Finite Group Databasebeta

← #15638596

Subgroups — #15638596

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×#10623337C211yesmaximal, characteristic, complemented
3#13080581C214yesmaximal, complemented
4#13080573C214yesmaximal, complemented
5#13080096C214yesmaximal, complemented
6#13080089C214yesmaximal, complemented
7#13079600C212yesmaximal, complemented
8#13079414C212yesmaximal, complemented
9#13079374C211yesmaximal, characteristic, complemented
10#13079373C211yesmaximal, characteristic, complemented
11#13078702C212yesmaximal, complemented
12#13077863C212yesmaximal, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C2×C11×#447C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic, complemented
17C2×#67037—21no—
18C22×#4341C2211yescharacteristic, complemented
19C22×C11×D8C2212yescomplemented
20C2×C11×#121C2211yescharacteristic
21C2×#67006—21no—
22C22×C22⋊Dic11—21no—
23#10623337—22no—
24#10623337—22no—
25#10623337C2214yescomplemented
26#10623337C2214yescomplemented
27#10623335—21no—
28C2×#66992—21no—
29D4×C22⋊D11C2212yescomplemented
30C2×#66991C2211yescharacteristic, complemented
31C2×#66989C2211yescharacteristic, complemented
32C2×#66988—21no—
33C2×D4×Dic11C2211yescharacteristic, complemented
34C22×#4323C2212yescomplemented
35C2×#66983C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×#66977C2211yescharacteristic, complemented
38C2×#66964C2214yescomplemented
39#10623142C2212yescomplemented
40#10623141—22no—
41#10623140C2212yescomplemented
42#10623136—21no—
43D11×#121C2212yescomplemented
44#10623128—21no—
45#10623127C2212yescomplemented
46#10623038C2212yescomplemented
47#10623021—22no—
48C11×#447C2214yescomplemented
49C11×#447C2212yescomplemented
50C11×#447C2212yescomplemented
51C2×C11×#102C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622831C2212yescomplemented
54#10622830C2214yescomplemented
55#10622830C2212yescomplemented
56#10622830C2212yescomplemented
57C2×#66896C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622772C2214yescomplemented
60#10622771C2214yescomplemented
61#10622769C2214yescomplemented
62#10622767C2214yescomplemented
63#10622766C2214yescomplemented
64#10622765C2214yescomplemented
65#10622763C2214yescomplemented
66#10622727C2214yescomplemented
67#10622724C2214yescomplemented
68#10622654C2214yescomplemented
69#10622653C2212yescomplemented
70#10622647C2212yescomplemented
71#10622584C2212yescomplemented
72#10622400C2214yescomplemented
73#10622398C2214yescomplemented
74#10622395C2214yescomplemented
75#10622394C2214yescomplemented
76#10622390C2214yescomplemented
77#10622384C2214yescomplemented
78#10622378C2214yescomplemented
79#10622374C2214yescomplemented
80#10622351C2212yescomplemented
81#10622348C2212yescomplemented
82#10622344C2212yescomplemented
83#10622343C2214yescomplemented
84#10622339C2212yescomplemented
85#10622334C2212yescomplemented
86#10622332C2212yescomplemented
87C25×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—44no—
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2312yes—
95C22×D4×C11C2312yes—
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—22no—
103C22×C22⋊D11D411yescharacteristic
104C23×Dic11—21no—
105C23×Dic11—21no—
106#67037—48no—
107C2×#4341—22no—
108C2×#4341—22no—
109C2×#4341—22no—
110C2×#4341—44no—
111C2×#4341C2314yes—
112C2×D4×D11—22no—
113C2×D4×D11—22no—
114C2×D4×D11C2312yescomplemented
115C2×#4339—22no—
116C22×D44C2311yescharacteristic
117C22×C4×D11C2311yescharacteristic
118C22×Dic22C2311yescharacteristic
119C2×C11×D8—44no—
120C2×C11×D8C2314yes—
121C2×C11×D8C2314yes—
122C22×C8×C11C2312yes—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4—21no—
129#67006—24no—
130#67006—24no—
131#67006—22no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×C22⋊Dic11—21no—
137C2×C22⋊Dic11—24no—
138C2×C22⋊Dic11—24no—
139C2×C22⋊Dic11D411yescharacteristic
140#66993C2312yescomplemented
141#66992—22no—
142#66992—22no—
143#66992—24no—
144#66992—24no—
145#66992—22no—
146#66991—22no—
147#66991C2314yes—
148#66991C2312yescomplemented
149#66990—22no—
150#66990—22no—
151#66989—22no—
152#66989C2314yes—
153#66988—22no—
154#66988—24no—
155#66988—24no—
156D4×Dic11—22no—
157D4×Dic11C2314yes—
158D4×Dic11C2312yescomplemented
159C2×#4324C2314yescomplemented
160C2×#4323—44no—
161C2×#4323C2314yes—
162C2×#4323C2314yes—
163#66983—21no—
164#66983—21no—
165#66983C2312yes—
166#66983C2312yes—
167#66982—22no—
168C4×C22⋊D11D412yes—
169C4×C22⋊D11D412yes—
170C4×C22⋊D11C2312yes—
171C4×C22⋊D11C2312yes—
172C2×(C2×D11)⋊C4—21no—
173C2×(C2×D11)⋊C4D411yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176#66977—21no—
177#66977—21no—
178#66977C2312yes—
179#66977C2312yes—
180C2×Dic11⋊C4—21no—
181C2×Dic11⋊C4D411yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C22×C11⋊C8C2312yes—
184#66964—48no—
185C2×#4314C2314yescomplemented
186C2×#4313C2314yescomplemented
187#66949—22no—
188#66948C2312yescomplemented
189#66947—22no—
190#66946C2312yescomplemented
191C4⋊C4×D11C2312yescomplemented
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×#102C2314yes—
202C11×#102C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66896C2314yes—
206#66896C2314yes—
207#66896C2314yescomplemented
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yescomplemented
212#66881C2314yescomplemented
213#66880C2314yescomplemented
214#66879C2314yescomplemented
215Dic11⋊C8C2314yescomplemented
216#66874C2314yescomplemented
217#66872C2314yescomplemented
218#61569—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11—22no—
222C24×C11—22no—
223C24×C11—21no—
224C24×C11—44no—
225C24×C11—44no—
226C24×C11—82no—
227C24×C11C2×D411yescharacteristic
228C23×D11—21no—
229C23×D11—22no—
230C23×D11C2×D411yescharacteristic
231C2×D4×C11—24no—
232C2×D4×C11—24no—
233C2×D4×C11—24no—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—21no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—42no—
242C2×D4×C11—42no—
243C2×D4×C11—42no—
244C2×D4×C11—42no—
245C2×D4×C11—44no—
246C2×D4×C11—44no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11C2412yes—
250C2×D4×C11C2412yes—
251C2×D4×C11C2412yes—
252C22×C4×C11—21no—
253C22×C4×C11—42no—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—24no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267C2×C22⋊D11—24no—
268C2×C22⋊D11—24no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—48no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—82no—
273C2×C22⋊D11C2×D412yes—
274C2×C22⋊D11C2×D412yes—
275C22×Dic11—22no—
276C22×Dic11—24no—
277C22×Dic11—24no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—44no—
282C22×Dic11—82no—
283C22×Dic11C2×D411yescharacteristic
284C22×Dic11C2×D411yescharacteristic
285C22×Dic11C2×D411yescharacteristic
286#4341—28no—
287#4341—44no—
288#4341—48no—
289#4341—48no—
290#4341—48no—
291D4×D11—44no—
292D4×D11—48no—
293D4×D11—48no—
294#4339—48no—
295C2×D44—22no—
296C2×D44—21no—
297C2×D44—42no—
298C2×D44C2412yes—
299C2×C4×D11—22no—
300C2×C4×D11—22no—
301C2×C4×D11—42no—
302C2×C4×D11C2×D412yes—
303C2×C4×D11C2412yes—
304C2×Dic22—22no—
305C2×Dic22—21no—
306C2×Dic22—42no—
307C2×Dic22C2412yes—
308C11×D8—28no—
309C11×D8—44no—
310C2×C8×C11—42no—
311C2×C8×C11C2414yes—
312C11×C4⋊C4—21no—
313C11×C4⋊C4C2412yes—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321C22⋊Dic11—24no—
322C22⋊Dic11—22no—
323C22⋊Dic11—22no—
324C22⋊Dic11C2×D412yes—
325C22⋊Dic11C2×D412yes—
326#4324—44no—
327#4323—28no—
328#4323—44no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4C2×D412yes—
334(C2×D11)⋊C4C2×D412yes—
335C4⋊Dic11—21no—
336C4⋊Dic11—21no—
337C4⋊Dic11C2412yes—
338C4⋊Dic11C2412yes—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343Dic11⋊C4C2×D412yes—
344Dic11⋊C4C2×D412yes—
345C4×Dic11C2×D412yes—
346C4×Dic11C2412yes—
347C2×C11⋊C8—42no—
348C2×C11⋊C8C2414yes—
349#4314—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#3187—111no—
361#3109—112no—
362#3006—112no—
363C2×#447—111no—
364C2×#447D1111yescharacteristic, complemented
365#2973—111no—
366C23×C11—24no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—42no—
377C23×C11—42no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—42no—
381C23×C11—42no—
382C23×C11—82no—
383C23×C11—82no—
384C23×C11—81no—
385C23×C11—81no—
386C23×C11—816no—
387C23×C11AGL(1,ℤ/8)14yescomplemented
388C23×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—44no—
396C22×D11—42no—
397C22×D11—82no—
398C22×D11—82no—
399C22×D11—81no—
400C22×D11—81no—
401C22×D11C22×D412yes—
402D4×C11—24no—
403D4×C11—22no—
404D4×C11—22no—
405D4×C11—24no—
406D4×C11—22no—
407D4×C11—44no—
408D4×C11—44no—
409D4×C11—42no—
410D4×C11—44no—
411D4×C11—44no—
412D4×C11—81no—
413D4×C11H(5,𝔽2)14yescomplemented
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—42no—
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C2511yescharacteristic
426C22⋊D11—24no—
427C22⋊D11—24no—
428C22⋊D11—44no—
429C22⋊D11—48no—
430C22⋊D11—44no—
431C22⋊D11—44no—
432C22⋊D11—44no—
433C22⋊D11—82no—
434C22⋊D11—82no—
435C22⋊D11—84no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—48no—
443C2×Dic11—44no—
444C2×Dic11—42no—
445C2×Dic11—42no—
446C2×Dic11—42no—
447C2×Dic11—84no—
448C2×Dic11C22×D412yes—
449C2×Dic11C22×D412yes—
450C2×Dic11C22×D412yes—
451D44—24no—
452D44—44no—
453D44—81no—
454C4×D11—24no—
455C4×D11—42no—
456C4×D11—44no—
457C4×D11—44no—
458Dic22—24no—
459Dic22—44no—
460Dic22—42no—
461C8×C11—24no—
462C11⋊C8—24no—
463C2×H(5,𝔽2)—221no—
464C22×#41—111no—
465C23×D4C2×D1111yescharacteristic, complemented
466C2×AGL(1,ℤ/8)—114no—
467C22×D8—112no—
468C22×D8C2×D1112yescomplemented
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⋊Q8—111no—
486C2×#121—111no—
487C2×#121—111no—
488C2×#121—112no—
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#483—112no—
499#481—112no—
500#481—114no—
501#481—112no—
502#476—114no—
503#469—114no—
504#469—114no—
505#465—114no—
506#465—114no—
507#463—114no—
508#463—114no—
509#459—114no—
510#450—112no—
511#450—112no—
512#449—114no—
513#449—114no—
514#448—112no—
515#448—112no—
516#447—112no—
517#447—112no—
518#447—114no—
519#447—114no—
520#447C2×D1112yescomplemented
521#447C2×D1112yescomplemented
522#447C2×D1114yescomplemented
523#442—114no—
524#442—114no—
525#435—114no—
526#435—114no—
527#432—112no—
528#417—114no—
529C2×#102—112no—
530C2×#102C2×D1112yescomplemented
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—24no—
541C22×C11—44no—
542C22×C11—48no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—88no—
552C22×C11—88no—
553C22×C11—84no—
554C22×C11—162no—
555C22×C11C2×AGL(1,ℤ/8)12yes—
556C22×C11C2×AGL(1,ℤ/8)12yes—
557C22×C11C2×AGL(1,ℤ/8)12yes—
558C22×C11C23×D411yescharacteristic
559C2×D11—22no—
560C2×D11—22no—
561C2×D11—22no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11—42no—
565C2×D11—82no—
566C2×D11—164no—
567C2×D11—162no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—21no—
571C4×C11—42no—
572C4×C11C2×H(5,𝔽2)12yes—
573Dic11—22no—
574Dic11—22no—
575Dic11—22no—
576Dic11—42no—
577Dic11—42no—
578Dic11—42no—
579C25—21no—
580H(5,𝔽2)—448no—
581C2×#41—114no—
582C2×#41—222no—
583C2×#41—222no—
584C2×#41—222no—
585C2×#41—222no—
586C2×#41—444no—
587C22×Q8—111no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—44no—
593C22×D4—111no—
594C22×D4—112no—
595C22×D4—111no—
596C22×D4—222no—
597C22×D4—222no—
598C22×D4—222no—
599C22×D4—221no—
600C22×D4—221no—
601C22×D4—221no—
602C22×D4C22×D1111yescharacteristic
603C22×D4C22×D1112yes—
604C22×D4C22×D1112yes—
605C22×D4C22×D1111yescharacteristic
606C22×D4C22×D1111yescharacteristic
607C23×C4—111no—
608C23×C4—221no—
609C23×C4—221no—
610C23×C4C22×D1111yescharacteristic
611AGL(1,ℤ/8)—448no—
612C2×SD16—114no—
613C2×SD16—114no—
614C2×D8—44no—
615C2×D8—114no—
616C2×D8—114no—
617C2×D8—444no—
618C2×D8C22×D1114yes—
619C2×D8C22×D1114yes—
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—112no—
635C22⋊Q8—112no—
636C22⋊Q8—222no—
637C22⋊Q8—222no—
638C22⋊Q8—221no—
639C22⋊Q8—221no—
640#121—21no—
641#121—21no—
642#121—112no—
643#121—114no—
644#121—112no—
645#121—112no—
646#121—112no—
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—222no—
661#120—222no—
662#120—222no—
663#120—224no—
664#120—224no—
665C4×D4—112no—
666C4×D4—112no—
667C4×D4—112no—
668C4×D4—112no—
669C4×D4—114no—
670C4×D4—112no—
671C4×D4—112no—
672C4×D4—222no—
673C4×D4—222no—
674C2×C4⋊C4—111no—
675C2×C4⋊C4—111no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—221no—
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—111no—
682C2×C22⋊C4—111no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—224no—
685C2×C22⋊C4—224no—
686C2×C22⋊C4—221no—
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#106—114no—
695C4⋊C8—114no—
696#103—114no—
697#103—114no—
698#102—114no—
699#102—114no—
700#102—114no—
701#102—114no—
702#102C22×D1114yes—
703#102C22×D1114yes—
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—44no—
714C2×C11—82no—
715C2×C11—82no—
716C2×C11#348411yescharacteristic
717C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
718C2×C11#358511yescharacteristic
719D11—42no—
720D11—82no—
721C24—21no—
722C24—21no—
723C24—22no—
724C24—22no—
725C24—21no—
726C24—44no—
727C24—44no—
728C24—82no—
729C24—111no—
730C24—222no—
731C24—221no—
732C24D4×D1111yescharacteristic
733#41—228no—
734#41—448no—
735#41—444no—
736#41—448no—
737#41—448no—
738#41—448no—
739C2×Q8—112no—
740C2×Q8—222no—
741C2×Q8—221no—
742C2×Q8—442no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—112no—
762C2×D4—112no—
763C2×D4—112no—
764C2×D4—222no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—222no—
768C2×D4—224no—
769C2×D4—224no—
770C2×D4—222no—
771C2×D4—222no—
772C2×D4—222no—
773C2×D4—224no—
774C2×D4—221no—
775C2×D4—442no—
776C2×D4—444no—
777C2×D4—448no—
778C2×D4—448no—
779C2×D4—448no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4—882no—
783C2×D4C23×D1112yes—
784C2×D4C23×D1112yes—
785C2×D4C23×D1112yes—
786C22×C4—21no—
787C22×C4—42no—
788C22×C4—111no—
789C22×C4—111no—
790C22×C4—111no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—224no—
796C22×C4—222no—
797C22×C4—224no—
798C22×C4—221no—
799C22×C4—221no—
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—444no—
811SD16—444no—
812D8—28no—
813D8—44no—
814D8—228no—
815D8—444no—
816M16—444no—
817C2×C8—42no—
818C2×C8—114no—
819C2×C8—442no—
820C2×C8C23×D1114yes—
821C4⋊C4—21no—
822C4⋊C4—112no—
823C4⋊C4—112no—
824C4⋊C4—112no—
825C4⋊C4—112no—
826C4⋊C4—222no—
827C4⋊C4—222no—
828C4⋊C4—221no—
829C4⋊C4—221no—
830C4⋊C4—222no—
831C4⋊C4—222no—
832C4⋊C4C23×D1112yes—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—112no—
836C22⋊C4—112no—
837C22⋊C4—112no—
838C22⋊C4—112no—
839C22⋊C4—222no—
840C22⋊C4—222no—
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—24no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—41no—
859C23—41no—
860C23—44no—
861C23—44no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—44no—
867C23—44no—
868C23—42no—
869C23—42no—
870C23—82no—
871C23—82no—
872C23—81no—
873C23—81no—
874C23—816no—
875C23—112no—
876C23—222no—
877C23—222no—
878C23—441no—
879C23—441no—
880C23—444no—
881C23—442no—
882C23—881no—
883C23—881no—
884C23—882no—
885C23—882no—
886C23#6696414yescomplemented
887C23C2×D4×D1111yescharacteristic
888C23C2×D4×D1111yescharacteristic
889C23C2×D4×D1111yescharacteristic
890Q8—224no—
891Q8—442no—
892Q8—444no—
893D4—24no—
894D4—22no—
895D4—24no—
896D4—22no—
897D4—22no—
898D4—44no—
899D4—44no—
900D4—42no—
901D4—44no—
902D4—44no—
903D4—81no—
904D4—224no—
905D4—224no—
906D4—224no—
907D4—444no—
908D4—444no—
909D4—448no—
910D4—444no—
911D4—444no—
912D4—444no—
913D4—881no—
914D4—882no—
915D4—882no—
916D4—884no—
917D4#6703714yescomplemented
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
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—222no—
934C2×C4—442no—
935C2×C4—444no—
936C2×C4—444no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—448no—
940C2×C4—444no—
941C2×C4—442no—
942C2×C4—442no—
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—24no—
958C22—44no—
959C22—48no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—88no—
969C22—88no—
970C22—84no—
971C22—162no—
972C22—222no—
973C22—222no—
974C22—222no—
975C22—442no—
976C22—442no—
977C22—442no—
978C22—882no—
979C22—1762no—
980C22—1764no—
981C22C2×#6696412yes—
982C22C2×#6696412yes—
983C22C2×#6696412yes—
984C22C22×D4×D1111yescharacteristic
985C4—21no—
986C4—21no—
987C4—21no—
988C4—42no—
989C4—222no—
990C4—222no—
991C4—222no—
992C4—442no—
993C4—442no—
994C4—442no—
995C4C2×#6703712yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—44no—
1000C2—82no—
1001C2—82no—
1002C2—442no—
1003C2—882no—
1004C2#1308224511yescharacteristic
1005C2C22×#6696411yescharacteristic
1006C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC22×C11C23×D4
hypercenterC2×#447D11
hypocenterC11#61569
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #13082373C2semidirect
2. C2×#10623337C2semidirect
3. #13080581C2semidirect
4. #13080573C2semidirect
5. #13080096C2semidirect
6. #13080089C2semidirect
7. #13079600C2semidirect
8. #13079414C2semidirect
9. #13079374C2semidirect
10. #13079373C2semidirect
11. #13078702C2semidirect
12. #13077863C2semidirect
13. C2×#10622830C2semidirect
14. #13077642C2semidirect
15. C2×C11×#447C2semidirect
16. C23×D4×C11C22semidirect
18. C22×#4341C22semidirect
19. C22×C11×D8C22semidirect
25. #10623337C22semidirect
26. #10623337C22semidirect
29. D4×C22⋊D11C22semidirect
30. C2×#66991C22semidirect
31. C2×#66989C22semidirect
33. C2×D4×Dic11C22semidirect
34. C22×#4323C22semidirect
37. C2×#66977C22semidirect
38. C2×#66964C22semidirect
39. #10623142C22semidirect
41. #10623140C22semidirect
43. D11×#121C22semidirect
45. #10623127C22semidirect
46. #10623038C22semidirect
48. C11×#447C22semidirect
49. C11×#447C22semidirect
50. C11×#447C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622831C22semidirect
54. #10622830C22semidirect
55. #10622830C22semidirect
56. #10622830C22semidirect
57. C2×#66896C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622772C22semidirect
60. #10622771C22semidirect
61. #10622769C22semidirect
62. #10622767C22semidirect
63. #10622766C22semidirect
64. #10622765C22semidirect
65. #10622763C22semidirect
66. #10622727C22semidirect
67. #10622724C22semidirect
68. #10622654C22semidirect
69. #10622653C22semidirect
70. #10622647C22semidirect
71. #10622584C22semidirect
72. #10622400C22semidirect
73. #10622398C22semidirect
74. #10622395C22semidirect
75. #10622394C22semidirect
76. #10622390C22semidirect
77. #10622384C22semidirect
78. #10622378C22semidirect
79. #10622374C22semidirect
80. #10622351C22semidirect
81. #10622348C22semidirect
82. #10622344C22semidirect
83. #10622343C22semidirect
84. #10622339C22semidirect
85. #10622334C22semidirect
86. #10622332C22semidirect
114. C2×D4×D11C23semidirect
140. #66993C23semidirect
148. #66991C23semidirect
158. D4×Dic11C23semidirect
159. C2×#4324C23semidirect
185. C2×#4314C23semidirect
186. C2×#4313C23semidirect
188. #66948C23semidirect
190. #66946C23semidirect
191. C4⋊C4×D11C23semidirect
192. #66941C23semidirect
207. #66896C23semidirect
210. #66885C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. #66881C23semidirect
213. #66880C23semidirect
214. #66879C23semidirect
215. Dic11⋊C8C23semidirect
216. #66874C23semidirect
217. #66872C23semidirect
364. C2×#447D11semidirect
387. C23×C11AGL(1,ℤ/8)semidirect
413. D4×C11H(5,𝔽2)semidirect
465. C23×D4C2×D11semidirect
468. C22×D8C2×D11semidirect
520. #447C2×D11semidirect
521. #447C2×D11semidirect
522. #447C2×D11semidirect
530. C2×#102C2×D11semidirect
533. C2×C22⋊C8C2×D11semidirect
853. C11#61569semidirect
886. C23#66964semidirect
917. D4#67037semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106233372
#130805812
#130805732
#130800962
#130800892
#130796002
#130794142
#130793742
#130793732
#130787022
#130778632
C2×#106228302
#130776422
C2×C11×#4472
#6156911