Finite Group Databasebeta

← #25968357

Subgroups — #25968357

Order 11008.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148507C211yesmaximal, characteristic, complemented
2#19148368C211yesmaximal, characteristic, complemented
3#19145696C214yesmaximal, complemented
4#19145695C214yesmaximal, complemented
5#19145548C211yesmaximal, characteristic, complemented
6#19145533C211yesmaximal, characteristic, complemented
7#19145532C211yesmaximal, characteristic, complemented
8#19145531C211yesmaximal, characteristic, complemented
9#19145528C211yesmaximal, characteristic, complemented
10#19145515C211yesmaximal, characteristic, complemented
11#19145514C211yesmaximal, characteristic, complemented
12#19145042C211yesmaximal, characteristic, complemented
13#19145024C211yesmaximal, characteristic, complemented
14#19144990C211yesmaximal, characteristic, complemented
15#486×D43C211yesmaximal, characteristic, complemented
16#19144137C214yesmaximal, complemented
17#19143903C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3210C211yesmaximal, characteristic, complemented
20C2×#13063371C2212yes—
21C2×#13063352C2214yescomplemented
22C2×#13063348C2214yescomplemented
23#14583621—21no—
24#14583612—21no—
25#14583605—21no—
26#14583602—21no—
27#14583593—21no—
28#14583570—21no—
29#14583570—21no—
30#14583561—21no—
31#14583559—21no—
32#14583551—21no—
33D4×D172—21no—
34D4×D172—21no—
35#14583533—21no—
36#14583533—21no—
37#14583533—21no—
38#14583533—21no—
39#14583522C2212yescomplemented
40#14583521C2212yescomplemented
41#14583479C2212yes—
42#14583467C2212yes—
43#14583467C2212yes—
44#14583463C2212yes—
45#14583454C2211yescharacteristic, complemented
46#14583450C2211yescharacteristic
47#14583450C2211yescharacteristic
48#14583450C2211yescharacteristic, complemented
49#14583450C2211yescharacteristic, complemented
50#14583449C2211yescharacteristic, complemented
51C4⋊Q8×D43C2211yescharacteristic, complemented
52C2×#13063322C2211yescharacteristic
53#127×D43C2211yescharacteristic
54#127×D43C2211yescharacteristic
55#14583381C2212yescomplemented
56C4×#10621898C2211yescharacteristic
57#14583285C2214yescomplemented
58#14583284C2214yescomplemented
59#14583276C2211yescharacteristic, complemented
60#14583276C2211yescharacteristic, complemented
61#14583275C2211yescharacteristic, complemented
62#14583273C2211yescharacteristic, complemented
63#14583273C2211yescharacteristic, complemented
64#14583273C2211yescharacteristic, complemented
65#14583260C2214yescomplemented
66#14583249C2211yescharacteristic, complemented
67#14583247C2211yescharacteristic, complemented
68#14583247C2211yescharacteristic, complemented
69#14583246C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583245C2211yescharacteristic, complemented
72#14583244C2214yescomplemented
73#14583123C2214yescomplemented
74#14583117C2214yescomplemented
75#14583111C2214yescomplemented
76#14583099C2214yescomplemented
77#14583097C2214yescomplemented
78#14583095C2214yescomplemented
79#14583093C2214yescomplemented
80#14583060C2214yescomplemented
81#14583049C2214yescomplemented
82#14583048C2214yescomplemented
83#14583047C2214yescomplemented
84#14583044C2214yescomplemented
85#14583035C2214yescomplemented
86#14583034C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yescomplemented
93#14582899C2214yescomplemented
94#102×D43C2214yescomplemented
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic, complemented
97C4×C8×D43C2211yescharacteristic, complemented
98C43×#533C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic
100C43×#494C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#464C2214yescomplemented
105C43×#452C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063371—48no—
108C2×#10621902—21no—
109C2×#10621902C2312yes—
110C2×#10621902C2312yes—
111C2×#10621902C2312yes—
112C2×#10621898—21no—
113C2×#10621898—22no—
114C2×#10621898C2311yescharacteristic
115C2×Q8×D43—21no—
116C22×D172—21no—
117C22×D172—21no—
118C22×D172—22no—
119C22×D172C2312yes—
120C2×D4×D43—22no—
121C2×D4×D43—22no—
122C2×D4×D43—21no—
123C2×D4×D43—21no—
124C2×D4×D43—21no—
125C2×D4×D43—21no—
126C2×D4×D43C2312yes—
127C2×D4×D43C2312yes—
128#13063352—48no—
129#13063348—48no—
130C2×#10621884C2314yes—
131C2×#10621884C2314yes—
132C2×#10621884C2314yes—
133C2×D344C2314yes—
134C2×D344C2314yes—
135C2×#10621882C2314yes—
136C2×#10621872C2312yes—
137C2×C8×D43C2312yes—
138#13063325C2311yescharacteristic
139#13063324—21no—
140#13063324C2312yes—
141#13063323—21no—
142#13063322—21no—
143#13063322—21no—
144#13063322C2312yes—
145#13063322C2311yescharacteristic
146#13063322C2311yescharacteristic
147#13063322C2311yescharacteristic
148#13063321—21no—
149#13063321—21no—
150#13063321—21no—
151#13063321—21no—
152#13063321C2312yes—
153#13063321C2312yes—
154#13063320—22no—
155#13063319—22no—
156#13063316—21no—
157#13063314—21no—
158#13063314C2312yes—
159#13063314C2312yes—
160#13063314C2312yes—
161#13063313—21no—
162#13063313—22no—
163#13063311—22no—
164#13063310—22no—
165#13063307—22no—
166#13063305—21no—
167#13063305—22no—
168#13063303—22no—
169#13063303—22no—
170#13063301C2312yes—
171#13063300—22no—
172#13063300—21no—
173#13063300—21no—
174#13063300—21no—
175#13063300—21no—
176#13063300—21no—
177#13063300—21no—
178#13063300—21no—
179#13063300C2312yes—
180#13063299—21no—
181#13063299—22no—
182#13063299—22no—
183#13063299C2312yes—
184#13063298—22no—
185#13063298—22no—
186#13063298—22no—
187#13063298—22no—
188#13063298—22no—
189#13063298—22no—
190#13063295—22no—
191#13063295—22no—
192#13063295—22no—
193#13063295—22no—
194#13063293—22no—
195#13063293—22no—
196Q8×Dic43C2312yes—
197C4×Dic86D411yescharacteristic
198C4×Dic86D411yescharacteristic
199#13063290—21no—
200C4×D172—21no—
201C4×D172—22no—
202C4×D172D411yescharacteristic
203C4×D172D411yescharacteristic
204C4×D172C2312yes—
205#13063287—22no—
206#13063287—21no—
207#13063287—21no—
208#13063287—21no—
209#13063287—21no—
210#13063287—21no—
211#13063287—21no—
212#13063287—21no—
213#13063287C2312yes—
214C4×C22⋊D43D411yescharacteristic
215C4×C22⋊D43D411yescharacteristic
216C4×C22⋊D43D411yescharacteristic
217C4×C22⋊D43D411yescharacteristic
218#13063284C2311yescharacteristic
219#13063283—21no—
220#13063282—22no—
221#13063282C2311yescharacteristic
222#13063282C2311yescharacteristic
223C4⋊C4×D43—21no—
224C4⋊C4×D43—22no—
225C4⋊C4×D43C2312yes—
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×C43C2312yes—
245C2×Q16×C43C2314yes—
246C2×SD16×C43C2314yes—
247C4⋊Q8×C43C2311yescharacteristic
248C4⋊Q8×C43C2311yescharacteristic
249C4⋊Q8×C43C2311yescharacteristic
250#127×C43C2311yescharacteristic
251#125×C43—21no—
252#124×C43C2312yes—
253C22⋊Q8×C43—21no—
254C22⋊Q8×C43C2312yes—
255#121×C43—21no—
256#121×C43—21no—
257C4×Q8×C43—21no—
258C4×Q8×C43C2312yes—
259C4×D4×C43—21no—
260C4×D4×C43—21no—
261#117×C43—21no—
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—
272#41×C43—44no—
273C2×Q8×C43—21no—
274C2×Q8×C43C2412yes—
275C2×Q8×C43C2412yes—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—22no—
279C2×D4×C43C2412yes—
280C22×C4×C43—22no—
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2411yescharacteristic
284C2×C22⋊D43—22no—
285C2×C22⋊D43—22no—
286C2×C22⋊D43—22no—
287C2×C22⋊D43—22no—
288C2×C22⋊D43—22no—
289C2×C22⋊D43—22no—
290C2×C22⋊D43—22no—
291C2×C22⋊D43C2×D411yescharacteristic
292C2×C22⋊D43C2×D411yescharacteristic
293#10621902—28no—
294#10621902—28no—
295#10621902—44no—
296#10621902—82no—
297Q8×D43—82no—
298D4×D43—28no—
299D4×D43—44no—
300D4×D43—48no—
301D4×D43—48no—
302D4×D43—82no—
303D4×D43—82no—
304D4×D43—82no—
305D4×D43—82no—
306#10621898—24no—
307#10621898—48no—
308#10621898—82no—
309C2×D172—21no—
310C2×D172—21no—
311C2×D172—21no—
312C2×D172—21no—
313C2×D172—21no—
314C2×D172—21no—
315C2×D172—22no—
316C2×D172—22no—
317C2×D172—22no—
318C2×D172—22no—
319C2×D172—22no—
320C2×D172—22no—
321C2×D172—22no—
322C2×D172—44no—
323C2×D172—48no—
324C2×D172—82no—
325C2×D172—82no—
326C2×D172C2×D411yescharacteristic
327C2×D172C2412yes—
328C2×D172C2412yes—
329C2×D172C2412yes—
330C2×C4×D43—22no—
331C2×C4×D43—22no—
332C2×C4×D43—22no—
333C2×C4×D43—22no—
334C2×C4×D43—22no—
335C2×C4×D43—22no—
336C2×C4×D43C2×D411yescharacteristic
337C2×C4×D43C2×D411yescharacteristic
338C2×C4×D43C2×D411yescharacteristic
339C2×C4×D43C2×D411yescharacteristic
340C2×C4×D43C2411yescharacteristic
341C2×C4×D43C2411yescharacteristic
342C2×Dic86—21no—
343C2×Dic86—22no—
344C2×Dic86C2×D411yescharacteristic
345Q16×C43—44no—
346SD16×C43—44no—
347C2×C8×C43C2412yes—
348C2×C8×C43C2412yes—
349C4⋊C4×C43—21no—
350C4⋊C4×C43—21no—
351C4⋊C4×C43—21no—
352C4⋊C4×C43—21no—
353C4⋊C4×C43—21no—
354C4⋊C4×C43—22no—
355C4⋊C4×C43—22no—
356C4⋊C4×C43C2412yes—
357C22⋊C4×C43—22no—
358C22⋊C4×C43—22no—
359C22⋊C4×C43—22no—
360C42×C43—22no—
361C42×C43C2×D411yescharacteristic
362C42×C43C2×D411yescharacteristic
363C42×C43C2411yescharacteristic
364C42×C43C2411yescharacteristic
365C22⋊Dic43C2×D411yescharacteristic
366C22⋊Dic43C2×D411yescharacteristic
367#10621884—44no—
368#10621884—44no—
369#10621884—44no—
370#10621882—44no—
371(C2×D43)⋊C4—22no—
372(C2×D43)⋊C4—22no—
373(C2×D43)⋊C4—22no—
374(C2×D43)⋊C4—22no—
375(C2×D43)⋊C4—22no—
376(C2×D43)⋊C4—22no—
377(C2×D43)⋊C4—22no—
378(C2×D43)⋊C4—22no—
379(C2×D43)⋊C4—22no—
380(C2×D43)⋊C4—22no—
381(C2×D43)⋊C4—22no—
382(C2×D43)⋊C4C2×D411yescharacteristic
383(C2×D43)⋊C4C2×D411yescharacteristic
384(C2×D43)⋊C4C2×D411yescharacteristic
385(C2×D43)⋊C4C2×D411yescharacteristic
386C4⋊Dic43—21no—
387C4⋊Dic43—22no—
388C4⋊Dic43C2×D411yescharacteristic
389C4⋊Dic43C2×D411yescharacteristic
390C4⋊Dic43C2412yes—
391Dic43⋊C4—22no—
392Dic43⋊C4—22no—
393Dic43⋊C4—22no—
394Dic43⋊C4C2×D411yescharacteristic
395Dic43⋊C4C2×D411yescharacteristic
396Dic43⋊C4C2×D411yescharacteristic
397Dic43⋊C4C2×D411yescharacteristic
398C4×Dic43—22no—
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2411yescharacteristic
404C4×Dic43C2411yescharacteristic
405C2×C43⋊C8C2412yes—
406C2×C43⋊C8C2412yes—
407D344—44no—
408D344—44no—
409#10621872—24no—
410C8×D43—24no—
411C23×C43—22no—
412C23×C43C22×D411yescharacteristic
413C22×D43—22no—
414C22×D43—22no—
415C22×D43—22no—
416C22×D43—44no—
417C22×D43—44no—
418C22×D43—44no—
419C22×D43—82no—
420C22×D43—82no—
421C22×D43—82no—
422C22×D43—82no—
423C22×D43—82no—
424C22×D43—82no—
425C22×D43C22×D411yescharacteristic
426C22×D43C22×D411yescharacteristic
427Q8×C43—24no—
428Q8×C43—24no—
429Q8×C43—42no—
430D4×C43—24no—
431D4×C43—44no—
432D4×C43—42no—
433D4×C43—42no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—44no—
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C22×D411yescharacteristic
445C2×C4×C43C22×D411yescharacteristic
446C2×C4×C43C2511yescharacteristic
447C22⋊D43—22no—
448C22⋊D43—22no—
449C22⋊D43—44no—
450C22⋊D43—44no—
451C22⋊D43—82no—
452C22⋊D43—82no—
453C22⋊D43—82no—
454C22⋊D43—82no—
455C22⋊D43—82no—
456C2×Dic43—22no—
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459C2×Dic43C22×D411yescharacteristic
460C2×Dic43C22×D411yescharacteristic
461C2×Dic43C22×D411yescharacteristic
462C2×Dic43C22×D411yescharacteristic
463D172—22no—
464D172—24no—
465D172—24no—
466D172—24no—
467D172—44no—
468D172—44no—
469D172—44no—
470D172—44no—
471D172—42no—
472D172—42no—
473D172—42no—
474D172—42no—
475D172—42no—
476D172—42no—
477D172—82no—
478D172—82no—
479D172—82no—
480C4×D43—22no—
481C4×D43—22no—
482C4×D43—22no—
483C4×D43—22no—
484C4×D43—22no—
485C4×D43—44no—
486C4×D43—44no—
487C4×D43—44no—
488C4×D43—82no—
489C4×D43—82no—
490C4×D43—82no—
491C4×D43H(5,𝔽2)14yes—
492Dic86—22no—
493Dic86—42no—
494Dic86—82no—
495C8×C43—22no—
496C8×C43—22no—
497C43⋊C8—22no—
498C43⋊C8—22no—
499#60822—431nomaximal, Sylow
500C22×C43—21no—
501C22×C43—21no—
502C22×C43—21no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43C23×D411yescharacteristic
507C2×D43—21no—
508C2×D43—21no—
509C2×D43—21no—
510C2×D43—21no—
511C2×D43—21no—
512C2×D43—42no—
513C2×D43—42no—
514C2×D43—42no—
515C2×D43—42no—
516C2×D43—42no—
517C2×D43—42no—
518C2×D43—42no—
519C2×D43—42no—
520C2×D43—42no—
521C2×D43—164no—
522C2×D43—164no—
523C2×D43—164no—
524C2×D43#53512yes—
525C4×C43—21no—
526C4×C43—21no—
527C4×C43—21no—
528C4×C43—42no—
529C4×C43—42no—
530C4×C43—42no—
531C4×C43#57612yes—
532C4×C43#57712yes—
533C4×C43C2×H(5,𝔽2)12yes—
534Dic43—21no—
535Dic43—21no—
536Dic43—21no—
537Dic43—21no—
538Dic43—21no—
539Dic43—42no—
540Dic43#53512yes—
541#3511—431no—
542#3498—431no—
543#3224—434no—
544#3224—434no—
545#3210—431no—
546#3210D4311yescharacteristic, complemented
547#3208—431no—
548#3208—431no—
549#3207—431no—
550#3207—431no—
551#3205—431no—
552#3205—431no—
553#3151—431no—
554#3147—431no—
555#3141—431no—
556C2×#486—431no—
557#3045—434no—
558#3012—434no—
559#2922—431no—
560C2×C43—41no—
561C2×C43—82no—
562C2×C43C2×#53511yescharacteristic
563C2×C43C2×#57611yescharacteristic
564C2×C43C2×#57711yescharacteristic
565D43—22no—
566D43—41no—
567D43—82no—
568D43—82no—
569D43—82no—
570C2×H(5,𝔽2)—432no—
571C2×AGL(1,ℤ/8)—434no—
572C2×#135—434no—
573#556—861no—
574#555—861no—
575#554—861no—
576#553—861no—
577#553—861no—
578#550—861no—
579#550—861no—
580#548—861no—
581#548—861no—
582#547—861no—
583D42—861no—
584D42—861no—
585D42—861no—
586D42—861no—
587D42—861no—
588D42—861no—
589#542—432no—
590#542—432no—
591#537—432no—
592#535—432no—
593#535—432no—
594#535—432no—
595#533—431no—
596#533C2×D4311yescharacteristic, complemented
597#532—431no—
598#532—431no—
599#532—431no—
600#532—431no—
601#532—431no—
602#532C2×D4311yescharacteristic
603C2×C4⋊Q8—431no—
604C2×#127—431no—
605C2×#127—431no—
606C2×#127—431no—
607#520—432no—
608C4×#41—431no—
609#496—434no—
610#495—434no—
611#494C2×D4311yescharacteristic, complemented
612#493—431no—
613#493—431no—
614#493—431no—
615#492—431no—
616#492—431no—
617#492—431no—
618#492C2×D4311yescharacteristic, complemented
619#489—434no—
620#487—431no—
621#487C2×D4311yescharacteristic, complemented
622#486—431no—
623#486—431no—
624#486—431no—
625#486—434no—
626#486—431no—
627#486—431no—
628#486C2×D4311yescharacteristic, complemented
629#464—434no—
630#464C2×D4314yescomplemented
631#463—434no—
632#463—434no—
633#460—434no—
634#460—434no—
635#459—434no—
636#459—434no—
637#452—434no—
638#452C2×D4314yescomplemented
639#450—434no—
640#450—434no—
641#449—434no—
642#449—434no—
643#447—434no—
644#447—434no—
645#433—432no—
646#433—432no—
647#431—431no—
648#431—431no—
649#431—431no—
650#431C2×D4311yescharacteristic, complemented
651#424—432no—
652#417—434no—
653C2×#102—434no—
654#408—432no—
655C4×M16—431no—
656C2×C4×C8—431no—
657C43#6082211yescharacteristic, complemented, Sylow
658H(5,𝔽2)—1728no—
659C2×#41—431no—
660C2×#41—432no—
661C2×#41—432no—
662C2×#41—432no—
663C2×#41—862no—
664C2×#41—861no—
665C2×#41—861no—
666C2×#41C22×D4312yes—
667C22×Q8—861no—
668C22×D4—432no—
669C22×D4—432no—
670C22×D4—432no—
671C22×D4—862no—
672C22×D4—861no—
673C22×D4—861no—
674C22×D4—861no—
675C22×D4—861no—
676C22×D4—862no—
677C22×D4—862no—
678C22×D4—861no—
679C22×D4—861no—
680AGL(1,ℤ/8)—1728no—
681#135—1728no—
682C2×Q16C22×D4314yes—
683C2×SD16—434no—
684C2×SD16—434no—
685C2×SD16—434no—
686C2×SD16C22×D4314yes—
687C2×D8—434no—
688C2×D8—434no—
689C2×D8—434no—
690C2×M16—432no—
691C22×C8—432no—
692C4⋊Q8—432no—
693C4⋊Q8—431no—
694C4⋊Q8—861no—
695C4⋊Q8—861no—
696C4⋊Q8C22×D4311yescharacteristic
697C4⋊Q8C22×D4311yescharacteristic
698C4⋊Q8C22×D4311yescharacteristic
699#127—432no—
700#127—432no—
701#127—431no—
702#127—431no—
703#127—432no—
704#127—431no—
705#127—861no—
706#127—861no—
707#127—861no—
708#127—861no—
709#127—861no—
710#127—861no—
711#127C22×D4311yescharacteristic
712#126—862no—
713#126—862no—
714#125—21no—
715#125—861no—
716#124—432no—
717#124—432no—
718#124—432no—
719#124—862no—
720#124—861no—
721#124—862no—
722#124—861no—
723#124C22×D4312yes—
724#123—862no—
725#123—862no—
726C22⋊Q8—21no—
727C22⋊Q8—432no—
728C22⋊Q8—862no—
729C22⋊Q8—862no—
730C22⋊Q8—861no—
731C22⋊Q8—862no—
732C22⋊Q8C22×D4312yes—
733#121—21no—
734#121—21no—
735#121—432no—
736#121—432no—
737#121—862no—
738#121—862no—
739#121—862no—
740#121—862no—
741#121—862no—
742#121—862no—
743#121—861no—
744#121—861no—
745#121—861no—
746#121—861no—
747#121—861no—
748#121—861no—
749#121—861no—
750#121—862no—
751#121—862no—
752#121—862no—
753#121—861no—
754#120—862no—
755#120—862no—
756#120—862no—
757#120—862no—
758#120—862no—
759#120—862no—
760C4×Q8—21no—
761C4×Q8—431no—
762C4×Q8—431no—
763C4×Q8—432no—
764C4×Q8—861no—
765C4×Q8C22×D4312yes—
766C4×D4—21no—
767C4×D4—21no—
768C4×D4—431no—
769C4×D4—431no—
770C4×D4—431no—
771C4×D4—431no—
772C4×D4—432no—
773C4×D4—431no—
774C4×D4—431no—
775C4×D4—432no—
776C4×D4—862no—
777C4×D4—861no—
778C4×D4—861no—
779C4×D4—861no—
780C4×D4—861no—
781C4×D4—861no—
782C4×D4—861no—
783C4×D4—861no—
784C4×D4—862no—
785C4×D4—861no—
786#117—21no—
787#117—431no—
788#117—431no—
789#117—431no—
790#117—862no—
791#117—861no—
792C2×C4⋊C4—432no—
793C2×C4⋊C4—862no—
794C2×C4⋊C4—861no—
795C2×C42—431no—
796C2×C42—431no—
797C2×C42C22×D4311yescharacteristic
798C4⋊C8—432no—
799C4⋊C8—432no—
800C4⋊C8—432no—
801C4⋊C8C22×D4312yes—
802#103—434no—
803#103C22×D4314yes—
804#102—434no—
805#102—434no—
806#102—434no—
807#102—434no—
808#102—434no—
809#102C22×D4314yes—
810C22⋊C8—432no—
811C22⋊C8—432no—
812C22⋊C8—432no—
813C22⋊C8C22×D4312yes—
814#97—432no—
815C4×C8—432no—
816C4×C8—431no—
817C4×C8—431no—
818C4×C8C22×D4311yescharacteristic
819C4×C8C22×D4311yescharacteristic
820C24—862no—
821C24—862no—
822C24—862no—
823#41—44no—
824#41—864no—
825#41—868no—
826#41—868no—
827#41—3442no—
828#41—3442no—
829#41—1728no—
830#41—1724no—
831C2×Q8—21no—
832C2×Q8—431no—
833C2×Q8—862no—
834C2×Q8—861no—
835C2×Q8—3442no—
836C2×Q8C23×D4312yes—
837C2×Q8C23×D4312yes—
838C2×D4—22no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—431no—
842C2×D4—431no—
843C2×D4—431no—
844C2×D4—432no—
845C2×D4—432no—
846C2×D4—432no—
847C2×D4—862no—
848C2×D4—862no—
849C2×D4—862no—
850C2×D4—862no—
851C2×D4—868no—
852C2×D4—862no—
853C2×D4—862no—
854C2×D4—862no—
855C2×D4—862no—
856C2×D4—862no—
857C2×D4—862no—
858C2×D4—862no—
859C2×D4—862no—
860C2×D4—862no—
861C2×D4—861no—
862C2×D4—861no—
863C2×D4—861no—
864C2×D4—861no—
865C2×D4—861no—
866C2×D4—861no—
867C2×D4—862no—
868C2×D4—3442no—
869C2×D4—3442no—
870C2×D4—3442no—
871C2×D4—3442no—
872C2×D4—3442no—
873C2×D4—3442no—
874C2×D4—1724no—
875C2×D4—1728no—
876C2×D4—1724no—
877C2×D4—1728no—
878C2×D4—1728no—
879C2×D4C23×D4312yes—
880C22×C4—22no—
881C22×C4—431no—
882C22×C4—431no—
883C22×C4—431no—
884C22×C4—431no—
885C22×C4—431no—
886C22×C4—431no—
887C22×C4—862no—
888C22×C4—862no—
889C22×C4—862no—
890C22×C4—862no—
891C22×C4—862no—
892C22×C4—862no—
893C22×C4D4×D4311yescharacteristic
894C22×C4D4×D4311yescharacteristic
895C22×C4C23×D4311yescharacteristic
896Q16—44no—
897SD16—44no—
898SD16—1724no—
899SD16—1724no—
900SD16—1724no—
901D8—1724no—
902D8—1724no—
903D8—1724no—
904M16—864no—
905C2×C8—432no—
906C2×C8—432no—
907C2×C8—864no—
908C2×C8C23×D4312yes—
909C2×C8C23×D4312yes—
910C4⋊C4—21no—
911C4⋊C4—22no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—22no—
917C4⋊C4—431no—
918C4⋊C4—431no—
919C4⋊C4—431no—
920C4⋊C4—431no—
921C4⋊C4—431no—
922C4⋊C4—431no—
923C4⋊C4—432no—
924C4⋊C4—862no—
925C4⋊C4—862no—
926C4⋊C4—862no—
927C4⋊C4—862no—
928C4⋊C4—861no—
929C4⋊C4C23×D4312yes—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—22no—
933C22⋊C4—431no—
934C22⋊C4—431no—
935C22⋊C4—431no—
936C22⋊C4—431no—
937C22⋊C4—431no—
938C22⋊C4—431no—
939C22⋊C4—862no—
940C22⋊C4—862no—
941C22⋊C4—862no—
942C22⋊C4—862no—
943C22⋊C4—862no—
944C22⋊C4—862no—
945C22⋊C4—862no—
946C22⋊C4—862no—
947C22⋊C4—862no—
948C22⋊C4—862no—
949C22⋊C4—862no—
950C42—22no—
951C42—431no—
952C42—431no—
953C42—431no—
954C42—431no—
955C42—431no—
956C42—431no—
957C42—862no—
958C42D4×D4311yescharacteristic
959C42D4×D4311yescharacteristic
960C42C23×D4311yescharacteristic
961C42C23×D4311yescharacteristic
962C23—22no—
963C23—431no—
964C23—431no—
965C23—862no—
966C23—862no—
967C23—862no—
968C23—3442no—
969C23—3442no—
970C23—3442no—
971C23—3442no—
972C23—3442no—
973C23—3442no—
974C23—1724no—
975C23—1724no—
976C23—1724no—
977C23C2×D4×D4311yescharacteristic
978Q8—24no—
979Q8—24no—
980Q8—42no—
981Q8—862no—
982Q8—3442no—
983Q8—1722no—
984D4—24no—
985D4—44no—
986D4—42no—
987D4—42no—
988D4—862no—
989D4—862no—
990D4—862no—
991D4—864no—
992D4—864no—
993D4—864no—
994D4—3442no—
995D4—3442no—
996D4—3442no—
997D4—3442no—
998D4—3442no—
999D4—3442no—
1000D4—3442no—
1001D4—3442no—
1002D4—1724no—
1003D4—1724no—
1004D4—1724no—
1005D4—1724no—
1006D4—1724no—
1007D4—1724no—
1008D4—1722no—
1009D4—1722no—
1010D4—1722no—
1011D4—1722no—
1012D4—1722no—
1013D4—1722no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—44no—
1021C2×C4—431no—
1022C2×C4—434no—
1023C2×C4—431no—
1024C2×C4—431no—
1025C2×C4—431no—
1026C2×C4—431no—
1027C2×C4—431no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—3442no—
1035C2×C4—3442no—
1036C2×C4—3442no—
1037C2×C4—1724no—
1038C2×C4—1724no—
1039C2×C4—1724no—
1040C2×C4C2×D4×D4311yescharacteristic
1041C2×C4C2×D4×D4311yescharacteristic
1042C2×C4C2×D4×D4311yescharacteristic
1043C2×C4C2×D4×D4311yescharacteristic
1044C2×C4C2×D4×D4311yescharacteristic
1045C2×C4C24×D4311yescharacteristic
1046C8—22no—
1047C8—22no—
1048C8—862no—
1049C8—862no—
1050C22—21no—
1051C22—21no—
1052C22—21no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—432no—
1057C22—861no—
1058C22—861no—
1059C22—861no—
1060C22—861no—
1061C22—861no—
1062C22—1722no—
1063C22—1722no—
1064C22—1722no—
1065C22—1722no—
1066C22—1722no—
1067C22—1722no—
1068C22—1722no—
1069C22—1722no—
1070C22—1722no—
1071C22—6884no—
1072C22—6884no—
1073C22—6884no—
1074C22C22×D4×D4311yescharacteristic
1075C4—21no—
1076C4—21no—
1077C4—21no—
1078C4—42no—
1079C4—42no—
1080C4—42no—
1081C4—432no—
1082C4—861no—
1083C4—861no—
1084C4—861no—
1085C4—861no—
1086C4—861no—
1087C4—1722no—
1088C4#1458370112yes—
1089C4#1458370812yes—
1090C4H(5,𝔽2)×D4312yes—
1091C2—41no—
1092C2—82no—
1093C2—862no—
1094C2—3442no—
1095C2—3442no—
1096C2—3442no—
1097C2—1721no—
1098C2#535×D4311yescharacteristic
1099C2C2×#1458370111yescharacteristic
1100C2C2×#1458370811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3210C2
socleC22×C43C23×D4
hypercenter#3210D43
hypocenterC43#60822
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3210

Complements

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

NH ≅ G/Ntype
1. #19148507C2semidirect
2. #19148368C2semidirect
3. #19145696C2semidirect
4. #19145695C2semidirect
5. #19145548C2semidirect
6. #19145533C2semidirect
7. #19145532C2semidirect
8. #19145531C2semidirect
9. #19145528C2semidirect
10. #19145515C2semidirect
11. #19145514C2semidirect
12. #19145042C2semidirect
13. #19145024C2semidirect
14. #19144990C2semidirect
15. #486×D43C2semidirect
16. #19144137C2semidirect
17. #19143903C2semidirect
18. #19143234C2semidirect
19. C43×#3210C2semidirect
21. C2×#13063352C22semidirect
22. C2×#13063348C22semidirect
39. #14583522C22semidirect
40. #14583521C22semidirect
45. #14583454C22semidirect
48. #14583450C22semidirect
49. #14583450C22semidirect
50. #14583449C22semidirect
51. C4⋊Q8×D43C22semidirect
55. #14583381C22semidirect
57. #14583285C22semidirect
58. #14583284C22semidirect
59. #14583276C22semidirect
60. #14583276C22semidirect
61. #14583275C22semidirect
62. #14583273C22semidirect
63. #14583273C22semidirect
64. #14583273C22semidirect
65. #14583260C22semidirect
66. #14583249C22semidirect
67. #14583247C22semidirect
68. #14583247C22semidirect
69. #14583246C22semidirect
70. #14583246C22semidirect
71. #14583245C22semidirect
72. #14583244C22semidirect
73. #14583123C22semidirect
74. #14583117C22semidirect
75. #14583111C22semidirect
76. #14583099C22semidirect
77. #14583097C22semidirect
78. #14583095C22semidirect
79. #14583093C22semidirect
80. #14583060C22semidirect
81. #14583049C22semidirect
82. #14583048C22semidirect
83. #14583047C22semidirect
84. #14583044C22semidirect
85. #14583035C22semidirect
86. #14583034C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
92. #14582924C22semidirect
93. #14582899C22semidirect
94. #102×D43C22semidirect
96. C4×#10621872C22semidirect
97. C4×C8×D43C22semidirect
98. C43×#533C22semidirect
100. C43×#494C22semidirect
101. C43×#492C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#464C22semidirect
105. C43×#452C22semidirect
106. C43×#431C22semidirect
546. #3210D43semidirect
596. #533C2×D43semidirect
611. #494C2×D43semidirect
618. #492C2×D43semidirect
621. #487C2×D43semidirect
628. #486C2×D43semidirect
630. #464C2×D43semidirect
638. #452C2×D43semidirect
650. #431C2×D43semidirect
657. C43#60822semidirect

Maximal subgroups

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

subgroupindex
#191485072
#191483682
#191456962
#191456952
#191455482
#191455332
#191455322
#191455312
#191455282
#191455152
#191455142
#191450422
#191450242
#191449902
#486×D432
#191441372
#191439032
#191432342
C43×#32102
#6082243