Finite Group Databasebeta

← #15638692

Subgroups — #15638692

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#13082468C211yesmaximal, characteristic, complemented
2C2×#10623081C211yesmaximal, characteristic, complemented
3#13080774C214yesmaximal, complemented
4#13080654C214yesmaximal, complemented
5#13080161C214yesmaximal, complemented
6#13080146C214yesmaximal, complemented
7#13079621C211yesmaximal, characteristic, complemented
8#13079605C211yesmaximal, characteristic, complemented
9#13079448C212yesmaximal, complemented
10#13079383C212yesmaximal, complemented
11#13078716C211yesmaximal, characteristic, complemented
12#13078708C211yesmaximal, characteristic, complemented
13#13077846C212yesmaximal, complemented
14#13077838C212yesmaximal, complemented
15C11×#2973C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19#10623336—21no—
20C2×#66990—21no—
21#10623322C2212yes—
22#10623322C2212yescomplemented
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66961C2214yescomplemented
26C2×#66957C2214yescomplemented
27#10623094C2212yescomplemented
28#10623090—22no—
29#10623089—22no—
30#10623084C2212yescomplemented
31#10623082C2212yescomplemented
32#10623081—22no—
33#10623081—22no—
34#10623081C2214yes—
35#10623081C2214yes—
36#10623073C2212yescomplemented
37C2×#66947—21no—
38#10623035—21no—
39#10623025—21no—
40#10623025—21no—
41C2×#66937—21no—
42C2×C22⋊C4×D11—21no—
43#10623008C2211yescharacteristic, complemented
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46#10623001C2211yescharacteristic, complemented
47C11×#435C2214yescomplemented
48C11×#435C2214yescomplemented
49C11×#432C2211yescharacteristic, complemented
50C11×#432C2211yescharacteristic, complemented
51C11×#407C2212yes—
52C2×C11×C22⋊C8C2212yescomplemented
53#10622750C2214yescomplemented
54#10622747C2214yescomplemented
55#10622744C2214yescomplemented
56#10622728C2214yescomplemented
57#10622727C2214yescomplemented
58#10622726C2214yescomplemented
59#10622459C2212yescomplemented
60#10622458C2214yescomplemented
61#10622457C2214yescomplemented
62#10622456C2212yescomplemented
63#10622455C2212yescomplemented
64#10622454C2212yescomplemented
65#10622352C2212yescomplemented
66#10622351C2212yescomplemented
67#10622350C2214yescomplemented
68#10622348C2212yescomplemented
69#10622347C2214yescomplemented
70#10622347C2214yescomplemented
71#10622346C2214yescomplemented
72#10622346C2214yescomplemented
73#10622345C2212yes—
74#10622345C2212yes—
75#10622345C2214yescomplemented
76#10622344C2212yes—
77#10622344C2212yes—
78#10622344C2214yescomplemented
79#10622336C2214yescomplemented
80#10622335C2212yescomplemented
81#10622328C2212yescomplemented
82#10622327C2212yescomplemented
83#10622327C2212yescomplemented
84#10622325C2212yescomplemented
85#10622324C2214yescomplemented
86#10622323C2214yescomplemented
87C24×D11—21no—
88C22×D4×C11D411yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C2×#4339—21no—
94C2×#4339—22no—
95C2×#4339—44no—
96C2×#4339C2314yes—
97C2×#4339C2312yes—
98C2×#4339C2312yescomplemented
99C22×D44—21no—
100C22×D44—22no—
101C22×D44—44no—
102C22×D44C2311yescharacteristic
103C22×D44C2314yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×Dic22C2311yescharacteristic
108C2×C11×M16C2314yes—
109C22×C8×C11C2314yescomplemented
110C4×D4×C11D412yes—
111C4×D4×C11D412yes—
112C4×D4×C11C2312yes—
113C4×D4×C11C2312yes—
114C2×C11×C4⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C42×C11C2311yescharacteristic
118#67006—22no—
119#67006—22no—
120C2×C22⋊Dic11—21no—
121#66993—22no—
122#66991—22no—
123#66991—22no—
124#66990—24no—
125#66990—24no—
126#66989—22no—
127#66983—21no—
128#66983—22no—
129#66983C2314yes—
130#66983C2312yes—
131#66983C2312yes—
132#66983C2312yescomplemented
133#66982—22no—
134#66982—22no—
135C4×C22⋊D11—22no—
136C4×C22⋊D11—22no—
137C4×C22⋊D11—22no—
138C4×C22⋊D11—22no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143#66979—21no—
144#66979C2312yes—
145#66979C2312yescomplemented
146C2×C4⋊Dic11C2311yescharacteristic
147#66977—21no—
148#66977—22no—
149#66977C2312yes—
150#66977C2314yes—
151#66977C2312yes—
152#66977C2312yescomplemented
153C2×Dic11⋊C4—21no—
154#66961—48no—
155C2×Dic44C2314yescomplemented
156#66957—48no—
157C2×D88C2314yes—
158C2×D88C2314yes—
159C2×#4314C2314yes—
160C2×#4314C2314yes—
161C2×#4314C2314yescomplemented
162#66947—24no—
163#66947—24no—
164#66946—22no—
165#66945—22no—
166C4⋊C4×D11—22no—
167#66940—22no—
168#66938—22no—
169#66938—22no—
170#66937—24no—
171#66937—24no—
172#66937—22no—
173#66937—22no—
174#66936—22no—
175#66936—22no—
176C22⋊C4×D11—24no—
177C22⋊C4×D11—24no—
178#66932—22no—
179#66932—22no—
180#66928—21no—
181#66928—21no—
182#66928—21no—
183#66928C2312yes—
184#66928C2312yes—
185#66927C2311yescharacteristic, complemented
186C4×D44—21no—
187C4×D44—21no—
188C4×D44—21no—
189C4×D44C2312yes—
190C4×D44C2312yes—
191C4×D44C2312yescomplemented
192#66923—21no—
193#66922C2311yescharacteristic, complemented
194#66922C2311yescharacteristic, complemented
195#66922C2311yescharacteristic, complemented
196C4×Dic22—21no—
197C4×Dic22C2312yescomplemented
198C11×C4⋊C8C2312yescomplemented
199C11×C4⋊C8C2312yescomplemented
200C11×C22⋊C8C2312yes—
201C11×C22⋊C8C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2314yescomplemented
204C11×#97C2312yescomplemented
205C11×#97C2312yescomplemented
206#66885C2314yes—
207#66885C2314yes—
208#66885C2314yes—
209#66885C2314yes—
210#66885C2314yescomplemented
211#66882C2314yescomplemented
212#66881C2314yescomplemented
213#66880C2314yescomplemented
214#66880C2314yescomplemented
215#66880C2314yescomplemented
216#61576—111nomaximal, Sylow
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—24no—
222C23×D11—44no—
223C23×D11—44no—
224C23×D11—82no—
225C2×D4×C11—42no—
226C2×D4×C11C2×D412yes—
227C2×D4×C11C2×D412yes—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2411yescharacteristic
237C22×C4×C11C2412yes—
238C22×C4×C11C2412yes—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—22no—
241C2×C22⋊D11—22no—
242C2×C22⋊D11—22no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—22no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—82no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250#4339—28no—
251#4339—44no—
252#4339—44no—
253#4339—44no—
254#4339—44no—
255#4339—48no—
256C2×D44—24no—
257C2×D44—28no—
258C2×D44—21no—
259C2×D44—21no—
260C2×D44—21no—
261C2×D44—24no—
262C2×D44—21no—
263C2×D44—44no—
264C2×D44—42no—
265C2×D44—44no—
266C2×D44—48no—
267C2×D44C2412yes—
268C2×D44C2412yes—
269C2×D44C2412yes—
270C2×C4×D11—22no—
271C2×C4×D11—24no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×C4×D11—44no—
277C2×C4×D11—82no—
278C2×Dic22—21no—
279C2×Dic22—21no—
280C2×Dic22—21no—
281C2×Dic22—42no—
282C2×Dic22C2412yes—
283C2×Dic22C2412yes—
284C11×M16—44no—
285C2×C8×C11—44no—
286C2×C8×C11C2414yes—
287C2×C8×C11C2414yes—
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D412yes—
290C11×C22⋊C4C2×D412yes—
291C11×C22⋊C4C2×D412yes—
292C11×C22⋊C4C2×D412yes—
293C11×C22⋊C4C2×D412yes—
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302C22⋊Dic11—24no—
303C22⋊Dic11—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315C4⋊Dic11—21no—
316C4⋊Dic11—21no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11C2412yes—
321C4⋊Dic11C2412yes—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—24no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331Dic44—44no—
332D88—28no—
333D88—44no—
334#4314—28no—
335#4314—44no—
336#4314—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#3109—111no—
349#3003—112no—
350#3002—112no—
351#2973D1111yescharacteristic, complemented
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11C22×D412yes—
359C23×C11C22×D412yes—
360C23×C11C22×D411yescharacteristic
361C22×D11—24no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—48no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—48no—
371C22×D11—42no—
372C22×D11—84no—
373C22×D11—816no—
374D4×C11—42no—
375D4×C11—42no—
376C2×C4×C11—22no—
377C2×C4×C11—24no—
378C2×C4×C11—24no—
379C2×C4×C11—22no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—42no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—48no—
394C22⋊D11—44no—
395C22⋊D11—82no—
396C22⋊D11—82no—
397C22⋊D11—82no—
398C22⋊D11—82no—
399C22⋊D11—84no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407D44—24no—
408D44—22no—
409D44—24no—
410D44—24no—
411D44—48no—
412D44—42no—
413D44—42no—
414D44—81no—
415D44H(5,𝔽2)14yes—
416C4×D11—48no—
417C4×D11—44no—
418C4×D11—82no—
419C4×D11—82no—
420C4×D11—82no—
421C4×D11—82no—
422Dic22—24no—
423Dic22—24no—
424Dic22—42no—
425Dic22—42no—
426Dic22—81no—
427C8×C11—24no—
428C8×C11—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#532—111no—
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#481—112no—
468#476—112no—
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#459—112no—
478#452—114no—
479#452—114no—
480#451—112no—
481#450—112no—
482#450—112no—
483#450—114no—
484#449—114no—
485#449—114no—
486#448—112no—
487#447—112no—
488#447—112no—
489#447—114no—
490#442—114no—
491#440—114no—
492#435C2×D1114yescomplemented
493#435C2×D1114yescomplemented
494#432C2×D1111yescharacteristic, complemented
495#432C2×D1111yescharacteristic, complemented
496#418—114no—
497#416—114no—
498#407C2×D1112yes—
499C2×C22⋊C8C2×D1112yescomplemented
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—44no—
509C22×C11—82no—
510C22×C11#57512yes—
511C22×C11C23×D411yescharacteristic
512C2×D11—24no—
513C2×D11—48no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—816no—
523C2×D11—84no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—22no—
528C4×C11—22no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11C2×H(5,𝔽2)12yes—
532Dic11—42no—
533Dic11—42no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537C25—221no—
538C2×#41—114no—
539C2×#41—112no—
540C2×#41—112no—
541C2×#41—221no—
542C2×#41—222no—
543C2×#41—444no—
544C22×Q8—111no—
545C22×D4—111no—
546C22×D4—114no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—222no—
552C22×D4—444no—
553C22×D4D4411yescharacteristic
554C23×C4—221no—
555C23×C4—221no—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558AGL(1,ℤ/8)—448no—
559#135—448no—
560C2×Q16—114no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—114no—
564C2×D8—114no—
565C2×D8—114no—
566C2×M16C22×D1114yes—
567C22×C8C22×D1114yescomplemented
568C4⋊Q8—111no—
569C4⋊Q8—111no—
570C4⋊Q8—111no—
571#127—111no—
572#127—222no—
573#126—222no—
574#126—222no—
575#125—221no—
576#124—112no—
577#124—112no—
578#124—222no—
579#124—222no—
580#124—222no—
581#124—221no—
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—114no—
591C22⋊Q8—112no—
592C22⋊Q8—112no—
593C22⋊Q8—112no—
594C22⋊Q8—222no—
595C22⋊Q8—221no—
596#121—114no—
597#121—112no—
598#121—112no—
599#121—112no—
600#121—222no—
601#121—222no—
602#121—222no—
603#121—221no—
604#121—224no—
605#121—224no—
606#121—222no—
607#121—222no—
608#120—222no—
609#120—222no—
610#120—224no—
611#120—224no—
612C4×Q8—112no—
613C4×Q8—222no—
614C4×Q8—221no—
615C4×D4—112no—
616C4×D4—112no—
617C4×D4—112no—
618C4×D4—222no—
619C4×D4—222no—
620C4×D4—222no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—221no—
624C4×D4—221no—
625C4×D4—221no—
626C4×D4D4412yes—
627C4×D4D4412yes—
628C4×D4C22×D1112yes—
629C4×D4C22×D1112yes—
630#117—112no—
631#117—112no—
632#117—221no—
633#117—222no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—221no—
636C2×C4⋊C4—222no—
637C2×C4⋊C4D4411yescharacteristic
638C2×C22⋊C4—221no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4—221no—
642C2×C22⋊C4—221no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4D4411yescharacteristic
646C2×C22⋊C4D4411yescharacteristic
647C2×C42C22×D1111yescharacteristic
648#107—114no—
649#106—114no—
650C4⋊C8C22×D1112yescomplemented
651C4⋊C8C22×D1112yescomplemented
652#103—114no—
653#103—114no—
654#103—114no—
655#102—114no—
656#102—114no—
657#102—114no—
658#102—114no—
659#102—114no—
660C22⋊C8C22×D1112yes—
661C22⋊C8C22×D1112yes—
662C22⋊C8C22×D1114yes—
663C22⋊C8C22×D1114yescomplemented
664#97C22×D1112yescomplemented
665#97C22×D1112yescomplemented
666C2×C11—22no—
667C2×C11—42no—
668C2×C11—42no—
669C2×C11#348411yescharacteristic
670C2×C11C2×#57511yescharacteristic
671C2×C11#358511yescharacteristic
672D11—44no—
673D11—82no—
674D11—82no—
675C24—221no—
676C24—221no—
677C24—224no—
678C24—444no—
679C24—444no—
680C24—882no—
681C24C2×D4411yescharacteristic
682C24C2×D4411yescharacteristic
683#41—228no—
684#41—444no—
685#41—444no—
686#41—444no—
687#41—444no—
688#41—448no—
689C2×Q8—112no—
690C2×Q8—112no—
691C2×Q8—221no—
692C2×Q8—221no—
693C2×Q8—221no—
694C2×Q8—442no—
695C2×D4—42no—
696C2×D4—112no—
697C2×D4—112no—
698C2×D4—112no—
699C2×D4—224no—
700C2×D4—228no—
701C2×D4—222no—
702C2×D4—224no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—224no—
706C2×D4—222no—
707C2×D4—222no—
708C2×D4—221no—
709C2×D4—221no—
710C2×D4—224no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—444no—
714C2×D4—442no—
715C2×D4—448no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—882no—
719C2×D4C2×D4412yes—
720C2×D4C2×D4412yes—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—224no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—444no—
732C22×C4—882no—
733C22×C4C2×D4411yescharacteristic
734C22×C4C2×D4411yescharacteristic
735C22×C4C2×D4411yescharacteristic
736C22×C4C2×D4411yescharacteristic
737C22×C4C2×D4412yes—
738C22×C4C2×D4412yes—
739C22×C4C23×D1111yescharacteristic
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742Q16—444no—
743SD16—228no—
744SD16—444no—
745SD16—444no—
746D8—228no—
747D8—444no—
748M16—44no—
749C2×C8—44no—
750C2×C8C23×D1114yes—
751C2×C8C23×D1114yes—
752C4⋊C4—112no—
753C4⋊C4—112no—
754C4⋊C4—112no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—222no—
758C4⋊C4—222no—
759C4⋊C4—224no—
760C4⋊C4—221no—
761C4⋊C4—222no—
762C4⋊C4—221no—
763C4⋊C4—222no—
764C4⋊C4—221no—
765C4⋊C4C2×D4412yes—
766C4⋊C4C2×D4412yes—
767C22⋊C4—224no—
768C22⋊C4—222no—
769C22⋊C4—222no—
770C22⋊C4—222no—
771C22⋊C4—222no—
772C22⋊C4—222no—
773C22⋊C4—224no—
774C22⋊C4—222no—
775C22⋊C4—222no—
776C22⋊C4—222no—
777C22⋊C4—222no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4C2×D4412yes—
785C22⋊C4C2×D4412yes—
786C22⋊C4C2×D4412yes—
787C22⋊C4C2×D4412yes—
788C42—222no—
789C42—222no—
790C42—222no—
791C42C2×D4411yescharacteristic
792C42C2×D4411yescharacteristic
793C42C23×D1111yescharacteristic
794C42C23×D1111yescharacteristic
795C11#6157611yescharacteristic, complemented, Sylow
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—224no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—448no—
807C23—442no—
808C23—442no—
809C23—442no—
810C23—448no—
811C23—442no—
812C23—442no—
813C23—884no—
814C23—8816no—
815C23C22×D4412yes—
816C23C22×D4412yes—
817C23C22×D4411yescharacteristic
818Q8—224no—
819Q8—224no—
820Q8—442no—
821Q8—442no—
822Q8—881no—
823D4—42no—
824D4—42no—
825D4—114no—
826D4—224no—
827D4—222no—
828D4—224no—
829D4—224no—
830D4—448no—
831D4—442no—
832D4—442no—
833D4—448no—
834D4—444no—
835D4—881no—
836D4—884no—
837D4—882no—
838D4—882no—
839D4—882no—
840D4—882no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—448no—
856C2×C4—444no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—882no—
860C2×C4—882no—
861C2×C4—882no—
862C2×C4—882no—
863C2×C4C22×D4411yescharacteristic
864C2×C4C22×D4412yes—
865C2×C4C22×D4412yes—
866C2×C4C22×D4411yescharacteristic
867C2×C4C22×D4411yescharacteristic
868C2×C4C22×D4411yescharacteristic
869C2×C4C22×D4411yescharacteristic
870C2×C4C24×D1111yescharacteristic
871C8—24no—
872C8—24no—
873C22—21no—
874C22—21no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—44no—
882C22—82no—
883C22—224no—
884C22—448no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—884no—
894C22—8816no—
895C22#1062327912yes—
896C22C23×D4411yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—22no—
901C4—22no—
902C4—21no—
903C4—21no—
904C4—442no—
905C4—442no—
906C4—442no—
907C4—442no—
908C4—442no—
909C4D11×H(5,𝔽2)12yes—
910C2—22no—
911C2—42no—
912C2—42no—
913C2—444no—
914C2—882no—
915C2—882no—
916C2#1308225211yescharacteristic
917C2C2×#1062327911yescharacteristic
918C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2973C2
socleC22×C11C23×D4
hypercenter#2973D11
hypocenterC11#61576
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
1. #13082468C2semidirect
2. C2×#10623081C2semidirect
3. #13080774C2semidirect
4. #13080654C2semidirect
5. #13080161C2semidirect
6. #13080146C2semidirect
7. #13079621C2semidirect
8. #13079605C2semidirect
9. #13079448C2semidirect
10. #13079383C2semidirect
11. #13078716C2semidirect
12. #13078708C2semidirect
13. #13077846C2semidirect
14. #13077838C2semidirect
15. C11×#2973C2semidirect
22. #10623322C22semidirect
25. C2×#66961C22semidirect
26. C2×#66957C22semidirect
27. #10623094C22semidirect
30. #10623084C22semidirect
31. #10623082C22semidirect
36. #10623073C22semidirect
43. #10623008C22semidirect
46. #10623001C22semidirect
47. C11×#435C22semidirect
48. C11×#435C22semidirect
49. C11×#432C22semidirect
50. C11×#432C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622750C22semidirect
54. #10622747C22semidirect
55. #10622744C22semidirect
56. #10622728C22semidirect
57. #10622727C22semidirect
58. #10622726C22semidirect
59. #10622459C22semidirect
60. #10622458C22semidirect
61. #10622457C22semidirect
62. #10622456C22semidirect
63. #10622455C22semidirect
64. #10622454C22semidirect
65. #10622352C22semidirect
66. #10622351C22semidirect
67. #10622350C22semidirect
68. #10622348C22semidirect
69. #10622347C22semidirect
70. #10622347C22semidirect
71. #10622346C22semidirect
72. #10622346C22semidirect
75. #10622345C22semidirect
78. #10622344C22semidirect
79. #10622336C22semidirect
80. #10622335C22semidirect
81. #10622328C22semidirect
82. #10622327C22semidirect
83. #10622327C22semidirect
84. #10622325C22semidirect
85. #10622324C22semidirect
86. #10622323C22semidirect
98. C2×#4339C23semidirect
109. C22×C8×C11C23semidirect
132. #66983C23semidirect
145. #66979C23semidirect
152. #66977C23semidirect
155. C2×Dic44C23semidirect
161. C2×#4314C23semidirect
185. #66927C23semidirect
191. C4×D44C23semidirect
193. #66922C23semidirect
194. #66922C23semidirect
195. #66922C23semidirect
197. C4×Dic22C23semidirect
198. C11×C4⋊C8C23semidirect
199. C11×C4⋊C8C23semidirect
203. C11×C22⋊C8C23semidirect
204. C11×#97C23semidirect
205. C11×#97C23semidirect
210. #66885C23semidirect
211. #66882C23semidirect
212. #66881C23semidirect
213. #66880C23semidirect
214. #66880C23semidirect
215. #66880C23semidirect
351. #2973D11semidirect
492. #435C2×D11semidirect
493. #435C2×D11semidirect
494. #432C2×D11semidirect
495. #432C2×D11semidirect
499. C2×C22⋊C8C2×D11semidirect
567. C22×C8C22×D11semidirect
650. C4⋊C8C22×D11semidirect
651. C4⋊C8C22×D11semidirect
663. C22⋊C8C22×D11semidirect
664. #97C22×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
#130824682
C2×#106230812
#130807742
#130806542
#130801612
#130801462
#130796212
#130796052
#130794482
#130793832
#130787162
#130787082
#130778462
#130778382
C11×#29732
#6157611