Finite Group Databasebeta

← #25968280

Subgroups — #25968280

Order 11008.

2258 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C211yesmaximal, characteristic, complemented
2#19148368C211yesmaximal, characteristic, complemented
3#19145643C214yesmaximal, complemented
4#19145642C214yesmaximal, complemented
5#19145531C211yesmaximal, characteristic, complemented
6#19145528C211yesmaximal, characteristic, complemented
7#19145525C211yesmaximal, characteristic, complemented
8#19145515C211yesmaximal, characteristic, complemented
9#19145514C211yesmaximal, characteristic, complemented
10#19145510C211yesmaximal, characteristic, complemented
11#19145509C211yesmaximal, characteristic, complemented
12#19145042C211yesmaximal, characteristic, complemented
13#493×D43C211yesmaximal, characteristic, complemented
14#19144966C211yesmaximal, characteristic, complemented
15#19144919C211yesmaximal, characteristic, complemented
16#19144096C214yesmaximal, complemented
17#19143860C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3207C211yesmaximal, characteristic, complemented
20C2×#13063371C2212yes—
21C2×#13063352C2214yescomplemented
22C2×D8×D43C2214yescomplemented
23#14583632—21no—
24#14583631—21no—
25#14583570—21no—
26#14583570—21no—
27#14583568—21no—
28#14583567—21no—
29#14583546—21no—
30#14583544—21no—
31#14583542—21no—
32#14583537—21no—
33D4×D172—21no—
34D4×D172—21no—
35#14583533—21no—
36#14583533—21no—
37#14583533—21no—
38#14583533—21no—
39#14583502C2212yescomplemented
40#14583500C2212yescomplemented
41#14583467C2212yes—
42#14583467C2212yescomplemented
43#14583465C2212yes—
44#14583463C2212yescomplemented
45#14583454C2211yescharacteristic, complemented
46#14583450C2211yescharacteristic
47#14583450C2211yescharacteristic, complemented
48#14583450C2211yescharacteristic, complemented
49#14583449C2211yescharacteristic, complemented
50#14583447C2211yescharacteristic, complemented
51C2×#13063322C2211yescharacteristic, complemented
52#127×D43C2211yescharacteristic
53#127×D43C2211yescharacteristic, complemented
54#127×D43C2211yescharacteristic, complemented
55#14583371C2212yescomplemented
56C4×#10621898C2211yescharacteristic
57#14583285C2214yescomplemented
58#14583276C2211yescharacteristic, complemented
59#14583276C2211yescharacteristic, complemented
60#14583275C2211yescharacteristic, complemented
61#14583275C2211yescharacteristic, complemented
62#14583275C2211yescharacteristic, complemented
63#14583274C2214yescomplemented
64#14583273C2211yescharacteristic, complemented
65#14583262C2214yescomplemented
66#14583255C2214yescomplemented
67#14583249C2211yescharacteristic, complemented
68#14583247C2211yescharacteristic, complemented
69#14583247C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583246C2211yescharacteristic, complemented
72#14583245C2211yescharacteristic, complemented
73#14583117C2214yescomplemented
74#14583116C2214yescomplemented
75#14583111C2214yescomplemented
76#14583095C2214yescomplemented
77#14583094C2214yescomplemented
78#14583093C2214yescomplemented
79#14583092C2214yescomplemented
80#14583047C2214yescomplemented
81#14583044C2214yescomplemented
82#14583043C2214yescomplemented
83#14583035C2214yescomplemented
84#14583034C2214yescomplemented
85#14583032C2214yescomplemented
86#14583031C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yescomplemented
93#14582902C2214yescomplemented
94#14582894C2214yescomplemented
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic, complemented
97C4×C8×D43C2211yescharacteristic, complemented
98C43×#532C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic, complemented
100C43×#493C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#463C2214yescomplemented
105C43×#449C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063371—48no—
108C2×#10621902—21no—
109C2×#10621902C2312yes—
110C2×#10621902C2312yes—
111C2×#10621898—21no—
112C2×#10621898—22no—
113C2×#10621898C2311yescharacteristic
114C2×#10621900—21no—
115C22×D172—21no—
116C22×D172—21no—
117C22×D172—22no—
118C22×D172C2312yes—
119C2×D4×D43—22no—
120C2×D4×D43—22no—
121C2×D4×D43—21no—
122C2×D4×D43—21no—
123C2×D4×D43—21no—
124C2×D4×D43—21no—
125C2×D4×D43—21no—
126C2×D4×D43—21no—
127C2×D4×D43C2312yes—
128C2×D4×D43C2312yes—
129C2×D4×D43C2312yes—
130#13063352—48no—
131C2×#10621884C2314yes—
132C2×D344C2314yes—
133C2×D344C2314yes—
134C2×#10621882C2314yes—
135C2×#10621882C2314yes—
136C2×#10621882C2314yes—
137D8×D43—48no—
138C2×#10621872C2312yes—
139C2×C8×D43C2312yes—
140#13063325C2311yescharacteristic
141#13063322—21no—
142#13063322—21no—
143#13063322C2312yes—
144#13063322C2311yescharacteristic
145#13063322C2311yescharacteristic
146#13063322C2311yescharacteristic
147#13063321—22no—
148#13063321—21no—
149#13063321—21no—
150#13063321—21no—
151#13063321—21no—
152#13063321—21no—
153#13063321—21no—
154#13063321C2312yes—
155#13063321C2312yes—
156#13063321C2312yes—
157#13063316C2312yes—
158#13063314—21no—
159#13063314C2312yes—
160#13063314C2312yes—
161#13063313—21no—
162#13063312—21no—
163#13063311—22no—
164#13063309—22no—
165#13063308—22no—
166#13063307—22no—
167#13063307—22no—
168#13063305—21no—
169#13063301—21no—
170#13063300—21no—
171#13063300—21no—
172#13063300—21no—
173#13063300—21no—
174#13063300—21no—
175#13063300C2312yes—
176#13063299—21no—
177#13063299—22no—
178#13063299—22no—
179#13063299—22no—
180#13063299C2312yes—
181#13063298—22no—
182#13063298—22no—
183#13063298—22no—
184#13063298—22no—
185#13063298—22no—
186#13063297—22no—
187#13063296—21no—
188#13063296—22no—
189#13063296C2312yes—
190#13063295—22no—
191#13063295—22no—
192#13063295—22no—
193#13063295—22no—
194#13063295—22no—
195#13063293—22no—
196#13063293—22no—
197#13063293—22no—
198Q8×Dic43—21no—
199C4×Dic86D411yescharacteristic
200C4×Dic86D411yescharacteristic
201#13063290—21no—
202C4×D172—21no—
203C4×D172D411yescharacteristic
204C4×D172D411yescharacteristic
205C4×D172C2312yes—
206D4×Dic43—21no—
207D4×Dic43C2312yes—
208#13063287—21no—
209#13063287—21no—
210#13063287—21no—
211#13063287—21no—
212#13063287—21no—
213#13063287C2312yes—
214C4×C22⋊D43—22no—
215C4×C22⋊D43D411yescharacteristic
216C4×C22⋊D43D411yescharacteristic
217C4×C22⋊D43D411yescharacteristic
218C4×C22⋊D43D411yescharacteristic
219(C22⋊D43)⋊C4—22no—
220#13063284C2311yescharacteristic
221#13063283C2312yes—
222#13063282C2311yescharacteristic
223#13063282C2311yescharacteristic
224C2×(C2×D43)⋊C4—22no—
225C22⋊C4×D43—22no—
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228C4⋊(C43⋊C8)C2312yes—
229Dic43⋊C8C2312yes—
230Dic43⋊C8C2312yes—
231#13063249C2314yes—
232#13063247C2314yes—
233#13063247C2314yes—
234#13063246C2314yes—
235#13063245C2314yes—
236#13063245C2314yes—
237C22⋊(C43⋊C8)C2312yes—
238(C2×D43)⋊C8C2312yes—
239(C2×D43)⋊C8C2312yes—
240#13063235C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2311yescharacteristic
243C8×Dic43C2312yes—
244C2×#41×C43—21no—
245C2×#41×C43C2312yes—
246C2×SD16×C43C2314yes—
247C2×D8×C43C2314yes—
248C4⋊Q8×C43C2311yescharacteristic
249C4⋊Q8×C43C2311yescharacteristic
250#127×C43C2311yescharacteristic
251#127×C43C2311yescharacteristic
252#124×C43—21no—
253#124×C43C2312yes—
254#121×C43—21no—
255#121×C43—21no—
256#121×C43—21no—
257#121×C43C2312yes—
258C4×D4×C43—21no—
259C4×D4×C43—21no—
260C4×D4×C43—21no—
261C4×D4×C43C2312yes—
262C2×C42×C43C2311yescharacteristic
263C4⋊C8×C43C2312yes—
264#103×C43C2314yes—
265#102×C43C2314yes—
266C22⋊C8×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C4×C8×C43C2311yescharacteristic
269C23×D43—22no—
270C23×D43—22no—
271C23×D43—22no—
272C23×D43—22no—
273#41×C43—44no—
274#41×C43—82no—
275C2×Q8×C43—21no—
276C2×Q8×C43C2412yes—
277C2×D4×C43—21no—
278C2×D4×C43—21no—
279C2×D4×C43—21no—
280C2×D4×C43—21no—
281C2×D4×C43—22no—
282C2×D4×C43—22no—
283C2×D4×C43C2412yes—
284C2×D4×C43C2412yes—
285C22×C4×C43—22no—
286C22×C4×C43—22no—
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C2×C22⋊D43—22no—
291C2×C22⋊D43—22no—
292C2×C22⋊D43—22no—
293C2×C22⋊D43—22no—
294C2×C22⋊D43—22no—
295C2×C22⋊D43—22no—
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—22no—
301C2×C22⋊D43C2×D411yescharacteristic
302C2×C22⋊D43C2×D411yescharacteristic
303C22×Dic43—22no—
304#10621902—28no—
305#10621902—44no—
306#10621902—82no—
307#10621900—82no—
308D4×D43—28no—
309D4×D43—28no—
310D4×D43—44no—
311D4×D43—48no—
312D4×D43—48no—
313D4×D43—82no—
314D4×D43—82no—
315D4×D43—82no—
316D4×D43—82no—
317D4×D43—82no—
318D4×D43—82no—
319#10621898—24no—
320#10621898—48no—
321#10621898—82no—
322C2×D172—21no—
323C2×D172—21no—
324C2×D172—21no—
325C2×D172—21no—
326C2×D172—21no—
327C2×D172—21no—
328C2×D172—22no—
329C2×D172—22no—
330C2×D172—22no—
331C2×D172—22no—
332C2×D172—22no—
333C2×D172—22no—
334C2×D172—44no—
335C2×D172—48no—
336C2×D172—82no—
337C2×D172—82no—
338C2×D172C2×D411yescharacteristic
339C2×D172C2412yes—
340C2×D172C2412yes—
341C2×D172C2412yes—
342C2×C4×D43—22no—
343C2×C4×D43—22no—
344C2×C4×D43—22no—
345C2×C4×D43—22no—
346C2×C4×D43C2×D411yescharacteristic
347C2×C4×D43C2×D411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×C4×D43C2×D411yescharacteristic
350C2×C4×D43C2411yescharacteristic
351C2×C4×D43C2411yescharacteristic
352C2×Dic86—21no—
353C2×Dic86C2×D411yescharacteristic
354SD16×C43—44no—
355D8×C43—44no—
356C2×C8×C43C2412yes—
357C2×C8×C43C2412yes—
358C4⋊C4×C43—21no—
359C4⋊C4×C43—21no—
360C4⋊C4×C43—21no—
361C4⋊C4×C43C2412yes—
362C22⋊C4×C43—22no—
363C22⋊C4×C43—22no—
364C22⋊C4×C43—22no—
365C22⋊C4×C43—22no—
366C42×C43C2×D411yescharacteristic
367C42×C43C2×D411yescharacteristic
368C42×C43C2411yescharacteristic
369C42×C43C2411yescharacteristic
370C22⋊Dic43—22no—
371C22⋊Dic43—22no—
372C22⋊Dic43C2×D411yescharacteristic
373C22⋊Dic43C2×D411yescharacteristic
374#10621884—44no—
375#10621882—44no—
376#10621882—44no—
377#10621882—44no—
378(C2×D43)⋊C4—22no—
379(C2×D43)⋊C4—22no—
380(C2×D43)⋊C4—22no—
381(C2×D43)⋊C4—22no—
382(C2×D43)⋊C4—22no—
383(C2×D43)⋊C4—22no—
384(C2×D43)⋊C4—22no—
385(C2×D43)⋊C4—22no—
386(C2×D43)⋊C4—22no—
387(C2×D43)⋊C4C2×D411yescharacteristic
388(C2×D43)⋊C4C2×D411yescharacteristic
389(C2×D43)⋊C4C2×D411yescharacteristic
390(C2×D43)⋊C4C2×D411yescharacteristic
391C4⋊Dic43—21no—
392C4⋊Dic43—22no—
393C4⋊Dic43C2×D411yescharacteristic
394C4⋊Dic43C2×D411yescharacteristic
395C4⋊Dic43C2412yes—
396Dic43⋊C4—22no—
397Dic43⋊C4C2×D411yescharacteristic
398Dic43⋊C4C2×D411yescharacteristic
399Dic43⋊C4C2×D411yescharacteristic
400Dic43⋊C4C2×D411yescharacteristic
401C4×Dic43—22no—
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2×D411yescharacteristic
404C4×Dic43C2×D411yescharacteristic
405C4×Dic43C2×D411yescharacteristic
406C4×Dic43C2411yescharacteristic
407C4×Dic43C2411yescharacteristic
408C2×C43⋊C8C2412yes—
409C2×C43⋊C8C2412yes—
410D344—44no—
411D344—44no—
412#10621872—24no—
413C8×D43—24no—
414C23×C43—22no—
415C23×C43—22no—
416C23×C43C22×D411yescharacteristic
417C22×D43—22no—
418C22×D43—22no—
419C22×D43—22no—
420C22×D43—44no—
421C22×D43—44no—
422C22×D43—44no—
423C22×D43—44no—
424C22×D43—82no—
425C22×D43—82no—
426C22×D43—82no—
427C22×D43—82no—
428C22×D43—82no—
429C22×D43—82no—
430C22×D43—82no—
431C22×D43—82no—
432C22×D43C22×D411yescharacteristic
433C22×D43C22×D411yescharacteristic
434Q8×C43—24no—
435Q8×C43—42no—
436D4×C43—24no—
437D4×C43—24no—
438D4×C43—44no—
439D4×C43—42no—
440D4×C43—42no—
441D4×C43—42no—
442D4×C43—42no—
443D4×C43—82no—
444C2×C4×C43—22no—
445C2×C4×C43—22no—
446C2×C4×C43—22no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—44no—
450C2×C4×C43—82no—
451C2×C4×C43C22×D411yescharacteristic
452C2×C4×C43C22×D411yescharacteristic
453C2×C4×C43C22×D411yescharacteristic
454C2×C4×C43C22×D411yescharacteristic
455C2×C4×C43C22×D411yescharacteristic
456C2×C4×C43C2511yescharacteristic
457C22⋊D43—22no—
458C22⋊D43—22no—
459C22⋊D43—44no—
460C22⋊D43—44no—
461C22⋊D43—44no—
462C22⋊D43—82no—
463C22⋊D43—82no—
464C22⋊D43—82no—
465C22⋊D43—82no—
466C22⋊D43—82no—
467C22⋊D43—82no—
468C22⋊D43—82no—
469C22⋊D43—82no—
470C2×Dic43—22no—
471C2×Dic43—82no—
472C2×Dic43C22×D411yescharacteristic
473C2×Dic43C22×D411yescharacteristic
474C2×Dic43C22×D411yescharacteristic
475C2×Dic43C22×D411yescharacteristic
476C2×Dic43C22×D411yescharacteristic
477C2×Dic43C22×D411yescharacteristic
478D172—22no—
479D172—24no—
480D172—24no—
481D172—24no—
482D172—44no—
483D172—44no—
484D172—44no—
485D172—42no—
486D172—42no—
487D172—42no—
488D172—42no—
489D172—42no—
490D172—42no—
491D172—82no—
492D172—82no—
493D172—82no—
494C4×D43—22no—
495C4×D43—22no—
496C4×D43—22no—
497C4×D43—22no—
498C4×D43—22no—
499C4×D43—44no—
500C4×D43—44no—
501C4×D43—82no—
502C4×D43—82no—
503C4×D43H(5,𝔽2)14yes—
504Dic86—22no—
505Dic86—42no—
506C8×C43—22no—
507C8×C43—22no—
508C43⋊C8—22no—
509C43⋊C8—22no—
510#60817—431nomaximal, Sylow
511C22×C43—21no—
512C22×C43—21no—
513C22×C43—21no—
514C22×C43—42no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43C23×D411yescharacteristic
521C2×D43—21no—
522C2×D43—21no—
523C2×D43—21no—
524C2×D43—21no—
525C2×D43—21no—
526C2×D43—42no—
527C2×D43—42no—
528C2×D43—42no—
529C2×D43—42no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—164no—
536C2×D43—164no—
537C2×D43—164no—
538C2×D43—164no—
539C2×D43#53512yes—
540C4×C43—21no—
541C4×C43—21no—
542C4×C43—21no—
543C4×C43—42no—
544C4×C43—42no—
545C4×C43#57612yes—
546C4×C43#57612yes—
547C4×C43C2×H(5,𝔽2)12yes—
548Dic43—21no—
549Dic43—21no—
550Dic43—21no—
551Dic43—21no—
552Dic43—21no—
553Dic43—42no—
554Dic43#53512yes—
555#3508—431no—
556#3498—431no—
557#3220—434no—
558#3220—434no—
559#3207—431no—
560#3207—431no—
561#3207—431no—
562#3207D4311yescharacteristic, complemented
563#3205—431no—
564#3205—431no—
565#3205—431no—
566#3205—431no—
567#3151—431no—
568C2×#493—431no—
569#3138—431no—
570#3131—431no—
571#3041—434no—
572#3008—434no—
573#2922—431no—
574C2×C43—41no—
575C2×C43—82no—
576C2×C43—82no—
577C2×C43C2×#53511yescharacteristic
578C2×C43C2×#57611yescharacteristic
579C2×C43C2×#57611yescharacteristic
580D43—22no—
581D43—41no—
582D43—82no—
583D43—82no—
584D43—82no—
585C2×H(5,𝔽2)—432no—
586C2×AGL(1,ℤ/8)—434no—
587C22×D8—434no—
588#559—861no—
589#559—861no—
590#550—861no—
591#550—861no—
592#550—861no—
593#550—861no—
594#546—861no—
595#546—861no—
596#546—861no—
597#546—861no—
598D42—861no—
599D42—861no—
600D42—861no—
601D42—861no—
602D42—861no—
603D42—861no—
604#540—432no—
605#540—432no—
606#535—432no—
607#535—432no—
608#535—432no—
609#535—432no—
610#533—431no—
611#532—431no—
612#532—431no—
613#532—431no—
614#532—431no—
615#532—431no—
616#532C2×D4311yescharacteristic, complemented
617#532C2×D4311yescharacteristic, complemented
618C2×#127—431no—
619C2×#127—431no—
620C2×#127—431no—
621C2×#127—431no—
622#518—432no—
623C4×#41—431no—
624#496—434no—
625#493—434no—
626#493—431no—
627#493—431no—
628#493—431no—
629#493—431no—
630#493—431no—
631#493C2×D4311yescharacteristic, complemented
632#492—431no—
633#492C2×D4311yescharacteristic, complemented
634#490—434no—
635#488—434no—
636#487—431no—
637#487C2×D4311yescharacteristic, complemented
638#486—431no—
639#486—431no—
640#486—431no—
641#486—431no—
642#486—431no—
643#486C2×D4311yescharacteristic, complemented
644#463—434no—
645#463—434no—
646#463—434no—
647#463C2×D4314yescomplemented
648#459—434no—
649#459—434no—
650#459—434no—
651#459—434no—
652#449—434no—
653#449—434no—
654#449—434no—
655#449C2×D4314yescomplemented
656#447—434no—
657#447—434no—
658#447—434no—
659#447—434no—
660#433—432no—
661#433—432no—
662#431—431no—
663#431—431no—
664#431—431no—
665#431C2×D4311yescharacteristic, complemented
666#424—432no—
667#418—434no—
668#416—434no—
669#408—432no—
670C4×M16—431no—
671C2×C4×C8—431no—
672C43#6081711yescharacteristic, complemented, Sylow
673H(5,𝔽2)—1728no—
674C2×#41—21no—
675C2×#41—431no—
676C2×#41—432no—
677C2×#41—432no—
678C2×#41—862no—
679C2×#41—861no—
680C2×#41—861no—
681C2×#41—861no—
682C2×#41C22×D4312yes—
683C22×D4—432no—
684C22×D4—432no—
685C22×D4—432no—
686C22×D4—432no—
687C22×D4—862no—
688C22×D4—861no—
689C22×D4—861no—
690C22×D4—861no—
691C22×D4—861no—
692C22×D4—861no—
693C22×D4—861no—
694C22×D4—862no—
695C22×D4—862no—
696C22×D4—861no—
697C22×D4—861no—
698AGL(1,ℤ/8)—1728no—
699C2×SD16—434no—
700C2×SD16C22×D4314yes—
701C2×D8—434no—
702C2×D8—434no—
703C2×D8—434no—
704C2×D8—434no—
705C2×D8—434no—
706C2×D8—1728no—
707C2×D8C22×D4314yes—
708C2×M16—432no—
709C22×C8—432no—
710C4⋊Q8—431no—
711C4⋊Q8C22×D4311yescharacteristic
712C4⋊Q8C22×D4311yescharacteristic
713#127—432no—
714#127—432no—
715#127—432no—
716#127—431no—
717#127—431no—
718#127—431no—
719#127—432no—
720#127—861no—
721#127—861no—
722#127—861no—
723#127—861no—
724#127—861no—
725#127—861no—
726#127—862no—
727#127—861no—
728#127—861no—
729#127C22×D4311yescharacteristic
730#127C22×D4311yescharacteristic
731#125—432no—
732#124—21no—
733#124—432no—
734#124—432no—
735#124—861no—
736#124—861no—
737#124—862no—
738#124—861no—
739#124C22×D4312yes—
740#123—862no—
741#123—862no—
742#123—862no—
743#123—862no—
744C22⋊Q8—861no—
745C22⋊Q8—861no—
746#121—21no—
747#121—21no—
748#121—21no—
749#121—432no—
750#121—432no—
751#121—432no—
752#121—862no—
753#121—862no—
754#121—862no—
755#121—862no—
756#121—862no—
757#121—862no—
758#121—862no—
759#121—862no—
760#121—861no—
761#121—861no—
762#121—861no—
763#121—861no—
764#121—861no—
765#121—862no—
766#121—862no—
767#121—861no—
768#121—861no—
769#121C22×D4312yes—
770#120—862no—
771#120—862no—
772#120—862no—
773#120—862no—
774#120—862no—
775#120—862no—
776#120—862no—
777#120—862no—
778C4×Q8—431no—
779C4×Q8—431no—
780C4×Q8—861no—
781C4×Q8—861no—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4—431no—
786C4×D4—431no—
787C4×D4—431no—
788C4×D4—431no—
789C4×D4—432no—
790C4×D4—432no—
791C4×D4—431no—
792C4×D4—431no—
793C4×D4—432no—
794C4×D4—861no—
795C4×D4—861no—
796C4×D4—861no—
797C4×D4—861no—
798C4×D4—861no—
799C4×D4—861no—
800C4×D4—862no—
801C4×D4—862no—
802C4×D4—861no—
803C4×D4C22×D4312yes—
804#117—431no—
805#117—431no—
806#117—431no—
807#117—432no—
808C2×C22⋊C4—862no—
809C2×C22⋊C4—862no—
810C2×C42—431no—
811C2×C42—431no—
812C2×C42C22×D4311yescharacteristic
813C4⋊C8—432no—
814C4⋊C8—432no—
815C4⋊C8—432no—
816C4⋊C8C22×D4312yes—
817#103—434no—
818#103C22×D4314yes—
819#102—434no—
820#102—434no—
821#102—434no—
822#102—434no—
823#102—434no—
824#102C22×D4314yes—
825C22⋊C8—432no—
826C22⋊C8—432no—
827C22⋊C8—432no—
828C22⋊C8C22×D4312yes—
829#97—432no—
830C4×C8—432no—
831C4×C8—431no—
832C4×C8—431no—
833C4×C8C22×D4311yescharacteristic
834C4×C8C22×D4311yescharacteristic
835C24—862no—
836C24—862no—
837C24—862no—
838C24—862no—
839#41—44no—
840#41—82no—
841#41—864no—
842#41—868no—
843#41—3442no—
844#41—3442no—
845#41—3442no—
846#41—1728no—
847#41—1724no—
848C2×Q8—21no—
849C2×Q8—431no—
850C2×Q8—861no—
851C2×Q8C23×D4312yes—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—431no—
859C2×D4—431no—
860C2×D4—431no—
861C2×D4—432no—
862C2×D4—432no—
863C2×D4—432no—
864C2×D4—862no—
865C2×D4—862no—
866C2×D4—862no—
867C2×D4—868no—
868C2×D4—868no—
869C2×D4—862no—
870C2×D4—862no—
871C2×D4—862no—
872C2×D4—862no—
873C2×D4—862no—
874C2×D4—862no—
875C2×D4—862no—
876C2×D4—862no—
877C2×D4—862no—
878C2×D4—862no—
879C2×D4—862no—
880C2×D4—862no—
881C2×D4—862no—
882C2×D4—861no—
883C2×D4—861no—
884C2×D4—861no—
885C2×D4—861no—
886C2×D4—861no—
887C2×D4—861no—
888C2×D4—862no—
889C2×D4—3442no—
890C2×D4—3442no—
891C2×D4—3442no—
892C2×D4—3442no—
893C2×D4—3442no—
894C2×D4—3442no—
895C2×D4—3442no—
896C2×D4—3442no—
897C2×D4—1724no—
898C2×D4—1728no—
899C2×D4—1724no—
900C2×D4—1728no—
901C2×D4—1728no—
902C2×D4C23×D4312yes—
903C2×D4C23×D4312yes—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—431no—
907C22×C4—431no—
908C22×C4—431no—
909C22×C4—431no—
910C22×C4—431no—
911C22×C4—431no—
912C22×C4—862no—
913C22×C4—862no—
914C22×C4—862no—
915C22×C4—862no—
916C22×C4—862no—
917C22×C4D4×D4311yescharacteristic
918C22×C4D4×D4311yescharacteristic
919C22×C4C23×D4311yescharacteristic
920SD16—44no—
921SD16—1724no—
922D8—44no—
923D8—1724no—
924D8—1724no—
925D8—1724no—
926D8—1724no—
927D8—1724no—
928M16—864no—
929C2×C8—432no—
930C2×C8—432no—
931C2×C8—864no—
932C2×C8C23×D4312yes—
933C2×C8C23×D4312yes—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—431no—
938C4⋊C4—431no—
939C4⋊C4—431no—
940C4⋊C4—431no—
941C4⋊C4—431no—
942C4⋊C4—431no—
943C4⋊C4—432no—
944C4⋊C4—862no—
945C4⋊C4—862no—
946C4⋊C4—861no—
947C4⋊C4C23×D4312yes—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—431no—
953C22⋊C4—431no—
954C22⋊C4—431no—
955C22⋊C4—431no—
956C22⋊C4—431no—
957C22⋊C4—431no—
958C22⋊C4—862no—
959C22⋊C4—862no—
960C22⋊C4—862no—
961C22⋊C4—862no—
962C22⋊C4—862no—
963C22⋊C4—862no—
964C22⋊C4—862no—
965C22⋊C4—862no—
966C22⋊C4—862no—
967C22⋊C4—862no—
968C22⋊C4—862no—
969C42—431no—
970C42—431no—
971C42—431no—
972C42—431no—
973C42—431no—
974C42—431no—
975C42—862no—
976C42D4×D4311yescharacteristic
977C42D4×D4311yescharacteristic
978C42C23×D4311yescharacteristic
979C42C23×D4311yescharacteristic
980C23—22no—
981C23—22no—
982C23—431no—
983C23—431no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—3442no—
988C23—3442no—
989C23—3442no—
990C23—3442no—
991C23—3442no—
992C23—3442no—
993C23—3442no—
994C23—3442no—
995C23—1724no—
996C23—1724no—
997C23—1724no—
998C23—1724no—
999C23C2×D4×D4311yescharacteristic
1000Q8—24no—
1001Q8—42no—
1002Q8—862no—
1003Q8—1722no—
1004D4—24no—
1005D4—24no—
1006D4—44no—
1007D4—42no—
1008D4—42no—
1009D4—42no—
1010D4—42no—
1011D4—82no—
1012D4—862no—
1013D4—862no—
1014D4—862no—
1015D4—864no—
1016D4—864no—
1017D4—864no—
1018D4—3442no—
1019D4—3442no—
1020D4—3442no—
1021D4—3442no—
1022D4—3442no—
1023D4—3442no—
1024D4—3442no—
1025D4—3442no—
1026D4—3442no—
1027D4—3442no—
1028D4—3442no—
1029D4—1724no—
1030D4—1724no—
1031D4—1724no—
1032D4—1724no—
1033D4—1724no—
1034D4—1724no—
1035D4—1722no—
1036D4—1722no—
1037D4—1722no—
1038D4—1722no—
1039D4—1722no—
1040D4—1722no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—44no—
1047C2×C4—82no—
1048C2×C4—431no—
1049C2×C4—434no—
1050C2×C4—431no—
1051C2×C4—431no—
1052C2×C4—431no—
1053C2×C4—431no—
1054C2×C4—431no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—3442no—
1062C2×C4—3442no—
1063C2×C4—3442no—
1064C2×C4—1724no—
1065C2×C4—1724no—
1066C2×C4C2×D4×D4311yescharacteristic
1067C2×C4C2×D4×D4311yescharacteristic
1068C2×C4C2×D4×D4311yescharacteristic
1069C2×C4C2×D4×D4311yescharacteristic
1070C2×C4C2×D4×D4311yescharacteristic
1071C2×C4C24×D4311yescharacteristic
1072C8—22no—
1073C8—22no—
1074C8—862no—
1075C8—862no—
1076C22—21no—
1077C22—21no—
1078C22—21no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—432no—
1086C22—861no—
1087C22—861no—
1088C22—861no—
1089C22—861no—
1090C22—861no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—6884no—
1101C22—6884no—
1102C22—6884no—
1103C22—6884no—
1104C22C22×D4×D4311yescharacteristic
1105C4—21no—
1106C4—21no—
1107C4—21no—
1108C4—42no—
1109C4—42no—
1110C4—432no—
1111C4—861no—
1112C4—861no—
1113C4—861no—
1114C4—861no—
1115C4—861no—
1116C4—1722no—
1117C4#1458370112yes—
1118C4#1458370312yes—
1119C4H(5,𝔽2)×D4312yes—
1120C2—41no—
1121C2—82no—
1122C2—82no—
1123C2—862no—
1124C2—3442no—
1125C2—3442no—
1126C2—3442no—
1127C2—1721no—
1128C2#535×D4311yescharacteristic
1129C2C2×#1458370111yescharacteristic
1130C2C2×#1458370311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3207C2
socleC22×C43C23×D4
hypercenter#3207D43
hypocenterC43#60817
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #19148464C2semidirect
2. #19148368C2semidirect
3. #19145643C2semidirect
4. #19145642C2semidirect
5. #19145531C2semidirect
6. #19145528C2semidirect
7. #19145525C2semidirect
8. #19145515C2semidirect
9. #19145514C2semidirect
10. #19145510C2semidirect
11. #19145509C2semidirect
12. #19145042C2semidirect
13. #493×D43C2semidirect
14. #19144966C2semidirect
15. #19144919C2semidirect
16. #19144096C2semidirect
17. #19143860C2semidirect
18. #19143234C2semidirect
19. C43×#3207C2semidirect
21. C2×#13063352C22semidirect
22. C2×D8×D43C22semidirect
39. #14583502C22semidirect
40. #14583500C22semidirect
42. #14583467C22semidirect
44. #14583463C22semidirect
45. #14583454C22semidirect
47. #14583450C22semidirect
48. #14583450C22semidirect
49. #14583449C22semidirect
50. #14583447C22semidirect
51. C2×#13063322C22semidirect
53. #127×D43C22semidirect
54. #127×D43C22semidirect
55. #14583371C22semidirect
57. #14583285C22semidirect
58. #14583276C22semidirect
59. #14583276C22semidirect
60. #14583275C22semidirect
61. #14583275C22semidirect
62. #14583275C22semidirect
63. #14583274C22semidirect
64. #14583273C22semidirect
65. #14583262C22semidirect
66. #14583255C22semidirect
67. #14583249C22semidirect
68. #14583247C22semidirect
69. #14583247C22semidirect
70. #14583246C22semidirect
71. #14583246C22semidirect
72. #14583245C22semidirect
73. #14583117C22semidirect
74. #14583116C22semidirect
75. #14583111C22semidirect
76. #14583095C22semidirect
77. #14583094C22semidirect
78. #14583093C22semidirect
79. #14583092C22semidirect
80. #14583047C22semidirect
81. #14583044C22semidirect
82. #14583043C22semidirect
83. #14583035C22semidirect
84. #14583034C22semidirect
85. #14583032C22semidirect
86. #14583031C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
92. #14582924C22semidirect
93. #14582902C22semidirect
94. #14582894C22semidirect
96. C4×#10621872C22semidirect
97. C4×C8×D43C22semidirect
98. C43×#532C22semidirect
99. C43×#532C22semidirect
100. C43×#493C22semidirect
101. C43×#492C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#463C22semidirect
105. C43×#449C22semidirect
106. C43×#431C22semidirect
562. #3207D43semidirect
616. #532C2×D43semidirect
617. #532C2×D43semidirect
631. #493C2×D43semidirect
633. #492C2×D43semidirect
637. #487C2×D43semidirect
643. #486C2×D43semidirect
647. #463C2×D43semidirect
655. #449C2×D43semidirect
665. #431C2×D43semidirect
672. C43#60817semidirect

Maximal subgroups

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

subgroupindex
#191484642
#191483682
#191456432
#191456422
#191455312
#191455282
#191455252
#191455152
#191455142
#191455102
#191455092
#191450422
#493×D432
#191449662
#191449192
#191440962
#191438602
#191432342
C43×#32072
#6081743