Finite Group Databasebeta

← #25968354

Subgroups — #25968354

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#19148371C211yesmaximal, characteristic, complemented
3#19145694C214yesmaximal, complemented
4#19145693C214yesmaximal, complemented
5#19145547C211yesmaximal, characteristic, complemented
6#19145546C211yesmaximal, characteristic, complemented
7#19145532C211yesmaximal, characteristic, complemented
8#19145530C211yesmaximal, characteristic, complemented
9#19145529C211yesmaximal, characteristic, complemented
10#19145514C211yesmaximal, characteristic, complemented
11#19145513C211yesmaximal, characteristic, complemented
12#19145042C211yesmaximal, characteristic, complemented
13#19145018C211yesmaximal, characteristic, complemented
14#19144985C211yesmaximal, characteristic, complemented
15#486×D43C211yesmaximal, characteristic, complemented
16#19144131C214yesmaximal, complemented
17#19143900C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3208C211yesmaximal, characteristic, complemented
20C2×#13063370C2212yes—
21C2×#13063352C2214yescomplemented
22C2×#13063346C2214yescomplemented
23#14583621—21no—
24#14583612—21no—
25#14583605—21no—
26#14583602—21no—
27#14583593—21no—
28#14583569—21no—
29#14583569—21no—
30#14583561—21no—
31#14583559—21no—
32#14583551—21no—
33#14583534—21no—
34#14583534—21no—
35D4×C22⋊D43—21no—
36D4×C22⋊D43—21no—
37D4×C22⋊D43—21no—
38D4×C22⋊D43—21no—
39#14583522C2212yescomplemented
40#14583521C2212yescomplemented
41#14583479C2212yes—
42#14583466C2212yes—
43#14583462C2212yes—
44#14583462C2212yes—
45#14583454C2211yescharacteristic, complemented
46#14583450C2211yescharacteristic, complemented
47#14583450C2211yescharacteristic, complemented
48#14583449C2211yescharacteristic
49#14583449C2211yescharacteristic, complemented
50#14583447C2211yescharacteristic
51#14583447C2211yescharacteristic
52C4⋊Q8×D43C2211yescharacteristic, complemented
53#127×D43C2211yescharacteristic
54#127×D43C2211yescharacteristic
55#14583381C2212yescomplemented
56C4×#10621898C2211yescharacteristic
57#14583285C2214yescomplemented
58#14583280C2214yescomplemented
59#14583278C2211yescharacteristic, complemented
60#14583276C2211yescharacteristic, complemented
61#14583275C2211yescharacteristic, complemented
62#14583275C2211yescharacteristic, complemented
63#14583273C2211yescharacteristic, complemented
64#14583272C2211yescharacteristic, complemented
65#14583257C2214yescomplemented
66#14583251C2211yescharacteristic, complemented
67#14583250C2211yescharacteristic, complemented
68#14583247C2211yescharacteristic, complemented
69#14583246C2211yescharacteristic, complemented
70#14583245C2211yescharacteristic, complemented
71#14583245C2211yescharacteristic, complemented
72#14583244C2214yescomplemented
73#14583121C2214yescomplemented
74#14583119C2214yescomplemented
75#14583115C2214yescomplemented
76#14583113C2214yescomplemented
77#14583097C2214yescomplemented
78#14583093C2214yescomplemented
79#14583091C2214yescomplemented
80#14583059C2214yescomplemented
81#14583058C2214yescomplemented
82#14583048C2214yescomplemented
83#14583046C2214yescomplemented
84#14583045C2214yescomplemented
85#14583034C2214yescomplemented
86#14583033C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yescomplemented
93#14582897C2214yescomplemented
94#102×D43C2214yescomplemented
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic, complemented
97C4×C8×D43C2211yescharacteristic, complemented
98C43×#533C2211yescharacteristic, complemented
99C2×#127×C43C2211yescharacteristic
100C43×#492C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#486C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#460C2214yescomplemented
105C43×#450C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063370—48no—
108C2×#10621902—21no—
109C2×#10621902C2312yes—
110C2×#10621898—21no—
111C2×#10621898C2311yescharacteristic
112C2×#10621898C2312yes—
113C2×#10621900—22no—
114C2×#10621900C2312yes—
115C2×#10621900C2312yes—
116C2×Q8×D43—21no—
117C22×C22⋊D43—22no—
118C22×C22⋊D43—22no—
119C2×D4×D43—22no—
120C2×D4×D43—21no—
121C2×D4×D43—21no—
122C2×D4×D43—21no—
123C2×D4×D43—21no—
124C2×D4×D43C2312yes—
125C2×D4×D43C2312yes—
126#13063352—48no—
127#13063346—48no—
128C2×#10621885C2314yes—
129C2×#10621873C2314yes—
130C2×#10621884C2314yes—
131C2×D344C2314yes—
132C2×#10621882C2314yes—
133C2×#10621882C2314yes—
134C2×#10621872C2312yes—
135C2×C8×D43C2312yes—
136#13063325C2311yescharacteristic
137#13063325C2311yescharacteristic
138#13063324—21no—
139#13063324C2312yes—
140#13063323—21no—
141#13063322C2311yescharacteristic
142#13063322C2311yescharacteristic
143#13063321—21no—
144#13063321—21no—
145#13063321—21no—
146#13063321—21no—
147#13063321C2312yes—
148#13063321C2312yes—
149#13063320—22no—
150#13063319—22no—
151#13063316—21no—
152#13063314—21no—
153#13063314C2312yes—
154#13063313—21no—
155#13063313—22no—
156#13063313C2312yes—
157#13063312C2312yes—
158#13063312C2312yes—
159#13063311—22no—
160#13063310—22no—
161#13063307—22no—
162#13063305—21no—
163#13063305—22no—
164#13063303—22no—
165#13063303—22no—
166#13063301C2312yes—
167#13063300—22no—
168#13063300—21no—
169#13063300—21no—
170#13063300—21no—
171#13063300C2312yes—
172#13063299—21no—
173#13063299—21no—
174#13063299—21no—
175#13063299C2312yes—
176#13063298—22no—
177#13063298—22no—
178#13063297—22no—
179#13063297—22no—
180#13063297—22no—
181#13063297—22no—
182#13063296—21no—
183#13063296—21no—
184#13063296—21no—
185#13063296—21no—
186#13063296—22no—
187#13063296—22no—
188#13063294—22no—
189#13063294—22no—
190#13063293—22no—
191#13063293—22no—
192#13063293—22no—
193#13063293—22no—
194Q8×Dic43C2312yes—
195C4×Dic86D411yescharacteristic
196C4×Dic86D411yescharacteristic
197#13063290—21no—
198C4×D172—21no—
199C4×D172—21no—
200C4×D172—21no—
201C4×D172—22no—
202C4×D172D411yescharacteristic
203C4×D172D411yescharacteristic
204C4×D172C2312yes—
205D4×Dic43—21no—
206D4×Dic43—21no—
207D4×Dic43—21no—
208D4×Dic43—21no—
209#13063287—22no—
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#13063250C2314yes—
232#13063248C2314yes—
233#13063247C2314yes—
234#13063246C2314yes—
235#13063246C2314yes—
236#13063245C2314yes—
237C22⋊(C43⋊C8)C2312yes—
238(C2×D43)⋊C8C2312yes—
239(C2×D43)⋊C8C2312yes—
240#13063235C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2311yescharacteristic
243C8×Dic43C2312yes—
244C22×D4×C43—21no—
245C22×D4×C43—21no—
246C22×D4×C43C2312yes—
247C2×SD16×C43C2314yes—
248C2×SD16×C43C2314yes—
249C4⋊Q8×C43C2311yescharacteristic
250C4⋊Q8×C43C2311yescharacteristic
251#127×C43—21no—
252#127×C43—21no—
253#127×C43C2312yes—
254#127×C43C2311yescharacteristic
255#127×C43C2311yescharacteristic
256#125×C43—21no—
257C22⋊Q8×C43—21no—
258C22⋊Q8×C43C2312yes—
259C4×Q8×C43—21no—
260C4×Q8×C43C2312yes—
261#117×C43—21no—
262C2×C42×C43C2311yescharacteristic
263C4⋊C8×C43C2312yes—
264#102×C43C2314yes—
265#102×C43C2314yes—
266C22⋊C8×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C4×C8×C43C2311yescharacteristic
269C24×C43—22no—
270C23×D43—22no—
271C23×D43—22no—
272C2×Q8×C43—21no—
273C2×Q8×C43C2412yes—
274C2×D4×C43—22no—
275C2×D4×C43—21no—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—21no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C2×D4×C43—44no—
282C2×D4×C43—82no—
283C2×D4×C43—82no—
284C2×D4×C43C2412yes—
285C2×D4×C43C2412yes—
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C2×C22⋊D43—22no—
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—48no—
300C2×C22⋊D43—48no—
301C2×C22⋊D43C2×D411yescharacteristic
302C2×C22⋊D43C2×D411yescharacteristic
303C22×Dic43—22no—
304C22×Dic43—22no—
305#10621902—28no—
306#10621902—82no—
307Q8×D43—82no—
308#10621900—28no—
309#10621900—44no—
310#10621900—48no—
311D4×D43—28no—
312D4×D43—44no—
313D4×D43—48no—
314D4×D43—82no—
315D4×D43—82no—
316D4×D43—82no—
317D4×D43—82no—
318#10621898—24no—
319#10621898—44no—
320#10621898—82no—
321C2×D172—21no—
322C2×D172—21no—
323C2×D172—21no—
324C2×D172—21no—
325C2×D172—22no—
326C2×D172—22no—
327C2×D172C2×D411yescharacteristic
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×D43C2×D411yescharacteristic
336C2×C4×D43C2×D411yescharacteristic
337C2×C4×D43C2×D411yescharacteristic
338C2×C4×D43C2×D411yescharacteristic
339C2×C4×D43C2411yescharacteristic
340C2×C4×D43C2411yescharacteristic
341C2×Dic86—21no—
342C2×Dic86—22no—
343C2×Dic86C2×D411yescharacteristic
344C2×Dic86C2412yes—
345SD16×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—22no—
353C4⋊C4×C43—22no—
354C4⋊C4×C43C2412yes—
355C22⋊C4×C43—22no—
356C42×C43—22no—
357C42×C43C2×D411yescharacteristic
358C42×C43C2×D411yescharacteristic
359C42×C43C2411yescharacteristic
360C42×C43C2411yescharacteristic
361C22⋊Dic43—22no—
362C22⋊Dic43—22no—
363C22⋊Dic43—22no—
364C22⋊Dic43—22no—
365C22⋊Dic43C2×D411yescharacteristic
366C22⋊Dic43C2×D411yescharacteristic
367#10621885—44no—
368#10621884—44no—
369#10621882—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)⋊C4C2×D411yescharacteristic
381(C2×D43)⋊C4C2×D411yescharacteristic
382(C2×D43)⋊C4C2×D411yescharacteristic
383(C2×D43)⋊C4C2×D411yescharacteristic
384C4⋊Dic43—21no—
385C4⋊Dic43—21no—
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—
408#10621873—44no—
409#10621872—24no—
410C8×D43—24no—
411C23×C43—22no—
412C23×C43—22no—
413C23×C43—44no—
414C23×C43—82no—
415C23×C43—82no—
416C23×C43C22×D411yescharacteristic
417C22×D43—22no—
418C22×D43—22no—
419C22×D43—44no—
420C22×D43—44no—
421C22×D43—82no—
422C22×D43—82no—
423C22×D43—82no—
424C22×D43—82no—
425C22×D43C22×D411yescharacteristic
426C22×D43C22×D411yescharacteristic
427Q8×C43—24no—
428Q8×C43—42no—
429D4×C43—24no—
430D4×C43—24no—
431D4×C43—44no—
432D4×C43—42no—
433D4×C43—42no—
434D4×C43—42no—
435D4×C43—42no—
436D4×C43—82no—
437D4×C43—82no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C22×D411yescharacteristic
445C2×C4×C43C22×D411yescharacteristic
446C2×C4×C43C22×D411yescharacteristic
447C2×C4×C43C22×D411yescharacteristic
448C2×C4×C43C2511yescharacteristic
449C22⋊D43—22no—
450C22⋊D43—22no—
451C22⋊D43—44no—
452C22⋊D43—44no—
453C22⋊D43—44no—
454C22⋊D43—44no—
455C22⋊D43—44no—
456C22⋊D43—82no—
457C22⋊D43—82no—
458C22⋊D43—82no—
459C22⋊D43—82no—
460C22⋊D43—82no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—44no—
464C2×Dic43—44no—
465C2×Dic43C22×D411yescharacteristic
466C2×Dic43C22×D411yescharacteristic
467C2×Dic43C22×D411yescharacteristic
468C2×Dic43C22×D411yescharacteristic
469C2×Dic43C22×D411yescharacteristic
470C2×Dic43C22×D411yescharacteristic
471D172—22no—
472D172—24no—
473D172—24no—
474D172—44no—
475D172—42no—
476D172—42no—
477D172—42no—
478D172—42no—
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—82no—
488C4×D43—82no—
489C4×D43—82no—
490C4×D43H(5,𝔽2)14yes—
491Dic86—22no—
492Dic86—24no—
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×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—164no—
510C22×C43C23×D411yescharacteristic
511C2×D43—21no—
512C2×D43—21no—
513C2×D43—21no—
514C2×D43—21no—
515C2×D43—21no—
516C2×D43—42no—
517C2×D43—42no—
518C2×D43—42no—
519C2×D43—42no—
520C2×D43—42no—
521C2×D43—42no—
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#57612yes—
531C4×C43#57712yes—
532C4×C43C2×H(5,𝔽2)12yes—
533Dic43—21no—
534Dic43—21no—
535Dic43—21no—
536Dic43—21no—
537Dic43—21no—
538Dic43—42no—
539Dic43—42no—
540Dic43#53512yes—
541#3511—431no—
542#3498—431no—
543#3224—434no—
544#3224—434no—
545#3210—431no—
546#3210—431no—
547#3208—431no—
548#3208D4311yescharacteristic, complemented
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×C43—82no—
563C2×C43C2×#53511yescharacteristic
564C2×C43C2×#57611yescharacteristic
565C2×C43C2×#57711yescharacteristic
566D43—22no—
567D43—41no—
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#532—431no—
603C2×C4⋊Q8—431no—
604C2×#127—431no—
605C2×#127—431no—
606C2×#127C2×D4311yescharacteristic
607#520—432no—
608C4×#41—431no—
609#496—434no—
610#495—434no—
611#494—431no—
612#493—431no—
613#493—431no—
614#493—431no—
615#492—431no—
616#492—431no—
617#492C2×D4311yescharacteristic, complemented
618#492C2×D4311yescharacteristic, complemented
619#489—434no—
620#487—431no—
621#487—431no—
622#486—431no—
623#486—431no—
624#486—431no—
625#486—434no—
626#486—431no—
627#486C2×D4311yescharacteristic, complemented
628#486C2×D4311yescharacteristic, complemented
629#464—434no—
630#464—434no—
631#463—434no—
632#463—434no—
633#460—434no—
634#460C2×D4314yescomplemented
635#459—434no—
636#459—434no—
637#452—434no—
638#452—434no—
639#450—434no—
640#450C2×D4314yescomplemented
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—432no—
664C2×#41—861no—
665C2×#41—862no—
666C2×#41—861no—
667C22×Q8—861no—
668C22×D4—21no—
669C22×D4—21no—
670C22×D4—432no—
671C22×D4—432no—
672C22×D4—861no—
673C22×D4—861no—
674C22×D4—861no—
675C22×D4—861no—
676C22×D4—862no—
677C22×D4—862no—
678C22×D4—862no—
679C22×D4C22×D4312yes—
680AGL(1,ℤ/8)—1728no—
681#135—1728no—
682C2×Q16—434no—
683C2×SD16—434no—
684C2×SD16—434no—
685C2×SD16C22×D4314yes—
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—431no—
695C4⋊Q8—861no—
696C4⋊Q8—861no—
697C4⋊Q8C22×D4311yescharacteristic
698C4⋊Q8C22×D4311yescharacteristic
699#127—21no—
700#127—21no—
701#127—432no—
702#127—432no—
703#127—431no—
704#127—431no—
705#127—861no—
706#127—861no—
707#127—861no—
708#127—861no—
709#127C22×D4311yescharacteristic
710#127C22×D4311yescharacteristic
711#127C22×D4312yes—
712#126—862no—
713#126—862no—
714#125—21no—
715#125—861no—
716#124—432no—
717#124—432no—
718#124—432no—
719#124—432no—
720#124—862no—
721#124—861no—
722#124—862no—
723#124—861no—
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—432no—
734#121—432no—
735#121—862no—
736#121—862no—
737#121—861no—
738#121—861no—
739#121—861no—
740#121—862no—
741#121—862no—
742#121—862no—
743#121—862no—
744#121—862no—
745#121—862no—
746#121—862no—
747#121—861no—
748#121—861no—
749#121—861no—
750#121—861no—
751#121—861no—
752#121—861no—
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—431no—
767C4×D4—431no—
768C4×D4—431no—
769C4×D4—431no—
770C4×D4—432no—
771C4×D4—431no—
772C4×D4—431no—
773C4×D4—432no—
774C4×D4—862no—
775C4×D4—861no—
776C4×D4—861no—
777C4×D4—861no—
778C4×D4—861no—
779C4×D4—861no—
780C4×D4—861no—
781C4×D4—861no—
782C4×D4—862no—
783C4×D4—861no—
784C4×D4—861no—
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#103—434no—
804#102—434no—
805#102—434no—
806#102—434no—
807#102—434no—
808#102C22×D4314yes—
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—22no—
821C24—862no—
822C24—862no—
823#41—864no—
824#41—868no—
825#41—868no—
826#41—3442no—
827#41—3442no—
828#41—1724no—
829#41—1724no—
830#41—1728no—
831C2×Q8—21no—
832C2×Q8—431no—
833C2×Q8—432no—
834C2×Q8—862no—
835C2×Q8—861no—
836C2×Q8—3442no—
837C2×Q8C23×D4312yes—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—44no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—431no—
849C2×D4—431no—
850C2×D4—431no—
851C2×D4—432no—
852C2×D4—432no—
853C2×D4—862no—
854C2×D4—862no—
855C2×D4—868no—
856C2×D4—862no—
857C2×D4—862no—
858C2×D4—862no—
859C2×D4—862no—
860C2×D4—862no—
861C2×D4—862no—
862C2×D4—862no—
863C2×D4—862no—
864C2×D4—862no—
865C2×D4—862no—
866C2×D4—861no—
867C2×D4—861no—
868C2×D4—861no—
869C2×D4—861no—
870C2×D4—3442no—
871C2×D4—3442no—
872C2×D4—3442no—
873C2×D4—3442no—
874C2×D4—1724no—
875C2×D4—1728no—
876C2×D4—1728no—
877C2×D4—1728no—
878C2×D4C23×D4312yes—
879C2×D4C23×D4312yes—
880C22×C4—431no—
881C22×C4—431no—
882C22×C4—431no—
883C22×C4—431no—
884C22×C4—431no—
885C22×C4—431no—
886C22×C4—862no—
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—1724no—
897SD16—44no—
898SD16—44no—
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—22no—
915C4⋊C4—431no—
916C4⋊C4—431no—
917C4⋊C4—431no—
918C4⋊C4—431no—
919C4⋊C4—431no—
920C4⋊C4—431no—
921C4⋊C4—432no—
922C4⋊C4—862no—
923C4⋊C4—862no—
924C4⋊C4—862no—
925C4⋊C4—862no—
926C4⋊C4—861no—
927C4⋊C4—861no—
928C4⋊C4—861no—
929C4⋊C4C23×D4312yes—
930C22⋊C4—22no—
931C22⋊C4—431no—
932C22⋊C4—431no—
933C22⋊C4—431no—
934C22⋊C4—431no—
935C22⋊C4—431no—
936C22⋊C4—431no—
937C22⋊C4—862no—
938C22⋊C4—862no—
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—22no—
964C23—44no—
965C23—82no—
966C23—82no—
967C23—431no—
968C23—431no—
969C23—862no—
970C23—862no—
971C23—3442no—
972C23—3442no—
973C23—3442no—
974C23—3442no—
975C23—1724no—
976C23—1724no—
977C23C2×D4×D4311yescharacteristic
978Q8—24no—
979Q8—42no—
980Q8—862no—
981Q8—864no—
982Q8—3442no—
983Q8—1722no—
984D4—24no—
985D4—24no—
986D4—44no—
987D4—42no—
988D4—42no—
989D4—42no—
990D4—42no—
991D4—82no—
992D4—82no—
993D4—862no—
994D4—862no—
995D4—862no—
996D4—864no—
997D4—864no—
998D4—3442no—
999D4—3442no—
1000D4—3442no—
1001D4—3442no—
1002D4—3442no—
1003D4—3442no—
1004D4—1724no—
1005D4—1724no—
1006D4—1724no—
1007D4—1724no—
1008D4—1724no—
1009D4—1724no—
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—431no—
1020C2×C4—434no—
1021C2×C4—431no—
1022C2×C4—431no—
1023C2×C4—431no—
1024C2×C4—431no—
1025C2×C4—431no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—3442no—
1034C2×C4—3442no—
1035C2×C4—3442no—
1036C2×C4—1724no—
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—42no—
1057C22—42no—
1058C22—42no—
1059C22—164no—
1060C22—432no—
1061C22—861no—
1062C22—861no—
1063C22—861no—
1064C22—861no—
1065C22—861no—
1066C22—1722no—
1067C22—1722no—
1068C22—1722no—
1069C22—1722no—
1070C22—1722no—
1071C22—1722no—
1072C22—6884no—
1073C22—6884no—
1074C22C22×D4×D4311yescharacteristic
1075C4—21no—
1076C4—21no—
1077C4—21no—
1078C4—42no—
1079C4—42no—
1080C4—432no—
1081C4—861no—
1082C4—861no—
1083C4—861no—
1084C4—861no—
1085C4—861no—
1086C4—1722no—
1087C4—1722no—
1088C4#1458370312yes—
1089C4#1458370512yes—
1090C4H(5,𝔽2)×D4312yes—
1091C2—41no—
1092C2—82no—
1093C2—82no—
1094C2—862no—
1095C2—3442no—
1096C2—3442no—
1097C2—1721no—
1098C2#535×D4311yescharacteristic
1099C2C2×#1458370311yescharacteristic
1100C2C2×#1458370511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3208C2
socleC22×C43C23×D4
hypercenter#3208D43
hypocenterC43#60822
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #19148507C2semidirect
2. #19148371C2semidirect
3. #19145694C2semidirect
4. #19145693C2semidirect
5. #19145547C2semidirect
6. #19145546C2semidirect
7. #19145532C2semidirect
8. #19145530C2semidirect
9. #19145529C2semidirect
10. #19145514C2semidirect
11. #19145513C2semidirect
12. #19145042C2semidirect
13. #19145018C2semidirect
14. #19144985C2semidirect
15. #486×D43C2semidirect
16. #19144131C2semidirect
17. #19143900C2semidirect
18. #19143234C2semidirect
19. C43×#3208C2semidirect
21. C2×#13063352C22semidirect
22. C2×#13063346C22semidirect
39. #14583522C22semidirect
40. #14583521C22semidirect
45. #14583454C22semidirect
46. #14583450C22semidirect
47. #14583450C22semidirect
49. #14583449C22semidirect
52. C4⋊Q8×D43C22semidirect
55. #14583381C22semidirect
57. #14583285C22semidirect
58. #14583280C22semidirect
59. #14583278C22semidirect
60. #14583276C22semidirect
61. #14583275C22semidirect
62. #14583275C22semidirect
63. #14583273C22semidirect
64. #14583272C22semidirect
65. #14583257C22semidirect
66. #14583251C22semidirect
67. #14583250C22semidirect
68. #14583247C22semidirect
69. #14583246C22semidirect
70. #14583245C22semidirect
71. #14583245C22semidirect
72. #14583244C22semidirect
73. #14583121C22semidirect
74. #14583119C22semidirect
75. #14583115C22semidirect
76. #14583113C22semidirect
77. #14583097C22semidirect
78. #14583093C22semidirect
79. #14583091C22semidirect
80. #14583059C22semidirect
81. #14583058C22semidirect
82. #14583048C22semidirect
83. #14583046C22semidirect
84. #14583045C22semidirect
85. #14583034C22semidirect
86. #14583033C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
92. #14582924C22semidirect
93. #14582897C22semidirect
94. #102×D43C22semidirect
96. C4×#10621872C22semidirect
97. C4×C8×D43C22semidirect
98. C43×#533C22semidirect
100. C43×#492C22semidirect
101. C43×#492C22semidirect
102. C43×#486C22semidirect
103. C43×#486C22semidirect
104. C43×#460C22semidirect
105. C43×#450C22semidirect
106. C43×#431C22semidirect
548. #3208D43semidirect
596. #533C2×D43semidirect
617. #492C2×D43semidirect
618. #492C2×D43semidirect
627. #486C2×D43semidirect
628. #486C2×D43semidirect
634. #460C2×D43semidirect
640. #450C2×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
#191483712
#191456942
#191456932
#191455472
#191455462
#191455322
#191455302
#191455292
#191455142
#191455132
#191450422
#191450182
#191449852
#486×D432
#191441312
#191439002
#191432342
C43×#32082
#6082243