Finite Group Databasebeta

← #15638598

Subgroups — #15638598

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic, complemented
2C2×#10623161C211yesmaximal, characteristic, complemented
3#13080583C214yesmaximal, complemented
4#13080575C214yesmaximal, complemented
5#13080100C214yesmaximal, complemented
6#13080093C214yesmaximal, complemented
7#13079602C212yesmaximal, complemented
8#13079415C212yesmaximal, complemented
9#13079369C211yesmaximal, characteristic, complemented
10#13078704C212yesmaximal, complemented
11#13077867C212yesmaximal, complemented
12C2×#10622345C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C11×#3187C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic, complemented
17C2×#67037—21no—
18C23×D44C2211yescharacteristic, complemented
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21C2×#67000C2211yescharacteristic, complemented
22#10623335—21no—
23D4×C22⋊D11C2212yescomplemented
24C22×#4323C2212yescomplemented
25C2×#66983C2211yescharacteristic
26C2×C4×C22⋊D11C2211yescharacteristic
27C2×#66967C2214yescomplemented
28C22×D88C2212yescomplemented
29#10623161—22no—
30#10623161—22no—
31#10623161C2214yescomplemented
32#10623161C2214yescomplemented
33#10623142C2212yescomplemented
34#10623141—22no—
35#10623140C2212yescomplemented
36#10623136—21no—
37D11×#121C2212yescomplemented
38#10623128—21no—
39#10623127C2212yescomplemented
40#10623038C2212yescomplemented
41C2×#66948—21no—
42C2×#66948C2211yescharacteristic, complemented
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic, complemented
45#10623021—22no—
46C2×#66935—21no—
47C2×C22⋊C4×D11—21no—
48C11×#483C2212yescomplemented
49C11×#481C2212yescomplemented
50C11×#465C2214yescomplemented
51C11×#450C2212yescomplemented
52C11×#448C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54#10622840C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622789C2214yescomplemented
57#10622785C2214yescomplemented
58#10622778C2214yescomplemented
59C2×#66885C2212yescomplemented
60#10622724C2214yescomplemented
61#10622661C2214yescomplemented
62#10622659C2212yescomplemented
63#10622656C2212yescomplemented
64#10622649C2214yescomplemented
65#10622649C2212yescomplemented
66#10622649C2212yescomplemented
67#10622581C2212yescomplemented
68C2×#66873C2212yescomplemented
69#10622483C2214yescomplemented
70#10622482C2214yescomplemented
71#10622478C2214yescomplemented
72#10622476C2214yescomplemented
73#10622432C2214yescomplemented
74#10622424C2214yescomplemented
75#10622416C2214yescomplemented
76#10622408C2214yescomplemented
77#10622399C2214yescomplemented
78#10622398C2214yescomplemented
79#10622395C2214yescomplemented
80#10622386C2214yescomplemented
81#10622345C2214yescomplemented
82#10622345C2212yescomplemented
83#10622345C2212yescomplemented
84#10622343C2214yescomplemented
85#10622339C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—21no—
93C22×C22⋊D11—22no—
94C22×C22⋊D11D411yescharacteristic
95C2×#4343—22no—
96C2×#4343—44no—
97C2×#4343C2314yes—
98#67037—48no—
99C2×#4341—22no—
100C2×#4341—22no—
101C2×D4×D11—22no—
102C2×D4×D11—22no—
103C2×D4×D11C2312yescomplemented
104C2×#4339—22no—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—21no—
109C22×D44—21no—
110C22×D44—44no—
111C22×D44C2311yescharacteristic
112C22×D44C2312yes—
113C22×D44C2312yes—
114C22×D44C2311yescharacteristic
115C22×D44C2311yescharacteristic
116C22×C4×D11—21no—
117C22×C4×D11—21no—
118C22×C4×D11C2311yescharacteristic
119C2×C11×SD16C2314yescomplemented
120C22×C8×C11C2312yes—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8C2312yes—
124C11×C22⋊Q8C2312yes—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121C2312yes—
128C11×#121C2312yes—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134#67006—22no—
135C2×C22⋊Dic11D411yescharacteristic
136#67000—22no—
137#67000C2314yes—
138C2×#4325C2314yescomplemented
139#66993C2312yescomplemented
140#66992—22no—
141#66992—22no—
142#66992—22no—
143#66991C2312yescomplemented
144#66990—22no—
145#66990—22no—
146#66988—22no—
147D4×Dic11C2312yescomplemented
148C2×#4323—44no—
149C2×#4323C2314yes—
150C2×#4323C2314yes—
151#66983—21no—
152#66983—21no—
153#66983C2312yes—
154#66983C2312yes—
155#66982—22no—
156C4×C22⋊D11D412yes—
157C4×C22⋊D11D412yes—
158C4×C22⋊D11C2312yes—
159C4×C22⋊D11C2312yes—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4D411yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167C2×Dic11⋊C4D411yescharacteristic
168C2×C4×Dic11C2311yescharacteristic
169C22×C11⋊C8C2312yes—
170#66967—48no—
171C2×D88—44no—
172C2×D88C2314yes—
173C2×D88C2314yes—
174C2×#4313C2314yescomplemented
175#66949—22no—
176#66948—22no—
177#66948—24no—
178#66948—24no—
179#66948C2314yes—
180#66948C2312yescomplemented
181#66947—22no—
182#66947—24no—
183#66947—24no—
184#66946—22no—
185#66946C2314yes—
186#66946C2312yescomplemented
187C4⋊C4×D11C2312yescomplemented
188#66941C2312yescomplemented
189#66938—22no—
190#66937—22no—
191#66937—22no—
192#66936—22no—
193#66935—24no—
194#66935—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×#103C2314yescomplemented
203C11×#102C2314yescomplemented
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yes—
206#66899C2314yescomplemented
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209#66885C2314yes—
210#66885C2314yes—
211(C2×D11)⋊C8C2314yescomplemented
212#66879C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214#66873C2314yes—
215#66873C2314yes—
216#66873C2314yescomplemented
217#66872C2314yescomplemented
218#61569—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—22no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—82no—
230C23×D11C2×D411yescharacteristic
231C2×Q8×C11—21no—
232C2×Q8×C11—42no—
233C2×Q8×C11C2412yes—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—21no—
237C2×D4×C11—42no—
238C2×D4×C11—44no—
239C2×D4×C11C2412yes—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—42no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—22no—
251C2×C22⋊D11—22no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—48no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11C2×D412yes—
260C2×C22⋊D11C2×D412yes—
261C22×Dic11—22no—
262C22×Dic11—21no—
263C22×Dic11C2×D411yescharacteristic
264C22×Dic11C2×D411yescharacteristic
265C22×Dic11C2×D411yescharacteristic
266#4343—28no—
267#4343—44no—
268#4343—48no—
269#4341—48no—
270#4341—48no—
271D4×D11—44no—
272D4×D11—48no—
273D4×D11—48no—
274#4339—48no—
275C2×D44—24no—
276C2×D44—24no—
277C2×D44—22no—
278C2×D44—24no—
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×D44—82no—
295C2×D44C2412yes—
296C2×D44C2412yes—
297C2×D44C2412yes—
298C2×C4×D11—24no—
299C2×C4×D11—22no—
300C2×C4×D11—24no—
301C2×C4×D11—22no—
302C2×C4×D11—42no—
303C2×C4×D11—44no—
304C2×C4×D11—82no—
305C2×C4×D11C2×D412yes—
306C2×C4×D11C2412yes—
307C2×Dic22—22no—
308C11×SD16—44no—
309C2×C8×C11—42no—
310C2×C8×C11C2414yes—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—22no—
313C11×C4⋊C4—22no—
314C11×C4⋊C4—21no—
315C11×C4⋊C4C2412yes—
316C11×C4⋊C4C2412yes—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C22⋊Dic11—22no—
322C22⋊Dic11—22no—
323C22⋊Dic11C2×D412yes—
324C22⋊Dic11C2×D412yes—
325#4325—44no—
326#4323—28no—
327#4323—44no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
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)⋊C4—22no—
336(C2×D11)⋊C4C2×D412yes—
337(C2×D11)⋊C4C2×D412yes—
338C4⋊Dic11—21no—
339C4⋊Dic11C2412yes—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4C2×D412yes—
343Dic11⋊C4C2×D412yes—
344C4×Dic11C2×D412yes—
345C4×Dic11C2412yes—
346C2×C11⋊C8—42no—
347C2×C11⋊C8C2414yes—
348D88—28no—
349D88—44no—
350#4313—44no—
351#3496—111no—
352C2×#546—111no—
353#3306—114no—
354#3306—114no—
355#3264—114no—
356#3264—114no—
357#3213—112no—
358#3192—112no—
359#3187—111no—
360#3187D1111yescharacteristic, complemented
361#3109—112no—
362#3006—112no—
363C2×#447—111no—
364C2×#447—111no—
365#2973—111no—
366C23×C11—22no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—42no—
370C23×C11—81no—
371C23×C11—81no—
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—44no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—42no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—42no—
393C22×D11—42no—
394C22×D11—82no—
395C22×D11—82no—
396C22×D11—82no—
397C22×D11—82no—
398C22×D11—81no—
399C22×D11—81no—
400C22×D11—816no—
401C22×D11C22×D412yes—
402Q8×C11—24no—
403Q8×C11—42no—
404D4×C11—24no—
405D4×C11—44no—
406D4×C11—44no—
407D4×C11—81no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—42no—
418C2×C4×C11—42no—
419C2×C4×C11—42no—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C2511yescharacteristic
424C22⋊D11—24no—
425C22⋊D11—24no—
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—41no—
435C2×Dic11—41no—
436C2×Dic11—44no—
437C2×Dic11—42no—
438C2×Dic11C22×D412yes—
439C2×Dic11C22×D412yes—
440C2×Dic11C22×D412yes—
441D44—24no—
442D44—22no—
443D44—24no—
444D44—22no—
445D44—22no—
446D44—44no—
447D44—44no—
448D44—42no—
449D44—48no—
450D44—44no—
451D44—81no—
452D44—84no—
453D44H(5,𝔽2)14yescomplemented
454C4×D11—24no—
455C4×D11—42no—
456C4×D11—48no—
457C4×D11—44no—
458C4×D11—44no—
459C4×D11—84no—
460Dic22—44no—
461C8×C11—24no—
462C11⋊C8—24no—
463C2×H(5,𝔽2)—221no—
464C22×#41—111no—
465C23×D4—111no—
466C2×AGL(1,ℤ/8)—114no—
467C22×D8—112no—
468C22×D8—112no—
469#547—112no—
470#547—112no—
471#546—114no—
472#546—114no—
473#546—222no—
474#546—222no—
475#546—222no—
476#546—222no—
477D42—112no—
478D42—112no—
479#537—221no—
480#534—221no—
481#534—221no—
482#532—112no—
483C2×#124—111no—
484C2×#123—221no—
485C2×C22⋊Q8C2×D1111yescharacteristic, complemented
486C2×#121—111no—
487C2×#121—112no—
488C2×#121—111no—
489C2×#121—221no—
490C2×#121C2×D1111yescharacteristic
491C2×#120—221no—
492C2×C4×D4—111no—
493C2×C4×D4—111no—
494C22×C22⋊C4—221no—
495#496—114no—
496#489—114no—
497#483—112no—
498#483C2×D1112yescomplemented
499#481—112no—
500#481—114no—
501#481C2×D1112yescomplemented
502#476—114no—
503#469—114no—
504#469—114no—
505#465—114no—
506#465C2×D1114yescomplemented
507#463—114no—
508#463—114no—
509#459—114no—
510#450—112no—
511#450C2×D1112yescomplemented
512#449—114no—
513#449—114no—
514#448—112no—
515#448C2×D1112yescomplemented
516#447—112no—
517#447—112no—
518#447—114no—
519#447—114no—
520#447—112no—
521#447—112no—
522#447—114no—
523#442—114no—
524#442—114no—
525#435—114no—
526#435—114no—
527#432—112no—
528#417—114no—
529C2×#102—112no—
530C2×#102—112no—
531#407—112no—
532C2×C22⋊C8—111no—
533C2×C22⋊C8C2×D1111yescharacteristic, complemented
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—44no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—162no—
545C22×C11C2×AGL(1,ℤ/8)12yes—
546C22×C11C2×AGL(1,ℤ/8)12yes—
547C22×C11C2×AGL(1,ℤ/8)12yes—
548C22×C11C23×D411yescharacteristic
549C2×D11—22no—
550C2×D11—24no—
551C2×D11—22no—
552C2×D11—22no—
553C2×D11—48no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—82no—
563C2×D11—88no—
564C2×D11—88no—
565C2×D11—84no—
566C2×D11—164no—
567C2×D11—162no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—21no—
571C4×C11—42no—
572C4×C11—42no—
573C4×C11—42no—
574C4×C11C2×H(5,𝔽2)12yes—
575Dic11—22no—
576Dic11—22no—
577Dic11—22no—
578Dic11—42no—
579C25—221no—
580H(5,𝔽2)—448no—
581C2×#41—114no—
582C2×#41—222no—
583C2×#41—222no—
584C2×#41—222no—
585C2×#41—222no—
586C2×#41—444no—
587C22×Q8C22×D1111yescharacteristic
588C22×D4—21no—
589C22×D4—111no—
590C22×D4—112no—
591C22×D4—111no—
592C22×D4—112no—
593C22×D4—112no—
594C22×D4—111no—
595C22×D4—111no—
596C22×D4—221no—
597C22×D4—221no—
598C22×D4—222no—
599C22×D4—222no—
600C22×D4—222no—
601C22×D4—221no—
602C22×D4—221no—
603C22×D4—221no—
604C22×D4—221no—
605C22×D4—444no—
606C22×D4C22×D1111yescharacteristic
607C23×C4—111no—
608C23×C4—221no—
609C23×C4—221no—
610C23×C4C22×D1111yescharacteristic
611AGL(1,ℤ/8)—448no—
612C2×SD16—114no—
613C2×SD16C22×D1114yescomplemented
614C2×D8—114no—
615C2×D8—114no—
616C2×D8—114no—
617C2×D8—114no—
618C2×D8—444no—
619C2×D8—444no—
620C2×M16—114no—
621C22×C8—112no—
622C22×C8C22×D1112yes—
623C4⋊Q8—112no—
624#127—112no—
625#124—114no—
626#124—222no—
627#124—222no—
628#123—222no—
629#123—222no—
630#123—222no—
631#123—222no—
632#123—224no—
633#123—224no—
634C22⋊Q8—21no—
635C22⋊Q8—21no—
636C22⋊Q8—222no—
637C22⋊Q8—222no—
638C22⋊Q8C22×D1112yes—
639C22⋊Q8C22×D1112yes—
640#121—21no—
641#121—21no—
642#121—112no—
643#121—112no—
644#121—112no—
645#121—112no—
646#121—114no—
647#121—222no—
648#121—222no—
649#121—224no—
650#121—224no—
651#121—222no—
652#121—222no—
653#121—222no—
654#121—222no—
655#121—221no—
656#121—221no—
657#121C22×D1112yes—
658#121C22×D1112yes—
659#120—222no—
660#120—224no—
661#120—224no—
662#120—222no—
663#120—222no—
664#120—222no—
665C4×D4—112no—
666C4×D4—112no—
667C4×D4—112no—
668C4×D4—112no—
669C4×D4—112no—
670C4×D4—114no—
671C4×D4—112no—
672C4×D4—222no—
673C4×D4—222no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—111no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4C22×D1111yescharacteristic
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—111no—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—224no—
685C2×C22⋊C4—224no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C22⋊C4—221no—
690C2×C22⋊C4—221no—
691C2×C22⋊C4—221no—
692C2×C42—111no—
693#106—114no—
694#106C22×D1114yescomplemented
695C4⋊C8—114no—
696#103—114no—
697#103C22×D1114yescomplemented
698#102—114no—
699#102—114no—
700#102—114no—
701#102—114no—
702#102—114no—
703#102C22×D1114yescomplemented
704C22⋊C8—112no—
705C22⋊C8—112no—
706C22⋊C8—114no—
707C22⋊C8C22×D1112yes—
708C22⋊C8C22×D1112yes—
709#97—114no—
710C2×C11—22no—
711C2×C11—22no—
712C2×C11—22no—
713C2×C11—82no—
714C2×C11#348411yescharacteristic
715C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
716C2×C11#358511yescharacteristic
717D11—42no—
718D11—44no—
719D11—82no—
720D11—82no—
721C24—21no—
722C24—111no—
723C24—222no—
724C24—221no—
725C24—221no—
726C24—222no—
727C24—222no—
728C24—221no—
729C24—444no—
730C24—444no—
731C24—882no—
732C24D4×D1111yescharacteristic
733#41—228no—
734#41—448no—
735#41—448no—
736#41—444no—
737#41—448no—
738#41—448no—
739C2×Q8—21no—
740C2×Q8—42no—
741C2×Q8—222no—
742C2×Q8C23×D1112yes—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—42no—
747C2×D4—44no—
748C2×D4—112no—
749C2×D4—112no—
750C2×D4—112no—
751C2×D4—112no—
752C2×D4—112no—
753C2×D4—224no—
754C2×D4—224no—
755C2×D4—224no—
756C2×D4—224no—
757C2×D4—222no—
758C2×D4—224no—
759C2×D4—222no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—224no—
763C2×D4—222no—
764C2×D4—222no—
765C2×D4—222no—
766C2×D4—221no—
767C2×D4—222no—
768C2×D4—222no—
769C2×D4—221no—
770C2×D4—221no—
771C2×D4—442no—
772C2×D4—442no—
773C2×D4—442no—
774C2×D4—442no—
775C2×D4—444no—
776C2×D4—444no—
777C2×D4—444no—
778C2×D4—444no—
779C2×D4—444no—
780C2×D4—448no—
781C2×D4—448no—
782C2×D4—448no—
783C2×D4—444no—
784C2×D4—882no—
785C2×D4C23×D1112yes—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—42no—
790C22×C4—111no—
791C22×C4—111no—
792C22×C4—111no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—224no—
796C22×C4—222no—
797C22×C4—224no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—221no—
801C22×C4—442no—
802C22×C4—444no—
803C22×C4—882no—
804C22×C4D4×D1111yescharacteristic
805C22×C4D4×D1111yescharacteristic
806C22×C4D4×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1111yescharacteristic
810SD16—44no—
811SD16—444no—
812D8—228no—
813D8—228no—
814D8—444no—
815D8—444no—
816M16—444no—
817C2×C8—42no—
818C2×C8—114no—
819C2×C8—442no—
820C2×C8C23×D1114yes—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—112no—
826C4⋊C4—112no—
827C4⋊C4—112no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—221no—
831C4⋊C4C23×D1112yes—
832C4⋊C4C23×D1112yes—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—22no—
836C22⋊C4—22no—
837C22⋊C4—112no—
838C22⋊C4—112no—
839C22⋊C4—112no—
840C22⋊C4—112no—
841C22⋊C4—224no—
842C22⋊C4—224no—
843C22⋊C4—224no—
844C22⋊C4—224no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C22⋊C4—222no—
848C22⋊C4—222no—
849C22⋊C4—222no—
850C22⋊C4—222no—
851C42—112no—
852C42—112no—
853C11#6156911yescharacteristic, complemented, Sylow
854C23—22no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—81no—
859C23—81no—
860C23—112no—
861C23—224no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—441no—
867C23—441no—
868C23—444no—
869C23—444no—
870C23—442no—
871C23—442no—
872C23—442no—
873C23—444no—
874C23—442no—
875C23—444no—
876C23—444no—
877C23—442no—
878C23—442no—
879C23—882no—
880C23—882no—
881C23—881no—
882C23—881no—
883C23—882no—
884C23—882no—
885C23—8816no—
886C23#6696714yescomplemented
887C23C2×D4×D1111yescharacteristic
888C23C2×D4×D1111yescharacteristic
889C23C2×D4×D1111yescharacteristic
890Q8—24no—
891Q8—42no—
892Q8—444no—
893D4—24no—
894D4—44no—
895D4—44no—
896D4—81no—
897D4—114no—
898D4—224no—
899D4—224no—
900D4—224no—
901D4—222no—
902D4—224no—
903D4—222no—
904D4—222no—
905D4—444no—
906D4—444no—
907D4—442no—
908D4—448no—
909D4—444no—
910D4—444no—
911D4—444no—
912D4—444no—
913D4—444no—
914D4—881no—
915D4—884no—
916D4—882no—
917D4—882no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—112no—
931C2×C4—112no—
932C2×C4—112no—
933C2×C4—222no—
934C2×C4—224no—
935C2×C4—222no—
936C2×C4—442no—
937C2×C4—448no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—444no—
943C2×C4—442no—
944C2×C4—884no—
945C2×C4C2×D4×D1111yescharacteristic
946C2×C4C2×D4×D1111yescharacteristic
947C2×C4C2×D4×D1111yescharacteristic
948C2×C4C24×D1111yescharacteristic
949C8—24no—
950C8—224no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—44no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—162no—
962C22—222no—
963C22—222no—
964C22—224no—
965C22—222no—
966C22—448no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—442no—
975C22—882no—
976C22—888no—
977C22—888no—
978C22—884no—
979C22—1762no—
980C22—1764no—
981C22C2×#6696712yes—
982C22C2×#6696712yes—
983C22C2×#6696712yes—
984C22C22×D4×D1111yescharacteristic
985C4—21no—
986C4—21no—
987C4—21no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—222no—
992C4—222no—
993C4—222no—
994C4—442no—
995C4D11×H(5,𝔽2)12yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—82no—
1000C2—442no—
1001C2—444no—
1002C2—882no—
1003C2—882no—
1004C2#1308224811yescharacteristic
1005C2C22×#6696711yescharacteristic
1006C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3187C2
socleC22×C11C23×D4
hypercenter#3187D11
hypocenterC11#61569
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. #13082373C2semidirect
2. C2×#10623161C2semidirect
3. #13080583C2semidirect
4. #13080575C2semidirect
5. #13080100C2semidirect
6. #13080093C2semidirect
7. #13079602C2semidirect
8. #13079415C2semidirect
9. #13079369C2semidirect
10. #13078704C2semidirect
11. #13077867C2semidirect
12. C2×#10622345C2semidirect
13. C2×#10622649C2semidirect
14. #13077642C2semidirect
15. C11×#3187C2semidirect
16. C22×#4343C22semidirect
18. C23×D44C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
21. C2×#67000C22semidirect
23. D4×C22⋊D11C22semidirect
24. C22×#4323C22semidirect
27. C2×#66967C22semidirect
28. C22×D88C22semidirect
31. #10623161C22semidirect
32. #10623161C22semidirect
33. #10623142C22semidirect
35. #10623140C22semidirect
37. D11×#121C22semidirect
39. #10623127C22semidirect
40. #10623038C22semidirect
42. C2×#66948C22semidirect
44. C2×#66946C22semidirect
48. C11×#483C22semidirect
49. C11×#481C22semidirect
50. C11×#465C22semidirect
51. C11×#450C22semidirect
52. C11×#448C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622840C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622789C22semidirect
57. #10622785C22semidirect
58. #10622778C22semidirect
59. C2×#66885C22semidirect
60. #10622724C22semidirect
61. #10622661C22semidirect
62. #10622659C22semidirect
63. #10622656C22semidirect
64. #10622649C22semidirect
65. #10622649C22semidirect
66. #10622649C22semidirect
67. #10622581C22semidirect
68. C2×#66873C22semidirect
69. #10622483C22semidirect
70. #10622482C22semidirect
71. #10622478C22semidirect
72. #10622476C22semidirect
73. #10622432C22semidirect
74. #10622424C22semidirect
75. #10622416C22semidirect
76. #10622408C22semidirect
77. #10622399C22semidirect
78. #10622398C22semidirect
79. #10622395C22semidirect
80. #10622386C22semidirect
81. #10622345C22semidirect
82. #10622345C22semidirect
83. #10622345C22semidirect
84. #10622343C22semidirect
85. #10622339C22semidirect
86. #10622332C22semidirect
103. C2×D4×D11C23semidirect
119. C2×C11×SD16C23semidirect
138. C2×#4325C23semidirect
139. #66993C23semidirect
143. #66991C23semidirect
147. D4×Dic11C23semidirect
174. C2×#4313C23semidirect
180. #66948C23semidirect
186. #66946C23semidirect
187. C4⋊C4×D11C23semidirect
188. #66941C23semidirect
201. C11×#106C23semidirect
202. C11×#103C23semidirect
203. C11×#102C23semidirect
206. #66899C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. #66879C23semidirect
213. Dic11⋊C8C23semidirect
216. #66873C23semidirect
217. #66872C23semidirect
360. #3187D11semidirect
372. C23×C11AGL(1,ℤ/8)semidirect
453. D44H(5,𝔽2)semidirect
485. C2×C22⋊Q8C2×D11semidirect
498. #483C2×D11semidirect
501. #481C2×D11semidirect
506. #465C2×D11semidirect
511. #450C2×D11semidirect
515. #448C2×D11semidirect
533. C2×C22⋊C8C2×D11semidirect
613. C2×SD16C22×D11semidirect
694. #106C22×D11semidirect
697. #103C22×D11semidirect
703. #102C22×D11semidirect
853. C11#61569semidirect
886. C23#66967semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106231612
#130805832
#130805752
#130801002
#130800932
#130796022
#130794152
#130793692
#130787042
#130778672
C2×#106223452
C2×#106226492
#130776422
C11×#31872
#6156911