Finite Group Databasebeta

← #25968323

Subgroups — #25968323

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C211yesmaximal, characteristic, complemented
2#19148375C211yesmaximal, characteristic, complemented
3#19145654C214yesmaximal, complemented
4#19145653C214yesmaximal, complemented
5#19145529C211yesmaximal, characteristic, complemented
6#19145528C211yesmaximal, characteristic, complemented
7#19145523C211yesmaximal, characteristic, complemented
8#19145522C211yesmaximal, characteristic, complemented
9#19145521C211yesmaximal, characteristic, complemented
10#19145517C211yesmaximal, characteristic, complemented
11#19145516C211yesmaximal, characteristic, complemented
12#19145046C211yesmaximal, characteristic, complemented
13#492×D43C211yesmaximal, characteristic, complemented
14#19144972C211yesmaximal, characteristic, complemented
15#19144914C211yesmaximal, characteristic, complemented
16#19144105C214yesmaximal, complemented
17#19143878C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3207C211yesmaximal, characteristic, complemented
20C2×#13063372C2212yes—
21C2×#13063349C2214yes—
22C2×SD16×D43C2214yes—
23#14583632—21no—
24#14583631—21no—
25#14583568—21no—
26#14583567—21no—
27D4×Dic86—21no—
28D4×Dic86—21no—
29#14583554—21no—
30#14583554—21no—
31#14583549—21no—
32#14583549—21no—
33#14583549—21no—
34#14583549—21no—
35#14583546—21no—
36#14583544—21no—
37#14583542—21no—
38#14583537—21no—
39#14583502C2212yes—
40#14583500C2212yes—
41#14583470C2212yescomplemented
42#14583469C2212yes—
43#14583469C2212yescomplemented
44#14583465C2212yes—
45#14583454C2211yescharacteristic
46#14583450C2211yescharacteristic
47#14583449C2211yescharacteristic
48#14583447C2211yescharacteristic
49#14583447C2211yescharacteristic
50#14583447C2211yescharacteristic, complemented
51C2×#13063325C2211yescharacteristic, complemented
52C4⋊Q8×D43C2211yescharacteristic
53C4⋊Q8×D43C2211yescharacteristic, complemented
54#127×D43C2211yescharacteristic
55#14583371C2212yes—
56C4×#10621898C2211yescharacteristic
57#14583287C2214yes—
58#14583275C2211yescharacteristic
59#14583273C2211yescharacteristic
60#14583272C2211yescharacteristic
61#14583272C2211yescharacteristic
62#14583271C2211yescharacteristic
63#14583271C2211yescharacteristic
64#14583270C2214yes—
65#14583266C2214yescomplemented
66#14583252C2214yescomplemented
67#14583251C2211yescharacteristic, complemented
68#14583251C2211yescharacteristic, complemented
69#14583250C2211yescharacteristic, complemented
70#14583250C2211yescharacteristic, complemented
71#14583249C2211yescharacteristic, complemented
72#14583245C2211yescharacteristic, complemented
73#14583113C2214yescomplemented
74#14583112C2214yescomplemented
75#14583111C2214yescomplemented
76#14583105C2214yescomplemented
77#14583104C2214yescomplemented
78#14583103C2214yescomplemented
79#14583102C2214yescomplemented
80#14583045C2214yescomplemented
81#14583044C2214yescomplemented
82#14583041C2214yescomplemented
83#14583040C2214yescomplemented
84#14583039C2214yescomplemented
85#14583037C2214yescomplemented
86#14583036C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yes—
93#14582906C2214yes—
94#14582892C2214yes—
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#532C2211yescharacteristic
99C43×#532C2211yescharacteristic, complemented
100C43×#493C2211yescharacteristic
101C43×#492C2211yescharacteristic
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#463C2214yescomplemented
105C43×#449C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063372—48no—
108C2×#10621902—21no—
109C2×#10621898—21no—
110C2×#10621898—22no—
111C2×#10621898C2311yescharacteristic
112C2×#10621900—22no—
113C2×#10621900—22no—
114C2×#10621900—21no—
115C2×#10621900C2312yes—
116C2×#10621900C2312yes—
117C22×Dic86—22no—
118C22×Dic86C2312yes—
119C2×Q8×D43C2312yes—
120C2×Q8×D43C2312yes—
121C2×D4×D43—21no—
122C2×D4×D43—21no—
123C2×D4×D43C2312yes—
124#13063349—48no—
125C2×#10621873C2314yes—
126C2×#10621873C2314yes—
127C2×#10621883C2314yes—
128C2×#10621883C2314yes—
129C2×#10621884C2314yes—
130SD16×D43—48no—
131C2×#10621882C2314yes—
132C2×#10621872C2312yes—
133C2×C8×D43C2312yes—
134#13063325—21no—
135#13063325—21no—
136#13063325C2312yes—
137#13063325C2311yescharacteristic
138#13063325C2311yescharacteristic
139#13063325C2311yescharacteristic
140#13063324—21no—
141#13063324—21no—
142#13063324—21no—
143#13063324—21no—
144#13063323C2312yes—
145#13063323C2312yes—
146#13063322C2311yescharacteristic
147#13063321—22no—
148#13063321—21no—
149#13063321—21no—
150#13063321C2312yes—
151#13063316C2312yes—
152#13063314—21no—
153#13063313—21no—
154#13063312—21no—
155#13063312C2312yes—
156#13063312C2312yes—
157#13063311—22no—
158#13063309—22no—
159#13063308—22no—
160#13063307—22no—
161#13063307—22no—
162#13063307—22no—
163#13063307—22no—
164#13063307—22no—
165#13063307—22no—
166#13063306—22no—
167#13063306—22no—
168#13063305—21no—
169#13063304—22no—
170#13063304—22no—
171#13063302—22no—
172#13063302—22no—
173#13063302—22no—
174#13063302—22no—
175#13063301—21no—
176#13063300—21no—
177#13063300C2312yes—
178#13063299—21no—
179#13063299—22no—
180#13063299C2312yes—
181#13063298—22no—
182#13063297—22no—
183#13063296—21no—
184#13063296—21no—
185#13063296—21no—
186#13063296—21no—
187#13063296—21no—
188#13063296—22no—
189#13063296C2312yes—
190#13063295—22no—
191#13063293—22no—
192Q8×Dic43—21no—
193C4×Dic86D411yescharacteristic
194C4×Dic86D411yescharacteristic
195#13063290—21no—
196C4×D172—21no—
197C4×D172D411yescharacteristic
198C4×D172D411yescharacteristic
199C4×D172C2312yes—
200D4×Dic43—21no—
201D4×Dic43—21no—
202D4×Dic43—21no—
203D4×Dic43—21no—
204D4×Dic43—21no—
205D4×Dic43C2312yes—
206#13063287—21no—
207#13063287C2312yes—
208C4×C22⋊D43—22no—
209C4×C22⋊D43D411yescharacteristic
210C4×C22⋊D43D411yescharacteristic
211C4×C22⋊D43D411yescharacteristic
212C4×C22⋊D43D411yescharacteristic
213(C22⋊D43)⋊C4—22no—
214#13063284C2311yescharacteristic
215#13063283C2312yes—
216#13063282C2311yescharacteristic
217#13063282C2311yescharacteristic
218C2×C4⋊Dic43—21no—
219C2×C4⋊Dic43—21no—
220C4⋊C4×D43—21no—
221C4⋊C4×D43—21no—
222C4⋊C4×D43—21no—
223C4⋊C4×D43—21no—
224C2×(C2×D43)⋊C4—22no—
225C22⋊C4×D43—22no—
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228C4⋊(C43⋊C8)C2312yes—
229Dic43⋊C8C2312yes—
230Dic43⋊C8C2312yes—
231#13063250C2314yes—
232#13063250C2314yes—
233#13063249C2314yes—
234#13063248C2314yes—
235#13063248C2314yes—
236#13063246C2314yes—
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—
270#41×C43—44no—
271#41×C43—82no—
272C2×Q8×C43—21no—
273C2×Q8×C43C2412yes—
274C2×D4×C43—21no—
275C2×D4×C43—21no—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—22no—
279C2×D4×C43—22no—
280C2×D4×C43C2412yes—
281C2×D4×C43C2412yes—
282C22×C4×C43—22no—
283C22×C4×C43—22no—
284C22×C4×C43C2×D411yescharacteristic
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2411yescharacteristic
287C2×C22⋊D43—22no—
288C2×C22⋊D43—22no—
289C2×C22⋊D43—22no—
290C2×C22⋊D43—22no—
291C2×C22⋊D43—22no—
292C2×C22⋊D43—22no—
293C2×C22⋊D43—22no—
294C2×C22⋊D43C2×D411yescharacteristic
295C2×C22⋊D43C2×D411yescharacteristic
296C22×Dic43—22no—
297C22×Dic43—22no—
298C22×Dic43—22no—
299C22×Dic43—22no—
300#10621902—82no—
301Q8×D43—28no—
302Q8×D43—44no—
303#10621900—28no—
304#10621900—44no—
305#10621900—48no—
306#10621900—48no—
307#10621900—82no—
308D4×D43—28no—
309D4×D43—82no—
310D4×D43—82no—
311#10621898—24no—
312#10621898—48no—
313#10621898—82no—
314C2×D172—21no—
315C2×D172—21no—
316C2×D172—22no—
317C2×D172C2×D411yescharacteristic
318C2×D172C2412yes—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43C2×D411yescharacteristic
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2411yescharacteristic
328C2×C4×D43C2411yescharacteristic
329C2×Dic86—21no—
330C2×Dic86—22no—
331C2×Dic86—22no—
332C2×Dic86—22no—
333C2×Dic86—44no—
334C2×Dic86—48no—
335C2×Dic86C2×D411yescharacteristic
336C2×Dic86C2412yes—
337C2×Dic86C2412yes—
338SD16×C43—44no—
339D8×C43—44no—
340C2×C8×C43C2412yes—
341C2×C8×C43C2412yes—
342C4⋊C4×C43—21no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43C2412yes—
346C22⋊C4×C43—22no—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—22no—
350C42×C43C2×D411yescharacteristic
351C42×C43C2×D411yescharacteristic
352C42×C43C2411yescharacteristic
353C42×C43C2411yescharacteristic
354C22⋊Dic43—22no—
355C22⋊Dic43—22no—
356C22⋊Dic43—22no—
357C22⋊Dic43—22no—
358C22⋊Dic43—22no—
359C22⋊Dic43—22no—
360C22⋊Dic43C2×D411yescharacteristic
361C22⋊Dic43C2×D411yescharacteristic
362#10621884—44no—
363#10621883—44no—
364#10621883—44no—
365#10621882—44no—
366(C2×D43)⋊C4—22no—
367(C2×D43)⋊C4—22no—
368(C2×D43)⋊C4—22no—
369(C2×D43)⋊C4—22no—
370(C2×D43)⋊C4—22no—
371(C2×D43)⋊C4C2×D411yescharacteristic
372(C2×D43)⋊C4C2×D411yescharacteristic
373(C2×D43)⋊C4C2×D411yescharacteristic
374(C2×D43)⋊C4C2×D411yescharacteristic
375C4⋊Dic43—21no—
376C4⋊Dic43—21no—
377C4⋊Dic43—21no—
378C4⋊Dic43—21no—
379C4⋊Dic43—22no—
380C4⋊Dic43—22no—
381C4⋊Dic43—21no—
382C4⋊Dic43—22no—
383C4⋊Dic43C2×D411yescharacteristic
384C4⋊Dic43C2×D411yescharacteristic
385C4⋊Dic43C2412yes—
386Dic43⋊C4—22no—
387Dic43⋊C4—22no—
388Dic43⋊C4—22no—
389Dic43⋊C4—22no—
390Dic43⋊C4—22no—
391Dic43⋊C4C2×D411yescharacteristic
392Dic43⋊C4C2×D411yescharacteristic
393Dic43⋊C4C2×D411yescharacteristic
394Dic43⋊C4C2×D411yescharacteristic
395C4×Dic43—22no—
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2411yescharacteristic
401C4×Dic43C2411yescharacteristic
402C2×C43⋊C8C2412yes—
403C2×C43⋊C8C2412yes—
404#10621873—44no—
405#10621873—44no—
406#10621872—24no—
407C8×D43—24no—
408C23×C43—22no—
409C23×C43—22no—
410C23×C43C22×D411yescharacteristic
411C22×D43—22no—
412C22×D43—44no—
413C22×D43—82no—
414C22×D43—82no—
415C22×D43C22×D411yescharacteristic
416C22×D43C22×D411yescharacteristic
417Q8×C43—24no—
418Q8×C43—42no—
419D4×C43—24no—
420D4×C43—24no—
421D4×C43—44no—
422D4×C43—42no—
423D4×C43—42no—
424D4×C43—42no—
425D4×C43—42no—
426D4×C43—82no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—44no—
433C2×C4×C43—82no—
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C2511yescharacteristic
440C22⋊D43—22no—
441C22⋊D43—22no—
442C22⋊D43—44no—
443C22⋊D43—44no—
444C22⋊D43—44no—
445C22⋊D43—82no—
446C22⋊D43—82no—
447C22⋊D43—82no—
448C22⋊D43—82no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—44no—
453C2×Dic43—44no—
454C2×Dic43—44no—
455C2×Dic43—82no—
456C2×Dic43C22×D411yescharacteristic
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459C2×Dic43C22×D411yescharacteristic
460C2×Dic43C22×D411yescharacteristic
461C2×Dic43C22×D411yescharacteristic
462D172—22no—
463D172—24no—
464D172—42no—
465D172—42no—
466D172—82no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—22no—
470C4×D43—22no—
471C4×D43—22no—
472C4×D43—44no—
473C4×D43—44no—
474C4×D43—82no—
475C4×D43—82no—
476C4×D43H(5,𝔽2)14yes—
477Dic86—22no—
478Dic86—24no—
479Dic86—24no—
480Dic86—44no—
481Dic86—44no—
482Dic86—42no—
483Dic86—44no—
484C8×C43—22no—
485C8×C43—22no—
486C43⋊C8—22no—
487C43⋊C8—22no—
488#60820—431nomaximal, Sylow
489C22×C43—21no—
490C22×C43—21no—
491C22×C43—21no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—42no—
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43C23×D411yescharacteristic
499C2×D43—21no—
500C2×D43—21no—
501C2×D43—21no—
502C2×D43—21no—
503C2×D43—21no—
504C2×D43—42no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—164no—
508C2×D43#53512yes—
509C4×C43—21no—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43—42no—
513C4×C43—42no—
514C4×C43#57712yes—
515C4×C43#57712yes—
516C4×C43C2×H(5,𝔽2)12yes—
517Dic43—21no—
518Dic43—21no—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—42no—
523Dic43—42no—
524Dic43—42no—
525Dic43#53512yes—
526#3508—431no—
527#3499—431no—
528#3221—434no—
529#3221—434no—
530#3207—431no—
531#3207—431no—
532#3207—431no—
533#3207D4311yescharacteristic, complemented
534#3206—431no—
535#3206—431no—
536#3206—431no—
537#3206—431no—
538#3151—431no—
539C2×#492—431no—
540#3139—431no—
541#3131—431no—
542#3042—434no—
543#3010—434no—
544#2922—431no—
545C2×C43—41no—
546C2×C43—82no—
547C2×C43—82no—
548C2×C43C2×#53511yescharacteristic
549C2×C43C2×#57711yescharacteristic
550C2×C43C2×#57711yescharacteristic
551D43—22no—
552D43—41no—
553D43—82no—
554C2×2−1+4—432no—
555C2×AGL(1,ℤ/8)—434no—
556C22×SD16—434no—
557#559—861no—
558#559—861no—
559#550—861no—
560#550—861no—
561D4×Q8—861no—
562D4×Q8—861no—
563#547—861no—
564#547—861no—
565#547—861no—
566#547—861no—
567#547—861no—
568#547—861no—
569#546—861no—
570#546—861no—
571#546—861no—
572#546—861no—
573#540—432no—
574#540—432no—
575#536—432no—
576#536—432no—
577#536—432no—
578#535—432no—
579#533—431no—
580#532—431no—
581#532—431no—
582#532—431no—
583#532—431no—
584#532—431no—
585#532C2×D4311yescharacteristic
586#532C2×D4311yescharacteristic, complemented
587C2×C4⋊Q8—431no—
588C2×C4⋊Q8—431no—
589C2×C4⋊Q8—431no—
590C2×#127—431no—
591#518—432no—
592C4×#41—431no—
593#496—434no—
594#493—431no—
595#493C2×D4311yescharacteristic
596#492—434no—
597#492—431no—
598#492—431no—
599#492—431no—
600#492—431no—
601#492—431no—
602#492C2×D4311yescharacteristic
603#491—434no—
604#488—434no—
605#487—431no—
606#487—431no—
607#487—431no—
608#487—431no—
609#487—431no—
610#487C2×D4311yescharacteristic, complemented
611#486—431no—
612#486C2×D4311yescharacteristic, complemented
613#463—434no—
614#463—434no—
615#463—434no—
616#463C2×D4314yescomplemented
617#461—434no—
618#461—434no—
619#461—434no—
620#461—434no—
621#449—434no—
622#449—434no—
623#449—434no—
624#449C2×D4314yescomplemented
625#448—434no—
626#448—434no—
627#448—434no—
628#448—434no—
629#433—432no—
630#433—432no—
631#431—431no—
632#431—431no—
633#431—431no—
634#431C2×D4311yescharacteristic, complemented
635#424—432no—
636#419—434no—
637#416—434no—
638#408—432no—
639C4×M16—431no—
640C2×C4×C8—431no—
641C43#6082011yescharacteristic, complemented, Sylow
6422−1+4—1728no—
643C2×#41—21no—
644C2×#41—431no—
645C2×#41—432no—
646C2×#41—432no—
647C2×#41—862no—
648C2×#41—861no—
649C2×#41—861no—
650C2×#41—862no—
651C2×#41—862no—
652C2×#41—861no—
653C2×#41C22×D4312yes—
654C22×Q8—432no—
655C22×Q8—432no—
656C22×Q8—432no—
657C22×Q8—862no—
658C22×D4—432no—
659C22×D4—861no—
660C22×D4—861no—
661AGL(1,ℤ/8)—1728no—
662C2×SD16—434no—
663C2×SD16—434no—
664C2×SD16—434no—
665C2×SD16—434no—
666C2×SD16—434no—
667C2×SD16—1728no—
668C2×SD16C22×D4314yes—
669C2×D8—434no—
670C2×D8C22×D4314yes—
671C2×M16—432no—
672C22×C8—432no—
673C4⋊Q8—432no—
674C4⋊Q8—432no—
675C4⋊Q8—431no—
676C4⋊Q8—431no—
677C4⋊Q8—431no—
678C4⋊Q8—432no—
679C4⋊Q8—861no—
680C4⋊Q8—861no—
681C4⋊Q8—861no—
682C4⋊Q8—861no—
683C4⋊Q8—861no—
684C4⋊Q8—861no—
685C4⋊Q8C22×D4311yescharacteristic
686C4⋊Q8C22×D4311yescharacteristic
687#127—432no—
688#127—431no—
689#127—861no—
690#127—861no—
691#127—862no—
692#127C22×D4311yescharacteristic
693#127C22×D4311yescharacteristic
694#125—432no—
695#124—21no—
696#124—432no—
697#124—432no—
698#124—861no—
699#124—861no—
700#124—862no—
701#124—861no—
702#124C22×D4312yes—
703#123—862no—
704#123—862no—
705#123—862no—
706#123—862no—
707#123—862no—
708#123—862no—
709#123—862no—
710#123—862no—
711#123—862no—
712#123—862no—
713C22⋊Q8—862no—
714C22⋊Q8—862no—
715C22⋊Q8—862no—
716C22⋊Q8—862no—
717C22⋊Q8—861no—
718C22⋊Q8—862no—
719C22⋊Q8—862no—
720C22⋊Q8—861no—
721#121—21no—
722#121—21no—
723#121—21no—
724#121—432no—
725#121—432no—
726#121—432no—
727#121—862no—
728#121—862no—
729#121—862no—
730#121—862no—
731#121—861no—
732#121—861no—
733#121—861no—
734#121—861no—
735#121—861no—
736#121—861no—
737#121—861no—
738#121C22×D4312yes—
739#120—862no—
740#120—862no—
741C4×Q8—431no—
742C4×Q8—431no—
743C4×Q8—861no—
744C4×Q8—861no—
745C4×D4—21no—
746C4×D4—21no—
747C4×D4—21no—
748C4×D4—431no—
749C4×D4—431no—
750C4×D4—431no—
751C4×D4—431no—
752C4×D4—432no—
753C4×D4—432no—
754C4×D4—431no—
755C4×D4—431no—
756C4×D4—432no—
757C4×D4—861no—
758C4×D4—861no—
759C4×D4—861no—
760C4×D4—861no—
761C4×D4—861no—
762C4×D4—861no—
763C4×D4—862no—
764C4×D4—862no—
765C4×D4—861no—
766C4×D4C22×D4312yes—
767#117—431no—
768#117—431no—
769#117—431no—
770#117—432no—
771C2×C4⋊C4—861no—
772C2×C4⋊C4—861no—
773C2×C4⋊C4—861no—
774C2×C4⋊C4—861no—
775C2×C4⋊C4—861no—
776C2×C4⋊C4—861no—
777C2×C22⋊C4—862no—
778C2×C22⋊C4—862no—
779C2×C42—431no—
780C2×C42—431no—
781C2×C42C22×D4311yescharacteristic
782C4⋊C8—432no—
783C4⋊C8—432no—
784C4⋊C8—432no—
785C4⋊C8C22×D4312yes—
786#103—434no—
787#103—434no—
788#103—434no—
789#103—434no—
790#103—434no—
791#103C22×D4314yes—
792#102—434no—
793#102C22×D4314yes—
794C22⋊C8—432no—
795C22⋊C8—432no—
796C22⋊C8—432no—
797C22⋊C8C22×D4312yes—
798#97—432no—
799C4×C8—432no—
800C4×C8—431no—
801C4×C8—431no—
802C4×C8C22×D4311yescharacteristic
803C4×C8C22×D4311yescharacteristic
804C24—862no—
805#41—44no—
806#41—82no—
807#41—864no—
808#41—868no—
809#41—3442no—
810#41—3442no—
811#41—3442no—
812#41—1728no—
813#41—1724no—
814#41—1728no—
815#41—1728no—
816C2×Q8—21no—
817C2×Q8—431no—
818C2×Q8—432no—
819C2×Q8—432no—
820C2×Q8—862no—
821C2×Q8—862no—
822C2×Q8—868no—
823C2×Q8—861no—
824C2×Q8—862no—
825C2×Q8—1724no—
826C2×Q8—1728no—
827C2×Q8—1724no—
828C2×Q8C23×D4312yes—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—431no—
836C2×D4—431no—
837C2×D4—431no—
838C2×D4—432no—
839C2×D4—862no—
840C2×D4—868no—
841C2×D4—862no—
842C2×D4—862no—
843C2×D4—862no—
844C2×D4—862no—
845C2×D4—862no—
846C2×D4—862no—
847C2×D4—862no—
848C2×D4—861no—
849C2×D4—861no—
850C2×D4—3442no—
851C2×D4—3442no—
852C2×D4C23×D4312yes—
853C2×D4C23×D4312yes—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—431no—
862C22×C4—862no—
863C22×C4—862no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—862no—
868C22×C4—862no—
869C22×C4—862no—
870C22×C4D4×D4311yescharacteristic
871C22×C4D4×D4311yescharacteristic
872C22×C4C23×D4311yescharacteristic
873SD16—44no—
874SD16—1724no—
875SD16—1724no—
876SD16—1724no—
877SD16—1724no—
878SD16—1724no—
879D8—44no—
880D8—1724no—
881M16—864no—
882C2×C8—432no—
883C2×C8—432no—
884C2×C8—864no—
885C2×C8C23×D4312yes—
886C2×C8C23×D4312yes—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—431no—
891C4⋊C4—431no—
892C4⋊C4—431no—
893C4⋊C4—431no—
894C4⋊C4—431no—
895C4⋊C4—431no—
896C4⋊C4—432no—
897C4⋊C4—862no—
898C4⋊C4—862no—
899C4⋊C4—862no—
900C4⋊C4—862no—
901C4⋊C4—862no—
902C4⋊C4—862no—
903C4⋊C4—861no—
904C4⋊C4—861no—
905C4⋊C4—861no—
906C4⋊C4—861no—
907C4⋊C4—862no—
908C4⋊C4—862no—
909C4⋊C4—861no—
910C4⋊C4C23×D4312yes—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—431no—
916C22⋊C4—431no—
917C22⋊C4—431no—
918C22⋊C4—431no—
919C22⋊C4—431no—
920C22⋊C4—431no—
921C22⋊C4—862no—
922C22⋊C4—862no—
923C22⋊C4—862no—
924C22⋊C4—862no—
925C22⋊C4—862no—
926C22⋊C4—862no—
927C22⋊C4—862no—
928C22⋊C4—862no—
929C22⋊C4—862no—
930C22⋊C4—862no—
931C22⋊C4—862no—
932C42—431no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—431no—
938C42—862no—
939C42D4×D4311yescharacteristic
940C42D4×D4311yescharacteristic
941C42C23×D4311yescharacteristic
942C42C23×D4311yescharacteristic
943C23—22no—
944C23—22no—
945C23—431no—
946C23—431no—
947C23—862no—
948C23—3442no—
949C23—3442no—
950C23—1724no—
951C23C2×D4×D4311yescharacteristic
952Q8—24no—
953Q8—42no—
954Q8—862no—
955Q8—864no—
956Q8—864no—
957Q8—1724no—
958Q8—1724no—
959Q8—1724no—
960Q8—1722no—
961D4—24no—
962D4—24no—
963D4—44no—
964D4—42no—
965D4—42no—
966D4—42no—
967D4—42no—
968D4—82no—
969D4—862no—
970D4—862no—
971D4—862no—
972D4—864no—
973D4—3442no—
974D4—3442no—
975D4—3442no—
976D4—3442no—
977D4—3442no—
978D4—1724no—
979D4—1724no—
980D4—1724no—
981D4—1722no—
982D4—1722no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—44no—
989C2×C4—82no—
990C2×C4—431no—
991C2×C4—434no—
992C2×C4—431no—
993C2×C4—431no—
994C2×C4—431no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—3442no—
1006C2×C4—3442no—
1007C2×C4—3442no—
1008C2×C4—1724no—
1009C2×C4—1724no—
1010C2×C4—1724no—
1011C2×C4—1724no—
1012C2×C4—1724no—
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C2×D4×D4311yescharacteristic
1015C2×C4C2×D4×D4311yescharacteristic
1016C2×C4C2×D4×D4311yescharacteristic
1017C2×C4C2×D4×D4311yescharacteristic
1018C2×C4C24×D4311yescharacteristic
1019C8—22no—
1020C8—22no—
1021C8—862no—
1022C8—862no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—432no—
1033C22—861no—
1034C22—861no—
1035C22—861no—
1036C22—861no—
1037C22—861no—
1038C22—1722no—
1039C22—1722no—
1040C22—1722no—
1041C22—6884no—
1042C22C22×D4×D4311yescharacteristic
1043C4—21no—
1044C4—21no—
1045C4—21no—
1046C4—42no—
1047C4—42no—
1048C4—432no—
1049C4—861no—
1050C4—861no—
1051C4—861no—
1052C4—861no—
1053C4—861no—
1054C4—1722no—
1055C4—1722no—
1056C4—1722no—
1057C4#1458370612yes—
1058C4#1458370912yes—
1059C4H(5,𝔽2)×D4312yes—
1060C2—41no—
1061C2—82no—
1062C2—82no—
1063C2—862no—
1064C2—3442no—
1065C2—1721no—
1066C2#535×D4311yescharacteristic
1067C2C2×#1458370611yescharacteristic
1068C2C2×#1458370911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3207C2
socleC22×C43C23×D4
hypercenter#3207D43
hypocenterC43#60820
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. #19148375C2semidirect
3. #19145654C2semidirect
4. #19145653C2semidirect
5. #19145529C2semidirect
6. #19145528C2semidirect
7. #19145523C2semidirect
8. #19145522C2semidirect
9. #19145521C2semidirect
10. #19145517C2semidirect
11. #19145516C2semidirect
12. #19145046C2semidirect
13. #492×D43C2semidirect
14. #19144972C2semidirect
15. #19144914C2semidirect
16. #19144105C2semidirect
17. #19143878C2semidirect
18. #19143234C2semidirect
19. C43×#3207C2semidirect
41. #14583470C22semidirect
43. #14583469C22semidirect
50. #14583447C22semidirect
51. C2×#13063325C22semidirect
53. C4⋊Q8×D43C22semidirect
65. #14583266C22semidirect
66. #14583252C22semidirect
67. #14583251C22semidirect
68. #14583251C22semidirect
69. #14583250C22semidirect
70. #14583250C22semidirect
71. #14583249C22semidirect
72. #14583245C22semidirect
73. #14583113C22semidirect
74. #14583112C22semidirect
75. #14583111C22semidirect
76. #14583105C22semidirect
77. #14583104C22semidirect
78. #14583103C22semidirect
79. #14583102C22semidirect
80. #14583045C22semidirect
81. #14583044C22semidirect
82. #14583041C22semidirect
83. #14583040C22semidirect
84. #14583039C22semidirect
85. #14583037C22semidirect
86. #14583036C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
99. C43×#532C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#463C22semidirect
105. C43×#449C22semidirect
106. C43×#431C22semidirect
533. #3207D43semidirect
586. #532C2×D43semidirect
610. #487C2×D43semidirect
612. #486C2×D43semidirect
616. #463C2×D43semidirect
624. #449C2×D43semidirect
634. #431C2×D43semidirect
641. C43#60820semidirect

Maximal subgroups

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

subgroupindex
#191484642
#191483752
#191456542
#191456532
#191455292
#191455282
#191455232
#191455222
#191455212
#191455172
#191455162
#191450462
#492×D432
#191449722
#191449142
#191441052
#191438782
#191432342
C43×#32072
#6082043