Finite Group Databasebeta

← #15632556

Subgroups — #15632556

Order 2816.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13081213C212yesmaximal, complemented
4#13081202C212yesmaximal, complemented
5#13081091C214yesmaximal, complemented
6#13081061C214yesmaximal, complemented
7#13080975C212yesmaximal, complemented
8#13080965C212yesmaximal, complemented
9#13079162C211yesmaximal, characteristic, complemented
10#13078554C212yesmaximal, complemented
11#13078537C212yesmaximal, complemented
12#13078431C211yesmaximal, characteristic, complemented
13#13078413C211yesmaximal, characteristic, complemented
14#13078229C212yesmaximal, complemented
15M16×D44C211yesmaximal, characteristic, complemented
16D11×#428C212yesmaximal, complemented
17C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
18C22×#4339—21no—
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22#10623359C2212yes—
23C2×#66991C2212yes—
24C2×#66977—21no—
25C2×M16×D11C2212yes—
26#10623115C2211yescharacteristic, complemented
27#10623112C2212yescomplemented
28#10623110C2211yescharacteristic, complemented
29#10623094C2211yescharacteristic, complemented
30#10623089C2212yescomplemented
31#10623087—22no—
32#10623082—21no—
33#10623082—21no—
34#10623082—22no—
35#10623082C2214yes—
36#10623082C2212yes—
37#10623082C2212yes—
38#10623082C2211yescharacteristic, complemented
39#10623081—21no—
40#10623072—21no—
41#10623059—22no—
42D11×#117C2212yes—
43C2×C4⋊C4×D11C2212yes—
44C2×#66936—22no—
45#10623010—21no—
46C4×#4339—21no—
47C2×C4×D44C2211yescharacteristic
48#10623001C2211yescharacteristic
49C2×#66922C2211yescharacteristic
50C11×#442C2212yescomplemented
51C11×#440C2212yescomplemented
52C4×C11×SD16C2212yescomplemented
53C4×C11×D8C2212yescomplemented
54C11×#428C2211yescharacteristic
55C11×#418C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C4×C11×M16C2211yescharacteristic
58#10622845C2212yes—
59#10622828C2212yes—
60#10622787C2214yescomplemented
61#10622784C2214yescomplemented
62#10622772C2214yescomplemented
63#10622770C2214yescomplemented
64#10622739C2212yes—
65#10622734C2212yes—
66#10622734C2212yes—
67#10622634C2212yescomplemented
68#10622633C2212yescomplemented
69#10622622C2214yescomplemented
70#10622621C2212yescomplemented
71#10622621C2212yescomplemented
72#10622620C2212yescomplemented
73#10622620C2212yescomplemented
74#10622608C2212yes—
75#10622577C2212yes—
76#10622537C2211yescharacteristic
77#10622494C2214yescomplemented
78D11×#107C2214yescomplemented
79#10622474C2214yescomplemented
80D11×#106C2214yescomplemented
81#10622422C2214yescomplemented
82#10622418C2214yescomplemented
83#10622397C2214yescomplemented
84#10622392C2214yescomplemented
85#10622390C2214yescomplemented
86#10622390C2214yescomplemented
87#10622387C2214yescomplemented
88#10622387C2214yescomplemented
89#10622319C2214yescomplemented
90#10622315C2214yescomplemented
91#10622301C2212yescomplemented
92C8×D44C2212yescomplemented
93#10622295C2212yescomplemented
94#10622293C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C22×C22⋊D11—22no—
99C2×#4339—21no—
100C2×#4339—22no—
101C2×#4339—24no—
102C2×#4339—22no—
103C2×#4339—48no—
104C22×D44D411yescharacteristic
105C22×C4×D11—22no—
106C22×C4×D11C2312yes—
107C22×Dic22—21no—
108C11×AGL(1,ℤ/8)—24no—
109C2×C11×SD16C2312yes—
110C2×C11×D8C2312yes—
111C2×C11×M16C2311yescharacteristic
112C2×C11×M16C2311yescharacteristic
113C4×Q8×C11C2311yescharacteristic
114C4×Q8×C11C2311yescharacteristic
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11C2312yes—
120C4×D4×C11C2312yes—
121C4×D4×C11C2311yescharacteristic
122C4×D4×C11C2311yescharacteristic
123C11×#117—21no—
124C11×#117C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C2×C22⋊Dic11—22no—
130#66999C2312yes—
131#66999C2312yes—
132#66991—22no—
133#66991—22no—
134#66991C2312yes—
135#66991C2314yes—
136#66991C2312yes—
137#66991C2314yes—
138#66990—22no—
139#66988—22no—
140#66983—21no—
141#66982—22no—
142C4×C22⋊D11—22no—
143C4×C22⋊D11—22no—
144C4×C22⋊D11—22no—
145C2×(C2×D11)⋊C4D412yes—
146#66979—21no—
147#66979C2312yes—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11D411yescharacteristic
150C2×C4⋊Dic11C2312yes—
151#66977—21no—
152#66977—21no—
153#66977—21no—
154#66977—22no—
155#66977—22no—
156#66977—24no—
157C2×Dic11⋊C4—22no—
158C2×#4318C2312yes—
159M16×D11—28no—
160C2×#4313C2314yes—
161C2×C8×D11C2314yes—
162#66951—22no—
163#66949—22no—
164#66947—22no—
165#66945C2312yes—
166#66945C2312yes—
167C4⋊C4×D11—22no—
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2312yes—
170C4⋊C4×D11C2314yes—
171C4⋊C4×D11C2314yes—
172C4⋊C4×D11C2312yes—
173#66942—22no—
174#66938—22no—
175#66937—22no—
176#66936—24no—
177#66936—24no—
178#66936—24no—
179#66936—24no—
180#66936—22no—
181C22⋊C4×D11—22no—
182#66932—22no—
183#66930—22no—
184#66929—22no—
185#66928—21no—
186C4×D44—21no—
187C4×D44D411yescharacteristic
188C4×D44D411yescharacteristic
189C4×D44D412yes—
190C4×D44C2311yescharacteristic
191C4×D44C2311yescharacteristic
192C4×D44C2312yes—
193#66925—22no—
194#66925—22no—
195C42×D11—22no—
196#66923—21no—
197#66923C2312yes—
198#66922—21no—
199#66922—21no—
200#66922C2312yes—
201#66922C2312yes—
202#66922C2311yescharacteristic
203#66922C2311yescharacteristic
204C4×Dic22—21no—
205C4×Dic22—21no—
206C4×Dic22—21no—
207C11×#107C2312yes—
208C11×#106C2312yes—
209C11×#103C2312yes—
210C11×#102C2312yes—
211C11×#102C2312yes—
212C11×#102C2312yes—
213C11×#97C2312yes—
214C4×C8×C11C2312yes—
215#66899C2314yes—
216#66896C2314yes—
217#66896C2314yes—
218#66896C2314yes—
219(C2×D11)⋊C8C2314yes—
220(C2×D11)⋊C8C2314yes—
221#66882C2314yes—
222#66882C2314yes—
223#66881C2314yes—
224#66881C2314yes—
225#66872C2314yes—
226#66872C2314yes—
227#66871C2314yes—
228#66871C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#61252—111nomaximal, Sylow
232C24×C11—21no—
233C23×D11C2×D412yes—
234C11×#41—22no—
235C11×#41—22no—
236C2×Q8×C11C2411yescharacteristic
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11C2411yescharacteristic
242C2×D4×C11C2412yes—
243C22×C4×C11—21no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—44no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—48no—
258C22×Dic11—22no—
259C22×Dic11C2×D412yes—
260#4339—416no—
261#4339—48no—
262#4339—44no—
263#4339—48no—
264C2×D44—24no—
265C2×D44C2×D411yescharacteristic
266C2×D44C2×D412yes—
267C2×D44C2×D411yescharacteristic
268C2×C4×D11—22no—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—22no—
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—48no—
275C2×C4×D11C2×D412yes—
276C2×C4×D11C2×D412yes—
277C2×C4×D11C2412yes—
278C2×C4×D11C2412yes—
279C2×Dic22—21no—
280C2×Dic22—22no—
281C2×Dic22—22no—
282C2×Dic22—21no—
283C2×Dic22—44no—
284C11×SD16—24no—
285C11×D8—24no—
286C11×M16—22no—
287C11×M16#4114yescomplemented
288C2×C8×C11C2412yes—
289C2×C8×C11C2412yes—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4C2411yescharacteristic
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2411yescharacteristic
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—21no—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306C42×C11C2411yescharacteristic
307C42×C11C2411yescharacteristic
308C22⋊Dic11—22no—
309C22⋊Dic11—22no—
310C22⋊Dic11—24no—
311C22⋊Dic11—24no—
312C22⋊Dic11—22no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4C2×D412yes—
318(C2×D11)⋊C4C2×D412yes—
319(C2×D11)⋊C4C2×D412yes—
320(C2×D11)⋊C4C2×D412yes—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11C2×D411yescharacteristic
327C4⋊Dic11C2×D411yescharacteristic
328C4⋊Dic11C2×D412yes—
329C4⋊Dic11C2412yes—
330C4⋊Dic11C2414yes—
331C4⋊Dic11C2412yes—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343#4318—24no—
344C2×C11⋊C8C2414yes—
345#4313—28no—
346C8×D11—28no—
347#3475—111no—
348C2×#547—111no—
349#3354—112no—
350#3353—112no—
351#3345—114no—
352#3343—114no—
353#3335—112no—
354#3334—112no—
355#3165—111no—
356#3094—112no—
357#3092—112no—
358#3079—111no—
359#3077—111no—
360#3055—112no—
361C4×AGL(1,ℤ/8)D1111yescharacteristic, complemented
362D4×M16—111no—
363C2×#428—112no—
364C23×C11—21no—
365C23×C11—22no—
366C23×C11—42no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11C22×D411yescharacteristic
370C22×D11—24no—
371C22×D11—24no—
372C22×D11—42no—
373C22×D11C22×D412yes—
374C22×D11C22×D412yes—
375Q8×C11—21no—
376Q8×C11—21no—
377D4×C11—21no—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—21no—
381D4×C11—42no—
382D4×C11—42no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—41no—
389C2×C4×C11—44no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11—44no—
393C2×C4×C11—42no—
394C2×C4×C11—81no—
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C2×#4112yes—
401C2×C4×C112−1+412yes—
402C2×C4×C11C2511yescharacteristic
403C22⋊D11—48no—
404C22⋊D11—48no—
405C22⋊D11—44no—
406C22⋊D11—82no—
407C2×Dic11—24no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—24no—
411C2×Dic11—44no—
412C2×Dic11C22×D412yes—
413C2×Dic11C22×D412yes—
414D44—24no—
415D44—22no—
416D44AGL(1,ℤ/8)14yescomplemented
417C4×D11—24no—
418C4×D11—24no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—22no—
422C4×D11—22no—
423C4×D11—48no—
424C4×D11—48no—
425C4×D11—44no—
426C4×D11—82no—
427Dic22—44no—
428Dic22—44no—
429Dic22—42no—
430Dic22—81no—
431C8×C11—22no—
432C8×C11C2×#4114yescomplemented
433C11⋊C8—24no—
434C22×#41—221no—
435C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
436C22×M16—112no—
437#556—111no—
438#555—111no—
439#554—111no—
440#553—112no—
441#552—112no—
442#552—221no—
443#551—222no—
444#547—111no—
445#547—112no—
446#547—114no—
447#547—112no—
448#547—221no—
449#547—222no—
450#547—221no—
451#546—221no—
452#533—111no—
453C2×C4⋊Q8—111no—
454#529—221no—
455#529—222no—
456#525—112no—
457C2×#123—222no—
458C2×C22⋊Q8—221no—
459C2×#121—112no—
460C4×#41—221no—
461C4×#41C2×D1111yescharacteristic
462C2×C4×D4—111no—
463C2×C4×D4C2×D1111yescharacteristic
464C2×#117—112no—
465C22×C4⋊C4—112no—
466#501—114no—
467#500—112no—
468#498—112no—
469#484—114no—
470#483—114no—
471#482—114no—
472#482—114no—
473#481—114no—
474#481—114no—
475#480—114no—
476#480—114no—
477#478—114no—
478#477—112no—
479#476—112no—
480#476—112no—
481#475—112no—
482#474—112no—
483#474—112no—
484#469—114no—
485#468—114no—
486#466—114no—
487#465—114no—
488#442C2×D1112yescomplemented
489#440C2×D1112yescomplemented
490C4×SD16C2×D1112yescomplemented
491C4×D8C2×D1112yescomplemented
492#436—112no—
493#435—114no—
494C8×D4—112no—
495#428—112no—
496#428—112no—
497#428—112no—
498#428—112no—
499#428—114no—
500#428—114no—
501#428C2×D1111yescharacteristic
502C2×#107—114no—
503C2×#106—114no—
504#423—111no—
505#418—112no—
506#418C2×D1111yescharacteristic
507#417—112no—
508#417C2×D1111yescharacteristic
509#407—112no—
510C4×M16C2×D1111yescharacteristic
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—41no—
514C22×C11—42no—
515C22×C11—41no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—41no—
519C22×C11—84no—
520C22×C11#54712yes—
521C22×C11C23×D411yescharacteristic
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—22no—
525C2×D11—22no—
526C2×D11—22no—
527C2×D11—48no—
528C2×D11C2×AGL(1,ℤ/8)14yes—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—21no—
532C4×C11—41no—
533C4×C11—41no—
534C4×C11—42no—
535C4×C11—41no—
536C4×C11#54712yes—
537C4×C11C2×AGL(1,ℤ/8)12yes—
538C4×C11C22×#4111yescharacteristic
539C4×C11C2×2−1+411yescharacteristic
540Dic11—22no—
541Dic11—22no—
542Dic11—42no—
543Dic11—44no—
544Dic11—42no—
545C2×#41—221no—
546C2×#41—222no—
547C2×#41—224no—
548C2×#41—222no—
549C2×#41—448no—
550C2×#41C22×D1111yescharacteristic
551C22×Q8—221no—
552C22×D4—111no—
553C22×D4—222no—
554C22×D4C22×D1111yescharacteristic
555C23×C4—21no—
556C23×C4—112no—
557C23×C4—222no—
558AGL(1,ℤ/8)—24no—
559C2×SD16C22×D1112yes—
560C2×D8C22×D1112yes—
561C2×M16—112no—
562C2×M16—114no—
563C2×M16—228no—
564C2×M16C22×D1111yescharacteristic
565C2×M16C22×D1111yescharacteristic
566C22×C8—114no—
567C4⋊Q8—112no—
568C4⋊Q8—112no—
569C4⋊Q8—111no—
570C4⋊Q8—111no—
571C4⋊Q8—221no—
572C4⋊Q8—221no—
573#126—222no—
574#126—222no—
575#126—222no—
576#125—112no—
577#125—221no—
578#125—222no—
579#124—221no—
580#124—222no—
581#123—224no—
582#123—224no—
583#123—224no—
584#123—224no—
585#123—222no—
586#123—222no—
587#123—222no—
588#123—222no—
589C22⋊Q8—112no—
590C22⋊Q8—112no—
591C22⋊Q8—222no—
592C22⋊Q8—222no—
593C22⋊Q8—222no—
594C22⋊Q8—224no—
595C22⋊Q8—221no—
596C22⋊Q8—221no—
597C22⋊Q8—221no—
598#121—114no—
599#121—114no—
600#121—112no—
601#121—112no—
602#121—222no—
603#121—221no—
604#121—222no—
605#121—222no—
606#120—222no—
607C4×Q8—221no—
608C4×Q8—221no—
609C4×Q8—221no—
610C4×Q8C22×D1111yescharacteristic
611C4×Q8C22×D1111yescharacteristic
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—111no—
617C4×D4—111no—
618C4×D4—112no—
619C4×D4—111no—
620C4×D4—112no—
621C4×D4—111no—
622C4×D4—221no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4C22×D1112yes—
627C4×D4C22×D1112yes—
628C4×D4C22×D1111yescharacteristic
629C4×D4C22×D1111yescharacteristic
630#117—21no—
631#117—112no—
632#117—112no—
633#117—112no—
634#117—222no—
635#117—222no—
636#117—222no—
637#117—221no—
638#117C22×D1111yescharacteristic
639C2×C4⋊C4—111no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—222no—
646C2×C4⋊C4—222no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4—221no—
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C22⋊C4—21no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C42—21no—
655C2×C42—222no—
656C2×C42C22×D1111yescharacteristic
657#107—114no—
658#107—114no—
659#107—114no—
660#107—114no—
661#107C22×D1112yes—
662#106—114no—
663#106—114no—
664#106—114no—
665#106—114no—
666#106C22×D1112yes—
667C4⋊C8—112no—
668C4⋊C8—112no—
669#103—114no—
670#103C22×D1112yes—
671#102—114no—
672#102—114no—
673#102—114no—
674#102C22×D1112yes—
675#102C22×D1112yes—
676#102C22×D1112yes—
677C22⋊C8—114no—
678C22⋊C8—114no—
679#97C22×D1112yes—
680C4×C8C22×D1112yes—
681C2×C11—22no—
682C2×C11—81no—
683C2×C11—82no—
684C2×C11C2×#54711yescharacteristic
685C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
686C2×C11#358611yescharacteristic
687D11—24no—
688D11—42no—
689C24—21no—
690C24—112no—
691#41—22no—
692#41—22no—
693#41—448no—
694#41—444no—
695#41—4416no—
696#41—448no—
697C2×Q8—221no—
698C2×Q8—222no—
699C2×Q8—222no—
700C2×Q8—221no—
701C2×Q8—444no—
702C2×Q8C23×D1111yescharacteristic
703C2×D4—21no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—22no—
707C2×D4—111no—
708C2×D4—112no—
709C2×D4—111no—
710C2×D4—224no—
711C2×D4—222no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—222no—
715C2×D4—448no—
716C2×D4C23×D1111yescharacteristic
717C2×D4C23×D1112yes—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—44no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—222no—
731C22×C4—224no—
732C22×C4—224no—
733C22×C4—222no—
734C22×C4—224no—
735C22×C4—224no—
736C22×C4—222no—
737C22×C4—448no—
738C22×C4D4×D1111yescharacteristic
739C22×C4D4×D1111yescharacteristic
740C22×C4C23×D1111yescharacteristic
741SD16—24no—
742D8—24no—
743M16—22no—
744M16—224no—
745M16—228no—
746M16#433914yescomplemented
747C2×C8—114no—
748C2×C8—228no—
749C2×C8C23×D1112yes—
750C2×C8C23×D1112yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—111no—
755C4⋊C4—111no—
756C4⋊C4—112no—
757C4⋊C4—112no—
758C4⋊C4—112no—
759C4⋊C4—114no—
760C4⋊C4—224no—
761C4⋊C4—224no—
762C4⋊C4—222no—
763C4⋊C4—222no—
764C4⋊C4—222no—
765C4⋊C4—222no—
766C4⋊C4—222no—
767C4⋊C4—222no—
768C4⋊C4—222no—
769C4⋊C4—221no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—221no—
773C4⋊C4C23×D1111yescharacteristic
774C4⋊C4C23×D1111yescharacteristic
775C4⋊C4C23×D1112yes—
776C22⋊C4—21no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—112no—
782C22⋊C4—112no—
783C22⋊C4—112no—
784C22⋊C4—112no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—222no—
792C22⋊C4—222no—
793C22⋊C4—222no—
794C42—21no—
795C42—21no—
796C42—21no—
797C42—222no—
798C42—222no—
799C42—222no—
800C42D4×D1111yescharacteristic
801C42D4×D1111yescharacteristic
802C42C23×D1111yescharacteristic
803C42C23×D1111yescharacteristic
804C11#6125211yescharacteristic, complemented, Sylow
805C23—21no—
806C23—22no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—112no—
811C23—112no—
812C23—224no—
813C23—224no—
814C23—442no—
815C23C2×D4×D1111yescharacteristic
816Q8—21no—
817Q8—21no—
818Q8—444no—
819Q8—444no—
820Q8—442no—
821Q8—881no—
822D4—21no—
823D4—22no—
824D4—22no—
825D4—21no—
826D4—42no—
827D4—42no—
828D4—114no—
829D4—224no—
830D4—222no—
831D4—448no—
832D4—444no—
833D4—448no—
834D4—882no—
835C2×C4—22no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—41no—
841C2×C4—44no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—81no—
847C2×C4—112no—
848C2×C4—112no—
849C2×C4—224no—
850C2×C4—224no—
851C2×C4—224no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—224no—
859C2×C4—448no—
860C2×C4—444no—
861C2×C4—448no—
862C2×C4—444no—
863C2×C4—882no—
864C2×C4C2×#433912yes—
865C2×C4C2×D4×D1111yescharacteristic
866C2×C4C2×D4×D1111yescharacteristic
867C2×C4C2×D4×D1111yescharacteristic
868C2×C4C2×D4×D1111yescharacteristic
869C2×C4C2×D4×D1111yescharacteristic
870C2×C4#6704312yes—
871C2×C4C24×D1111yescharacteristic
872C8—22no—
873C8—224no—
874C8C2×#433914yescomplemented
875C22—21no—
876C22—21no—
877C22—41no—
878C22—42no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—84no—
884C22—114no—
885C22—222no—
886C22—222no—
887C22—222no—
888C22—222no—
889C22—222no—
890C22—448no—
891C22#1062308212yes—
892C22C22×D4×D1111yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—41no—
897C4—42no—
898C4—41no—
899C4—41no—
900C4—222no—
901C4—222no—
902C4—442no—
903C4—444no—
904C4—442no—
905C4#1062308212yes—
906C4D11×AGL(1,ℤ/8)12yes—
907C4C22×#433911yescharacteristic
908C4C2×#6704311yescharacteristic
909C2—22no—
910C2—82no—
911C2—81no—
912C2—224no—
913C2—442no—
914C2C2×#1062308211yescharacteristic
915C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
916C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#61252
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. #13082180C2semidirect
2. C2×#10623082C2semidirect
3. #13081213C2semidirect
4. #13081202C2semidirect
5. #13081091C2semidirect
6. #13081061C2semidirect
7. #13080975C2semidirect
8. #13080965C2semidirect
9. #13079162C2semidirect
10. #13078554C2semidirect
11. #13078537C2semidirect
12. #13078431C2semidirect
13. #13078413C2semidirect
14. #13078229C2semidirect
15. M16×D44C2semidirect
16. D11×#428C2semidirect
17. C4×C11×AGL(1,ℤ/8)C2semidirect
26. #10623115C22semidirect
27. #10623112C22semidirect
28. #10623110C22semidirect
29. #10623094C22semidirect
30. #10623089C22semidirect
38. #10623082C22semidirect
50. C11×#442C22semidirect
51. C11×#440C22semidirect
52. C4×C11×SD16C22semidirect
53. C4×C11×D8C22semidirect
60. #10622787C22semidirect
61. #10622784C22semidirect
62. #10622772C22semidirect
63. #10622770C22semidirect
67. #10622634C22semidirect
68. #10622633C22semidirect
69. #10622622C22semidirect
70. #10622621C22semidirect
71. #10622621C22semidirect
72. #10622620C22semidirect
73. #10622620C22semidirect
77. #10622494C22semidirect
78. D11×#107C22semidirect
79. #10622474C22semidirect
80. D11×#106C22semidirect
81. #10622422C22semidirect
82. #10622418C22semidirect
83. #10622397C22semidirect
84. #10622392C22semidirect
85. #10622390C22semidirect
86. #10622390C22semidirect
87. #10622387C22semidirect
88. #10622387C22semidirect
89. #10622319C22semidirect
90. #10622315C22semidirect
91. #10622301C22semidirect
92. C8×D44C22semidirect
93. #10622295C22semidirect
94. #10622293C22semidirect
287. C11×M16#41semidirect
361. C4×AGL(1,ℤ/8)D11semidirect
416. D44AGL(1,ℤ/8)semidirect
432. C8×C11C2×#41semidirect
488. #442C2×D11semidirect
489. #440C2×D11semidirect
490. C4×SD16C2×D11semidirect
491. C4×D8C2×D11semidirect
746. M16#4339semidirect
804. C11#61252semidirect
874. C8C2×#4339semidirect

Maximal subgroups

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

subgroupindex
#130821802
C2×#106230822
#130812132
#130812022
#130810912
#130810612
#130809752
#130809652
#130791622
#130785542
#130785372
#130784312
#130784132
#130782292
M16×D442
D11×#4282
C4×C11×AGL(1,ℤ/8)2
#6125211