Finite Group Databasebeta

← AGL(1,ℤ/8)×Dic22 #15634348

Subgroups — AGL(1,ℤ/8)×Dic22 #15634348

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081538C214yesmaximal, complemented
4#13081535C212yesmaximal, complemented
5#13081516C214yesmaximal, complemented
6#13081513C212yesmaximal, complemented
7SD16×Dic22C212yesmaximal, complemented
8D8×Dic22C212yesmaximal, complemented
9#13079162C211yesmaximal, characteristic, complemented
10#13079160C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic, complemented
12#13078427C212yesmaximal, complemented
13#13078413C211yesmaximal, characteristic, complemented
14#13078410C212yesmaximal, complemented
15M16×Dic22C211yesmaximal, characteristic, complemented
16AGL(1,ℤ/8)×Dic11C212yesmaximal
17C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
18C23×Dic22—21no—
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22#41×Dic11C2212yes—
23C2×D4×Dic11C2212yes—
24C2×#66977—21no—
25#10623101C2211yescharacteristic, complemented
26#10623100C2212yescomplemented
27Q8×Dic22C2211yescharacteristic, complemented
28#10623074—21no—
29#10623074C2211yescharacteristic, complemented
30#10623070—22no—
31#10623070C2212yescomplemented
32D4×Dic22—21no—
33D4×Dic22—21no—
34D4×Dic22—21no—
35D4×Dic22—22no—
36D4×Dic22C2212yes—
37D4×Dic22C2212yes—
38D4×Dic22C2214yes—
39D4×Dic22C2211yescharacteristic, complemented
40#10623048—22no—
41#10623048C2212yes—
42C2×#66941C2212yes—
43C2×#66931—22no—
44#10623001—21no—
45#10623001C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22—21no—
48C2×C4×Dic22C2211yescharacteristic
49C11×#442C2212yes—
50C11×#440C2212yes—
51C4×C11×SD16C2212yes—
52C4×C11×D8C2212yes—
53C11×#428C2211yescharacteristic
54C11×#418C2211yescharacteristic
55C11×#417C2211yescharacteristic
56C4×C11×M16C2211yescharacteristic
57#10622845C2212yes—
58#10622828C2212yes—
59#10622777C2214yes—
60SD16×Dic11C2214yes—
61#10622765C2214yes—
62D8×Dic11C2214yes—
63#10622734C2212yes—
64#10622734C2212yes—
65#10622731C2212yes—
66M16×Dic11C2212yes—
67#10622634C2212yescomplemented
68#10622633C2212yescomplemented
69#10622622C2214yes—
70#10622621C2212yes—
71#10622621C2212yescomplemented
72#10622620C2212yes—
73#10622620C2212yescomplemented
74#10622608C2212yes—
75#10622577C2212yes—
76#10622537C2211yescharacteristic
77#10622489C2214yescomplemented
78#10622487C2214yescomplemented
79#10622469C2214yescomplemented
80#10622468C2214yescomplemented
81#10622407C2214yescomplemented
82#10622404C2214yescomplemented
83#10622379C2214yes—
84#10622376C2214yes—
85#10622374C2214yes—
86#10622374C2214yescomplemented
87#10622372C2214yes—
88#10622372C2214yescomplemented
89#10622315C2214yescomplemented
90#10622314C2214yescomplemented
91#10622295C2212yescomplemented
92#10622293C2212yescomplemented
93#10622292C2212yescomplemented
94C8×Dic22C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×Dic11—22no—
99C22×Dic22—21no—
100C22×Dic22—22no—
101C22×Dic22—21no—
102C22×Dic22—22no—
103C22×Dic22—24no—
104C22×Dic22—22no—
105C22×Dic22—48no—
106C22×Dic22D411yescharacteristic
107C11×AGL(1,ℤ/8)Q818yescomplemented
108C2×C11×SD16C2312yes—
109C2×C11×D8C2312yes—
110C2×C11×M16C2311yescharacteristic
111C2×C11×M16C2311yescharacteristic
112C4×Q8×C11C2311yescharacteristic
113C4×Q8×C11C2311yescharacteristic
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11C2312yes—
119C4×D4×C11C2312yes—
120C4×D4×C11C2311yescharacteristic
121C4×D4×C11C2311yescharacteristic
122C11×#117—21no—
123C11×#117C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C42×C11—21no—
127C2×C42×C11C2311yescharacteristic
128C2×C22⋊Dic11—22no—
129Q8×Dic11C2312yes—
130Q8×Dic11C2312yes—
131D4×Dic11—22no—
132D4×Dic11—22no—
133D4×Dic11—22no—
134D4×Dic11—22no—
135D4×Dic11C2312yes—
136D4×Dic11C2314yes—
137D4×Dic11C2312yes—
138D4×Dic11C2314yes—
139#66979—22no—
140#66979C2312yes—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11D411yescharacteristic
144C2×C4⋊Dic11C2312yes—
145#66977—21no—
146#66977—21no—
147#66977—21no—
148#66977—21no—
149#66977—22no—
150#66977—22no—
151#66977—24no—
152#66977—22no—
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4D412yes—
156C2×C4×Dic11—22no—
157C2×C4×Dic11C2312yes—
158C2×#4318C2312yes—
159#66943—22no—
160#66943—22no—
161#66943C2312yes—
162#66943C2312yes—
163#66941—22no—
164#66941—22no—
165#66941—22no—
166#66941—22no—
167#66941C2312yes—
168#66941C2314yes—
169#66941C2314yes—
170#66941C2312yes—
171#66931—22no—
172#66931—22no—
173#66931—22no—
174#66931—22no—
175#66931—24no—
176#66931—24no—
177#66931—24no—
178#66931—24no—
179#66931—22no—
180#66931—22no—
181#66923—22no—
182#66923C2312yes—
183#66922—21no—
184#66922—21no—
185#66922—21no—
186#66922—21no—
187#66922C2312yes—
188#66922C2312yes—
189#66922C2311yescharacteristic
190#66922C2311yescharacteristic
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22—21no—
195C4×Dic22—22no—
196C4×Dic22—22no—
197C4×Dic22—22no—
198C4×Dic22D411yescharacteristic
199C4×Dic22D411yescharacteristic
200C4×Dic22D412yes—
201C4×Dic22C2311yescharacteristic
202C4×Dic22C2311yescharacteristic
203C4×Dic22C2312yes—
204C11×#107C2312yes—
205C11×#106C2312yes—
206C11×#103C2312yes—
207C11×#102C2312yes—
208C11×#102C2312yes—
209C11×#102C2312yes—
210C11×#97C2312yes—
211C4×C8×C11C2312yes—
212#66899C2314yes—
213#66896C2314yes—
214#66896C2314yes—
215#66896C2314yes—
216#66882C2314yes—
217#66882C2314yes—
218#66881C2314yes—
219#66881C2314yes—
220#66879C2314yes—
221Dic11⋊C8C2314yes—
222Dic11⋊C8C2314yes—
223C8×Dic11C2314yes—
224#66872C2314yes—
225#66872C2314yes—
226#66871C2314yes—
227#66871C2314yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230Q8×AGL(1,ℤ/8)—111nomaximal, Sylow
231C24×C11—21no—
232C11×#41—22no—
233C11×#41C2×Q814yescomplemented
234C2×Q8×C11C2411yescharacteristic
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—22no—
238C2×D4×C11C2×Q814yescomplemented
239C2×D4×C11C2412yes—
240C2×D4×C11C2411yescharacteristic
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—21no—
247C22×C4×C11—44no—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×Dic11—22no—
252C22×Dic11—24no—
253C22×Dic11—24no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—48no—
257C22×Dic11C2×D412yes—
258C22×Dic11C2×D412yes—
259C2×Dic22—24no—
260C2×Dic22—22no—
261C2×Dic22—24no—
262C2×Dic22—24no—
263C2×Dic22—22no—
264C2×Dic22—21no—
265C2×Dic22—22no—
266C2×Dic22—22no—
267C2×Dic22—21no—
268C2×Dic22—44no—
269C2×Dic22—416no—
270C2×Dic22—48no—
271C2×Dic22—48no—
272C2×Dic22—44no—
273C2×Dic22—48no—
274C2×Dic22C2×D411yescharacteristic
275C2×Dic22C2×D412yes—
276C2×Dic22C2×D411yescharacteristic
277C11×SD16C2×Q818yescomplemented
278C11×D8C2×Q818yescomplemented
279C11×M16—22no—
280C11×M16C2×Q814yescomplemented
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4C2411yescharacteristic
287C11×C4⋊C4C2412yes—
288C11×C4⋊C4C2411yescharacteristic
289C11×C22⋊C4—21no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11C2×D411yescharacteristic
298C42×C11C2×D411yescharacteristic
299C42×C11C2411yescharacteristic
300C42×C11C2411yescharacteristic
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303C22⋊Dic11—24no—
304C22⋊Dic11—24no—
305C22⋊Dic11—22no—
306C4⋊Dic11—22no—
307C4⋊Dic11—22no—
308C4⋊Dic11—22no—
309C4⋊Dic11—22no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11—22no—
313C4⋊Dic11—22no—
314C4⋊Dic11—22no—
315C4⋊Dic11C2×D411yescharacteristic
316C4⋊Dic11C2×D411yescharacteristic
317C4⋊Dic11C2×D412yes—
318C4⋊Dic11C2412yes—
319C4⋊Dic11C2414yes—
320C4⋊Dic11C2412yes—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—24no—
326Dic11⋊C4—24no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4C2×D412yes—
330Dic11⋊C4C2×D412yes—
331Dic11⋊C4C2×D412yes—
332Dic11⋊C4C2×D412yes—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11C2×D412yes—
337C4×Dic11C2×D412yes—
338C4×Dic11C2412yes—
339C4×Dic11C2412yes—
340#4318—24no—
341C2×C11⋊C8C2414yes—
342Q8×#41—111no—
343C2×D4×Q8—111no—
344#3386—114no—
345#3386—112no—
346#3384—114no—
347#3384—112no—
348Q8×SD16—112no—
349Q8×D8—112no—
350#3165—112no—
351#3165—111no—
352#3079—112no—
353#3079—111no—
354#3077—112no—
355#3077—111no—
356Q8×M16—111no—
357C4×AGL(1,ℤ/8)—112no—
358C4×AGL(1,ℤ/8)D1111yescharacteristic
359C23×C11—24no—
360C23×C11—21no—
361C23×C11—22no—
362C23×C11—42no—
363C23×C11—42no—
364C23×C11C22×D411yescharacteristic
365Q8×C11—21no—
366Q8×C11C22×Q812yescomplemented
367D4×C11—24no—
368D4×C11—24no—
369D4×C11—22no—
370D4×C11—21no—
371D4×C11C22×Q814yes—
372D4×C11C22×Q812yescomplemented
373C2×C4×C11—21no—
374C2×C4×C11—24no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—41no—
380C2×C4×C11—44no—
381C2×C4×C11—42no—
382C2×C4×C11—44no—
383C2×C4×C11—42no—
384C2×C4×C11—81no—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×Q812yes—
391C2×C4×C112−1+412yes—
392C2×C4×C11C2511yescharacteristic
393C2×Dic11—24no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—24no—
397C2×Dic11—42no—
398C2×Dic11—48no—
399C2×Dic11—44no—
400C2×Dic11—48no—
401C2×Dic11—44no—
402C2×Dic11—82no—
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405C2×Dic11C22×D412yes—
406C2×Dic11C22×D412yes—
407Dic22—22no—
408Dic22—24no—
409Dic22—48no—
410Dic22—44no—
411Dic22—42no—
412Dic22—44no—
413Dic22—44no—
414Dic22—48no—
415Dic22—82no—
416Dic22—81no—
417Dic22AGL(1,ℤ/8)14yesdirect product factor
418C8×C11—22no—
419C8×C11C22×Q814yescomplemented
420C11⋊C8—24no—
421C23×Q8—221no—
422C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
423Q82—111no—
424#557—112no—
425#557—111no—
426#554—112no—
427#554—111no—
428#554—222no—
429#554—221no—
430D4×Q8—111no—
431D4×Q8—112no—
432D4×Q8—114no—
433D4×Q8—112no—
434D4×Q8—221no—
435D4×Q8—221no—
436D4×Q8—222no—
437D4×Q8—221no—
438#533—112no—
439#533—111no—
440#533—221no—
441#533—222no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8—111no—
444C2×C22⋊Q8—222no—
445C2×C22⋊Q8—221no—
446C4×#41—112no—
447C4×#41C2×D1111yescharacteristic
448C2×C4×Q8—111no—
449C2×C4×Q8—221no—
450C2×C4×D4—112no—
451C2×C4×D4C2×D1111yescharacteristic
452#501—114no—
453#501—114no—
454#501—114no—
455#500—114no—
456#500—112no—
457#498—114no—
458#498—112no—
459#478—114no—
460#478—114no—
461#478—114no—
462#477—112no—
463#477—114no—
464#476—112no—
465#476—112no—
466#476—114no—
467#476—114no—
468#475—112no—
469#475—114no—
470#474—112no—
471#474—112no—
472#474—114no—
473#474—114no—
474#446—114no—
475#446—112no—
476C8×Q8—112no—
477#442—114no—
478#442C2×D1112yes—
479#440—114no—
480#440C2×D1112yes—
481C4×SD16—114no—
482C4×SD16C2×D1112yes—
483C4×D8—114no—
484C4×D8C2×D1112yes—
485#428—112no—
486#428—112no—
487#428—112no—
488#428—112no—
489#428C2×D1111yescharacteristic
490#423—112no—
491#423—111no—
492#418—112no—
493#418C2×D1111yescharacteristic
494#417—112no—
495#417C2×D1111yescharacteristic
496C4×M16—112no—
497C4×M16C2×D1111yescharacteristic
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—22no—
501C22×C11—24no—
502C22×C11—48no—
503C22×C11—41no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—41no—
507C22×C11D4×Q812yes—
508C22×C11C23×D411yescharacteristic
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—22no—
512C4×C11—21no—
513C4×C11—41no—
514C4×C11—42no—
515C4×C11—41no—
516C4×C11D4×Q812yes—
517C4×C11C2×AGL(1,ℤ/8)12yes—
518C4×C11C23×Q811yescharacteristic
519C4×C11C2×2−1+411yescharacteristic
520Dic11—22no—
521Dic11—22no—
522Dic11—22no—
523Dic11—42no—
524Dic11—44no—
525Dic11—42no—
526Dic11C2×AGL(1,ℤ/8)14yes—
527C2×#41C22×D1111yescharacteristic
528C22×Q8—111no—
529C22×Q8—222no—
530C22×Q8—221no—
531C22×Q8—222no—
532C22×Q8—224no—
533C22×Q8—222no—
534C22×Q8—221no—
535C22×Q8—448no—
536C22×D4C22×D1111yescharacteristic
537C23×C4—21no—
538C23×C4—222no—
539AGL(1,ℤ/8)Dic2218yesdirect product factor
540C2×SD16C22×D1112yes—
541C2×D8C22×D1112yes—
542C2×M16—112no—
543C2×M16C22×D1111yescharacteristic
544C2×M16C22×D1111yescharacteristic
545C4⋊Q8—114no—
546C4⋊Q8—114no—
547C4⋊Q8—112no—
548C4⋊Q8—112no—
549C4⋊Q8—112no—
550C4⋊Q8—112no—
551C4⋊Q8—111no—
552C4⋊Q8—111no—
553C4⋊Q8—221no—
554C4⋊Q8—221no—
555C4⋊Q8—222no—
556C4⋊Q8—222no—
557C4⋊Q8—222no—
558C4⋊Q8—222no—
559C4⋊Q8—221no—
560C4⋊Q8—221no—
561#125—112no—
562#125—112no—
563#125—112no—
564#125—222no—
565#125—222no—
566#125—222no—
567C22⋊Q8—224no—
568C22⋊Q8—224no—
569C22⋊Q8—224no—
570C22⋊Q8—224no—
571C22⋊Q8—222no—
572C22⋊Q8—222no—
573C22⋊Q8—222no—
574C22⋊Q8—222no—
575C22⋊Q8—222no—
576C22⋊Q8—222no—
577C22⋊Q8—222no—
578C22⋊Q8—224no—
579C22⋊Q8—222no—
580C22⋊Q8—221no—
581C22⋊Q8—222no—
582C22⋊Q8—221no—
583C22⋊Q8—221no—
584C22⋊Q8—221no—
585C4×Q8—111no—
586C4×Q8—112no—
587C4×Q8—111no—
588C4×Q8—111no—
589C4×Q8—112no—
590C4×Q8—111no—
591C4×Q8—112no—
592C4×Q8—112no—
593C4×Q8—222no—
594C4×Q8—222no—
595C4×Q8—222no—
596C4×Q8—221no—
597C4×Q8—221no—
598C4×Q8—221no—
599C4×Q8—221no—
600C4×Q8C22×D1111yescharacteristic
601C4×Q8C22×D1111yescharacteristic
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—114no—
607C4×D4—114no—
608C4×D4—112no—
609C4×D4—112no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4C22×D1112yes—
615C4×D4C22×D1112yes—
616C4×D4C22×D1111yescharacteristic
617C4×D4C22×D1111yescharacteristic
618#117—21no—
619#117—112no—
620#117—222no—
621#117C22×D1111yescharacteristic
622C2×C4⋊C4—112no—
623C2×C4⋊C4—111no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—222no—
626C2×C4⋊C4—221no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4—221no—
629C2×C4⋊C4C22×D1111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—222no—
632C2×C42—21no—
633C2×C42—112no—
634C2×C42—222no—
635C2×C42C22×D1111yescharacteristic
636#107—114no—
637#107—114no—
638#107—114no—
639#107—114no—
640#107C22×D1112yes—
641#106—114no—
642#106—114no—
643#106—114no—
644#106—114no—
645#106C22×D1112yes—
646C4⋊C8—114no—
647C4⋊C8—114no—
648C4⋊C8—112no—
649C4⋊C8—112no—
650#103—114no—
651#103C22×D1112yes—
652#102—114no—
653#102—114no—
654#102—114no—
655#102C22×D1112yes—
656#102C22×D1112yes—
657#102C22×D1112yes—
658#97—114no—
659#97C22×D1112yes—
660C4×C8—114no—
661C4×C8C22×D1112yes—
662C2×C11—22no—
663C2×C11—42no—
664C2×C11—44no—
665C2×C11C2×D4×Q811yescharacteristic
666C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
667C2×C11#358611yescharacteristic
668C24—21no—
669#41—22no—
670#41C2×Dic2214yescomplemented
671C2×Q8—111no—
672C2×Q8—112no—
673C2×Q8—111no—
674C2×Q8—222no—
675C2×Q8—224no—
676C2×Q8—224no—
677C2×Q8—222no—
678C2×Q8—224no—
679C2×Q8—221no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—221no—
683C2×Q8—444no—
684C2×Q8—448no—
685C2×Q8—448no—
686C2×Q8—444no—
687C2×Q8—4416no—
688C2×Q8—448no—
689C2×Q8C23×D1111yescharacteristic
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—22no—
693C2×D4C2×Dic2214yescomplemented
694C2×D4C23×D1112yes—
695C2×D4C23×D1111yescharacteristic
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—44no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—222no—
706C22×C4—224no—
707C22×C4—224no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—448no—
711C22×C4D4×D1111yescharacteristic
712C22×C4D4×D1111yescharacteristic
713C22×C4C23×D1111yescharacteristic
714SD16C2×Dic2218yescomplemented
715D8C2×Dic2218yescomplemented
716M16—22no—
717M16—224no—
718M16C2×Dic2214yescomplemented
719C2×C8—114no—
720C2×C8C23×D1112yes—
721C2×C8C23×D1112yes—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—112no—
726C4⋊C4—111no—
727C4⋊C4—112no—
728C4⋊C4—112no—
729C4⋊C4—112no—
730C4⋊C4—112no—
731C4⋊C4—111no—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—114no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—221no—
748C4⋊C4—222no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—221no—
752C4⋊C4C23×D1111yescharacteristic
753C4⋊C4C23×D1111yescharacteristic
754C4⋊C4C23×D1112yes—
755C22⋊C4—21no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—222no—
763C22⋊C4—222no—
764C22⋊C4—222no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—112no—
769C42—112no—
770C42—112no—
771C42—112no—
772C42—222no—
773C42—222no—
774C42—222no—
775C42D4×D1111yescharacteristic
776C42D4×D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C42C23×D1111yescharacteristic
779C11Q8×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
780C23—24no—
781C23—21no—
782C23—22no—
783C23—42no—
784C23—42no—
785C23C2×D4×D1111yescharacteristic
786Q8—21no—
787Q8—114no—
788Q8—224no—
789Q8—222no—
790Q8—444no—
791Q8—448no—
792Q8—444no—
793Q8—448no—
794Q8—444no—
795Q8—442no—
796Q8—881no—
797Q8—882no—
798Q8C22×Dic2212yescomplemented
799D4—24no—
800D4—24no—
801D4—22no—
802D4—21no—
803D4C22×Dic2214yes—
804D4C22×Dic2212yescomplemented
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—41no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—81no—
817C2×C4—112no—
818C2×C4—112no—
819C2×C4—112no—
820C2×C4—112no—
821C2×C4—224no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—224no—
825C2×C4—448no—
826C2×C4—444no—
827C2×C4—442no—
828C2×C4—448no—
829C2×C4—444no—
830C2×C4—882no—
831C2×C4C22×Dic2212yes—
832C2×C4C2×D4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4C2×D4×D1111yescharacteristic
836C2×C4C2×D4×D1111yescharacteristic
837C2×C4#6704312yes—
838C2×C4C24×D1111yescharacteristic
839C8—22no—
840C8—224no—
841C8C22×Dic2214yescomplemented
842C22—21no—
843C22—21no—
844C22—22no—
845C22—24no—
846C22—48no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22D4×Dic2212yes—
852C22C22×D4×D1111yescharacteristic
853C4—21no—
854C4—21no—
855C4—21no—
856C4—22no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—114no—
861C4—222no—
862C4—222no—
863C4—222no—
864C4—442no—
865C4—444no—
866C4—442no—
867C4D4×Dic2212yes—
868C4D11×AGL(1,ℤ/8)12yes—
869C4C23×Dic2211yescharacteristic
870C4C2×#6704311yescharacteristic
871C2—22no—
872C2—44no—
873C2—42no—
874C2C2×D4×Dic2211yescharacteristic
875C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
876C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
prime radicalC2×C11×AGL(1,ℤ/8)C22
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×Dic22C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081538C2semidirect
4. #13081535C2semidirect
5. #13081516C2semidirect
6. #13081513C2semidirect
7. SD16×Dic22C2semidirect
8. D8×Dic22C2semidirect
9. #13079162C2semidirect
10. #13079160C2semidirect
11. #13078431C2semidirect
12. #13078427C2semidirect
13. #13078413C2semidirect
14. #13078410C2semidirect
15. M16×Dic22C2semidirect
25. #10623101C22semidirect
26. #10623100C22semidirect
27. Q8×Dic22C22semidirect
29. #10623074C22semidirect
31. #10623070C22semidirect
39. D4×Dic22C22semidirect
67. #10622634C22semidirect
68. #10622633C22semidirect
71. #10622621C22semidirect
73. #10622620C22semidirect
77. #10622489C22semidirect
78. #10622487C22semidirect
79. #10622469C22semidirect
80. #10622468C22semidirect
81. #10622407C22semidirect
82. #10622404C22semidirect
86. #10622374C22semidirect
88. #10622372C22semidirect
89. #10622315C22semidirect
90. #10622314C22semidirect
91. #10622295C22semidirect
92. #10622293C22semidirect
93. #10622292C22semidirect
94. C8×Dic22C22semidirect
107. C11×AGL(1,ℤ/8)Q8semidirect
233. C11×#41C2×Q8semidirect
238. C2×D4×C11C2×Q8semidirect
277. C11×SD16C2×Q8semidirect
278. C11×D8C2×Q8semidirect
280. C11×M16C2×Q8semidirect
366. Q8×C11C22×Q8semidirect
372. D4×C11C22×Q8semidirect
417. Dic22AGL(1,ℤ/8)direct (N × H)
419. C8×C11C22×Q8semidirect
539. AGL(1,ℤ/8)Dic22direct (N × H)
670. #41C2×Dic22semidirect
693. C2×D4C2×Dic22semidirect
714. SD16C2×Dic22semidirect
715. D8C2×Dic22semidirect
718. M16C2×Dic22semidirect
779. C11Q8×AGL(1,ℤ/8)semidirect
798. Q8C22×Dic22semidirect
804. D4C22×Dic22semidirect
841. C8C22×Dic22semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
C2×D4×Dic222
#130815382
#130815352
#130815162
#130815132
SD16×Dic222
D8×Dic222
#130791622
#130791602
#130784312
#130784272
#130784132
#130784102
M16×Dic222
AGL(1,ℤ/8)×Dic112
C4×C11×AGL(1,ℤ/8)2
Q8×AGL(1,ℤ/8)11