Finite Group Databasebeta

← #15638627

Subgroups — #15638627

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#13082457C211yesmaximal, characteristic, complemented
2C2×#10623140C211yesmaximal, characteristic, complemented
3#13080755C214yesmaximal, complemented
4#13080643C214yesmaximal, complemented
5#13080104C214yesmaximal, complemented
6#13080093C214yesmaximal, complemented
7#13079637C212yesmaximal, complemented
8#13079435C212yesmaximal, complemented
9#13079364C211yesmaximal, characteristic, complemented
10#13078757C212yesmaximal, complemented
11#13077844C212yesmaximal, complemented
12C2×#10622659C211yesmaximal, characteristic, complemented
13C2×#10622345C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C11×#3187C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic, complemented
18C23×D44C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21#10623348C2212yescomplemented
22C22×#4325C2212yescomplemented
23C2×#66993C2211yescharacteristic, complemented
24C2×#66990—21no—
25C2×#66983C2211yescharacteristic, complemented
26C2×C4×C22⋊D11C2211yescharacteristic
27C2×#66967C2214yescomplemented
28C22×D88C2212yescomplemented
29#10623176—21no—
30#10623175—21no—
31#10623173C2212yescomplemented
32#10623168—22no—
33#10623161C2212yescomplemented
34#10623158C2212yescomplemented
35#10623155C2212yescomplemented
36#10623140—22no—
37#10623140—22no—
38#10623140C2214yes—
39#10623140C2214yescomplemented
40#10623045—22no—
41#10623045C2212yescomplemented
42C2×#66948C2211yescharacteristic, complemented
43C2×#66946C2211yescharacteristic, complemented
44#10623024—21no—
45C2×#66937—21no—
46C2×#66935—21no—
47#10623017—21no—
48C11×#483C2212yescomplemented
49C11×#481C2212yescomplemented
50C11×#465C2214yescomplemented
51C11×#450C2212yescomplemented
52C11×#448C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54#10622830C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622789C2214yescomplemented
57#10622782C2214yescomplemented
58#10622776C2214yescomplemented
59C2×#66885C2212yescomplemented
60#10622724C2214yescomplemented
61#10622659C2212yescomplemented
62#10622659C2214yescomplemented
63#10622659C2212yescomplemented
64#10622651C2214yescomplemented
65#10622649C2212yescomplemented
66#10622646C2212yescomplemented
67#10622580C2212yescomplemented
68C2×#66873C2212yescomplemented
69#10622484C2214yescomplemented
70#10622482C2214yescomplemented
71#10622479C2214yescomplemented
72#10622478C2214yescomplemented
73#10622432C2214yescomplemented
74#10622430C2214yescomplemented
75#10622425C2214yescomplemented
76#10622424C2214yescomplemented
77#10622399C2214yescomplemented
78#10622386C2214yescomplemented
79#10622383C2214yescomplemented
80#10622377C2214yescomplemented
81#10622345C2212yes—
82#10622345C2214yescomplemented
83#10622345C2212yescomplemented
84#10622343C2214yescomplemented
85#10622339C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C24×D11—21no—
89C22×Q8×C11C2311yescharacteristic, complemented
90C22×D4×C11—21no—
91C22×D4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11D411yescharacteristic
98C2×#4343C2312yescomplemented
99C2×D4×D11—24no—
100C2×D4×D11—24no—
101C2×D4×D11—22no—
102C2×D4×D11—44no—
103C2×D4×D11—48no—
104C2×D4×D11C2314yes—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—21no—
109C22×D44—44no—
110C22×D44C2311yescharacteristic
111C22×D44C2312yes—
112C22×D44C2312yes—
113C22×D44C2311yescharacteristic
114C22×D44C2311yescharacteristic, complemented
115C22×C4×D11—21no—
116C22×C4×D11C2311yescharacteristic
117C2×C11×SD16C2314yescomplemented
118C22×C8×C11C2312yescomplemented
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8C2312yes—
122C11×C22⋊Q8C2312yescomplemented
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic, complemented
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C22⋊Dic11D411yescharacteristic
133#67000—22no—
134#67000C2312yescomplemented
135#66999—22no—
136#66999C2312yescomplemented
137Q8×Dic11C2312yescomplemented
138C2×#4325—44no—
139C2×#4325C2314yes—
140C2×#4325C2314yescomplemented
141#66993—22no—
142#66993C2314yes—
143#66990—24no—
144#66990—24no—
145C2×#4323C2314yescomplemented
146#66983—21no—
147#66983—21no—
148#66983—22no—
149#66983—22no—
150#66983C2312yes—
151#66983C2312yescomplemented
152C4×C22⋊D11—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11D412yes—
155C4×C22⋊D11D412yes—
156C4×C22⋊D11C2312yes—
157C4×C22⋊D11C2312yes—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4D411yescharacteristic
162C2×C4⋊Dic11C2311yescharacteristic, complemented
163C2×Dic11⋊C4D411yescharacteristic
164C2×C4×Dic11C2311yescharacteristic
165C22×C11⋊C8C2312yescomplemented
166#66967—48no—
167C2×D88—44no—
168C2×D88C2314yes—
169C2×D88C2314yescomplemented
170C2×#4313C2314yescomplemented
171#66951—22no—
172#66951—22no—
173#66951—22no—
174#66948—22no—
175#66948—22no—
176#66948C2314yes—
177#66948C2312yescomplemented
178#66947—22no—
179#66947—22no—
180#66947—22no—
181#66946—22no—
182#66946—22no—
183#66946C2314yes—
184#66946C2312yescomplemented
185#66945—22no—
186#66945C2312yescomplemented
187#66943—22no—
188#66943C2312yescomplemented
189#66939—22no—
190#66939—22no—
191#66937—24no—
192#66937—24no—
193#66935—22no—
194#66935—22no—
195#66935—24no—
196#66935—24no—
197(C22⋊D11)⋊C4—22no—
198(C22⋊D11)⋊C4—22no—
199C22⋊C4×D11—22no—
200#66930—22no—
201C11×#106C2314yescomplemented
202C11×#103C2314yescomplemented
203C11×#102C2314yescomplemented
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yescomplemented
206#66896C2314yescomplemented
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yescomplemented
212#66879C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214#66873C2314yes—
215#66873C2314yescomplemented
216#66873C2314yescomplemented
217#66871C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—21no—
226C23×D11—24no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—82no—
232C23×D11—82no—
233C23×D11C2×D411yescharacteristic
234C2×Q8×C11—21no—
235C2×Q8×C11—42no—
236C2×Q8×C11C2412yes—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—21no—
240C2×D4×C11—42no—
241C2×D4×C11—44no—
242C2×D4×C11C2412yes—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—42no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—82no—
263C2×C22⋊D11C2×D412yes—
264C2×C22⋊D11C2×D412yes—
265C22×Dic11—21no—
266C22×Dic11C2×D411yescharacteristic
267C22×Dic11C2×D411yescharacteristic
268C22×Dic11C2×D411yescharacteristic
269#4343—44no—
270D4×D11—28no—
271D4×D11—44no—
272D4×D11—48no—
273D4×D11—416no—
274D4×D11—416no—
275C2×D44—24no—
276C2×D44—24no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—24no—
280C2×D44—24no—
281C2×D44—21no—
282C2×D44—22no—
283C2×D44—22no—
284C2×D44—21no—
285C2×D44—21no—
286C2×D44—42no—
287C2×D44—42no—
288C2×D44—42no—
289C2×D44—42no—
290C2×D44—44no—
291C2×D44—44no—
292C2×D44—44no—
293C2×D44—44no—
294C2×D44C2412yes—
295C2×D44C2412yes—
296C2×D44C2412yes—
297C2×C4×D11—24no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—42no—
301C2×C4×D11—44no—
302C2×C4×D11C2×D412yes—
303C2×C4×D11C2412yes—
304C11×SD16—44no—
305C2×C8×C11—42no—
306C2×C8×C11C2414yes—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—21no—
310C11×C4⋊C4—21no—
311C11×C4⋊C4C2412yes—
312C11×C4⋊C4C2412yes—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C22⋊Dic11C2×D412yes—
318C22⋊Dic11C2×D412yes—
319#4325—28no—
320#4325—44no—
321#4323—44no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4C2×D412yes—
333(C2×D11)⋊C4C2×D412yes—
334C4⋊Dic11—22no—
335C4⋊Dic11—22no—
336C4⋊Dic11—21no—
337C4⋊Dic11C2412yes—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4C2×D412yes—
341Dic11⋊C4C2×D412yes—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11C2×D412yes—
345C4×Dic11C2412yes—
346C2×C11⋊C8—42no—
347C2×C11⋊C8C2414yes—
348D88—28no—
349D88—44no—
350#4313—44no—
351#3505—111no—
352C2×D42—111no—
353#3318—114no—
354#3310—114no—
355#3265—114no—
356#3264—114no—
357#3217—112no—
358#3194—112no—
359#3187D1111yescharacteristic, complemented
360#3186—111no—
361#3114—112no—
362#3003—112no—
363C2×#450—111no—
364C2×#447—111no—
365#2973—111no—
366C23×C11—22no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11AGL(1,ℤ/8)14yescomplemented
373C23×C11C22×D411yescharacteristic
374C23×C11C22×D411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C22×D11—24no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—48no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—48no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—42no—
390C22×D11—42no—
391C22×D11—42no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—42no—
395C22×D11—84no—
396C22×D11—82no—
397C22×D11—82no—
398C22×D11—816no—
399C22×D11—81no—
400C22×D11—81no—
401C22×D11—816no—
402C22×D11C22×D412yes—
403Q8×C11—24no—
404Q8×C11—81no—
405D4×C11—24no—
406D4×C11—42no—
407D4×C11—44no—
408D4×C11—44no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—42no—
419C2×C4×C11—81no—
420C2×C4×C11—81no—
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C2511yescharacteristic
425C22⋊D11—24no—
426C22⋊D11—24no—
427C22⋊D11—48no—
428C22⋊D11—48no—
429C22⋊D11—44no—
430C22⋊D11—44no—
431C22⋊D11—84no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—42no—
437C2×Dic11C22×D412yes—
438C2×Dic11C22×D412yes—
439C2×Dic11C22×D412yes—
440D44—24no—
441D44—22no—
442D44—24no—
443D44—22no—
444D44—22no—
445D44—44no—
446D44—44no—
447D44—42no—
448D44—48no—
449D44—81no—
450D44—82no—
451D44—82no—
452D44H(5,𝔽2)14yes—
453C4×D11—24no—
454C4×D11—42no—
455C4×D11—48no—
456C4×D11—82no—
457C4×D11—82no—
458C8×C11—24no—
459C11⋊C8—24no—
460C23×D4—111no—
461C23×D4—111no—
462C23×D4—221no—
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—114no—
473D42—114no—
474D42—222no—
475D42—222no—
476#539—221no—
477#538—221no—
478#534—221no—
479C2×#127—111no—
480#529—112no—
481#525—112no—
482C2×C22⋊Q8C2×D1111yescharacteristic, complemented
483C2×#121—111no—
484C2×#121—111no—
485C2×#121—221no—
486C2×#121C2×D1111yescharacteristic
487C2×#120—221no—
488C2×#120—221no—
489#518—221no—
490C2×C4×D4—111no—
491C2×C4×D4—111no—
492#496—114no—
493#490—114no—
494#483C2×D1112yescomplemented
495#482—114no—
496#481C2×D1112yescomplemented
497#480—112no—
498#480—112no—
499#478—114no—
500#469—114no—
501#468—114no—
502#466—114no—
503#465C2×D1114yescomplemented
504#463—114no—
505#460—114no—
506#459—114no—
507#450—114no—
508#450—112no—
509#450—112no—
510#450—114no—
511#450C2×D1112yescomplemented
512#449—114no—
513#448C2×D1112yescomplemented
514#447—112no—
515#447—112no—
516#447—114no—
517#447—112no—
518#447—112no—
519#447—114no—
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⋊C8C2×D1111yescharacteristic, complemented
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—44no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—84no—
542C22×C11C2×AGL(1,ℤ/8)12yes—
543C22×C11C2×AGL(1,ℤ/8)12yes—
544C22×C11C2×AGL(1,ℤ/8)12yes—
545C22×C11C23×D411yescharacteristic
546C2×D11—22no—
547C2×D11—24no—
548C2×D11—22no—
549C2×D11—22no—
550C2×D11—44no—
551C2×D11—48no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—816no—
561C2×D11—88no—
562C2×D11—88no—
563C2×D11—84no—
564C2×D11—162no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—42no—
569C4×C11—42no—
570C4×C11—42no—
571C4×C11C2×H(5,𝔽2)12yes—
572Dic11—22no—
573Dic11—22no—
574Dic11—22no—
575Dic11—42no—
576C25—221no—
577C25—221no—
578C2×#41—112no—
579C22×Q8C22×D1111yescharacteristic, complemented
580C22×D4—21no—
581C22×D4—111no—
582C22×D4—114no—
583C22×D4—111no—
584C22×D4—112no—
585C22×D4—112no—
586C22×D4—111no—
587C22×D4—111no—
588C22×D4—221no—
589C22×D4—222no—
590C22×D4—221no—
591C22×D4—221no—
592C22×D4—221no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—221no—
596C22×D4—221no—
597C22×D4—221no—
598C22×D4—221no—
599C22×D4—444no—
600C22×D4—444no—
601C22×D4—448no—
602C22×D4C22×D1111yescharacteristic
603C23×C4—111no—
604C23×C4—221no—
605C23×C4C22×D1111yescharacteristic
606AGL(1,ℤ/8)—448no—
607C2×SD16—114no—
608C2×SD16—114no—
609C2×SD16—444no—
610C2×SD16C22×D1114yescomplemented
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—444no—
615C2×M16—114no—
616C22×C8—112no—
617C22×C8C22×D1112yescomplemented
618#127—114no—
619#127—222no—
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—21no—
633C22⋊Q8—21no—
634C22⋊Q8—112no—
635C22⋊Q8—222no—
636C22⋊Q8C22×D1112yes—
637C22⋊Q8C22×D1112yescomplemented
638#121—21no—
639#121—21no—
640#121—112no—
641#121—112no—
642#121—114no—
643#121—112no—
644#121—224no—
645#121—224no—
646#121—222no—
647#121—222no—
648#121—222no—
649#121—222no—
650#121—221no—
651#121—221no—
652#121C22×D1112yes—
653#121C22×D1112yes—
654#120—224no—
655#120—224no—
656#120—222no—
657#120—222no—
658#120—224no—
659#120—224no—
660C4×Q8—112no—
661C4×D4—112no—
662C4×D4—112no—
663C4×D4—112no—
664C4×D4—112no—
665C4×D4—114no—
666C4×D4—112no—
667C4×D4—222no—
668C4×D4—222no—
669C4×D4—222no—
670C4×D4—222no—
671C4×D4—222no—
672C4×D4—222no—
673#117—112no—
674#117—222no—
675#117—222no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C4⋊C4C22×D1111yescharacteristic, complemented
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—111no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C42—111no—
690#107—114no—
691#106C22×D1114yescomplemented
692C4⋊C8—114no—
693#103C22×D1114yescomplemented
694#102—114no—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102C22×D1114yescomplemented
701C22⋊C8—112no—
702C22⋊C8—112no—
703C22⋊C8—114no—
704C22⋊C8C22×D1112yes—
705C22⋊C8C22×D1112yescomplemented
706#97—114no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—22no—
710C2×C11—82no—
711C2×C11#348411yescharacteristic
712C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
713C2×C11#358511yescharacteristic
714D11—42no—
715D11—44no—
716D11—82no—
717D11—82no—
718C24—21no—
719C24—111no—
720C24—224no—
721C24—221no—
722C24—221no—
723C24—222no—
724C24—222no—
725C24—221no—
726C24—444no—
727C24—444no—
728C24—444no—
729C24—444no—
730C24—882no—
731C24—882no—
732C24D4×D1111yescharacteristic
733#41—444no—
734C2×Q8—21no—
735C2×Q8—42no—
736C2×Q8C23×D1112yes—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—112no—
743C2×D4—112no—
744C2×D4—112no—
745C2×D4—112no—
746C2×D4—112no—
747C2×D4—224no—
748C2×D4—224no—
749C2×D4—224no—
750C2×D4—224no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—224no—
754C2×D4—224no—
755C2×D4—224no—
756C2×D4—228no—
757C2×D4—224no—
758C2×D4—222no—
759C2×D4—222no—
760C2×D4—221no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—221no—
764C2×D4—221no—
765C2×D4—442no—
766C2×D4—442no—
767C2×D4—442no—
768C2×D4—442no—
769C2×D4—444no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C2×D4—444no—
774C2×D4—444no—
775C2×D4—448no—
776C2×D4—4416no—
777C2×D4—4416no—
778C2×D4—444no—
779C2×D4—444no—
780C2×D4—882no—
781C2×D4C23×D1112yes—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—111no—
787C22×C4—111no—
788C22×C4—111no—
789C22×C4—112no—
790C22×C4—112no—
791C22×C4—224no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—221no—
795C22×C4—442no—
796C22×C4—444no—
797C22×C4D4×D1111yescharacteristic
798C22×C4D4×D1111yescharacteristic
799C22×C4D4×D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803SD16—44no—
804SD16—228no—
805SD16—444no—
806D8—228no—
807D8—444no—
808D8—444no—
809M16—444no—
810C2×C8—42no—
811C2×C8—114no—
812C2×C8—442no—
813C2×C8C23×D1114yes—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—112no—
819C4⋊C4—112no—
820C4⋊C4—112no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—221no—
826C4⋊C4C23×D1112yes—
827C4⋊C4C23×D1112yes—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—112no—
833C22⋊C4—112no—
834C22⋊C4—112no—
835C22⋊C4—112no—
836C22⋊C4—224no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—224no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C42—112no—
847C42—112no—
848C42—222no—
849C42—222no—
850C11#6157111yescharacteristic, complemented, Sylow
851C23—22no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—112no—
858C23—224no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—441no—
864C23—441no—
865C23—444no—
866C23—444no—
867C23—442no—
868C23—442no—
869C23—442no—
870C23—448no—
871C23—448no—
872C23—442no—
873C23—444no—
874C23—444no—
875C23—442no—
876C23—442no—
877C23—882no—
878C23—882no—
879C23—881no—
880C23—881no—
881C23—884no—
882C23—8816no—
883C23—8816no—
884C23#6696714yescomplemented
885C23C2×D4×D1111yescharacteristic
886C23C2×D4×D1111yescharacteristic
887C23C2×D4×D1111yescharacteristic
888Q8—24no—
889Q8—81no—
890D4—24no—
891D4—42no—
892D4—44no—
893D4—44no—
894D4—114no—
895D4—224no—
896D4—224no—
897D4—224no—
898D4—222no—
899D4—224no—
900D4—222no—
901D4—222no—
902D4—444no—
903D4—444no—
904D4—442no—
905D4—448no—
906D4—448no—
907D4—448no—
908D4—444no—
909D4—444no—
910D4—881no—
911D4—882no—
912D4—882no—
913D4—884no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—42no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—112no—
927C2×C4—112no—
928C2×C4—112no—
929C2×C4—222no—
930C2×C4—224no—
931C2×C4—222no—
932C2×C4—442no—
933C2×C4—448no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—442no—
937C2×C4—882no—
938C2×C4—882no—
939C2×C4C2×D4×D1111yescharacteristic
940C2×C4C2×D4×D1111yescharacteristic
941C2×C4C2×D4×D1111yescharacteristic
942C2×C4C24×D1111yescharacteristic
943C8—24no—
944C8—224no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—44no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—84no—
956C22—222no—
957C22—222no—
958C22—224no—
959C22—222no—
960C22—444no—
961C22—448no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—888no—
971C22—888no—
972C22—884no—
973C22—8816no—
974C22—1762no—
975C22C2×#6696712yes—
976C22C2×#6696712yes—
977C22C2×#6696712yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—222no—
986C4—222no—
987C4—222no—
988C4—442no—
989C4D11×H(5,𝔽2)12yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—82no—
994C2—442no—
995C2—444no—
996C2—882no—
997C2—882no—
998C2#1308224811yescharacteristic
999C2C22×#6696711yescharacteristic
1000C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3187C2
socleC22×C11C23×D4
hypercenter#3187D11
hypocenterC11#61571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
1. #13082457C2semidirect
2. C2×#10623140C2semidirect
3. #13080755C2semidirect
4. #13080643C2semidirect
5. #13080104C2semidirect
6. #13080093C2semidirect
7. #13079637C2semidirect
8. #13079435C2semidirect
9. #13079364C2semidirect
10. #13078757C2semidirect
11. #13077844C2semidirect
12. C2×#10622659C2semidirect
13. C2×#10622345C2semidirect
14. #13077642C2semidirect
15. C11×#3187C2semidirect
17. C22×D4×D11C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
21. #10623348C22semidirect
22. C22×#4325C22semidirect
23. C2×#66993C22semidirect
25. C2×#66983C22semidirect
27. C2×#66967C22semidirect
28. C22×D88C22semidirect
31. #10623173C22semidirect
33. #10623161C22semidirect
34. #10623158C22semidirect
35. #10623155C22semidirect
39. #10623140C22semidirect
41. #10623045C22semidirect
42. C2×#66948C22semidirect
43. C2×#66946C22semidirect
48. C11×#483C22semidirect
49. C11×#481C22semidirect
50. C11×#465C22semidirect
51. C11×#450C22semidirect
52. C11×#448C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622830C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622789C22semidirect
57. #10622782C22semidirect
58. #10622776C22semidirect
59. C2×#66885C22semidirect
60. #10622724C22semidirect
61. #10622659C22semidirect
62. #10622659C22semidirect
63. #10622659C22semidirect
64. #10622651C22semidirect
65. #10622649C22semidirect
66. #10622646C22semidirect
67. #10622580C22semidirect
68. C2×#66873C22semidirect
69. #10622484C22semidirect
70. #10622482C22semidirect
71. #10622479C22semidirect
72. #10622478C22semidirect
73. #10622432C22semidirect
74. #10622430C22semidirect
75. #10622425C22semidirect
76. #10622424C22semidirect
77. #10622399C22semidirect
78. #10622386C22semidirect
79. #10622383C22semidirect
80. #10622377C22semidirect
82. #10622345C22semidirect
83. #10622345C22semidirect
84. #10622343C22semidirect
85. #10622339C22semidirect
86. #10622332C22semidirect
89. C22×Q8×C11C23semidirect
98. C2×#4343C23semidirect
114. C22×D44C23semidirect
117. C2×C11×SD16C23semidirect
118. C22×C8×C11C23semidirect
122. C11×C22⋊Q8C23semidirect
129. C2×C11×C4⋊C4C23semidirect
134. #67000C23semidirect
136. #66999C23semidirect
137. Q8×Dic11C23semidirect
140. C2×#4325C23semidirect
145. C2×#4323C23semidirect
151. #66983C23semidirect
162. C2×C4⋊Dic11C23semidirect
165. C22×C11⋊C8C23semidirect
169. C2×D88C23semidirect
170. C2×#4313C23semidirect
177. #66948C23semidirect
184. #66946C23semidirect
186. #66945C23semidirect
188. #66943C23semidirect
201. C11×#106C23semidirect
202. C11×#103C23semidirect
203. C11×#102C23semidirect
205. C11×C22⋊C8C23semidirect
206. #66896C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. #66879C23semidirect
213. Dic11⋊C8C23semidirect
215. #66873C23semidirect
216. #66873C23semidirect
217. #66871C23semidirect
359. #3187D11semidirect
372. C23×C11AGL(1,ℤ/8)semidirect
482. C2×C22⋊Q8C2×D11semidirect
494. #483C2×D11semidirect
496. #481C2×D11semidirect
503. #465C2×D11semidirect
511. #450C2×D11semidirect
513. #448C2×D11semidirect
530. C2×C22⋊C8C2×D11semidirect
579. C22×Q8C22×D11semidirect
610. C2×SD16C22×D11semidirect
617. C22×C8C22×D11semidirect
637. C22⋊Q8C22×D11semidirect
680. C2×C4⋊C4C22×D11semidirect
691. #106C22×D11semidirect
693. #103C22×D11semidirect
700. #102C22×D11semidirect
705. C22⋊C8C22×D11semidirect
850. C11#61571semidirect
884. C23#66967semidirect

Maximal subgroups

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

subgroupindex
#130824572
C2×#106231402
#130807552
#130806432
#130801042
#130800932
#130796372
#130794352
#130793642
#130787572
#130778442
C2×#106226592
C2×#106223452
#130776422
C11×#31872
#6157111