Finite Group Databasebeta

← #15638687

Subgroups — #15638687

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082465C211yesmaximal, characteristic, complemented
2C2×#10623085C211yesmaximal, characteristic, complemented
3#13080777C214yesmaximal, complemented
4#13080649C214yesmaximal, complemented
5#13080162C214yesmaximal, complemented
6#13080143C214yesmaximal, complemented
7#13079621C211yesmaximal, characteristic, complemented
8#13079599C211yesmaximal, characteristic, complemented
9#13079445C212yesmaximal, complemented
10#13079380C212yesmaximal, complemented
11#13078715C211yesmaximal, characteristic, complemented
12#13077840C212yesmaximal, complemented
13#13077829C212yesmaximal, complemented
14#13077644C211yesmaximal, characteristic, complemented
15C11×#3109C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C11×#532C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20#10623361—21no—
21#10623358—21no—
22C2×#66983—21no—
23C22×(C2×D11)⋊C4—21no—
24C2×#66965C2214yescomplemented
25C2×#66964C2214yescomplemented
26#10623263C2212yescomplemented
27#10623249C2212yescomplemented
28#10623212—22no—
29#10623148—21no—
30#10623148—21no—
31#10623137C2212yes—
32#10623137C2212yescomplemented
33#10623096—22no—
34#10623094C2212yescomplemented
35#10623086C2212yescomplemented
36#10623085—22no—
37#10623085—22no—
38#10623085C2214yes—
39#10623085C2214yes—
40C2×#66950C2211yescharacteristic
41C2×#66948C2211yescharacteristic
42C2×#66939—21no—
43C2×#66935—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46#10623001C2211yescharacteristic, complemented
47C11×#481C2212yescomplemented
48C11×#476C2212yescomplemented
49C11×#459C2212yescomplemented
50C11×#447C2212yes—
51C11×#442C2214yescomplemented
52C11×#432C2211yescharacteristic, complemented
53#10622831C2212yes—
54#10622771C2214yescomplemented
55#10622769C2214yescomplemented
56#10622702C2212yescomplemented
57#10622687C2212yescomplemented
58#10622653C2212yescomplemented
59#10622649C2212yes—
60#10622632C2212yescomplemented
61#10622631C2214yescomplemented
62#10622629C2214yescomplemented
63#10622620C2212yescomplemented
64#10622583C2212yescomplemented
65#10622539C2211yescharacteristic, complemented
66#10622481C2214yescomplemented
67#10622480C2214yescomplemented
68#10622479C2214yescomplemented
69#10622477C2214yescomplemented
70#10622458C2214yescomplemented
71#10622449C2214yescomplemented
72#10622396C2214yescomplemented
73#10622396C2214yescomplemented
74#10622394C2214yescomplemented
75#10622393C2214yescomplemented
76#10622389C2214yescomplemented
77#10622388C2214yescomplemented
78#10622385C2214yescomplemented
79#10622383C2214yescomplemented
80#10622352C2212yescomplemented
81#10622344C2212yes—
82#10622339C2212yes—
83D11×C22⋊C8C2212yescomplemented
84#10622328C2212yescomplemented
85#10622327C2212yescomplemented
86#10622319C2214yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C23×Dic11—21no—
94C2×#4341—22no—
95C2×#4341—44no—
96C2×#4341C2314yes—
97C2×#4341C2312yes—
98C2×#4341C2312yescomplemented
99C2×D4×D11—22no—
100C2×D4×D11—44no—
101C2×D4×D11C2314yes—
102C22×D44—21no—
103C22×D44D411yescharacteristic
104C22×D44C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C2×C11×D8C2314yes—
109C11×C4⋊Q8C2311yescharacteristic, complemented
110C11×#127C2311yescharacteristic, complemented
111C11×#124—21no—
112C11×#121—21no—
113C11×#121C2312yes—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11C2312yes—
118C4×D4×C11C2312yes—
119C4×D4×C11C2312yescomplemented
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
122C2×C42×C11C2311yescharacteristic
123#67000—22no—
124Q8×Dic11—22no—
125#66993—22no—
126#66992—22no—
127#66992—22no—
128#66991C2312yes—
129#66991C2312yescomplemented
130#66990—22no—
131#66990—22no—
132D4×Dic11—22no—
133D4×Dic11—22no—
134D4×Dic11—22no—
135C2×#4324C2314yes—
136C2×#4324C2314yescomplemented
137C2×#4323C2314yes—
138#66983—22no—
139#66983—22no—
140#66983—24no—
141#66983—24no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4D411yescharacteristic
149C2×(C2×D11)⋊C4D411yescharacteristic
150#66979—21no—
151#66979—22no—
152C2×C4⋊Dic11—21no—
153C2×C4⋊Dic11—22no—
154C2×C4⋊Dic11D411yescharacteristic
155#66977—21no—
156#66977C2312yes—
157#66965—48no—
158#66964—48no—
159C2×Dic44C2314yescomplemented
160C2×#4314C2314yes—
161C2×#4313C2314yes—
162C2×C8×D11C2314yescomplemented
163#66951—22no—
164#66951—22no—
165#66950—22no—
166#66950C2314yes—
167#66950C2312yes—
168#66950C2312yescomplemented
169#66948—22no—
170#66948C2314yes—
171#66945C2312yes—
172#66945C2312yescomplemented
173#66939—22no—
174#66939—22no—
175#66939—24no—
176#66939—24no—
177#66938—22no—
178#66938—22no—
179#66936—22no—
180#66936—22no—
181#66935—24no—
182#66935—24no—
183(C22⋊D11)⋊C4—22no—
184(C22⋊D11)⋊C4—22no—
185#66928—21no—
186#66928—21no—
187#66928C2312yes—
188#66928C2312yes—
189C4×D44D412yes—
190C4×D44D412yes—
191C4×D44C2312yes—
192C4×D44C2312yes—
193#66923—21no—
194#66922C2311yescharacteristic, complemented
195#66922C2311yescharacteristic, complemented
196C4×Dic22—21no—
197C4×Dic22C2312yescomplemented
198C11×#106C2314yescomplemented
199C11×C4⋊C8C2312yescomplemented
200C11×#102C2314yes—
201C11×#102C2314yescomplemented
202C11×C22⋊C8C2312yes—
203C11×#97C2312yescomplemented
204#66896C2314yes—
205C22⋊(C11⋊C8)C2312yes—
206#66885C2314yes—
207(C2×D11)⋊C8C2314yes—
208(C2×D11)⋊C8C2314yescomplemented
209#66880C2314yescomplemented
210#66874C2314yescomplemented
211#66874C2314yescomplemented
212#66873C2314yes—
213#66871C2314yescomplemented
214C4⋊(C11⋊C8)C2312yescomplemented
215#66867C2312yescomplemented
216#61576—111nomaximal, Sylow
217C24×C11—21no—
218C23×D11—21no—
219C23×D11—24no—
220C23×D11—44no—
221C23×D11—44no—
222C23×D11—82no—
223C23×D11C2×D411yescharacteristic
224C23×D11C2×D411yescharacteristic
225C11×#41—44no—
226C2×Q8×C11—21no—
227C2×D4×C11—24no—
228C2×D4×C11—22no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11C2412yes—
233C2×D4×C11C2412yes—
234C22×C4×C11—21no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—82no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—22no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C22×Dic11—24no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—21no—
254C22×Dic11—44no—
255C22×Dic11C2×D411yescharacteristic
256C22×Dic11C2×D411yescharacteristic
257#4341—28no—
258#4341—44no—
259#4341—44no—
260#4341—44no—
261#4341—48no—
262D4×D11—28no—
263D4×D11—44no—
264D4×D11—48no—
265C2×D44—24no—
266C2×D44—21no—
267C2×D44—42no—
268C2×D44—42no—
269C2×D44—82no—
270C2×D44C2×D412yes—
271C2×D44C2×D412yes—
272C2×D44C2412yes—
273C2×C4×D11—42no—
274C2×C4×D11—42no—
275C2×C4×D11C2×D412yes—
276C2×C4×D11C2×D412yes—
277C2×C4×D11C2412yes—
278C2×C4×D11C2412yes—
279C2×Dic22—21no—
280C2×Dic22—21no—
281C2×Dic22—42no—
282C2×Dic22C2412yes—
283C2×Dic22C2412yes—
284C11×D8—28no—
285C2×C8×C11C2414yes—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2412yes—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300C22⋊Dic11—22no—
301#4324—28no—
302#4324—44no—
303#4323—44no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—22no—
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)⋊C4C2×D412yes—
315(C2×D11)⋊C4C2×D412yes—
316(C2×D11)⋊C4C2×D412yes—
317(C2×D11)⋊C4C2×D412yes—
318C4⋊Dic11—22no—
319C4⋊Dic11—22no—
320C4⋊Dic11—24no—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11C2×D412yes—
325C4⋊Dic11C2×D412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331C4×Dic11—22no—
332C2×C11⋊C8C2414yes—
333Dic44—44no—
334#4314—44no—
335#4313—44no—
336C8×D11—44no—
337#3506—111no—
338C2×#546—111no—
339#3319—114no—
340#3311—114no—
341#3268—114no—
342#3267—114no—
343#3215—111no—
344#3213—111no—
345#3196—112no—
346#3188—112no—
347#3110—111no—
348#3109D1111yescharacteristic, complemented
349#3003—112no—
350#3002—112no—
351#2973—111no—
352C23×C11—24no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11C22×D411yescharacteristic
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—48no—
366C22×D11—48no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—84no—
371C22×D11—816no—
372C22×D11C22×D412yes—
373C22×D11C22×D412yes—
374Q8×C11—42no—
375D4×C11—24no—
376D4×C11—22no—
377D4×C11—24no—
378D4×C11—42no—
379D4×C11—44no—
380D4×C11—81no—
381D4×C11H(5,𝔽2)14yes—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—41no—
387C2×C4×C11—44no—
388C2×C4×C11—42no—
389C2×C4×C11—82no—
390C2×C4×C11—82no—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C2511yescharacteristic
397C22⋊D11—48no—
398C22⋊D11—48no—
399C22⋊D11—82no—
400C22⋊D11—82no—
401C22⋊D11—82no—
402C22⋊D11—82no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—48no—
409C2×Dic11—42no—
410C2×Dic11—82no—
411C2×Dic11—82no—
412C2×Dic11C22×D412yes—
413C2×Dic11C22×D412yes—
414D44—24no—
415D44—42no—
416D44—42no—
417D44—42no—
418D44—84no—
419C4×D11—24no—
420C4×D11—24no—
421C4×D11—42no—
422C4×D11—42no—
423Dic22—24no—
424Dic22—24no—
425Dic22—42no—
426Dic22—81no—
427C8×C11—24no—
428C11⋊C8—24no—
429C22×#41—111no—
430C23×D4—111no—
431C2×AGL(1,ℤ/8)—114no—
432C2×#135—114no—
433#559—222no—
434#556—112no—
435#555—112no—
436#553—222no—
437#550—112no—
438#547—112no—
439#546—114no—
440#546—114no—
441#546—222no—
442#546—222no—
443#538—221no—
444#538—221no—
445#535—221no—
446#533—111no—
447#532C2×D1111yescharacteristic, complemented
448C2×#124—111no—
449#525—112no—
450#525—112no—
451C2×#123—221no—
452C2×C22⋊Q8—111no—
453C2×#121—111no—
454C2×#121—221no—
455C2×#120—221no—
456#520—221no—
457C2×C4×D4—111no—
458C2×C4×D4C2×D1111yescharacteristic
459C22×C22⋊C4—221no—
460#497—112no—
461#496—112no—
462#489—112no—
463#489—112no—
464#485—114no—
465#484—112no—
466#482—114no—
467#481C2×D1112yescomplemented
468#476C2×D1112yescomplemented
469#474—112no—
470#470—114no—
471#468—114no—
472#466—114no—
473#465—114no—
474#464—114no—
475#463—114no—
476#461—112no—
477#459C2×D1112yescomplemented
478#452—114no—
479#452—114no—
480#451—112no—
481#450—112no—
482#450—114no—
483#450—112no—
484#449—114no—
485#449—114no—
486#448—112no—
487#447—114no—
488#447—112no—
489#447C2×D1112yes—
490#442C2×D1114yescomplemented
491#440—114no—
492#435—114no—
493#435—114no—
494#432—111no—
495#432C2×D1111yescharacteristic, complemented
496#418—114no—
497#416—114no—
498#407—112no—
499C2×C22⋊C8—112no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—24no—
503C22×C11—48no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11#57512yes—
510C22×C11C23×D411yescharacteristic
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—22no—
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—44no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—82no—
522C2×D11—816no—
523C2×D11—84no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11C2×H(5,𝔽2)12yes—
532Dic11—22no—
533Dic11—22no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537C25—221no—
538C2×#41—21no—
539C2×#41—114no—
540C2×#41—112no—
541C2×#41—112no—
542C2×#41—222no—
543C2×#41—444no—
544C22×Q8—111no—
545C22×D4—114no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—222no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—444no—
553C22×D4C22×D1111yescharacteristic
554C23×C4—21no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—221no—
558AGL(1,ℤ/8)—448no—
559#135—448no—
560C2×Q16—114no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—114no—
564C2×D8—114no—
565C2×D8C22×D1114yes—
566C2×M16—114no—
567C22×C8—114no—
568C4⋊Q8—111no—
569C4⋊Q8—111no—
570C4⋊Q8C22×D1111yescharacteristic, complemented
571#127—222no—
572#127C22×D1111yescharacteristic, complemented
573#126—222no—
574#126—222no—
575#125—221no—
576#124—21no—
577#124—112no—
578#124—112no—
579#124—222no—
580#124—222no—
581#124—222no—
582#124—221no—
583#124—221no—
584#123—222no—
585#123—222no—
586#123—224no—
587#123—224no—
588#123—222no—
589#123—222no—
590C22⋊Q8—112no—
591C22⋊Q8—114no—
592C22⋊Q8—112no—
593C22⋊Q8—112no—
594C22⋊Q8—222no—
595C22⋊Q8—221no—
596#121—21no—
597#121—112no—
598#121—112no—
599#121—114no—
600#121—224no—
601#121—224no—
602#121—222no—
603#121—222no—
604#121—222no—
605#121—222no—
606#121—222no—
607#121C22×D1112yes—
608#120—224no—
609#120—224no—
610#120—222no—
611#120—222no—
612C4×Q8—112no—
613C4×Q8—222no—
614C4×Q8—221no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—112no—
619C4×D4—112no—
620C4×D4—112no—
621C4×D4—112no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4C22×D1112yes—
628C4×D4C22×D1112yes—
629C4×D4C22×D1112yescomplemented
630#117—112no—
631#117—112no—
632#117—222no—
633#117—221no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—222no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—221no—
645C2×C22⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C42C22×D1111yescharacteristic
648#107—114no—
649#106C22×D1114yescomplemented
650C4⋊C8—112no—
651C4⋊C8C22×D1112yescomplemented
652#103—114no—
653#103—114no—
654#103—114no—
655#102—114no—
656#102—114no—
657#102—114no—
658#102C22×D1114yes—
659#102C22×D1114yescomplemented
660C22⋊C8—112no—
661C22⋊C8—114no—
662C22⋊C8—114no—
663C22⋊C8C22×D1112yes—
664#97—112no—
665#97C22×D1112yescomplemented
666C2×C11—22no—
667C2×C11—44no—
668C2×C11—82no—
669C2×C11#348411yescharacteristic
670C2×C11C2×#57511yescharacteristic
671C2×C11#358511yescharacteristic
672D11—42no—
673D11—42no—
674D11—82no—
675C24—21no—
676C24—111no—
677C24—111no—
678C24—224no—
679C24—221no—
680C24—444no—
681C24—444no—
682C24—882no—
683#41—44no—
684#41—228no—
685#41—444no—
686#41—444no—
687#41—444no—
688#41—448no—
689C2×Q8—21no—
690C2×Q8—112no—
691C2×Q8—112no—
692C2×Q8—221no—
693C2×Q8—221no—
694C2×Q8—442no—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—112no—
701C2×D4—112no—
702C2×D4—112no—
703C2×D4—224no—
704C2×D4—224no—
705C2×D4—228no—
706C2×D4—224no—
707C2×D4—222no—
708C2×D4—222no—
709C2×D4—222no—
710C2×D4—222no—
711C2×D4—221no—
712C2×D4—442no—
713C2×D4—442no—
714C2×D4—444no—
715C2×D4—448no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—882no—
719C2×D4C23×D1112yes—
720C2×D4C23×D1112yes—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—82no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—224no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—221no—
736C22×C4—442no—
737C22×C4—442no—
738C22×C4—444no—
739C22×C4D4×D1111yescharacteristic
740C22×C4D4×D1111yescharacteristic
741C22×C4C23×D1111yescharacteristic
742Q16—444no—
743SD16—228no—
744SD16—444no—
745SD16—444no—
746D8—28no—
747D8—444no—
748M16—444no—
749C2×C8—114no—
750C2×C8—444no—
751C2×C8C23×D1114yes—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—112no—
755C4⋊C4—112no—
756C4⋊C4—112no—
757C4⋊C4—222no—
758C4⋊C4—222no—
759C4⋊C4—224no—
760C4⋊C4—221no—
761C4⋊C4—221no—
762C4⋊C4—222no—
763C4⋊C4—222no—
764C4⋊C4—221no—
765C4⋊C4C23×D1112yes—
766C4⋊C4C23×D1112yes—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—112no—
772C22⋊C4—112no—
773C22⋊C4—112no—
774C22⋊C4—112no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—222no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C42—222no—
789C42—222no—
790C42—222no—
791C42D4×D1111yescharacteristic
792C42D4×D1111yescharacteristic
793C42C23×D1111yescharacteristic
794C42C23×D1111yescharacteristic
795C11#6157611yescharacteristic, complemented, Sylow
796C23—24no—
797C23—22no—
798C23—22no—
799C23—42no—
800C23—42no—
801C23—112no—
802C23—112no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—448no—
811C23—442no—
812C23—442no—
813C23—448no—
814C23—442no—
815C23—884no—
816C23—8816no—
817C23C2×D4×D1111yescharacteristic
818Q8—42no—
819Q8—224no—
820Q8—224no—
821Q8—442no—
822Q8—881no—
823D4—24no—
824D4—22no—
825D4—24no—
826D4—42no—
827D4—44no—
828D4—81no—
829D4—224no—
830D4—442no—
831D4—442no—
832D4—442no—
833D4—448no—
834D4—448no—
835D4—884no—
836D4—882no—
837D4—882no—
838D4—882no—
839D4—882no—
840D4#6704214yes—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—112no—
851C2×C4—112no—
852C2×C4—224no—
853C2×C4—224no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—448no—
862C2×C4—442no—
863C2×C4—882no—
864C2×C4—882no—
865C2×C4C2×D4×D1111yescharacteristic
866C2×C4C2×D4×D1111yescharacteristic
867C2×C4C2×D4×D1111yescharacteristic
868C2×C4C2×D4×D1111yescharacteristic
869C2×C4C2×D4×D1111yescharacteristic
870C2×C4C24×D1111yescharacteristic
871C8—24no—
872C8—224no—
873C22—21no—
874C22—21no—
875C22—24no—
876C22—48no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—222no—
883C22—222no—
884C22—222no—
885C22—222no—
886C22—222no—
887C22—222no—
888C22—444no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—882no—
893C22—884no—
894C22—8816no—
895C22#1062330412yes—
896C22C22×D4×D1111yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—222no—
905C4—222no—
906C4—442no—
907C4—442no—
908C4—442no—
909C4C2×#6704212yes—
910C2—22no—
911C2—44no—
912C2—82no—
913C2—442no—
914C2—442no—
915C2—882no—
916C2#1308224911yescharacteristic
917C2C2×#1062330411yescharacteristic
918C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3109C2
socleC22×C11C23×D4
hypercenter#3109D11
hypocenterC11#61576
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #13082465C2semidirect
2. C2×#10623085C2semidirect
3. #13080777C2semidirect
4. #13080649C2semidirect
5. #13080162C2semidirect
6. #13080143C2semidirect
7. #13079621C2semidirect
8. #13079599C2semidirect
9. #13079445C2semidirect
10. #13079380C2semidirect
11. #13078715C2semidirect
12. #13077840C2semidirect
13. #13077829C2semidirect
14. #13077644C2semidirect
15. C11×#3109C2semidirect
18. C11×#532C22semidirect
24. C2×#66965C22semidirect
25. C2×#66964C22semidirect
26. #10623263C22semidirect
27. #10623249C22semidirect
32. #10623137C22semidirect
34. #10623094C22semidirect
35. #10623086C22semidirect
46. #10623001C22semidirect
47. C11×#481C22semidirect
48. C11×#476C22semidirect
49. C11×#459C22semidirect
51. C11×#442C22semidirect
52. C11×#432C22semidirect
54. #10622771C22semidirect
55. #10622769C22semidirect
56. #10622702C22semidirect
57. #10622687C22semidirect
58. #10622653C22semidirect
60. #10622632C22semidirect
61. #10622631C22semidirect
62. #10622629C22semidirect
63. #10622620C22semidirect
64. #10622583C22semidirect
65. #10622539C22semidirect
66. #10622481C22semidirect
67. #10622480C22semidirect
68. #10622479C22semidirect
69. #10622477C22semidirect
70. #10622458C22semidirect
71. #10622449C22semidirect
72. #10622396C22semidirect
73. #10622396C22semidirect
74. #10622394C22semidirect
75. #10622393C22semidirect
76. #10622389C22semidirect
77. #10622388C22semidirect
78. #10622385C22semidirect
79. #10622383C22semidirect
80. #10622352C22semidirect
83. D11×C22⋊C8C22semidirect
84. #10622328C22semidirect
85. #10622327C22semidirect
86. #10622319C22semidirect
98. C2×#4341C23semidirect
109. C11×C4⋊Q8C23semidirect
110. C11×#127C23semidirect
119. C4×D4×C11C23semidirect
129. #66991C23semidirect
136. C2×#4324C23semidirect
159. C2×Dic44C23semidirect
162. C2×C8×D11C23semidirect
168. #66950C23semidirect
172. #66945C23semidirect
194. #66922C23semidirect
195. #66922C23semidirect
197. C4×Dic22C23semidirect
198. C11×#106C23semidirect
199. C11×C4⋊C8C23semidirect
201. C11×#102C23semidirect
203. C11×#97C23semidirect
208. (C2×D11)⋊C8C23semidirect
209. #66880C23semidirect
210. #66874C23semidirect
211. #66874C23semidirect
213. #66871C23semidirect
214. C4⋊(C11⋊C8)C23semidirect
215. #66867C23semidirect
348. #3109D11semidirect
447. #532C2×D11semidirect
467. #481C2×D11semidirect
468. #476C2×D11semidirect
477. #459C2×D11semidirect
490. #442C2×D11semidirect
495. #432C2×D11semidirect
570. C4⋊Q8C22×D11semidirect
572. #127C22×D11semidirect
629. C4×D4C22×D11semidirect
649. #106C22×D11semidirect
651. C4⋊C8C22×D11semidirect
659. #102C22×D11semidirect
665. #97C22×D11semidirect
795. C11#61576semidirect

Maximal subgroups

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

subgroupindex
#130824652
C2×#106230852
#130807772
#130806492
#130801622
#130801432
#130796212
#130795992
#130794452
#130793802
#130787152
#130778402
#130778292
#130776442
C11×#31092
#6157611