Finite Group Databasebeta

← #15638629

Subgroups — #15638629

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic, complemented
2C2×#10623362C211yesmaximal, characteristic, complemented
3#13080608C214yesmaximal, complemented
4#13080600C214yesmaximal, complemented
5#13080114C214yesmaximal, complemented
6#13080105C214yesmaximal, complemented
7#13079600C212yesmaximal, complemented
8#13079423C211yesmaximal, characteristic, complemented
9#13079422C211yesmaximal, characteristic, complemented
10#13079365C212yesmaximal, complemented
11#13078733C212yesmaximal, complemented
12#13077868C211yesmaximal, characteristic, complemented
13D11×#448C212yesmaximal, complemented
14#13077643C211yesmaximal, characteristic, complemented
15C11×#3006C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic, complemented
17C22×Q8×D11C2211yescharacteristic, complemented
18C2×#67037—21no—
19C2×C11×AGL(1,ℤ/8)C2212yescomplemented
20C2×C11×#121C2211yescharacteristic
21#10623362—22no—
22#10623362—22no—
23#10623362C2214yescomplemented
24#10623362C2214yescomplemented
25C2×#67002C2212yescomplemented
26C2×Q8×Dic11C2211yescharacteristic, complemented
27#10623335—21no—
28D4×C22⋊D11C2212yescomplemented
29C2×#66991—21no—
30C2×#66991C2211yescharacteristic, complemented
31C2×#66989—21no—
32C2×#66989C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66977—21no—
37C2×#66977C2211yescharacteristic, complemented
38C2×SD16×D11C2214yescomplemented
39#10623142C2212yescomplemented
40#10623141—22no—
41#10623140C2212yescomplemented
42#10623136—21no—
43D11×#121C2212yes—
44#10623128—21no—
45#10623127C2212yes—
46#10623038C2212yescomplemented
47#10623021—22no—
48C11×#449C2214yescomplemented
49C11×#448C2212yescomplemented
50C11×#447C2212yescomplemented
51C11×#417C2212yescomplemented
52C11×#407C2211yescharacteristic, complemented
53#10622851C2214yescomplemented
54#10622845C2212yescomplemented
55#10622840C2212yescomplemented
56#10622831C2212yescomplemented
57#10622830C2212yescomplemented
58#10622820C2211yescharacteristic, complemented
59#10622783C2214yescomplemented
60#10622777C2214yescomplemented
61#10622776C2214yescomplemented
62#10622770C2214yescomplemented
63#10622769C2214yescomplemented
64#10622767C2214yescomplemented
65#10622766C2214yescomplemented
66#10622747C2214yescomplemented
67#10622740C2214yescomplemented
68#10622655C2214yescomplemented
69#10622653C2212yescomplemented
70#10622646C2212yescomplemented
71#10622583C2212yescomplemented
72#10622430C2214yescomplemented
73#10622419C2214yescomplemented
74D11×#103C2214yescomplemented
75#10622407C2214yescomplemented
76#10622400C2214yescomplemented
77#10622388C2214yescomplemented
78#10622387C2214yescomplemented
79#10622378C2214yescomplemented
80#10622351C2212yescomplemented
81#10622349C2212yescomplemented
82#10622344C2212yescomplemented
83#10622341C2214yescomplemented
84D11×C22⋊C8C2212yescomplemented
85#10622335C2212yescomplemented
86#10622332C2212yescomplemented
87C2×C11×#41—21no—
88C2×C11×#41—21no—
89C2×C11×#41—44no—
90C2×C11×#41C2312yes—
91C2×C11×#41C2312yes—
92C22×Q8×C11C2311yescharacteristic
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11C2311yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—22no—
102C22×C22⋊D11D411yescharacteristic
103C2×Q8×D11—22no—
104C2×Q8×D11—44no—
105C2×Q8×D11C2314yes—
106#67037—48no—
107C2×#4341—22no—
108C2×#4341—22no—
109C2×D4×D11—22no—
110C2×D4×D11—22no—
111C2×D4×D11C2312yes—
112C2×#4339—22no—
113C22×D44C2311yescharacteristic
114C22×C4×D11—21no—
115C22×C4×D11C2311yescharacteristic
116C22×Dic22—21no—
117C22×Dic22C2311yescharacteristic
118C11×AGL(1,ℤ/8)—44no—
119C2×C11×SD16C2314yes—
120C2×C11×D8C2314yes—
121C2×C11×M16C2312yes—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128#67006—22no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11D411yescharacteristic
134#67002—44no—
135Q8×Dic11—22no—
136Q8×Dic11C2314yes—
137C2×#4325C2314yes—
138#66993C2312yes—
139#66992—22no—
140#66992—22no—
141#66992—22no—
142#66991—24no—
143#66991—24no—
144#66991—22no—
145#66991C2314yes—
146#66991C2312yes—
147#66990—22no—
148#66990—22no—
149#66989—24no—
150#66989—24no—
151#66989—22no—
152#66989C2314yes—
153#66988—22no—
154D4×Dic11C2312yes—
155C2×#4324C2314yes—
156C2×#4323C2314yes—
157#66983—21no—
158#66983—21no—
159#66983C2312yes—
160#66983C2312yes—
161#66982—22no—
162C4×C22⋊D11—24no—
163C4×C22⋊D11—24no—
164C4×C22⋊D11D412yes—
165C4×C22⋊D11D412yes—
166C4×C22⋊D11C2312yes—
167C4×C22⋊D11C2312yes—
168C2×(C2×D11)⋊C4—21no—
169C2×(C2×D11)⋊C4D411yescharacteristic
170C2×C4⋊Dic11—21no—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173#66977—21no—
174#66977—21no—
175#66977—24no—
176#66977—24no—
177#66977C2312yes—
178#66977C2312yes—
179C2×Dic11⋊C4—21no—
180C2×Dic11⋊C4D411yescharacteristic
181C2×C4×Dic11—21no—
182C2×C4×Dic11C2311yescharacteristic
183C2×#4318C2312yes—
184SD16×D11—48no—
185C2×#4314C2314yes—
186C2×C8×D11C2314yes—
187#66949—22no—
188#66948C2312yes—
189#66947—22no—
190#66946C2312yes—
191C4⋊C4×D11C2312yes—
192#66941C2312yes—
193#66938—22no—
194#66937—22no—
195#66937—22no—
196#66936—22no—
197#66935—22no—
198(C22⋊D11)⋊C4—22no—
199C22⋊C4×D11—22no—
200#66931—22no—
201C11×#103C2314yes—
202C11×#102C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66899C2314yes—
206#66896C2314yes—
207#66896C2314yes—
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210#66885C2314yes—
211(C2×D11)⋊C8C2314yes—
212#66882C2314yes—
213#66880C2314yes—
214#66879C2314yes—
215Dic11⋊C8C2314yes—
216#66874C2314yes—
217#66871C2314yes—
218#61572—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C23×D11—22no—
224C23×D11C2×D411yescharacteristic
225C11×#41—24no—
226C11×#41—24no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—44no—
230C11×#41—44no—
231C2×Q8×C11—24no—
232C2×Q8×C11—21no—
233C2×Q8×C11C2412yes—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—42no—
241C2×D4×C11—42no—
242C2×D4×C11—44no—
243C2×D4×C11—44no—
244C2×D4×C11C2412yes—
245C2×D4×C11C2412yes—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—42no—
251C22×C4×C11—44no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—22no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—24no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—24no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—48no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11C2×D412yes—
270C2×C22⋊D11C2×D412yes—
271C22×Dic11—22no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11C2×D411yescharacteristic
276C22×Dic11C2×D411yescharacteristic
277C22×Dic11C2×D411yescharacteristic
278Q8×D11—28no—
279Q8×D11—44no—
280Q8×D11—48no—
281#4341—48no—
282#4341—48no—
283D4×D11—44no—
284D4×D11—48no—
285D4×D11—48no—
286#4339—48no—
287C2×D44—22no—
288C2×D44—21no—
289C2×D44—42no—
290C2×D44C2412yes—
291C2×C4×D11—22no—
292C2×C4×D11—22no—
293C2×C4×D11—24no—
294C2×C4×D11—42no—
295C2×C4×D11—44no—
296C2×C4×D11C2×D412yes—
297C2×C4×D11C2412yes—
298C2×Dic22—22no—
299C2×Dic22—24no—
300C2×Dic22—21no—
301C2×Dic22—42no—
302C2×Dic22—44no—
303C2×Dic22C2412yes—
304C11×SD16—28no—
305C11×D8—44no—
306C11×M16—42no—
307C2×C8×C11C2414yes—
308C11×C4⋊C4—21no—
309C11×C4⋊C4C2412yes—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314C22⋊Dic11—24no—
315C22⋊Dic11—24no—
316C22⋊Dic11—24no—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11C2×D412yes—
320C22⋊Dic11C2×D412yes—
321#4325—28no—
322#4324—44no—
323#4323—44no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4C2×D412yes—
329(C2×D11)⋊C4C2×D412yes—
330C4⋊Dic11—24no—
331C4⋊Dic11—21no—
332C4⋊Dic11—21no—
333C4⋊Dic11C2412yes—
334C4⋊Dic11C2412yes—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4C2×D412yes—
340Dic11⋊C4C2×D412yes—
341C4×Dic11—24no—
342C4×Dic11C2×D412yes—
343C4×Dic11C2412yes—
344#4318—42no—
345C2×C11⋊C8C2414yes—
346#4314—44no—
347C8×D11—44no—
348#3496—111no—
349C2×#548—111no—
350#3308—114no—
351#3308—114no—
352#3265—114no—
353#3265—114no—
354#3213—112no—
355#3193—111no—
356#3193—111no—
357#3186—112no—
358#3112—112no—
359#3006—111no—
360#3006D1111yescharacteristic, complemented
361C2×#448—112no—
362#2973—111no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—42no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—81no—
373C23×C11—81no—
374C23×C11C22×D411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C22×D11—22no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—42no—
381C22×D11—44no—
382C22×D11—82no—
383C22×D11—82no—
384C22×D11—81no—
385C22×D11—81no—
386C22×D11AGL(1,ℤ/8)14yescomplemented
387C22×D11C22×D412yes—
388Q8×C11—24no—
389Q8×C11—22no—
390Q8×C11H(5,𝔽2)14yescomplemented
391D4×C11—22no—
392D4×C11—24no—
393D4×C11—22no—
394D4×C11—44no—
395D4×C11—44no—
396D4×C11—42no—
397D4×C11—44no—
398D4×C11—44no—
399D4×C11—81no—
400C2×C4×C11—24no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—44no—
410C2×C4×C11—44no—
411C2×C4×C11—42no—
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C2511yescharacteristic
416C22⋊D11—24no—
417C22⋊D11—24no—
418C22⋊D11—44no—
419C22⋊D11—44no—
420C22⋊D11—44no—
421C22⋊D11—44no—
422C22⋊D11—48no—
423C22⋊D11—82no—
424C22⋊D11—82no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—44no—
432C2×Dic11—42no—
433C2×Dic11—42no—
434C2×Dic11—42no—
435C2×Dic11C22×D412yes—
436C2×Dic11C22×D412yes—
437C2×Dic11C22×D412yes—
438D44—24no—
439D44—44no—
440D44—81no—
441C4×D11—24no—
442C4×D11—42no—
443C4×D11—44no—
444C4×D11—48no—
445C4×D11—44no—
446Dic22—24no—
447Dic22—48no—
448Dic22—44no—
449Dic22—42no—
450C8×C11—24no—
451C11⋊C8—24no—
452C2×H(5,𝔽2)—221no—
453C22×#41C2×D1111yescharacteristic, complemented
454C23×Q8—111no—
455C2×AGL(1,ℤ/8)—112no—
456C2×AGL(1,ℤ/8)C2×D1112yescomplemented
457C22×SD16—114no—
458#548—114no—
459#548—114no—
460#548—222no—
461#548—222no—
462#547—112no—
463#547—112no—
464#546—222no—
465#546—222no—
466D42—112no—
467D42—112no—
468#537—221no—
469#534—221no—
470#534—221no—
471#532—112no—
472C2×#124—111no—
473C2×#124—221no—
474C2×C22⋊Q8—111no—
475C2×C22⋊Q8—221no—
476C2×#121—111no—
477C2×#121—111no—
478C2×#121—112no—
479C2×#121—221no—
480C2×#121C2×D1111yescharacteristic
481C2×C4×Q8—111no—
482C2×C4×D4—111no—
483C2×C4×D4—221no—
484#496—114no—
485#489—114no—
486#484—112no—
487#484—112no—
488#480—112no—
489#480—114no—
490#480—112no—
491#477—114no—
492#468—114no—
493#468—114no—
494#466—114no—
495#466—114no—
496#463—114no—
497#463—114no—
498#460—114no—
499#450—112no—
500#450—112no—
501#449—114no—
502#449C2×D1114yescomplemented
503#448—112no—
504#448—114no—
505#448—112no—
506#448—114no—
507#448—112no—
508#448C2×D1112yescomplemented
509#447—112no—
510#447—114no—
511#447C2×D1112yescomplemented
512#440—114no—
513#440—114no—
514#435—114no—
515#435—114no—
516#432—112no—
517#417—112no—
518#417C2×D1112yescomplemented
519C2×#103—114no—
520#407—111no—
521#407C2×D1111yescharacteristic, complemented
522C2×C22⋊C8—112no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—82no—
538C22×C11—84no—
539C22×C11—162no—
540C22×C11C2×AGL(1,ℤ/8)12yes—
541C22×C11C23×D411yescharacteristic
542C2×D11—22no—
543C2×D11—22no—
544C2×D11—44no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—164no—
549C2×D11—162no—
550C2×D11C2×AGL(1,ℤ/8)14yes—
551C4×C11—24no—
552C4×C11—21no—
553C4×C11—21no—
554C4×C11—21no—
555C4×C11—42no—
556C4×C11C2×H(5,𝔽2)12yes—
557Dic11—22no—
558Dic11—22no—
559Dic11—22no—
560Dic11—42no—
561Dic11—42no—
562Dic11—42no—
563H(5,𝔽2)—448no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—44no—
567C2×#41—222no—
568C2×#41—222no—
569C2×#41—222no—
570C2×#41C22×D1112yes—
571C2×#41C22×D1112yes—
572C22×Q8—114no—
573C22×Q8—111no—
574C22×Q8—221no—
575C22×Q8—222no—
576C22×Q8—444no—
577C22×Q8C22×D1111yescharacteristic
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—111no—
581C22×D4—112no—
582C22×D4—111no—
583C22×D4—222no—
584C22×D4—222no—
585C22×D4—222no—
586C22×D4—221no—
587C22×D4—221no—
588C22×D4C22×D1111yescharacteristic
589C22×D4C22×D1111yescharacteristic
590C23×C4—21no—
591C23×C4—111no—
592C23×C4—221no—
593C23×C4C22×D1111yescharacteristic
594AGL(1,ℤ/8)—44no—
595AGL(1,ℤ/8)—444no—
596C2×SD16—114no—
597C2×SD16—114no—
598C2×SD16—114no—
599C2×SD16—448no—
600C2×SD16C22×D1114yes—
601C2×D8—114no—
602C2×D8C22×D1114yes—
603C2×M16—112no—
604C2×M16C22×D1112yes—
605C22×C8—114no—
606C4⋊Q8—112no—
607#127—112no—
608#124—114no—
609#124—222no—
610#124—222no—
611#124—224no—
612#124—224no—
613#123—222no—
614#123—222no—
615#123—222no—
616#123—222no—
617C22⋊Q8—112no—
618C22⋊Q8—112no—
619C22⋊Q8—222no—
620C22⋊Q8—222no—
621C22⋊Q8—224no—
622C22⋊Q8—224no—
623C22⋊Q8—221no—
624C22⋊Q8—221no—
625#121—21no—
626#121—21no—
627#121—112no—
628#121—114no—
629#121—112no—
630#121—112no—
631#121—112no—
632#121—222no—
633#121—222no—
634#121—222no—
635#121—222no—
636#121—222no—
637#121—222no—
638#121—224no—
639#121—224no—
640#121—221no—
641#121—221no—
642#121C22×D1112yes—
643#121C22×D1112yes—
644#120—222no—
645#120—222no—
646#120—222no—
647#120—222no—
648C4×Q8—114no—
649C4×Q8—222no—
650C4×D4—112no—
651C4×D4—112no—
652C4×D4—112no—
653C4×D4—112no—
654C4×D4—112no—
655C4×D4—112no—
656C4×D4—222no—
657C4×D4—224no—
658C4×D4—224no—
659C2×C4⋊C4—111no—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4—221no—
664C2×C4⋊C4—221no—
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—111no—
668C2×C22⋊C4—111no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—221no—
671C2×C22⋊C4—221no—
672C2×C22⋊C4—221no—
673C2×C22⋊C4—221no—
674C2×C22⋊C4—221no—
675C2×C42—111no—
676C2×C42—221no—
677#107—114no—
678#107—114no—
679C4⋊C8—114no—
680#103—114no—
681#103—114no—
682#103—114no—
683#103C22×D1114yes—
684#102—114no—
685#102—114no—
686#102—114no—
687#102C22×D1114yes—
688C22⋊C8—112no—
689C22⋊C8—112no—
690C22⋊C8—114no—
691C22⋊C8C22×D1112yes—
692C22⋊C8C22×D1112yes—
693#97—114no—
694C2×C11—22no—
695C2×C11—41no—
696C2×C11—41no—
697C2×C11—82no—
698C2×C11—82no—
699C2×C11#348411yescharacteristic
700C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
701C2×C11#358611yescharacteristic
702D11—24no—
703D11—82no—
704C24—21no—
705C24—21no—
706C24—111no—
707C24—222no—
708C24—221no—
709C24D4×D1111yescharacteristic
710#41—24no—
711#41—24no—
712#41—42no—
713#41—42no—
714#41—44no—
715#41—44no—
716#41—448no—
717#41—448no—
718#41—448no—
719C2×Q8—24no—
720C2×Q8—21no—
721C2×Q8—112no—
722C2×Q8—224no—
723C2×Q8—222no—
724C2×Q8—221no—
725C2×Q8—228no—
726C2×Q8—442no—
727C2×Q8—444no—
728C2×Q8—444no—
729C2×Q8—448no—
730C2×Q8C23×D1112yes—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—112no—
742C2×D4—112no—
743C2×D4—112no—
744C2×D4—222no—
745C2×D4—222no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—224no—
749C2×D4—224no—
750C2×D4—222no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—221no—
754C2×D4—442no—
755C2×D4—444no—
756C2×D4—448no—
757C2×D4—448no—
758C2×D4—448no—
759C2×D4—444no—
760C2×D4—444no—
761C2×D4C23×D1112yes—
762C2×D4C23×D1112yes—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—42no—
768C22×C4—44no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—224no—
777C22×C4—222no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—442no—
782C22×C4—444no—
783C22×C4D4×D1111yescharacteristic
784C22×C4D4×D1111yescharacteristic
785C22×C4D4×D1111yescharacteristic
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789SD16—28no—
790SD16—228no—
791SD16—444no—
792SD16—444no—
793D8—44no—
794D8—444no—
795M16—42no—
796M16—442no—
797C2×C8—114no—
798C2×C8—444no—
799C2×C8C23×D1114yes—
800C4⋊C4—21no—
801C4⋊C4—112no—
802C4⋊C4—112no—
803C4⋊C4—112no—
804C4⋊C4—112no—
805C4⋊C4—222no—
806C4⋊C4—224no—
807C4⋊C4—222no—
808C4⋊C4—221no—
809C4⋊C4—221no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4C23×D1112yes—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—112no—
816C22⋊C4—112no—
817C22⋊C4—112no—
818C22⋊C4—112no—
819C22⋊C4—222no—
820C22⋊C4—222no—
821C22⋊C4—224no—
822C22⋊C4—222no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—222no—
826C22⋊C4—222no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C42—112no—
831C42—112no—
832C42—224no—
833C11#6157211yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—81no—
844C23—81no—
845C23—112no—
846C23—114no—
847C23—222no—
848C23—441no—
849C23—441no—
850C23—442no—
851C23—444no—
852C23—881no—
853C23—881no—
854C23—882no—
855C23—882no—
856C23C2×D4×D1111yescharacteristic
857C23C2×D4×D1111yescharacteristic
858C23C2×D4×D1111yescharacteristic
859Q8—24no—
860Q8—22no—
861Q8—224no—
862Q8—448no—
863Q8—442no—
864Q8—444no—
865Q8#6703714yescomplemented
866D4—22no—
867D4—24no—
868D4—22no—
869D4—44no—
870D4—44no—
871D4—42no—
872D4—44no—
873D4—44no—
874D4—81no—
875D4—224no—
876D4—224no—
877D4—224no—
878D4—444no—
879D4—444no—
880D4—444no—
881D4—444no—
882D4—448no—
883D4—444no—
884D4—881no—
885D4—882no—
886D4—882no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—44no—
897C2×C4—44no—
898C2×C4—42no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—222no—
903C2×C4—224no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—442no—
908C2×C4—448no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—444no—
914C2×C4—442no—
915C2×C4—442no—
916C2×C4—442no—
917C2×C4C2×D4×D1111yescharacteristic
918C2×C4C2×D4×D1111yescharacteristic
919C2×C4C2×D4×D1111yescharacteristic
920C2×C4C24×D1111yescharacteristic
921C8—24no—
922C8—224no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—82no—
938C22—84no—
939C22—114no—
940C22—162no—
941C22—222no—
942C22—222no—
943C22—444no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—1762no—
948C22—1764no—
949C22D11×AGL(1,ℤ/8)12yes—
950C22C22×D4×D1111yescharacteristic
951C4—24no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—42no—
956C4—222no—
957C4—222no—
958C4—222no—
959C4—442no—
960C4—442no—
961C4—442no—
962C4C2×#6703712yes—
963C2—22no—
964C2—41no—
965C2—41no—
966C2—82no—
967C2—82no—
968C2—224no—
969C2—882no—
970C2#1308224511yescharacteristic
971C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
972C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#61572
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. #13082373C2semidirect
2. C2×#10623362C2semidirect
3. #13080608C2semidirect
4. #13080600C2semidirect
5. #13080114C2semidirect
6. #13080105C2semidirect
7. #13079600C2semidirect
8. #13079423C2semidirect
9. #13079422C2semidirect
10. #13079365C2semidirect
11. #13078733C2semidirect
12. #13077868C2semidirect
13. D11×#448C2semidirect
14. #13077643C2semidirect
15. C11×#3006C2semidirect
16. C22×C11×#41C22semidirect
17. C22×Q8×D11C22semidirect
19. C2×C11×AGL(1,ℤ/8)C22semidirect
23. #10623362C22semidirect
24. #10623362C22semidirect
25. C2×#67002C22semidirect
26. C2×Q8×Dic11C22semidirect
28. D4×C22⋊D11C22semidirect
30. C2×#66991C22semidirect
32. C2×#66989C22semidirect
37. C2×#66977C22semidirect
38. C2×SD16×D11C22semidirect
39. #10623142C22semidirect
41. #10623140C22semidirect
46. #10623038C22semidirect
48. C11×#449C22semidirect
49. C11×#448C22semidirect
50. C11×#447C22semidirect
51. C11×#417C22semidirect
52. C11×#407C22semidirect
53. #10622851C22semidirect
54. #10622845C22semidirect
55. #10622840C22semidirect
56. #10622831C22semidirect
57. #10622830C22semidirect
58. #10622820C22semidirect
59. #10622783C22semidirect
60. #10622777C22semidirect
61. #10622776C22semidirect
62. #10622770C22semidirect
63. #10622769C22semidirect
64. #10622767C22semidirect
65. #10622766C22semidirect
66. #10622747C22semidirect
67. #10622740C22semidirect
68. #10622655C22semidirect
69. #10622653C22semidirect
70. #10622646C22semidirect
71. #10622583C22semidirect
72. #10622430C22semidirect
73. #10622419C22semidirect
74. D11×#103C22semidirect
75. #10622407C22semidirect
76. #10622400C22semidirect
77. #10622388C22semidirect
78. #10622387C22semidirect
79. #10622378C22semidirect
80. #10622351C22semidirect
81. #10622349C22semidirect
82. #10622344C22semidirect
83. #10622341C22semidirect
84. D11×C22⋊C8C22semidirect
85. #10622335C22semidirect
86. #10622332C22semidirect
360. #3006D11semidirect
386. C22×D11AGL(1,ℤ/8)semidirect
390. Q8×C11H(5,𝔽2)semidirect
453. C22×#41C2×D11semidirect
456. C2×AGL(1,ℤ/8)C2×D11semidirect
502. #449C2×D11semidirect
508. #448C2×D11semidirect
511. #447C2×D11semidirect
518. #417C2×D11semidirect
521. #407C2×D11semidirect
833. C11#61572semidirect
865. Q8#67037semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106233622
#130806082
#130806002
#130801142
#130801052
#130796002
#130794232
#130794222
#130793652
#130787332
#130778682
D11×#4482
#130776432
C11×#30062
#6157211