Finite Group Databasebeta

← #15638592

Subgroups — #15638592

Order 2816.

2514 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic, complemented
3#13080578C214yesmaximal, complemented
4#13080570C214yesmaximal, complemented
5#13080099C214yesmaximal, complemented
6#13080090C214yesmaximal, complemented
7#13079602C212yesmaximal, complemented
8#13079416C211yesmaximal, characteristic, complemented
9#13079413C211yesmaximal, characteristic, complemented
10#13079371C212yesmaximal, complemented
11#13078702C212yesmaximal, complemented
12#13077868C211yesmaximal, characteristic, complemented
13D11×#447C212yesmaximal, complemented
14#13077643C211yesmaximal, characteristic, complemented
15C11×#3006C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic, complemented
17C2×#67037—21no—
18C22×D4×D11C2211yescharacteristic, complemented
19C2×C11×AGL(1,ℤ/8)C2212yescomplemented
20C2×C11×#121C2211yescharacteristic, complemented
21#10623360—22no—
22#10623360—22no—
23#10623360C2214yescomplemented
24#10623360C2214yescomplemented
25C2×#67002C2212yescomplemented
26C2×#67000C2211yescharacteristic, complemented
27C2×#66999C2211yescharacteristic, complemented
28#10623335—21no—
29C2×#66992—21no—
30D4×C22⋊D11C2212yescomplemented
31C2×#66990—21no—
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic, complemented
34C2×#66983C2211yescharacteristic, complemented
35C2×#66982—21no—
36C2×C4×C22⋊D11C2211yescharacteristic
37C22×(C2×D11)⋊C4—21no—
38C2×D8×D11C2214yescomplemented
39#10623142C2212yescomplemented
40#10623141—22no—
41#10623140C2212yescomplemented
42#10623136—21no—
43D11×#121C2212yes—
44#10623128—21no—
45#10623127C2212yescomplemented
46#10623038C2212yescomplemented
47#10623021—22no—
48C11×#449C2214yescomplemented
49C11×#448C2212yescomplemented
50C11×#447C2212yescomplemented
51C11×#417C2212yescomplemented
52C11×#407C2211yescharacteristic, complemented
53#10622851C2214yescomplemented
54#10622845C2212yescomplemented
55#10622840C2212yescomplemented
56#10622830C2212yescomplemented
57#10622830C2212yescomplemented
58#10622820C2211yescharacteristic, complemented
59#10622789C2214yescomplemented
60#10622784C2214yescomplemented
61#10622782C2214yescomplemented
62#10622778C2214yescomplemented
63#10622769C2214yescomplemented
64#10622765C2214yescomplemented
65#10622763C2214yescomplemented
66#10622748C2214yescomplemented
67#10622740C2214yescomplemented
68#10622652C2214yescomplemented
69#10622649C2212yescomplemented
70#10622647C2212yescomplemented
71#10622581C2212yescomplemented
72#10622432C2214yescomplemented
73#10622420C2214yescomplemented
74#10622418C2214yescomplemented
75#10622408C2214yescomplemented
76#10622398C2214yescomplemented
77#10622386C2214yescomplemented
78D11×#102C2214yescomplemented
79#10622374C2214yescomplemented
80#10622348C2212yescomplemented
81#10622348C2212yescomplemented
82#10622345C2212yescomplemented
83#10622345C2212yescomplemented
84#10622341C2214yescomplemented
85D11×C22⋊C8C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41—44no—
91C2×C11×#41C2312yes—
92C2×C11×#41C2312yes—
93C22×Q8×C11C2311yescharacteristic
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic, complemented
98C23×C4×C11—21no—
99C23×C4×C11C2311yescharacteristic
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—22no—
103C22×C22⋊D11—21no—
104C22×C22⋊D11D411yescharacteristic
105C23×Dic11—21no—
106#67037—48no—
107C2×#4341—22no—
108C2×#4341—22no—
109C2×D4×D11—22no—
110C2×D4×D11—22no—
111C2×D4×D11—22no—
112C2×D4×D11—44no—
113C2×D4×D11C2314yes—
114C2×D4×D11C2312yes—
115C2×#4339—22no—
116C22×D44C2311yescharacteristic
117C22×D44C2311yescharacteristic, complemented
118C22×C4×D11C2311yescharacteristic
119C11×AGL(1,ℤ/8)—44no—
120C2×C11×SD16C2314yescomplemented
121C2×C11×D8C2314yes—
122C2×C11×M16C2312yescomplemented
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yescomplemented
127C2×C11×C4⋊C4C2311yescharacteristic, complemented
128C2×C11×C22⋊C4—21no—
129#67006—22no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11D411yescharacteristic
132#67002—44no—
133#67000—22no—
134#67000C2314yes—
135#66999—22no—
136#66999C2314yes—
137C2×#4325C2314yescomplemented
138#66993C2312yescomplemented
139#66992—22no—
140#66992—22no—
141#66992—24no—
142#66992—24no—
143#66992—22no—
144#66991C2312yes—
145#66990—24no—
146#66990—24no—
147#66990—22no—
148#66990—22no—
149#66988—22no—
150D4×Dic11—22no—
151D4×Dic11C2314yes—
152D4×Dic11C2312yescomplemented
153C2×#4323C2314yes—
154C2×#4323C2314yes—
155#66983—21no—
156#66983—21no—
157#66983—21no—
158#66983—21no—
159#66983C2312yes—
160#66983C2312yes—
161#66983C2312yes—
162#66983C2312yescomplemented
163#66982—22no—
164#66982—24no—
165#66982—24no—
166C4×C22⋊D11D412yes—
167C4×C22⋊D11D412yes—
168C4×C22⋊D11C2312yes—
169C4×C22⋊D11C2312yes—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4—21no—
173C2×(C2×D11)⋊C4—21no—
174C2×(C2×D11)⋊C4—21no—
175C2×(C2×D11)⋊C4—24no—
176C2×(C2×D11)⋊C4—24no—
177C2×(C2×D11)⋊C4D411yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic, complemented
180C2×Dic11⋊C4—21no—
181C2×Dic11⋊C4D411yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C2×#4318C2312yescomplemented
184D8×D11—48no—
185C2×D88C2314yes—
186C2×C8×D11C2314yes—
187#66949—22no—
188#66948C2312yes—
189#66947—22no—
190#66946C2312yescomplemented
191C4⋊C4×D11C2312yes—
192#66941C2312yescomplemented
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×#103C2314yescomplemented
202C11×#102C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yescomplemented
205#66899C2314yescomplemented
206#66896C2314yes—
207#66896C2314yescomplemented
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yescomplemented
210#66885C2314yes—
211#66885C2314yescomplemented
212(C2×D11)⋊C8C2314yes—
213#66881C2314yescomplemented
214#66879C2314yescomplemented
215Dic11⋊C8C2314yescomplemented
216#66873C2314yes—
217#66872C2314yescomplemented
218#61569—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—24no—
225C23×D11—22no—
226C23×D11—44no—
227C23×D11—44no—
228C23×D11—82no—
229C23×D11C2×D411yescharacteristic
230C11×#41—24no—
231C11×#41—24no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41—44no—
235C11×#41—44no—
236C2×Q8×C11—21no—
237C2×Q8×C11—42no—
238C2×Q8×C11C2412yes—
239C2×D4×C11—24no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—42no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11C2412yes—
250C2×D4×C11C2412yes—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—42no—
256C22×C4×C11—44no—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—22no—
264C2×C22⋊D11—24no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—22no—
271C2×C22⋊D11—24no—
272C2×C22⋊D11—22no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—48no—
276C2×C22⋊D11—82no—
277C2×C22⋊D11C2×D412yes—
278C2×C22⋊D11C2×D412yes—
279C22×Dic11—22no—
280C22×Dic11—24no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—82no—
284C22×Dic11C2×D411yescharacteristic
285C22×Dic11C2×D411yescharacteristic
286C22×Dic11C2×D411yescharacteristic
287#4341—48no—
288#4341—48no—
289D4×D11—28no—
290D4×D11—44no—
291D4×D11—48no—
292D4×D11—44no—
293D4×D11—48no—
294D4×D11—48no—
295#4339—48no—
296C2×D44—22no—
297C2×D44—21no—
298C2×D44—21no—
299C2×D44—42no—
300C2×D44—42no—
301C2×D44C2412yes—
302C2×D44C2412yes—
303C2×C4×D11—22no—
304C2×C4×D11—22no—
305C2×C4×D11—42no—
306C2×C4×D11C2×D412yes—
307C2×C4×D11C2412yes—
308C2×Dic22—22no—
309C11×SD16—44no—
310C11×D8—28no—
311C11×M16—42no—
312C2×C8×C11C2414yes—
313C11×C4⋊C4—21no—
314C11×C4⋊C4C2412yes—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11—24no—
320C22⋊Dic11C2×D412yes—
321C22⋊Dic11C2×D412yes—
322#4325—44no—
323#4323—28no—
324#4323—44no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334(C2×D11)⋊C4C2×D412yes—
335(C2×D11)⋊C4C2×D412yes—
336C4⋊Dic11—21no—
337C4⋊Dic11—21no—
338C4⋊Dic11C2412yes—
339C4⋊Dic11C2412yes—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4—24no—
343Dic11⋊C4C2×D412yes—
344Dic11⋊C4C2×D412yes—
345C4×Dic11C2×D412yes—
346C4×Dic11C2412yes—
347#4318—42no—
348C2×C11⋊C8C2414yes—
349D88—44no—
350C8×D11—44no—
351#3496—111no—
352C2×#546—111no—
353#3306—114no—
354#3306—114no—
355#3264—114no—
356#3264—114no—
357#3213—112no—
358#3192—111no—
359#3192—111no—
360#3187—112no—
361#3109—112no—
362#3006—111no—
363#3006D1111yescharacteristic, complemented
364C2×#447—112no—
365#2973—111no—
366C23×C11—24no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—81no—
376C23×C11—81no—
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—48no—
385C22×D11—42no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—48no—
390C22×D11—44no—
391C22×D11—84no—
392C22×D11—82no—
393C22×D11—82no—
394C22×D11—81no—
395C22×D11—81no—
396C22×D11—816no—
397C22×D11AGL(1,ℤ/8)14yescomplemented
398C22×D11C22×D412yes—
399Q8×C11—22no—
400Q8×C11—22no—
401Q8×C11—42no—
402D4×C11—24no—
403D4×C11—22no—
404D4×C11—24no—
405D4×C11—44no—
406D4×C11—44no—
407D4×C11—44no—
408D4×C11—44no—
409D4×C11—81no—
410D4×C11H(5,𝔽2)14yescomplemented
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11—42no—
422C2×C4×C11—42no—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C2511yescharacteristic
427C22⋊D11—24no—
428C22⋊D11—24no—
429C22⋊D11—48no—
430C22⋊D11—44no—
431C22⋊D11—44no—
432C22⋊D11—44no—
433C22⋊D11—44no—
434C22⋊D11—82no—
435C22⋊D11—82no—
436C22⋊D11—82no—
437C22⋊D11—82no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—44no—
444C2×Dic11—42no—
445C2×Dic11—42no—
446C2×Dic11—84no—
447C2×Dic11C22×D412yes—
448C2×Dic11C22×D412yes—
449C2×Dic11C22×D412yes—
450D44—24no—
451D44—24no—
452D44—42no—
453D44—44no—
454D44—81no—
455C4×D11—24no—
456C4×D11—42no—
457C4×D11—44no—
458C4×D11—44no—
459Dic22—44no—
460C8×C11—24no—
461C11⋊C8—24no—
462C2×H(5,𝔽2)—221no—
463C22×#41C2×D1111yescharacteristic, complemented
464C23×D4—111no—
465C2×AGL(1,ℤ/8)—112no—
466C2×AGL(1,ℤ/8)C2×D1112yescomplemented
467C22×D8—114no—
468#547—112no—
469#547—112no—
470#546—114no—
471#546—114no—
472#546—222no—
473#546—222no—
474#546—222no—
475#546—222no—
476D42—112no—
477D42—112no—
478#537—221no—
479#534—221no—
480#534—221no—
481#532—112no—
482C2×#124—111no—
483C2×#123—221no—
484C2×C22⋊Q8—111no—
485C2×#121—111no—
486C2×#121—111no—
487C2×#121—112no—
488C2×#121—221no—
489C2×#121C2×D1111yescharacteristic, complemented
490C2×#120—221no—
491C2×C4×D4—111no—
492C2×C4×D4—111no—
493C22×C22⋊C4—221no—
494#496—114no—
495#489—114no—
496#483—114no—
497#481—112no—
498#481—112no—
499#481—112no—
500#481—112no—
501#476—114no—
502#469—114no—
503#469—114no—
504#465—114no—
505#465—114no—
506#463—114no—
507#463—114no—
508#459—114no—
509#450—114no—
510#449—114no—
511#449C2×D1114yescomplemented
512#448—112no—
513#448C2×D1112yescomplemented
514#447—112no—
515#447—112no—
516#447—114no—
517#447—112no—
518#447—114no—
519#447—112no—
520#447—112no—
521#447C2×D1112yescomplemented
522#442—114no—
523#442—114no—
524#435—114no—
525#435—114no—
526#432—112no—
527#417—112no—
528#417C2×D1112yescomplemented
529C2×#102—114no—
530#407—111no—
531#407C2×D1111yescharacteristic, complemented
532C2×C22⋊C8—112no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—24no—
540C22×C11—21no—
541C22×C11—21no—
542C22×C11—48no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—82no—
549C22×C11—162no—
550C22×C11C2×AGL(1,ℤ/8)12yes—
551C22×C11C23×D411yescharacteristic
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—44no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—816no—
562C2×D11—84no—
563C2×D11—164no—
564C2×D11—162no—
565C2×D11C2×AGL(1,ℤ/8)14yes—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—42no—
570C4×C11—42no—
571C4×C11C2×H(5,𝔽2)12yes—
572Dic11—22no—
573Dic11—22no—
574Dic11—22no—
575Dic11—42no—
576Dic11—42no—
577C25—221no—
578H(5,𝔽2)—448no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—44no—
582C2×#41—222no—
583C2×#41—222no—
584C2×#41—222no—
585C2×#41C22×D1112yes—
586C2×#41C22×D1112yes—
587C22×Q8C22×D1111yescharacteristic
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—111no—
591C22×D4—114no—
592C22×D4—112no—
593C22×D4—111no—
594C22×D4—111no—
595C22×D4—222no—
596C22×D4—221no—
597C22×D4—222no—
598C22×D4—222no—
599C22×D4—222no—
600C22×D4—221no—
601C22×D4—221no—
602C22×D4—444no—
603C22×D4C22×D1111yescharacteristic
604C22×D4C22×D1111yescharacteristic, complemented
605C23×C4—21no—
606C23×C4—111no—
607C23×C4—221no—
608C23×C4C22×D1111yescharacteristic
609AGL(1,ℤ/8)—44no—
610AGL(1,ℤ/8)—444no—
611C2×SD16—114no—
612C2×SD16C22×D1114yescomplemented
613C2×D8—114no—
614C2×D8—114no—
615C2×D8—114no—
616C2×D8—448no—
617C2×D8C22×D1114yes—
618C2×M16—112no—
619C2×M16C22×D1112yescomplemented
620C22×C8—114no—
621C4⋊Q8—112no—
622#127—112no—
623#124—114no—
624#124—222no—
625#124—222no—
626#123—222no—
627#123—222no—
628#123—222no—
629#123—222no—
630#123—224no—
631#123—224no—
632C22⋊Q8—114no—
633C22⋊Q8—222no—
634C22⋊Q8—222no—
635C22⋊Q8—222no—
636#121—21no—
637#121—21no—
638#121—112no—
639#121—112no—
640#121—112no—
641#121—112no—
642#121—112no—
643#121—112no—
644#121—222no—
645#121—222no—
646#121—224no—
647#121—224no—
648#121—222no—
649#121—222no—
650#121—222no—
651#121—221no—
652#121—221no—
653#121—221no—
654#121—221no—
655#121C22×D1112yes—
656#121C22×D1112yescomplemented
657#120—222no—
658#120—222no—
659#120—222no—
660#120—222no—
661#120—224no—
662#120—224no—
663C4×D4—112no—
664C4×D4—112no—
665C4×D4—112no—
666C4×D4—112no—
667C4×D4—114no—
668C4×D4—112no—
669C4×D4—112no—
670C4×D4—222no—
671C4×D4—222no—
672C2×C4⋊C4—111no—
673C2×C4⋊C4—111no—
674C2×C4⋊C4—111no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—221no—
677C2×C4⋊C4C22×D1111yescharacteristic, complemented
678C2×C22⋊C4—21no—
679C2×C22⋊C4—111no—
680C2×C22⋊C4—111no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—224no—
683C2×C22⋊C4—224no—
684C2×C22⋊C4—221no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C22⋊C4—221no—
690C2×C42—111no—
691#106—114no—
692#106—114no—
693C4⋊C8—114no—
694#103—114no—
695#103C22×D1114yescomplemented
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102—114no—
701#102C22×D1114yes—
702C22⋊C8—112no—
703C22⋊C8—112no—
704C22⋊C8—114no—
705C22⋊C8C22×D1112yes—
706C22⋊C8C22×D1112yescomplemented
707#97—114no—
708C2×C11—22no—
709C2×C11—44no—
710C2×C11—41no—
711C2×C11—41no—
712C2×C11—82no—
713C2×C11#348411yescharacteristic
714C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
715C2×C11#358511yescharacteristic
716D11—24no—
717D11—82no—
718D11—82no—
719C24—21no—
720C24—21no—
721C24—111no—
722C24—224no—
723C24—222no—
724C24—221no—
725C24—221no—
726C24—444no—
727C24—444no—
728C24—882no—
729C24D4×D1111yescharacteristic
730#41—24no—
731#41—24no—
732#41—42no—
733#41—42no—
734#41—44no—
735#41—44no—
736#41—448no—
737#41—448no—
738#41—448no—
739C2×Q8—21no—
740C2×Q8—42no—
741C2×Q8—222no—
742C2×Q8C23×D1112yes—
743C2×D4—24no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—42no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—112no—
754C2×D4—112no—
755C2×D4—112no—
756C2×D4—112no—
757C2×D4—222no—
758C2×D4—224no—
759C2×D4—222no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—224no—
763C2×D4—228no—
764C2×D4—222no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—222no—
768C2×D4—222no—
769C2×D4—221no—
770C2×D4—221no—
771C2×D4—442no—
772C2×D4—442no—
773C2×D4—444no—
774C2×D4—444no—
775C2×D4—448no—
776C2×D4—448no—
777C2×D4—448no—
778C2×D4—448no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—882no—
782C2×D4C23×D1112yes—
783C2×D4C23×D1112yes—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—42no—
789C22×C4—44no—
790C22×C4—111no—
791C22×C4—111no—
792C22×C4—111no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—224no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—442no—
802C22×C4—882no—
803C22×C4D4×D1111yescharacteristic
804C22×C4D4×D1111yescharacteristic
805C22×C4D4×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809SD16—44no—
810SD16—444no—
811D8—28no—
812D8—228no—
813D8—444no—
814D8—444no—
815M16—42no—
816M16—442no—
817C2×C8—114no—
818C2×C8—444no—
819C2×C8C23×D1114yes—
820C4⋊C4—21no—
821C4⋊C4—112no—
822C4⋊C4—112no—
823C4⋊C4—112no—
824C4⋊C4—112no—
825C4⋊C4—222no—
826C4⋊C4—224no—
827C4⋊C4—222no—
828C4⋊C4—221no—
829C4⋊C4—221no—
830C4⋊C4C23×D1112yes—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—112no—
834C22⋊C4—112no—
835C22⋊C4—112no—
836C22⋊C4—112no—
837C22⋊C4—224no—
838C22⋊C4—224no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—224no—
842C22⋊C4—224no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C22⋊C4—222no—
848C22⋊C4—222no—
849C42—112no—
850C42—112no—
851C11#6156911yescharacteristic, complemented, Sylow
852C23—24no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—41no—
857C23—41no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—81no—
862C23—81no—
863C23—112no—
864C23—114no—
865C23—222no—
866C23—222no—
867C23—441no—
868C23—441no—
869C23—448no—
870C23—442no—
871C23—442no—
872C23—442no—
873C23—448no—
874C23—444no—
875C23—442no—
876C23—881no—
877C23—881no—
878C23—884no—
879C23—882no—
880C23—882no—
881C23—8816no—
882C23C2×D4×D1111yescharacteristic
883C23C2×D4×D1111yescharacteristic
884C23C2×D4×D1111yescharacteristic
885Q8—22no—
886Q8—22no—
887Q8—42no—
888Q8—444no—
889D4—24no—
890D4—22no—
891D4—24no—
892D4—44no—
893D4—44no—
894D4—44no—
895D4—44no—
896D4—81no—
897D4—224no—
898D4—224no—
899D4—224no—
900D4—224no—
901D4—442no—
902D4—444no—
903D4—448no—
904D4—444no—
905D4—444no—
906D4—444no—
907D4—444no—
908D4—881no—
909D4—882no—
910D4—882no—
911D4—882no—
912D4—882no—
913D4#6703714yescomplemented
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—112no—
927C2×C4—112no—
928C2×C4—112no—
929C2×C4—222no—
930C2×C4—224no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—442no—
934C2×C4—444no—
935C2×C4—444no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—444no—
939C2×C4—442no—
940C2×C4—442no—
941C2×C4—884no—
942C2×C4C2×D4×D1111yescharacteristic
943C2×C4C2×D4×D1111yescharacteristic
944C2×C4C2×D4×D1111yescharacteristic
945C2×C4C24×D1111yescharacteristic
946C8—24no—
947C8—224no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—24no—
955C22—21no—
956C22—21no—
957C22—48no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—82no—
964C22—114no—
965C22—162no—
966C22—222no—
967C22—222no—
968C22—444no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—442no—
975C22—884no—
976C22—8816no—
977C22—1762no—
978C22—1764no—
979C22D11×AGL(1,ℤ/8)12yes—
980C22C22×D4×D1111yescharacteristic
981C4—21no—
982C4—21no—
983C4—21no—
984C4—42no—
985C4—42no—
986C4—222no—
987C4—222no—
988C4—222no—
989C4—442no—
990C4—442no—
991C4C2×#6703712yes—
992C2—22no—
993C2—41no—
994C2—41no—
995C2—44no—
996C2—82no—
997C2—224no—
998C2—882no—
999C2—882no—
1000C2#1308224511yescharacteristic
1001C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1002C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#61569
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×#10623360C2semidirect
3. #13080578C2semidirect
4. #13080570C2semidirect
5. #13080099C2semidirect
6. #13080090C2semidirect
7. #13079602C2semidirect
8. #13079416C2semidirect
9. #13079413C2semidirect
10. #13079371C2semidirect
11. #13078702C2semidirect
12. #13077868C2semidirect
13. D11×#447C2semidirect
14. #13077643C2semidirect
15. C11×#3006C2semidirect
16. C22×C11×#41C22semidirect
18. C22×D4×D11C22semidirect
19. C2×C11×AGL(1,ℤ/8)C22semidirect
20. C2×C11×#121C22semidirect
23. #10623360C22semidirect
24. #10623360C22semidirect
25. C2×#67002C22semidirect
26. C2×#67000C22semidirect
27. C2×#66999C22semidirect
30. D4×C22⋊D11C22semidirect
32. C2×D4×Dic11C22semidirect
33. C2×#66983C22semidirect
34. C2×#66983C22semidirect
38. C2×D8×D11C22semidirect
39. #10623142C22semidirect
41. #10623140C22semidirect
45. #10623127C22semidirect
46. #10623038C22semidirect
48. C11×#449C22semidirect
49. C11×#448C22semidirect
50. C11×#447C22semidirect
51. C11×#417C22semidirect
52. C11×#407C22semidirect
53. #10622851C22semidirect
54. #10622845C22semidirect
55. #10622840C22semidirect
56. #10622830C22semidirect
57. #10622830C22semidirect
58. #10622820C22semidirect
59. #10622789C22semidirect
60. #10622784C22semidirect
61. #10622782C22semidirect
62. #10622778C22semidirect
63. #10622769C22semidirect
64. #10622765C22semidirect
65. #10622763C22semidirect
66. #10622748C22semidirect
67. #10622740C22semidirect
68. #10622652C22semidirect
69. #10622649C22semidirect
70. #10622647C22semidirect
71. #10622581C22semidirect
72. #10622432C22semidirect
73. #10622420C22semidirect
74. #10622418C22semidirect
75. #10622408C22semidirect
76. #10622398C22semidirect
77. #10622386C22semidirect
78. D11×#102C22semidirect
79. #10622374C22semidirect
80. #10622348C22semidirect
81. #10622348C22semidirect
82. #10622345C22semidirect
83. #10622345C22semidirect
84. #10622341C22semidirect
85. D11×C22⋊C8C22semidirect
86. #10622332C22semidirect
97. C22×D4×C11C23semidirect
117. C22×D44C23semidirect
120. C2×C11×SD16C23semidirect
122. C2×C11×M16C23semidirect
126. C11×#121C23semidirect
127. C2×C11×C4⋊C4C23semidirect
137. C2×#4325C23semidirect
138. #66993C23semidirect
152. D4×Dic11C23semidirect
162. #66983C23semidirect
179. C2×C4⋊Dic11C23semidirect
183. C2×#4318C23semidirect
190. #66946C23semidirect
192. #66941C23semidirect
201. C11×#103C23semidirect
204. C11×C22⋊C8C23semidirect
205. #66899C23semidirect
207. #66896C23semidirect
209. C22⋊(C11⋊C8)C23semidirect
211. #66885C23semidirect
213. #66881C23semidirect
214. #66879C23semidirect
215. Dic11⋊C8C23semidirect
217. #66872C23semidirect
363. #3006D11semidirect
397. C22×D11AGL(1,ℤ/8)semidirect
410. D4×C11H(5,𝔽2)semidirect
463. C22×#41C2×D11semidirect
466. C2×AGL(1,ℤ/8)C2×D11semidirect
489. C2×#121C2×D11semidirect
511. #449C2×D11semidirect
513. #448C2×D11semidirect
521. #447C2×D11semidirect
528. #417C2×D11semidirect
531. #407C2×D11semidirect
604. C22×D4C22×D11semidirect
612. C2×SD16C22×D11semidirect
619. C2×M16C22×D11semidirect
656. #121C22×D11semidirect
677. C2×C4⋊C4C22×D11semidirect
695. #103C22×D11semidirect
706. C22⋊C8C22×D11semidirect
851. C11#61569semidirect
913. D4#67037semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106233602
#130805782
#130805702
#130800992
#130800902
#130796022
#130794162
#130794132
#130793712
#130787022
#130778682
D11×#4472
#130776432
C11×#30062
#6156911