Finite Group Databasebeta

← #15638623

Subgroups — #15638623

Order 2816.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2#13080757C214yesmaximal, complemented
3#13080637C214yesmaximal, complemented
4#13080107C214yesmaximal, complemented
5#13080092C214yesmaximal, complemented
6#13079634C212yesmaximal, complemented
7#13079430C212yesmaximal, complemented
8#13079373C211yesmaximal, characteristic, complemented
9#13079364C211yesmaximal, characteristic, complemented
10#13078754C212yesmaximal, complemented
11#13077843C212yesmaximal, complemented
12C2×#10622831C211yesmaximal, characteristic, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C2×D42×C11C211yesmaximal, characteristic, complemented
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic, complemented
19D42×C11—22no—
20D42×C11—22no—
21D42×C11C2214yes—
22D42×C11C2214yescomplemented
23C2×C11×#127C2211yescharacteristic, complemented
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic, complemented
27C2×C11×#120—21no—
28C2×C11×#120—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic, complemented
31#10623335—21no—
32C22×#4324C2212yescomplemented
33C2×#66985C2214yescomplemented
34C22×#4323C2212yescomplemented
35#10623322C2212yescomplemented
36C2×#66983C2211yescharacteristic, complemented
37C2×#66977C2211yescharacteristic, complemented
38#10623096C2212yescomplemented
39#10623087—22no—
40#10623083C2212yescomplemented
41#10623081C2212yescomplemented
42#10623072C2212yescomplemented
43#10623071—22no—
44#10623046—21no—
45#10623025—21no—
46#10623017—21no—
47#10623010C2212yescomplemented
48#10622831C2212yescomplemented
49#10622831C2212yescomplemented
50#10622831C2212yescomplemented
51#10622831C2214yescomplemented
52#10622831C2214yescomplemented
53#10622830C2212yes—
54#10622830C2212yescomplemented
55#10622830C2212yescomplemented
56#10622830C2214yescomplemented
57#10622830C2214yescomplemented
58#10622828C2214yescomplemented
59C2×#66896C2212yescomplemented
60C2×#66896C2212yescomplemented
61#10622820C2212yescomplemented
62C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622688C2214yescomplemented
65#10622687C2214yescomplemented
66#10622685C2214yescomplemented
67#10622684C2214yescomplemented
68#10622655C2214yescomplemented
69#10622654C2214yescomplemented
70#10622653C2212yescomplemented
71#10622652C2214yescomplemented
72#10622651C2214yescomplemented
73#10622650C2214yescomplemented
74#10622649C2212yescomplemented
75#10622648C2214yescomplemented
76#10622647C2212yescomplemented
77#10622646C2212yescomplemented
78#10622631C2214yescomplemented
79#10622629C2214yescomplemented
80#10622627C2214yescomplemented
81#10622624C2214yescomplemented
82#10622624C2214yescomplemented
83#10622622C2214yescomplemented
84#10622584C2212yescomplemented
85#10622580C2212yescomplemented
86#10622539C2212yescomplemented
87C25×C11—21no—
88C25×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—24no—
92C22×D4×C11—24no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11—21no—
98C22×D4×C11—22no—
99C22×D4×C11—21no—
100C22×D4×C11—44no—
101C22×D4×C11—44no—
102C22×D4×C11—48no—
103C22×D4×C11D411yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2312yes—
106C22×D4×C11C2314yes—
107C22×D4×C11C2312yes—
108C22×D4×C11C2311yescharacteristic
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11—21no—
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C22×C22⋊D11—21no—
114C2×#4339C2312yescomplemented
115C22×D44C2311yescharacteristic, complemented
116C22×Dic22C2311yescharacteristic, complemented
117C11×#127—22no—
118C11×#127C2314yes—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—22no—
122C11×#121—24no—
123C11×#121—24no—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C11×#121C2314yes—
127C11×#120—24no—
128C11×#120—24no—
129C11×#120—24no—
130C11×#120—24no—
131C4×D4×C11—22no—
132C4×D4×C11D412yes—
133C4×D4×C11D412yes—
134C4×D4×C11C2314yes—
135C4×D4×C11C2312yes—
136C4×D4×C11C2312yes—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C11×C22⋊C4D411yescharacteristic
144C2×C42×C11C2311yescharacteristic
145#67006—22no—
146C2×C22⋊Dic11—21no—
147#66992—22no—
148#66992—22no—
149#66990—22no—
150#66988—22no—
151C2×#4324—44no—
152C2×#4324C2314yes—
153C2×#4324C2314yescomplemented
154C2×#4324C2314yescomplemented
155#66985—48no—
156C2×#4323—44no—
157C2×#4323C2314yes—
158C2×#4323C2314yescomplemented
159C2×#4323C2314yescomplemented
160#66983—21no—
161#66983—21no—
162#66983C2312yes—
163#66983C2312yescomplemented
164#66983C2312yescomplemented
165#66982—22no—
166#66982—22no—
167C4×C22⋊D11—22no—
168C4×C22⋊D11—22no—
169C4×C22⋊D11—22no—
170C2×(C2×D11)⋊C4—21no—
171#66979C2312yescomplemented
172C2×C4⋊Dic11C2311yescharacteristic, complemented
173C2×C4⋊Dic11C2311yescharacteristic, complemented
174#66977—21no—
175#66977—21no—
176#66977C2312yes—
177#66977C2312yescomplemented
178#66977C2312yescomplemented
179C2×Dic11⋊C4—21no—
180C2×#4318C2314yescomplemented
181C22×C11⋊C8C2312yescomplemented
182C22×C11⋊C8C2312yescomplemented
183#66951—22no—
184#66949—22no—
185#66947—22no—
186#66942—22no—
187#66938—22no—
188#66937—22no—
189#66936—22no—
190(C22⋊D11)⋊C4—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—22no—
193#66932—22no—
194#66930—22no—
195#66929—22no—
196#66928C2312yescomplemented
197C4×D44C2312yescomplemented
198#66925—22no—
199#66923C2312yescomplemented
200C4×Dic22C2312yescomplemented
201#66896C2314yes—
202#66896C2314yes—
203#66896C2314yescomplemented
204#66896C2314yescomplemented
205#66896C2314yescomplemented
206#66896C2314yescomplemented
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yescomplemented
210C22⋊(C11⋊C8)C2312yescomplemented
211C22⋊(C11⋊C8)C2314yescomplemented
212#66874C2314yescomplemented
213#66873C2314yescomplemented
214#66872C2314yescomplemented
215#66871C2314yescomplemented
216C4⋊(C11⋊C8)C2314yescomplemented
217#66867C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11—21no—
222C24×C11—24no—
223C24×C11—22no—
224C24×C11—22no—
225C24×C11—44no—
226C24×C11—44no—
227C24×C11—44no—
228C24×C11—44no—
229C24×C11—82no—
230C24×C11—82no—
231C24×C11C2×D411yescharacteristic
232C24×C11C2×D411yescharacteristic
233C23×D11—21no—
234C2×D4×C11—24no—
235C2×D4×C11—24no—
236C2×D4×C11—24no—
237C2×D4×C11—28no—
238C2×D4×C11—24no—
239C2×D4×C11—24no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—24no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—42no—
251C2×D4×C11—42no—
252C2×D4×C11—44no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11—44no—
256C2×D4×C11—44no—
257C2×D4×C11—44no—
258C2×D4×C11—48no—
259C2×D4×C11—416no—
260C2×D4×C11—416no—
261C2×D4×C11—44no—
262C2×D4×C11—44no—
263C2×D4×C11—44no—
264C2×D4×C11—44no—
265C2×D4×C11—82no—
266C2×D4×C11C2×D412yes—
267C2×D4×C11C2×D412yes—
268C2×D4×C11C2412yes—
269C2×D4×C11C2412yes—
270C2×D4×C11C2412yes—
271C22×C4×C11—21no—
272C22×C4×C11—24no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—44no—
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C2×C22⋊D11—22no—
288C2×C22⋊D11—22no—
289C2×C22⋊D11—22no—
290C2×C22⋊D11—22no—
291C2×C22⋊D11—44no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295#4339—44no—
296C2×D44—21no—
297C2×D44—42no—
298C2×D44C2412yes—
299C2×C4×D11—22no—
300C2×C4×D11—22no—
301C2×Dic22—21no—
302C2×Dic22—42no—
303C2×Dic22C2412yes—
304C11×C4⋊C4—21no—
305C11×C4⋊C4C2×D412yes—
306C11×C4⋊C4C2×D412yes—
307C11×C4⋊C4C2412yes—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—24no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C11×C22⋊C4C2×D412yes—
315C11×C22⋊C4C2×D412yes—
316C42×C11C2×D412yes—
317C42×C11C2412yes—
318C22⋊Dic11—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321C22⋊Dic11—22no—
322#4324—28no—
323#4324—44no—
324#4324—44no—
325#4323—28no—
326#4323—44no—
327#4323—44no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334C4⋊Dic11—21no—
335C4⋊Dic11—21no—
336C4⋊Dic11C2412yes—
337C4⋊Dic11C2412yes—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343Dic11⋊C4—22no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346#4318—44no—
347C2×C11⋊C8—42no—
348C2×C11⋊C8—42no—
349C2×C11⋊C8C2414yes—
350C2×C11⋊C8C2414yes—
351#3505—111no—
352C2×D42D1111yescharacteristic, complemented
353#3318—114no—
354#3310—114no—
355#3265—114no—
356#3264—114no—
357#3217—112no—
358#3194—112no—
359#3187—111no—
360#3186—111no—
361#3114—112no—
362#3003—112no—
363C2×#450—111no—
364C2×#447—111no—
365#2973—111no—
366C23×C11—24no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11—48no—
378C23×C11—42no—
379C23×C11—42no—
380C23×C11—42no—
381C23×C11—48no—
382C23×C11—42no—
383C23×C11—42no—
384C23×C11—42no—
385C23×C11—44no—
386C23×C11—44no—
387C23×C11—42no—
388C23×C11—42no—
389C23×C11—82no—
390C23×C11—82no—
391C23×C11—84no—
392C23×C11—816no—
393C23×C11—816no—
394C23×C11AGL(1,ℤ/8)14yescomplemented
395C23×C11C22×D412yes—
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C22×D411yescharacteristic
399C22×D11—22no—
400C22×D11—42no—
401C22×D11—81no—
402C22×D11—81no—
403D4×C11—24no—
404D4×C11—24no—
405D4×C11—24no—
406D4×C11—22no—
407D4×C11—22no—
408D4×C11—24no—
409D4×C11—22no—
410D4×C11—44no—
411D4×C11—48no—
412D4×C11—44no—
413D4×C11—42no—
414D4×C11—42no—
415D4×C11—48no—
416D4×C11—48no—
417D4×C11—44no—
418D4×C11—44no—
419D4×C11—84no—
420D4×C11H(5,𝔽2)14yes—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—24no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—41no—
428C2×C4×C11—42no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—48no—
434C2×C4×C11—42no—
435C2×C4×C11C22×D412yes—
436C2×C4×C11C22×D412yes—
437C2×C4×C11C22×D411yescharacteristic
438C2×C4×C11C22×D411yescharacteristic
439C2×C4×C11C22×D412yes—
440C2×C4×C11C22×D411yescharacteristic
441C2×C4×C11C2511yescharacteristic
442C22⋊D11—44no—
443C22⋊D11—44no—
444C22⋊D11—82no—
445C22⋊D11—82no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—42no—
450C2×Dic11—81no—
451C2×Dic11—81no—
452D44—24no—
453D44—81no—
454C4×D11—82no—
455C4×D11—82no—
456Dic22—24no—
457Dic22—81no—
458C11⋊C8—24no—
459C11⋊C8—24no—
460C23×D4—21no—
461C23×D4C2×D1111yescharacteristic
462C23×D4C2×D1111yescharacteristic, complemented
463C2×AGL(1,ℤ/8)—114no—
464C22×SD16—112no—
465C22×D8—112no—
466#553—112no—
467#553—222no—
468#552—112no—
469#551—222no—
470#548—112no—
471#546—112no—
472D42—22no—
473D42—22no—
474D42C2×D1114yes—
475D42C2×D1114yescomplemented
476#539—221no—
477#538—221no—
478#534—221no—
479C2×#127C2×D1111yescharacteristic, complemented
480#529—112no—
481#525—112no—
482C2×C22⋊Q8—111no—
483C2×#121—21no—
484C2×#121—111no—
485C2×#121C2×D1111yescharacteristic
486C2×#121C2×D1111yescharacteristic, complemented
487C2×#120—21no—
488C2×#120—21no—
489#518—221no—
490C2×C4×D4C2×D1111yescharacteristic
491C2×C4×D4C2×D1111yescharacteristic, complemented
492#496—114no—
493#490—114no—
494#483—112no—
495#482—114no—
496#481—112no—
497#480—112no—
498#480—112no—
499#478—114no—
500#469—114no—
501#468—114no—
502#466—114no—
503#465—114no—
504#463—114no—
505#460—114no—
506#459—114no—
507#450—112no—
508#450—112no—
509#450—112no—
510#450—114no—
511#450—114no—
512#449—114no—
513#448—112no—
514#447—112no—
515#447—112no—
516#447—112no—
517#447—114no—
518#447—114no—
519#447—112no—
520#442—114no—
521#440—114no—
522#435—114no—
523#435—114no—
524#432—112no—
525#418—114no—
526C2×#102—112no—
527C2×#102—112no—
528#407—112no—
529C2×C22⋊C8—111no—
530C2×C22⋊C8—111no—
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—22no—
538C22×C11—22no—
539C22×C11—24no—
540C22×C11—22no—
541C22×C11—44no—
542C22×C11—44no—
543C22×C11—48no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—88no—
553C22×C11—88no—
554C22×C11—84no—
555C22×C11—84no—
556C22×C11—816no—
557C22×C11C2×AGL(1,ℤ/8)12yes—
558C22×C11C2×AGL(1,ℤ/8)12yes—
559C22×C11C2×AGL(1,ℤ/8)12yes—
560C22×C11C23×D411yescharacteristic
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11—162no—
565C4×C11—22no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—22no—
569C4×C11—21no—
570C4×C11—22no—
571C4×C11—42no—
572C4×C11C2×H(5,𝔽2)12yes—
573Dic11—42no—
574Dic11—42no—
575Dic11—42no—
576C25—21no—
577C25—21no—
578C2×#41—112no—
579C22×Q8—111no—
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—24no—
583C22×D4—24no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—44no—
592C22×D4—44no—
593C22×D4—48no—
594C22×D4—111no—
595C22×D4—221no—
596C22×D4C22⋊D1111yescharacteristic
597C22×D4C22×D1111yescharacteristic
598C22×D4C22×D1112yes—
599C22×D4C22×D1114yes—
600C22×D4C22×D1112yes—
601C22×D4C22×D1111yescharacteristic
602C22×D4C22×D1111yescharacteristic
603C23×C4—21no—
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606AGL(1,ℤ/8)—448no—
607C2×SD16—114no—
608C2×SD16—114no—
609C2×SD16—114no—
610C2×SD16—444no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—444no—
615C2×M16—114no—
616C22×C8—112no—
617C22×C8—112no—
618#127—22no—
619#127C22×D1114yes—
620#126—222no—
621#126—222no—
622#126—222no—
623#125—112no—
624#125—222no—
625#124—112no—
626#124—222no—
627#123—222no—
628#123—222no—
629#123—222no—
630#123—222no—
631#123—222no—
632C22⋊Q8—112no—
633C22⋊Q8—112no—
634C22⋊Q8—112no—
635C22⋊Q8—221no—
636C22⋊Q8—221no—
637C22⋊Q8—222no—
638#121—21no—
639#121—21no—
640#121—22no—
641#121—24no—
642#121—24no—
643#121—112no—
644#121—112no—
645#121—112no—
646#121—222no—
647#121—222no—
648#121—221no—
649#121—221no—
650#121—222no—
651#121C22×D1112yes—
652#121C22×D1112yes—
653#121C22×D1114yes—
654#120—24no—
655#120—24no—
656#120—24no—
657#120—24no—
658#120—222no—
659#120—222no—
660C4×Q8—112no—
661C4×D4—22no—
662C4×D4—112no—
663C4×D4—222no—
664C4×D4—222no—
665C4×D4—222no—
666C4×D4—222no—
667C4×D4—222no—
668C4×D4C22⋊D1112yes—
669C4×D4C22⋊D1112yes—
670C4×D4C22×D1114yes—
671C4×D4C22×D1112yes—
672C4×D4C22×D1112yes—
673#117—112no—
674#117—222no—
675#117—222no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—221no—
679C2×C4⋊C4C22⋊D1111yescharacteristic
680C2×C4⋊C4C22×D1111yescharacteristic
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—221no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4C22⋊D1111yescharacteristic
688C2×C22⋊C4C22⋊D1111yescharacteristic
689C2×C42C22×D1111yescharacteristic
690#107—114no—
691#106—114no—
692C4⋊C8—114no—
693#103—114no—
694#102—114no—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102—114no—
701C22⋊C8—112no—
702C22⋊C8—112no—
703C22⋊C8—112no—
704C22⋊C8—112no—
705C22⋊C8—114no—
706#97—114no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—22no—
710C2×C11—42no—
711C2×C11—44no—
712C2×C11—82no—
713C2×C11—82no—
714C2×C11#348411yescharacteristic
715C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
716C2×C11#358511yescharacteristic
717D11—82no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—24no—
722C24—22no—
723C24—22no—
724C24—44no—
725C24—44no—
726C24—44no—
727C24—44no—
728C24—82no—
729C24—82no—
730C24—221no—
731C24C2×C22⋊D1111yescharacteristic
732C24C2×C22⋊D1111yescharacteristic
733#41—444no—
734C2×Q8—112no—
735C2×Q8—221no—
736C2×Q8—442no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—24no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—24no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—44no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—48no—
762C2×D4—416no—
763C2×D4—416no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—82no—
769C2×D4—112no—
770C2×D4—222no—
771C2×D4—222no—
772C2×D4—222no—
773C2×D4—222no—
774C2×D4—221no—
775C2×D4—442no—
776C2×D4—444no—
777C2×D4C2×C22⋊D1112yes—
778C2×D4C2×C22⋊D1112yes—
779C2×D4C23×D1112yes—
780C2×D4C23×D1112yes—
781C2×D4C23×D1112yes—
782C22×C4—21no—
783C22×C4—24no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—44no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4C2×C22⋊D1111yescharacteristic
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C2×C22⋊D1111yescharacteristic
797C22×C4C2×C22⋊D1111yescharacteristic
798C22×C4C2×C22⋊D1112yes—
799C22×C4C23×D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1112yes—
803SD16—228no—
804SD16—444no—
805SD16—444no—
806D8—228no—
807D8—444no—
808D8—444no—
809M16—444no—
810C2×C8—114no—
811C2×C8—114no—
812C2×C8—442no—
813C2×C8—442no—
814C4⋊C4—21no—
815C4⋊C4—112no—
816C4⋊C4—112no—
817C4⋊C4—221no—
818C4⋊C4—221no—
819C4⋊C4—222no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4C2×C22⋊D1112yes—
826C4⋊C4C2×C22⋊D1112yes—
827C4⋊C4C23×D1112yes—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—222no—
833C22⋊C4—222no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C22⋊C4—222no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4C2×C22⋊D1112yes—
843C22⋊C4C2×C22⋊D1112yes—
844C22⋊C4C2×C22⋊D1112yes—
845C22⋊C4C2×C22⋊D1112yes—
846C42—222no—
847C42—222no—
848C42C2×C22⋊D1112yes—
849C42C23×D1112yes—
850C11#6157111yescharacteristic, complemented, Sylow
851C23—24no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—44no—
861C23—44no—
862C23—48no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—48no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—44no—
871C23—44no—
872C23—42no—
873C23—42no—
874C23—82no—
875C23—82no—
876C23—84no—
877C23—816no—
878C23—816no—
879C23—222no—
880C23—442no—
881C23—881no—
882C23—881no—
883C23#6698514yescomplemented
884C23C22×C22⋊D1112yes—
885C23C22×C22⋊D1111yescharacteristic
886C23C22×C22⋊D1111yescharacteristic
887C23C22×C22⋊D1111yescharacteristic
888Q8—224no—
889Q8—881no—
890D4—24no—
891D4—24no—
892D4—24no—
893D4—22no—
894D4—22no—
895D4—24no—
896D4—22no—
897D4—48no—
898D4—44no—
899D4—44no—
900D4—42no—
901D4—42no—
902D4—48no—
903D4—48no—
904D4—44no—
905D4—44no—
906D4—84no—
907D4—224no—
908D4—444no—
909D4—444no—
910D4—881no—
911D4—882no—
912D4—882no—
913D4#6703714yes—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—42no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—48no—
927C2×C4—42no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—442no—
932C2×C4—882no—
933C2×C4—882no—
934C2×C4—881no—
935C2×C4—881no—
936C2×C4C22×C22⋊D1112yes—
937C2×C4C22×C22⋊D1112yes—
938C2×C4C22×C22⋊D1111yescharacteristic
939C2×C4C22×C22⋊D1112yes—
940C2×C4C22×C22⋊D1111yescharacteristic
941C2×C4C22×C22⋊D1111yescharacteristic
942C2×C4C24×D1111yescharacteristic
943C8—224no—
944C8—224no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—22no—
952C22—22no—
953C22—24no—
954C22—22no—
955C22—44no—
956C22—44no—
957C22—48no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—88no—
967C22—88no—
968C22—84no—
969C22—84no—
970C22—816no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—1762no—
975C22C2×#6698512yes—
976C22C2×#6698512yes—
977C22C2×#6698512yes—
978C22C23×C22⋊D1111yescharacteristic
979C4—22no—
980C4—21no—
981C4—22no—
982C4—21no—
983C4—21no—
984C4—22no—
985C4—42no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4C2×#6703712yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—42no—
994C2—44no—
995C2—82no—
996C2—82no—
997C2—882no—
998C2#1308225111yescharacteristic
999C2C22×#6698511yescharacteristic
1000C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D42×C11C2
socleC22×C11C23×D4
hypercenterC2×D42D11
hypocenterC11#61571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. #13080757C2semidirect
3. #13080637C2semidirect
4. #13080107C2semidirect
5. #13080092C2semidirect
6. #13079634C2semidirect
7. #13079430C2semidirect
8. #13079373C2semidirect
9. #13079364C2semidirect
10. #13078754C2semidirect
11. #13077843C2semidirect
12. C2×#10622831C2semidirect
13. C2×#10622830C2semidirect
14. #13077645C2semidirect
15. C2×D42×C11C2semidirect
18. C23×D4×C11C22semidirect
22. D42×C11C22semidirect
23. C2×C11×#127C22semidirect
26. C2×C11×#121C22semidirect
30. C2×C4×D4×C11C22semidirect
32. C22×#4324C22semidirect
33. C2×#66985C22semidirect
34. C22×#4323C22semidirect
35. #10623322C22semidirect
36. C2×#66983C22semidirect
37. C2×#66977C22semidirect
38. #10623096C22semidirect
40. #10623083C22semidirect
41. #10623081C22semidirect
42. #10623072C22semidirect
47. #10623010C22semidirect
48. #10622831C22semidirect
49. #10622831C22semidirect
50. #10622831C22semidirect
51. #10622831C22semidirect
52. #10622831C22semidirect
54. #10622830C22semidirect
55. #10622830C22semidirect
56. #10622830C22semidirect
57. #10622830C22semidirect
58. #10622828C22semidirect
59. C2×#66896C22semidirect
60. C2×#66896C22semidirect
61. #10622820C22semidirect
62. C2×C22⋊(C11⋊C8)C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622688C22semidirect
65. #10622687C22semidirect
66. #10622685C22semidirect
67. #10622684C22semidirect
68. #10622655C22semidirect
69. #10622654C22semidirect
70. #10622653C22semidirect
71. #10622652C22semidirect
72. #10622651C22semidirect
73. #10622650C22semidirect
74. #10622649C22semidirect
75. #10622648C22semidirect
76. #10622647C22semidirect
77. #10622646C22semidirect
78. #10622631C22semidirect
79. #10622629C22semidirect
80. #10622627C22semidirect
81. #10622624C22semidirect
82. #10622624C22semidirect
83. #10622622C22semidirect
84. #10622584C22semidirect
85. #10622580C22semidirect
86. #10622539C22semidirect
114. C2×#4339C23semidirect
115. C22×D44C23semidirect
116. C22×Dic22C23semidirect
153. C2×#4324C23semidirect
154. C2×#4324C23semidirect
158. C2×#4323C23semidirect
159. C2×#4323C23semidirect
163. #66983C23semidirect
164. #66983C23semidirect
171. #66979C23semidirect
172. C2×C4⋊Dic11C23semidirect
173. C2×C4⋊Dic11C23semidirect
177. #66977C23semidirect
178. #66977C23semidirect
180. C2×#4318C23semidirect
181. C22×C11⋊C8C23semidirect
182. C22×C11⋊C8C23semidirect
196. #66928C23semidirect
197. C4×D44C23semidirect
199. #66923C23semidirect
200. C4×Dic22C23semidirect
203. #66896C23semidirect
204. #66896C23semidirect
205. #66896C23semidirect
206. #66896C23semidirect
209. C22⋊(C11⋊C8)C23semidirect
210. C22⋊(C11⋊C8)C23semidirect
211. C22⋊(C11⋊C8)C23semidirect
212. #66874C23semidirect
213. #66873C23semidirect
214. #66872C23semidirect
215. #66871C23semidirect
216. C4⋊(C11⋊C8)C23semidirect
217. #66867C23semidirect
352. C2×D42D11semidirect
394. C23×C11AGL(1,ℤ/8)semidirect
462. C23×D4C2×D11semidirect
475. D42C2×D11semidirect
479. C2×#127C2×D11semidirect
486. C2×#121C2×D11semidirect
491. C2×C4×D4C2×D11semidirect
850. C11#61571semidirect
883. C23#66985semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130807572
#130806372
#130801072
#130800922
#130796342
#130794302
#130793732
#130793642
#130787542
#130778432
C2×#106228312
C2×#106228302
#130776452
C2×D42×C112
#6157111