no—
336C2×C11⋊C8—42no—
337C2×C11⋊C8—44no—
338C2×C11⋊C8C2414yes—
339C2×C11⋊C8C2414yes—
340#3505—111no—
341C2×#548D1111yescharacteristic, complemented
342#3301—114no—
343#3300—114no—
344#3285—114no—
345#3282—114no—
346#3211—112no—
347#3190—112no—
348#3187—111no—
349#3186—111no—
350#3108—112no—
351#3002—112no—
352C2×#451—111no—
353C2×#448—111no—
354#2972—111no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—42no—
362C23×C11—42no—
363C23×C11—42no—
364C23×C11#13514yescomplemented
365C23×C11C22×D412yes—
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—22no—
370C22×D11—42no—
371C22×D11—81no—
372C22×D11—81no—
373Q8×C11—24no—
374Q8×C11—22no—
375Q8×C11—22no—
376Q8×C11—22no—
377Q8×C11—44no—
378Q8×C11—44no—
379Q8×C11—42no—
380Q8×C11H(5,𝔽2)14yes—
381D4×C11—24no—
382D4×C11—24no—
383D4×C11—24no—
384D4×C11—48no—
385D4×C11—42no—
386D4×C11—44no—
387D4×C11—44no—
388C2×C4×C11—24no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—41no—
403C2×C4×C11—48no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11—42no—
407C2×C4×C11—42no—
408C2×C4×C11C22×D412yes—
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C2511yescharacteristic
415C22⋊D11—44no—
416C22⋊D11—44no—
417C22⋊D11—82no—
418C22⋊D11—82no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—42no—
423C2×Dic11—81no—
424C2×Dic11—81no—
425D44—24no—
426D44—81no—
427C4×D11—82no—
428C4×D11—82no—
429Dic22—24no—
430Dic22—81no—
431C11⋊C8—24no—
432C11⋊C8—24no—
433C22×#41C2×D1111yescharacteristic, complemented
434C23×Q8C2×D1111yescharacteristic
435C2×#135—114no—
436C22×Q16—112no—
437C22×SD16—112no—
438#553—112no—
439#553—222no—
440#552—112no—
441#551—222no—
442#548—22no—
443#548—22no—
444#548—112no—
445#548C2×D1114yes—
446#548C2×D1114yescomplemented
447#546—112no—
448#539—221no—
449#538—221no—
450#534—221no—
451#529—112no—
452C2×#124—21no—
453C2×#124C2×D1111yescharacteristic, complemented
454#525—112no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8C2×D1111yescharacteristic, complemented
458C2×#121—21no—
459C2×#121—111no—
460C2×#121C2×D1111yescharacteristic
461#518—221no—
462C2×C4×Q8C2×D1111yescharacteristic, complemented
463C2×C4×D4—21no—
464C2×C4×D4C2×D1111yescharacteristic
465#495—114no—
466#488—114no—
467#485—114no—
468#483—112no—
469#481—112no—
470#480—112no—
471#480—112no—
472#479—114no—
473#467—114no—
474#466—114no—
475#465—114no—
476#465—114no—
477#464—114no—
478#464—114no—
479#463—114no—
480#452—114no—
481#452—114no—
482#451—112no—
483#451—112no—
484#451—114no—
485#450—112no—
486#449—114no—
487#448—112no—
488#448—112no—
489#448—114no—
490#448—112no—
491#447—112no—
492#447—112no—
493C4×Q16—114no—
494C4×SD16—114no—
495C8×D4—114no—
496C8×D4—114no—
497#431—112no—
498#416—114no—
499C2×#103—112no—
500C2×#103—112no—
501C2×C22⋊C8—111no—
502C2×C22⋊C8—111no—
503C2×C22⋊C8—112no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—44no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—82no—
518C22×C11—84no—
519C22×C11C2×#13512yes—
520C22×C11C2×#13512yes—
521C22×C11C2×#13512yes—
522C22×C11C23×D411yescharacteristic
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—162no—
527C4×C11—22no—
528C4×C11—24no—
529C4×C11—22no—
530C4×C11—21no—
531C4×C11—21no—
532C4×C11—21no—
533C4×C11—22no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11C2×H(5,𝔽2)12yes—
537Dic11—42no—
538Dic11—42no—
539Dic11—42no—
540C2×#41—22no—
541C2×#41—44no—
542C2×#41—112no—
543C2×#41C22×D1114yes—
544C22×Q8—21no—
545C22×Q8—21no—
546C22×Q8—21no—
547C22×Q8—44no—
548C22×Q8—111no—
549C22×Q8C22×D1111yescharacteristic
550C22×Q8C22×D1112yes—
551C22×Q8C22×D1112yes—
552C22×Q8C22×D1111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—111no—
556C22×D4—221no—
557C22×D4C22⋊D1111yescharacteristic
558C22×D4C22×D1111yescharacteristic
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563#135—448no—
564C2×Q16—114no—
565C2×Q16—114no—
566C2×Q16—444no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—114no—
570C2×SD16—444no—
571C2×D8—114no—
572C22×C8—112no—
573C22×C8—112no—
574C22×C8—114no—
575#126—222no—
576#126—222no—
577#126—222no—
578#125—112no—
579#125—222no—
580#124—24no—
581#124—24no—
582#124—22no—
583#124—112no—
584#124—222no—
585#124C22×D1114yes—
586#123—222no—
587#123—222no—
588#123—222no—
589#123—222no—
590#123—222no—
591C22⋊Q8—22no—
592C22⋊Q8—24no—
593C22⋊Q8—24no—
594C22⋊Q8—112no—
595C22⋊Q8—112no—
596C22⋊Q8—112no—
597C22⋊Q8—221no—
598C22⋊Q8—221no—
599C22⋊Q8—222no—
600C22⋊Q8C22×D1114yes—
601#121—24no—
602#121—24no—
603#121—21no—
604#121—21no—
605#121—112no—
606#121—112no—
607#121—112no—
608#121—222no—
609#121—222no—
610#121—221no—
611#121—221no—
612#121—222no—
613#121C22×D1112yes—
614#121C22×D1112yes—
615#120—222no—
616#120—222no—
617C4×Q8—22no—
618C4×Q8—112no—
619C4×Q8C22×D1114yes—
620C4×D4—24no—
621C4×D4—24no—
622C4×D4—112no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4C22⋊D1112yes—
629C4×D4C22⋊D1112yes—
630C4×D4C22×D1112yes—
631C4×D4C22×D1112yes—
632#117—112no—
633#117—222no—
634#117—222no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—221no—
640C2×C4⋊C4C22⋊D1111yescharacteristic
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4C22⋊D1111yescharacteristic
650C2×C22⋊C4C22⋊D1111yescharacteristic
651C2×C42—21no—
652C2×C42C22×D1111yescharacteristic
653#107—114no—
654#106—114no—
655C4⋊C8—114no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#103—114no—
661#102—114no—
662#102—114no—
663#102—114no—
664C22⋊C8—112no—
665C22⋊C8—112no—
666C22⋊C8—112no—
667C22⋊C8—112no—
668C22⋊C8—114no—
669C4×C8—114no—
670C2×C11—22no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11—42no—
674C2×C11—82no—
675C2×C11#348411yescharacteristic
676C2×C11C22×#13511yescharacteristic
677C2×C11#358611yescharacteristic
678D11—82no—
679C24—21no—
680C24—221no—
681C24C2×C22⋊D1111yescharacteristic
682C24C2×C22⋊D1111yescharacteristic
683#41—28no—
684#41—44no—
685#41—48no—
686#41—444no—
687C2×Q8—24no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—21no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—42no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—112no—
701C2×Q8—221no—
702C2×Q8—442no—
703C2×Q8C23×D1112yes—
704C2×Q8C23×D1112yes—
705C2×D4—24no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—24no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—112no—
714C2×D4—222no—
715C2×D4—222no—
716C2×D4—222no—
717C2×D4—222no—
718C2×D4—221no—
719C2×D4—442no—
720C2×D4—444no—
721C2×D4C2×C22⋊D1112yes—
722C2×D4C2×C22⋊D1112yes—
723C2×D4C23×D1112yes—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4C2×C22⋊D1111yescharacteristic
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1111yescharacteristic
743C22×C4C2×C22⋊D1111yescharacteristic
744C22×C4C2×C22⋊D1111yescharacteristic
745C22×C4C2×C22⋊D1112yes—
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1112yes—
750Q16—228no—
751Q16—444no—
752SD16—228no—
753SD16—444no—
754SD16—444no—
755D8—444no—
756C2×C8—114no—
757C2×C8—114no—
758C2×C8—442no—
759C2×C8—442no—
760C2×C8—444no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—112no—
765C4⋊C4—112no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4—222no—
774C4⋊C4C2×C22⋊D1112yes—
775C4⋊C4C2×C22⋊D1112yes—
776C4⋊C4C23×D1112yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—22no—
781C22⋊C4—22no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4C2×C22⋊D1112yes—
793C22⋊C4C2×C22⋊D1112yes—
794C22⋊C4C2×C22⋊D1112yes—
795C22⋊C4C2×C22⋊D1112yes—
796C42—24no—
797C42—222no—
798C42—222no—
799C42C2×C22⋊D1112yes—
800C42C23×D1112yes—
801C11#6156411yescharacteristic, complemented, Sylow
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—222no—
812C23—442no—
813C23—881no—
814C23—881no—
815C23#6700314yescomplemented
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1111yescharacteristic
818C23C22×C22⋊D1111yescharacteristic
819C23C22×C22⋊D1111yescharacteristic
820Q8—24no—
821Q8—22no—
822Q8—22no—
823Q8—22no—
824Q8—44no—
825Q8—44no—
826Q8—42no—
827Q8—224no—
828Q8—881no—
829Q8#6703714yes—
830D4—24no—
831D4—24no—
832D4—24no—
833D4—48no—
834D4—42no—
835D4—44no—
836D4—44no—
837D4—224no—
838D4—444no—
839D4—444no—
840D4—881no—
841D4—882no—
842D4—882no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—41no—
858C2×C4—48no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—442no—
867C2×C4—882no—
868C2×C4—882no—
869C2×C4—881no—
870C2×C4—881no—
871C2×C4C22×C22⋊D1112yes—
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1111yescharacteristic
874C2×C4C22×C22⋊D1112yes—
875C2×C4C22×C22⋊D1111yescharacteristic
876C2×C4C22×C22⋊D1111yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—224no—
879C8—224no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—44no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—84no—
895C22—442no—
896C22—442no—
897C22—442no—
898C22—1762no—
899C22C2×#6700312yes—
900C22C2×#6700312yes—
901C22C2×#6700312yes—
902C22C23×C22⋊D1111yescharacteristic
903C4—22no—
904C4—24no—
905C4—22no—
906C4—21no—
907C4—21no—
908C4—21no—
909C4—22no—
910C4—42no—
911C4—42no—
912C4—442no—
913C4—442no—
914C4—442no—
915C4C2×#6703712yes—
916C2—22no—
917C2—22no—
918C2—22no—
919C2—42no—
920C2—82no—
921C2—882no—
922C2#1308225111yescharacteristic
923C2C22×#6700311yescharacteristic
924C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#548C2
socleC22×C11C23×D4
hypercenterC2×#548D11
hypocenterC11#61564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. #13080518C2semidirect
3. #13080503C2semidirect
4. #13080353C2semidirect
5. #13080324C2semidirect
6. #13079581C2semidirect
7. #13079397C2semidirect
8. #13079373C2semidirect
9. #13079364C2semidirect
10. #13078696C2semidirect
11. #13077834C2semidirect
12. C2×#10622841C2semidirect
13. C2×#10622840C2semidirect
14. #13077640C2semidirect
15. C2×C11×#548C2semidirect
16. C22×C11×#41C22semidirect
21. C11×#548C22semidirect
23. C2×C11×#124C22semidirect
25. C2×C11×C22⋊Q8C22semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×#67003C22semidirect
32. C22×#4326C22semidirect
33. C22×#4325C22semidirect
38. #10623096C22semidirect
40. #10623083C22semidirect
41. #10623081C22semidirect
42. #10623072C22semidirect
48. #10622852C22semidirect
49. #10622851C22semidirect
50. #10622846C22semidirect
51. #10622841C22semidirect
52. #10622841C22semidirect
53. #10622841C22semidirect
56. #10622840C22semidirect
57. C2×#66899C22semidirect
58. C2×#66899C22semidirect
59. #10622831C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622672C22semidirect
65. #10622670C22semidirect
66. #10622669C22semidirect
67. #10622667C22semidirect
68. #10622664C22semidirect
69. #10622661C22semidirect
70. #10622660C22semidirect
71. #10622658C22semidirect
72. #10622654C22semidirect
73. #10622653C22semidirect
74. #10622651C22semidirect
75. #10622649C22semidirect
76. #10622647C22semidirect
77. #10622646C22semidirect
78. C4×#4326C22semidirect
79. #10622641C22semidirect
80. C4×#4325C22semidirect
81. #10622635C22semidirect
82. D4×C11⋊C8C22semidirect
83. D4×C11⋊C8C22semidirect
84. #10622584C22semidirect
86. #10622538C22semidirect
341. C2×#548D11semidirect
364. C23×C11#135semidirect
433. C22×#41C2×D11semidirect
446. #548C2×D11semidirect
453. C2×#124C2×D11semidirect
457. C2×C22⋊Q8C2×D11semidirect
462. C2×C4×Q8C2×D11semidirect
801. C11#61564semidirect
815. C23#67003semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130805182
#130805032
#130803532
#130803242
#130795812
#130793972
#130793732
#130793642
#130786962
#130778342
C2×#106228412
C2×#106228402
#130776402
C2×C11×#5482
#6156411