Finite Group Databasebeta

← #15638595

Subgroups — #15638595

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic, complemented
2C2×#10623143C211yesmaximal, characteristic, complemented
3#13080580C214yesmaximal, complemented
4#13080572C214yesmaximal, complemented
5#13080103C214yesmaximal, complemented
6#13080094C214yesmaximal, complemented
7#13079600C212yesmaximal, complemented
8#13079413C211yesmaximal, characteristic, complemented
9#13079375C212yesmaximal, complemented
10#13078704C212yesmaximal, complemented
11#13077870C211yesmaximal, characteristic, complemented
12#13077866C211yesmaximal, characteristic, complemented
13D11×#447C212yesmaximal, complemented
14#13077643C211yesmaximal, characteristic, complemented
15C11×#3192C211yesmaximal, characteristic, complemented
16C2×#67037—21no—
17C22×D4×D11C2211yescharacteristic, complemented
18C22×#4339C2211yescharacteristic, complemented
19C2×C11×#121C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic, complemented
21#10623335—21no—
22D4×C22⋊D11C2212yescomplemented
23C2×#66991—21no—
24C2×#66990—21no—
25C2×#66989C2211yescharacteristic, complemented
26C2×#66985C2212yescomplemented
27C2×#66983C2211yescharacteristic, complemented
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×D8×D11C2214yescomplemented
30C2×#66961C2212yescomplemented
31#10623143—22no—
32#10623143—22no—
33#10623143C2214yescomplemented
34#10623143C2214yescomplemented
35#10623142C2212yescomplemented
36#10623141—22no—
37#10623140C2212yescomplemented
38#10623136—21no—
39D11×#121C2212yes—
40#10623128—21no—
41#10623127C2212yescomplemented
42C2×#66950C2211yescharacteristic, complemented
43#10623038C2212yescomplemented
44C2×#66946C2211yescharacteristic, complemented
45#10623021—22no—
46C2×#66936—21no—
47C2×C22⋊C4×D11—21no—
48C11×#481C2212yescomplemented
49C11×#481C2212yescomplemented
50C11×#469C2214yescomplemented
51C11×#447C2212yescomplemented
52C11×#447C2212yescomplemented
53C11×#407C2211yescharacteristic, complemented
54#10622830C2212yescomplemented
55#10622820C2211yescharacteristic, complemented
56#10622769C2214yescomplemented
57#10622767C2214yescomplemented
58#10622766C2214yescomplemented
59#10622746C2212yescomplemented
60#10622740C2214yescomplemented
61#10622653C2212yescomplemented
62#10622652C2214yescomplemented
63#10622650C2214yescomplemented
64#10622649C2212yescomplemented
65#10622649C2212yescomplemented
66#10622647C2212yescomplemented
67#10622581C2212yescomplemented
68#10622579C2212yescomplemented
69#10622483C2214yescomplemented
70#10622482C2214yescomplemented
71#10622477C2214yescomplemented
72#10622475C2214yescomplemented
73#10622400C2214yescomplemented
74#10622399C2214yescomplemented
75#10622398C2214yescomplemented
76#10622391C2214yescomplemented
77#10622389C2214yescomplemented
78#10622386C2214yescomplemented
79D11×#102C2214yescomplemented
80#10622378C2214yescomplemented
81#10622351C2212yescomplemented
82#10622347C2214yescomplemented
83#10622345C2212yescomplemented
84#10622341C2214yescomplemented
85D11×C22⋊C8C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2311yescharacteristic, complemented
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—22no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11D411yescharacteristic
98#67037—48no—
99C2×#4341—22no—
100C2×#4341—22no—
101C2×D4×D11—22no—
102C2×D4×D11—22no—
103C2×D4×D11—22no—
104C2×D4×D11—44no—
105C2×D4×D11C2314yes—
106C2×D4×D11C2312yes—
107C2×#4339—21no—
108C2×#4339—21no—
109C2×#4339—22no—
110C2×#4339—44no—
111C2×#4339C2312yes—
112C2×#4339C2312yes—
113C22×D44C2311yescharacteristic
114C22×D44C2311yescharacteristic, complemented
115C22×C4×D11—21no—
116C22×C4×D11—21no—
117C22×C4×D11C2311yescharacteristic
118C22×Dic22C2311yescharacteristic
119C2×C11×D8C2314yes—
120C2×C11×M16C2312yescomplemented
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C11×#121C2312yes—
128C11×#121C2312yescomplemented
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic, complemented
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133#67006—22no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×C22⋊Dic11D411yescharacteristic
137#66993C2312yescomplemented
138#66992—22no—
139#66992—22no—
140#66992—22no—
141#66991—24no—
142#66991—24no—
143#66991C2312yes—
144#66990—24no—
145#66990—24no—
146#66990—22no—
147#66990—22no—
148#66989—22no—
149#66989C2314yes—
150#66988—22no—
151D4×Dic11C2312yescomplemented
152C2×#4324C2314yescomplemented
153#66985—44no—
154C2×#4323C2314yes—
155C2×#4323C2314yes—
156#66983—21no—
157#66983—21no—
158#66983C2312yes—
159#66983C2312yescomplemented
160#66982—22no—
161C4×C22⋊D11D412yes—
162C4×C22⋊D11D412yes—
163C4×C22⋊D11C2312yes—
164C4×C22⋊D11C2312yes—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×(C2×D11)⋊C4—21no—
168C2×(C2×D11)⋊C4D411yescharacteristic
169C2×C4⋊Dic11—21no—
170C2×C4⋊Dic11C2311yescharacteristic, complemented
171C2×Dic11⋊C4D411yescharacteristic
172C2×C4×Dic11C2311yescharacteristic
173C2×#4318C2312yescomplemented
174D8×D11—48no—
175#66961—44no—
176C2×D88C2314yes—
177C2×#4314C2314yescomplemented
178C2×C8×D11C2314yes—
179#66950—22no—
180#66950C2314yes—
181#66949—22no—
182#66948C2312yes—
183#66947—22no—
184#66946—22no—
185#66946C2314yes—
186#66946C2312yescomplemented
187C4⋊C4×D11C2312yes—
188#66941C2312yescomplemented
189#66938—22no—
190#66937—22no—
191#66937—22no—
192#66936—22no—
193#66936—24no—
194#66936—24no—
195#66935—22no—
196(C22⋊D11)⋊C4—22no—
197C22⋊C4×D11—22no—
198C22⋊C4×D11—24no—
199C22⋊C4×D11—24no—
200#66931—22no—
201C11×#106C2314yescomplemented
202C11×#102C2314yes—
203C11×#102C2314yescomplemented
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yescomplemented
206#66896C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210(C2×D11)⋊C8C2314yes—
211#66880C2314yescomplemented
212#66879C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214#66874C2314yescomplemented
215#66873C2314yes—
216#66873C2314yescomplemented
217#66872C2314yescomplemented
218#61569—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—24no—
225C23×D11—22no—
226C23×D11—44no—
227C23×D11—44no—
228C23×D11—82no—
229C23×D11C2×D411yescharacteristic
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—42no—
237C2×D4×C11—42no—
238C2×D4×C11—44no—
239C2×D4×C11—82no—
240C2×D4×C11C2412yes—
241C2×D4×C11C2412yes—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—42no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—24no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—48no—
265C2×C22⋊D11C2×D412yes—
266C2×C22⋊D11C2×D412yes—
267C22×Dic11—22no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11C2×D411yescharacteristic
271C22×Dic11C2×D411yescharacteristic
272C22×Dic11C2×D411yescharacteristic
273#4341—48no—
274#4341—48no—
275D4×D11—28no—
276D4×D11—44no—
277D4×D11—44no—
278D4×D11—48no—
279D4×D11—48no—
280D4×D11—48no—
281#4339—24no—
282#4339—24no—
283#4339—42no—
284#4339—42no—
285#4339—44no—
286#4339—44no—
287#4339—48no—
288C2×D44—24no—
289C2×D44—22no—
290C2×D44—21no—
291C2×D44—21no—
292C2×D44—42no—
293C2×D44C2412yes—
294C2×D44C2412yes—
295C2×C4×D11—22no—
296C2×C4×D11—24no—
297C2×C4×D11—22no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—42no—
301C2×C4×D11—44no—
302C2×C4×D11—82no—
303C2×C4×D11C2×D412yes—
304C2×C4×D11C2412yes—
305C2×Dic22—22no—
306C2×Dic22—21no—
307C2×Dic22—42no—
308C2×Dic22C2412yes—
309C11×D8—44no—
310C11×M16—42no—
311C2×C8×C11C2414yes—
312C11×C4⋊C4—21no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4C2412yes—
315C11×C4⋊C4C2412yes—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C22⋊Dic11—22no—
321C22⋊Dic11—24no—
322C22⋊Dic11—24no—
323C22⋊Dic11—22no—
324C22⋊Dic11C2×D412yes—
325C22⋊Dic11C2×D412yes—
326#4324—44no—
327#4323—28no—
328#4323—44no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—22no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4C2×D412yes—
336(C2×D11)⋊C4C2×D412yes—
337C4⋊Dic11—24no—
338C4⋊Dic11—21no—
339C4⋊Dic11C2412yes—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4C2×D412yes—
343Dic11⋊C4C2×D412yes—
344C4×Dic11C2×D412yes—
345C4×Dic11C2412yes—
346#4318—42no—
347C2×C11⋊C8C2414yes—
348D88—28no—
349#4314—44no—
350C8×D11—44no—
351#3496—111no—
352C2×#546—111no—
353#3306—114no—
354#3306—114no—
355#3264—114no—
356#3264—114no—
357#3213—112no—
358#3192—111no—
359#3192D1111yescharacteristic, complemented
360#3187—112no—
361#3109—112no—
362#3006—111no—
363#3006—111no—
364C2×#447—112no—
365#2973—111no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—42no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—81no—
376C23×C11—81no—
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C22×D11—24no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—48no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—48no—
390C22×D11—44no—
391C22×D11—84no—
392C22×D11—82no—
393C22×D11—82no—
394C22×D11—816no—
395C22×D11—81no—
396C22×D11—81no—
397C22×D11AGL(1,ℤ/8)14yescomplemented
398C22×D11C22×D412yes—
399D4×C11—24no—
400D4×C11—24no—
401D4×C11—42no—
402D4×C11—44no—
403D4×C11—44no—
404D4×C11—81no—
405D4×C11—82no—
406D4×C11—82no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—42no—
416C2×C4×C11—42no—
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C2511yescharacteristic
421C22⋊D11—24no—
422C22⋊D11—24no—
423C22⋊D11—48no—
424C22⋊D11—44no—
425C22⋊D11—44no—
426C22⋊D11—44no—
427C22⋊D11—44no—
428C22⋊D11—44no—
429C22⋊D11—44no—
430C22⋊D11—82no—
431C22⋊D11—82no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—44no—
438C2×Dic11—42no—
439C2×Dic11—42no—
440C2×Dic11C22×D412yes—
441C2×Dic11C22×D412yes—
442C2×Dic11C22×D412yes—
443D44—24no—
444D44—22no—
445D44—24no—
446D44—44no—
447D44—81no—
448D44H(5,𝔽2)14yescomplemented
449C4×D11—24no—
450C4×D11—42no—
451C4×D11—44no—
452C4×D11—44no—
453C4×D11—44no—
454C4×D11—44no—
455C4×D11—84no—
456Dic22—22no—
457Dic22—22no—
458Dic22—44no—
459Dic22—42no—
460C8×C11—24no—
461C11⋊C8—24no—
462C2×H(5,𝔽2)—221no—
463C22×#41—111no—
464C23×D4—111no—
465C2×AGL(1,ℤ/8)—112no—
466C2×AGL(1,ℤ/8)—112no—
467C22×D8—114no—
468#547—112no—
469#547—112no—
470#546—114no—
471#546—114no—
472#546—222no—
473#546—222no—
474#546—222no—
475#546—222no—
476D42—112no—
477D42—112no—
478#537—221no—
479#534—221no—
480#534—221no—
481#532—112no—
482C2×#124—111no—
483C2×#123—221no—
484C2×C22⋊Q8—111no—
485C2×#121—111no—
486C2×#121—112no—
487C2×#121—221no—
488C2×#121C2×D1111yescharacteristic, complemented
489C2×#121C2×D1111yescharacteristic, complemented
490C2×#120—221no—
491C2×C4×D4—111no—
492C2×C4×D4—111no—
493C22×C22⋊C4—221no—
494#496—114no—
495#489—114no—
496#483—114no—
497#481—112no—
498#481—112no—
499#481C2×D1112yescomplemented
500#481C2×D1112yescomplemented
501#476—114no—
502#469—114no—
503#469C2×D1114yescomplemented
504#465—114no—
505#465—114no—
506#463—114no—
507#463—114no—
508#459—114no—
509#450—114no—
510#449—114no—
511#449—114no—
512#448—112no—
513#448—112no—
514#447—112no—
515#447—114no—
516#447—112no—
517#447—112no—
518#447—114no—
519#447—112no—
520#447C2×D1112yescomplemented
521#447C2×D1112yescomplemented
522#442—114no—
523#442—114no—
524#435—114no—
525#435—114no—
526#432—112no—
527#417—112no—
528#417—112no—
529C2×#102—114no—
530#407—111no—
531#407C2×D1111yescharacteristic, complemented
532C2×C22⋊C8—112no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—21no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—82no—
548C22×C11—84no—
549C22×C11—162no—
550C22×C11C2×AGL(1,ℤ/8)12yes—
551C22×C11C23×D411yescharacteristic
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—24no—
555C2×D11—44no—
556C2×D11—48no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—816no—
563C2×D11—164no—
564C2×D11—162no—
565C2×D11C2×AGL(1,ℤ/8)14yes—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—42no—
570C4×C11—42no—
571C4×C11C2×H(5,𝔽2)12yes—
572Dic11—22no—
573Dic11—22no—
574Dic11—22no—
575Dic11—42no—
576Dic11—42no—
577C25—221no—
578H(5,𝔽2)—448no—
579C2×#41—112no—
580C2×#41—112no—
581C2×#41—222no—
582C2×#41—222no—
583C2×#41—222no—
584C2×#41—221no—
585C2×#41—221no—
586C2×#41—444no—
587C22×Q8—111no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—111no—
591C22×D4—114no—
592C22×D4—112no—
593C22×D4—111no—
594C22×D4—111no—
595C22×D4—222no—
596C22×D4—221no—
597C22×D4—222no—
598C22×D4—222no—
599C22×D4—222no—
600C22×D4—221no—
601C22×D4—221no—
602C22×D4—444no—
603C22×D4C22×D1111yescharacteristic
604C22×D4C22×D1111yescharacteristic, complemented
605C23×C4—111no—
606C23×C4—221no—
607C23×C4—221no—
608C23×C4C22×D1111yescharacteristic
609AGL(1,ℤ/8)—444no—
610AGL(1,ℤ/8)—444no—
611C2×SD16—114no—
612C2×SD16—114no—
613C2×D8—114no—
614C2×D8—114no—
615C2×D8—114no—
616C2×D8—448no—
617C2×D8C22×D1114yes—
618C2×M16—112no—
619C2×M16C22×D1112yescomplemented
620C22×C8—114no—
621C4⋊Q8—112no—
622#127—112no—
623#124—114no—
624#124—222no—
625#124—222no—
626#123—222no—
627#123—224no—
628#123—224no—
629#123—222no—
630#123—222no—
631#123—222no—
632C22⋊Q8—114no—
633C22⋊Q8—222no—
634C22⋊Q8—222no—
635C22⋊Q8—222no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—112no—
641#121—112no—
642#121—112no—
643#121—112no—
644#121—222no—
645#121—222no—
646#121—224no—
647#121—224no—
648#121—222no—
649#121—222no—
650#121—222no—
651#121—221no—
652#121—221no—
653#121C22×D1112yes—
654#121C22×D1112yes—
655#121C22×D1112yes—
656#121C22×D1112yescomplemented
657#120—222no—
658#120—222no—
659#120—222no—
660#120—222no—
661#120—224no—
662#120—224no—
663C4×D4—112no—
664C4×D4—112no—
665C4×D4—112no—
666C4×D4—112no—
667C4×D4—112no—
668C4×D4—114no—
669C4×D4—112no—
670C4×D4—222no—
671C4×D4—222no—
672C2×C4⋊C4—111no—
673C2×C4⋊C4—111no—
674C2×C4⋊C4—112no—
675C2×C4⋊C4—221no—
676C2×C4⋊C4C22×D1111yescharacteristic
677C2×C4⋊C4C22×D1111yescharacteristic, complemented
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—111no—
681C2×C22⋊C4—111no—
682C2×C22⋊C4—224no—
683C2×C22⋊C4—224no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C22⋊C4—221no—
690C2×C42—111no—
691#106—114no—
692#106C22×D1114yescomplemented
693C4⋊C8—114no—
694#103—114no—
695#103—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102C22×D1114yes—
701#102C22×D1114yescomplemented
702C22⋊C8—112no—
703C22⋊C8—112no—
704C22⋊C8—114no—
705C22⋊C8C22×D1112yes—
706C22⋊C8C22×D1112yescomplemented
707#97—114no—
708C2×C11—22no—
709C2×C11—41no—
710C2×C11—41no—
711C2×C11—82no—
712C2×C11—82no—
713C2×C11#348411yescharacteristic
714C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
715C2×C11#358511yescharacteristic
716D11—24no—
717D11—44no—
718D11—82no—
719C24—21no—
720C24—21no—
721C24—111no—
722C24—224no—
723C24—222no—
724C24—221no—
725C24—221no—
726C24—444no—
727C24—444no—
728C24—882no—
729C24D4×D1111yescharacteristic
730#41—224no—
731#41—224no—
732#41—442no—
733#41—442no—
734#41—444no—
735#41—444no—
736#41—448no—
737#41—448no—
738#41—448no—
739C2×Q8—112no—
740C2×Q8—222no—
741C2×Q8—221no—
742C2×Q8—442no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—44no—
752C2×D4—82no—
753C2×D4—112no—
754C2×D4—112no—
755C2×D4—112no—
756C2×D4—112no—
757C2×D4—224no—
758C2×D4—222no—
759C2×D4—224no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—228no—
764C2×D4—224no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—222no—
768C2×D4—222no—
769C2×D4—222no—
770C2×D4—221no—
771C2×D4—221no—
772C2×D4—442no—
773C2×D4—444no—
774C2×D4—444no—
775C2×D4—448no—
776C2×D4—448no—
777C2×D4—448no—
778C2×D4—448no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4C23×D1112yes—
783C2×D4C23×D1112yes—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—42no—
787C22×C4—111no—
788C22×C4—111no—
789C22×C4—111no—
790C22×C4—112no—
791C22×C4—112no—
792C22×C4—222no—
793C22×C4—224no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—442no—
801C22×C4—444no—
802C22×C4—882no—
803C22×C4D4×D1111yescharacteristic
804C22×C4D4×D1111yescharacteristic
805C22×C4D4×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809SD16—444no—
810SD16—444no—
811D8—44no—
812D8—228no—
813D8—228no—
814D8—444no—
815M16—42no—
816M16—442no—
817C2×C8—114no—
818C2×C8—444no—
819C2×C8C23×D1114yes—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—112no—
823C4⋊C4—112no—
824C4⋊C4—112no—
825C4⋊C4—222no—
826C4⋊C4—224no—
827C4⋊C4—222no—
828C4⋊C4—221no—
829C4⋊C4C23×D1112yes—
830C4⋊C4C23×D1112yes—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—112no—
836C22⋊C4—112no—
837C22⋊C4—112no—
838C22⋊C4—112no—
839C22⋊C4—224no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4—224no—
843C22⋊C4—224no—
844C22⋊C4—224no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C22⋊C4—222no—
848C22⋊C4—222no—
849C42—112no—
850C42—112no—
851C11#6156911yescharacteristic, complemented, Sylow
852C23—22no—
853C23—22no—
854C23—22no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—81no—
862C23—81no—
863C23—112no—
864C23—114no—
865C23—224no—
866C23—222no—
867C23—222no—
868C23—441no—
869C23—441no—
870C23—442no—
871C23—442no—
872C23—448no—
873C23—444no—
874C23—448no—
875C23—442no—
876C23—881no—
877C23—881no—
878C23—884no—
879C23—882no—
880C23—882no—
881C23—8816no—
882C23C2×D4×D1111yescharacteristic
883C23C2×D4×D1111yescharacteristic
884C23C2×D4×D1111yescharacteristic
885Q8—222no—
886Q8—222no—
887Q8—442no—
888Q8—444no—
889D4—24no—
890D4—24no—
891D4—42no—
892D4—44no—
893D4—44no—
894D4—81no—
895D4—82no—
896D4—82no—
897D4—114no—
898D4—224no—
899D4—224no—
900D4—224no—
901D4—222no—
902D4—224no—
903D4—444no—
904D4—448no—
905D4—444no—
906D4—444no—
907D4—444no—
908D4—444no—
909D4—444no—
910D4—444no—
911D4—881no—
912D4—882no—
913D4—882no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—112no—
927C2×C4—222no—
928C2×C4—224no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—442no—
932C2×C4—444no—
933C2×C4—444no—
934C2×C4—444no—
935C2×C4—444no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—444no—
939C2×C4—442no—
940C2×C4—442no—
941C2×C4—884no—
942C2×C4C2×D4×D1111yescharacteristic
943C2×C4C2×D4×D1111yescharacteristic
944C2×C4C2×D4×D1111yescharacteristic
945C2×C4C24×D1111yescharacteristic
946C8—24no—
947C8—224no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—82no—
963C22—84no—
964C22—114no—
965C22—162no—
966C22—222no—
967C22—222no—
968C22—224no—
969C22—444no—
970C22—448no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—442no—
975C22—442no—
976C22—8816no—
977C22—1762no—
978C22—1764no—
979C22D11×AGL(1,ℤ/8)12yes—
980C22C22×D4×D1111yescharacteristic
981C4—21no—
982C4—21no—
983C4—21no—
984C4—42no—
985C4—42no—
986C4—222no—
987C4—222no—
988C4—222no—
989C4—442no—
990C4—442no—
991C4D11×H(5,𝔽2)12yes—
992C2—22no—
993C2—41no—
994C2—41no—
995C2—82no—
996C2—82no—
997C2—224no—
998C2—444no—
999C2—882no—
1000C2#1308224811yescharacteristic
1001C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1002C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3192C2
socleC22×C11C23×D4
hypercenter#3192D11
hypocenterC11#61569
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3192

Complements

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

NH ≅ G/Ntype
1. #13082373C2semidirect
2. C2×#10623143C2semidirect
3. #13080580C2semidirect
4. #13080572C2semidirect
5. #13080103C2semidirect
6. #13080094C2semidirect
7. #13079600C2semidirect
8. #13079413C2semidirect
9. #13079375C2semidirect
10. #13078704C2semidirect
11. #13077870C2semidirect
12. #13077866C2semidirect
13. D11×#447C2semidirect
14. #13077643C2semidirect
15. C11×#3192C2semidirect
17. C22×D4×D11C22semidirect
18. C22×#4339C22semidirect
19. C2×C11×#121C22semidirect
20. C2×C11×#121C22semidirect
22. D4×C22⋊D11C22semidirect
25. C2×#66989C22semidirect
26. C2×#66985C22semidirect
27. C2×#66983C22semidirect
29. C2×D8×D11C22semidirect
30. C2×#66961C22semidirect
33. #10623143C22semidirect
34. #10623143C22semidirect
35. #10623142C22semidirect
37. #10623140C22semidirect
41. #10623127C22semidirect
42. C2×#66950C22semidirect
43. #10623038C22semidirect
44. C2×#66946C22semidirect
48. C11×#481C22semidirect
49. C11×#481C22semidirect
50. C11×#469C22semidirect
51. C11×#447C22semidirect
52. C11×#447C22semidirect
53. C11×#407C22semidirect
54. #10622830C22semidirect
55. #10622820C22semidirect
56. #10622769C22semidirect
57. #10622767C22semidirect
58. #10622766C22semidirect
59. #10622746C22semidirect
60. #10622740C22semidirect
61. #10622653C22semidirect
62. #10622652C22semidirect
63. #10622650C22semidirect
64. #10622649C22semidirect
65. #10622649C22semidirect
66. #10622647C22semidirect
67. #10622581C22semidirect
68. #10622579C22semidirect
69. #10622483C22semidirect
70. #10622482C22semidirect
71. #10622477C22semidirect
72. #10622475C22semidirect
73. #10622400C22semidirect
74. #10622399C22semidirect
75. #10622398C22semidirect
76. #10622391C22semidirect
77. #10622389C22semidirect
78. #10622386C22semidirect
79. D11×#102C22semidirect
80. #10622378C22semidirect
81. #10622351C22semidirect
82. #10622347C22semidirect
83. #10622345C22semidirect
84. #10622341C22semidirect
85. D11×C22⋊C8C22semidirect
86. #10622332C22semidirect
91. C22×D4×C11C23semidirect
114. C22×D44C23semidirect
120. C2×C11×M16C23semidirect
128. C11×#121C23semidirect
130. C2×C11×C4⋊C4C23semidirect
137. #66993C23semidirect
151. D4×Dic11C23semidirect
152. C2×#4324C23semidirect
159. #66983C23semidirect
170. C2×C4⋊Dic11C23semidirect
173. C2×#4318C23semidirect
177. C2×#4314C23semidirect
186. #66946C23semidirect
188. #66941C23semidirect
201. C11×#106C23semidirect
203. C11×#102C23semidirect
205. C11×C22⋊C8C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
211. #66880C23semidirect
212. #66879C23semidirect
213. Dic11⋊C8C23semidirect
214. #66874C23semidirect
216. #66873C23semidirect
217. #66872C23semidirect
359. #3192D11semidirect
397. C22×D11AGL(1,ℤ/8)semidirect
448. D44H(5,𝔽2)semidirect
488. C2×#121C2×D11semidirect
489. C2×#121C2×D11semidirect
499. #481C2×D11semidirect
500. #481C2×D11semidirect
503. #469C2×D11semidirect
520. #447C2×D11semidirect
521. #447C2×D11semidirect
531. #407C2×D11semidirect
604. C22×D4C22×D11semidirect
619. C2×M16C22×D11semidirect
656. #121C22×D11semidirect
677. C2×C4⋊C4C22×D11semidirect
692. #106C22×D11semidirect
701. #102C22×D11semidirect
706. C22⋊C8C22×D11semidirect
851. C11#61569semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106231432
#130805802
#130805722
#130801032
#130800942
#130796002
#130794132
#130793752
#130787042
#130778702
#130778662
D11×#4472
#130776432
C11×#31922
#6156911