Finite Group Databasebeta

← #25968930

Subgroups — #25968930

Order 11008.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583454C211yesmaximal, characteristic, complemented
2#529×D43C211yesmaximal, characteristic
3#19145836C212yesmaximal, complemented
4#19145830C212yesmaximal, complemented
5#19145825C211yesmaximal, characteristic, complemented
6#19145818C211yesmaximal, characteristic, complemented
7#19145813C211yesmaximal, characteristic, complemented
8#19145778C212yesmaximal, complemented
9#19145772C212yesmaximal, complemented
10#19145768C212yesmaximal, complemented
11#19145762C212yesmaximal, complemented
12#19145146C212yesmaximal, complemented
13#19144980C212yesmaximal, complemented
14#19144540C212yesmaximal, complemented
15#19144532C212yesmaximal
16#19144395C212yesmaximal, complemented
17#19144387C212yesmaximal, complemented
18#19143225C211yesmaximal, characteristic, complemented
19C43×#3239C211yesmaximal, characteristic, complemented
20#14583454—21no—
21#14583454—21no—
22#14583454—21no—
23#14583454—21no—
24#14583454C2212yes—
25#14583454C2212yes—
26#14583454C2212yescomplemented
27#14583454C2212yescomplemented
28C2×#13063325C2211yescharacteristic, complemented
29#14583436C2211yescharacteristic
30#14583435C2211yescharacteristic
31#14583434C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583432—21no—
34#14583431C2211yescharacteristic
35#14583430C2211yescharacteristic
36#14583429—21no—
37#14583428C2211yescharacteristic
38#14583427—21no—
39#14583426—21no—
40#126×D43—21no—
41C2×#13063316C2212yescomplemented
42#125×D43C2211yescharacteristic
43#124×D43C2211yescharacteristic
44#123×D43—21no—
45C2×#13063305—21no—
46C2×#13063301—21no—
47C22⋊Q8×D43C2211yescharacteristic
48#121×D43C2211yescharacteristic
49C2×Q8×Dic43—21no—
50C2×#13063290—21no—
51C4×Q8×D43C2211yescharacteristic
52C4×D4×D43—21no—
53C4×D4×D43C2211yescharacteristic
54C2×#13063283C2212yes—
55#117×D43—21no—
56C2×C42×D43C2211yescharacteristic
57#14583309C2212yescomplemented
58#14583308C2212yescomplemented
59#14583305C2212yescomplemented
60#14583300C2214yescomplemented
61#14583299C2214yescomplemented
62#14583261C2212yescomplemented
63#14583259C2212yescomplemented
64#14583258C2212yescomplemented
65#14583255C2214yescomplemented
66#14583252C2214yescomplemented
67#14583242C2214yescomplemented
68#14583238C2214yescomplemented
69#14583234C2212yescomplemented
70#14583230C2212yescomplemented
71#14583227C2212yescomplemented
72#14583225C2214yes—
73#14583221C2214yes—
74#14583217C2212yes—
75#14583213C2212yes—
76#14583210C2212yes—
77#14583209C2214yescomplemented
78#14583208C2214yescomplemented
79#14583202C2214yescomplemented
80#14583201C2214yescomplemented
81#14583195C2212yescomplemented
82#14583194C2212yescomplemented
83#14583190C2212yescomplemented
84#14583189C2212yescomplemented
85#14583181C2212yescomplemented
86#14583176C2212yescomplemented
87#14582956C2211yescharacteristic, complemented
88#14582954C2212yescomplemented
89#14582951C2212yescomplemented
90#14582949C2212yescomplemented
91#14582940C2214yes—
92#14582938C2214yes—
93#14582921C2212yes—
94#14582906C2214yes—
95#14582902C2214yes—
96#14582861C2212yes—
97#14582851C2212yes—
98C2×C4⋊Q8×C43C2211yescharacteristic, complemented
99C43×#529C2211yescharacteristic
100C43×#501C2212yescomplemented
101C43×#489C2212yescomplemented
102C43×#484C2212yescomplemented
103C43×#481C2212yes—
104C43×#475C2212yescomplemented
105C43×#474C2212yescomplemented
106C43×#432C2211yescharacteristic, complemented
107C22×Dic86—21no—
108C2×Q8×D43C2311yescharacteristic
109C2×D4×D43—21no—
110C2×D4×D43C2311yescharacteristic
111C22×C4×D43—21no—
112C22×C4×D43D411yescharacteristic
113C22×C4×D43D411yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C2×#10621872C2314yes—
116#13063325—21no—
117#13063325—21no—
118#13063325C2312yes—
119#13063325C2312yes—
120#13063320—21no—
121#13063320—21no—
122#13063320—21no—
123#13063319—21no—
124#13063318—21no—
125#13063318—21no—
126#13063318—21no—
127#13063317C2311yescharacteristic
128#13063316—22no—
129#13063316—22no—
130#13063316C2311yescharacteristic
131#13063316C2314yes—
132#13063316C2311yescharacteristic
133#13063316C2314yes—
134#13063315—21no—
135#13063315—21no—
136#13063314C2311yescharacteristic
137#13063313C2311yescharacteristic
138#13063312C2311yescharacteristic
139#13063311—21no—
140#13063311—21no—
141#13063310—21no—
142#13063310—21no—
143#13063309—21no—
144#13063308—21no—
145#13063307—21no—
146#13063307—21no—
147#13063306—21no—
148#13063305—22no—
149#13063305—22no—
150#13063305—22no—
151#13063305—22no—
152#13063305C2311yescharacteristic
153#13063304C2311yescharacteristic
154#13063303—21no—
155#13063302—21no—
156#13063301—22no—
157#13063301—22no—
158#13063301—22no—
159#13063301—22no—
160#13063301C2311yescharacteristic
161#13063300C2311yescharacteristic
162#13063299C2311yescharacteristic
163#13063298—21no—
164#13063297—21no—
165#13063296C2311yescharacteristic
166Q8×Dic43—22no—
167Q8×Dic43—22no—
168Q8×Dic43—22no—
169Q8×Dic43—22no—
170Q8×Dic43C2311yescharacteristic
171C4×Dic86—21no—
172C4×Dic86C2311yescharacteristic
173#13063290—21no—
174#13063290—22no—
175#13063290—22no—
176#13063290—22no—
177#13063290—22no—
178#13063290C2311yescharacteristic
179C4×D172—21no—
180C4×D172C2311yescharacteristic
181D4×Dic43—21no—
182D4×Dic43C2311yescharacteristic
183#13063287—21no—
184#13063287C2311yescharacteristic
185C4×C22⋊D43—21no—
186C4×C22⋊D43—21no—
187C4×C22⋊D43—21no—
188(C22⋊D43)⋊C4—21no—
189(C22⋊D43)⋊C4—21no—
190(C22⋊D43)⋊C4—21no—
191#13063284—21no—
192#13063283—22no—
193#13063283—22no—
194#13063283—21no—
195#13063283—21no—
196#13063283C2314yes—
197#13063283C2314yes—
198#13063282—21no—
199#13063282—21no—
200#13063281—21no—
201#13063281—21no—
202C2×C4⋊Dic43—21no—
203C2×C4⋊Dic43—22no—
204C2×C4⋊Dic43C2312yes—
205C2×Dic43⋊C4—22no—
206C4⋊C4×D43—21no—
207C4⋊C4×D43—21no—
208C4⋊C4×D43—21no—
209C4⋊C4×D43—21no—
210C4⋊C4×D43C2311yescharacteristic
211C4⋊C4×D43C2311yescharacteristic
212C2×(C2×D43)⋊C4—22no—
213C22⋊C4×D43—21no—
214C22⋊C4×D43—21no—
215C22⋊C4×D43—21no—
216C22⋊C4×D43—21no—
217C22⋊C4×D43—21no—
218C2×C4×Dic43—22no—
219C2×C4×Dic43D411yescharacteristic
220C2×C4×Dic43D411yescharacteristic
221C2×C4×Dic43C2311yescharacteristic
222C42×D43—21no—
223C42×D43D411yescharacteristic
224C42×D43D411yescharacteristic
225C42×D43D411yescharacteristic
226C42×D43D411yescharacteristic
227C42×D43C2311yescharacteristic
228C42×D43C2311yescharacteristic
229C42×D43C2311yescharacteristic
230C42×D43C2311yescharacteristic
231#13063259C2314yes—
232#13063258C2314yes—
233#13063258C2314yes—
234#13063257C2314yes—
235#13063256C2314yes—
236#13063256C2314yes—
237C4⋊(C43⋊C8)C2312yes—
238Dic43⋊C8C2314yes—
239#13063250C2314yes—
240#13063249C2314yes—
241#13063248C2314yes—
242#13063247C2314yes—
243#13063246C2314yes—
244#13063245C2314yes—
245C22⋊(C43⋊C8)C2312yes—
246(C2×D43)⋊C8C2314yes—
247#13063236C2312yes—
248C8×Dic43C2314yes—
249C22×Q8×C43—21no—
250C4⋊Q8×C43—21no—
251C4⋊Q8×C43—21no—
252C4⋊Q8×C43C2312yes—
253C4⋊Q8×C43C2312yes—
254#126×C43—21no—
255#125×C43C2311yescharacteristic
256#124×C43C2311yescharacteristic
257#123×C43—21no—
258C22⋊Q8×C43C2311yescharacteristic
259#121×C43C2311yescharacteristic
260C4×Q8×C43C2311yescharacteristic
261C4×D4×C43—21no—
262C4×D4×C43C2311yescharacteristic
263#117×C43—21no—
264C2×C4⋊C4×C43—21no—
265C2×C4⋊C4×C43C2312yes—
266C2×C42×C43C2311yescharacteristic
267#107×C43C2314yes—
268#106×C43C2314yes—
269C4⋊C8×C43C2312yes—
270#103×C43C2314yes—
271#102×C43C2314yes—
272C22⋊C8×C43C2312yes—
273#97×C43C2312yes—
274C23×D43—21no—
275C23×D43C2×D411yescharacteristic
276C2×Q8×C43—22no—
277C2×Q8×C43—22no—
278C2×Q8×C43—44no—
279C2×Q8×C43C2411yescharacteristic
280C2×D4×C43—21no—
281C2×D4×C43C2411yescharacteristic
282C22×C4×C43—21no—
283C22×C4×C43—22no—
284C22×C4×C43C2×D411yescharacteristic
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2411yescharacteristic
287C2×C22⋊D43—21no—
288C2×C22⋊D43—21no—
289C2×C22⋊D43—21no—
290C22×Dic43—21no—
291C22×Dic43—22no—
292C22×Dic43C2×D411yescharacteristic
293C22×Dic43C2×D411yescharacteristic
294C22×Dic43C2×D411yescharacteristic
295Q8×D43—24no—
296D4×D43—24no—
297D4×D43—44no—
298C2×D172—21no—
299C2×D172C2411yescharacteristic
300C2×C4×D43—24no—
301C2×C4×D43—21no—
302C2×C4×D43—21no—
303C2×C4×D43—21no—
304C2×C4×D43—21no—
305C2×C4×D43—21no—
306C2×C4×D43—42no—
307C2×C4×D43—42no—
308C2×C4×D43—44no—
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×C4×D43C2×D411yescharacteristic
313C2×C4×D43C2×D411yescharacteristic
314C2×C4×D43C2×D411yescharacteristic
315C2×C4×D43C2×D411yescharacteristic
316C2×C4×D43C2×D411yescharacteristic
317C2×C4×D43C2×D411yescharacteristic
318C2×C4×D43C2×D411yescharacteristic
319C2×C4×D43C2411yescharacteristic
320C2×C4×D43C2411yescharacteristic
321C2×Dic86—22no—
322C2×Dic86—22no—
323C2×Dic86—21no—
324C2×Dic86—44no—
325C2×Dic86C2411yescharacteristic
326C2×C8×C43C2414yes—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—22no—
329C4⋊C4×C43—22no—
330C4⋊C4×C43—21no—
331C4⋊C4×C43—21no—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43C2414yes—
335C4⋊C4×C43C2411yescharacteristic
336C4⋊C4×C43C2411yescharacteristic
337C22⋊C4×C43—21no—
338C22⋊C4×C43—21no—
339C22⋊C4×C43—21no—
340C22⋊C4×C43—21no—
341C22⋊C4×C43—21no—
342C42×C43—21no—
343C42×C43C2×D411yescharacteristic
344C42×C43C2×D411yescharacteristic
345C42×C43C2411yescharacteristic
346C42×C43C2411yescharacteristic
347C22⋊Dic43—21no—
348C22⋊Dic43—21no—
349C22⋊Dic43—21no—
350C22⋊Dic43—21no—
351C22⋊Dic43—21no—
352(C2×D43)⋊C4—21no—
353(C2×D43)⋊C4—21no—
354(C2×D43)⋊C4—21no—
355(C2×D43)⋊C4—21no—
356(C2×D43)⋊C4—21no—
357(C2×D43)⋊C4—21no—
358(C2×D43)⋊C4—21no—
359(C2×D43)⋊C4—21no—
360(C2×D43)⋊C4—21no—
361(C2×D43)⋊C4—21no—
362(C2×D43)⋊C4—24no—
363(C2×D43)⋊C4—24no—
364C4⋊Dic43—22no—
365C4⋊Dic43—22no—
366C4⋊Dic43—22no—
367C4⋊Dic43—21no—
368C4⋊Dic43—21no—
369C4⋊Dic43—21no—
370C4⋊Dic43—21no—
371C4⋊Dic43—24no—
372C4⋊Dic43—24no—
373C4⋊Dic43C2414yes—
374C4⋊Dic43C2411yescharacteristic
375C4⋊Dic43C2411yescharacteristic
376Dic43⋊C4—21no—
377Dic43⋊C4—21no—
378Dic43⋊C4—21no—
379Dic43⋊C4—21no—
380Dic43⋊C4—21no—
381Dic43⋊C4—21no—
382Dic43⋊C4—21no—
383Dic43⋊C4—21no—
384Dic43⋊C4—21no—
385Dic43⋊C4—21no—
386Dic43⋊C4—24no—
387Dic43⋊C4—24no—
388C4×Dic43—21no—
389C4×Dic43—21no—
390C4×Dic43—21no—
391C4×Dic43—24no—
392C4×Dic43—24no—
393C4×Dic43C2×D411yescharacteristic
394C4×Dic43C2×D411yescharacteristic
395C4×Dic43C2×D411yescharacteristic
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2411yescharacteristic
404C4×Dic43C2411yescharacteristic
405C2×C43⋊C8C2414yes—
406#10621872—28no—
407C23×C43—21no—
408C23×C43C22×D411yescharacteristic
409C22×D43—22no—
410C22×D43—22no—
411C22×D43—21no—
412C22×D43—41no—
413C22×D43—42no—
414C22×D43—42no—
415C22×D43—42no—
416C22×D43C22×D411yescharacteristic
417C22×D43C22×D411yescharacteristic
418Q8×C43—22no—
419Q8×C43—44no—
420Q8×C43—44no—
421D4×C43—22no—
422D4×C43—42no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—24no—
427C2×C4×C43—21no—
428C2×C4×C43—21no—
429C2×C4×C43—21no—
430C2×C4×C43—44no—
431C2×C4×C43—42no—
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C2511yescharacteristic
438C22⋊D43—42no—
439C22⋊D43—42no—
440C22⋊D43—42no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—21no—
444C2×Dic43—21no—
445C2×Dic43—24no—
446C2×Dic43—21no—
447C2×Dic43—41no—
448C2×Dic43—42no—
449C2×Dic43—44no—
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C2×Dic43C22×D411yescharacteristic
456D172—22no—
457D172—42no—
458C4×D43—22no—
459C4×D43—22no—
460C4×D43—22no—
461C4×D43—22no—
462C4×D43—22no—
463C4×D43—41no—
464C4×D43—41no—
465C4×D43—41no—
466C4×D43—41no—
467C4×D43—41no—
468C4×D43—41no—
469C4×D43—42no—
470C4×D43—42no—
471C4×D43—42no—
472C4×D43—42no—
473C4×D43—42no—
474C4×D432−1+414yes—
475Dic86—22no—
476Dic86—44no—
477Dic86—44no—
478Dic86—42no—
479C8×C43—24no—
480C43⋊C8—24no—
481#60866—431nomaximal, Sylow
482C22×C43—21no—
483C22×C43—21no—
484C22×C43—41no—
485C22×C43—41no—
486C22×C43—41no—
487C22×C43#57512yes—
488C22×C43C23×D411yescharacteristic
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—44no—
495C2×D43—41no—
496C2×D43—41no—
497C2×D43—41no—
498C2×D43—84no—
499C2×D43#53612yes—
500C4×C43—21no—
501C4×C43—21no—
502C4×C43—21no—
503C4×C43—21no—
504C4×C43—41no—
505C4×C43—41no—
506C4×C43—41no—
507C4×C43—44no—
508C4×C43#57512yes—
509C4×C43C2×2−1+412yes—
510Dic43—21no—
511Dic43—21no—
512Dic43—21no—
513Dic43—21no—
514Dic43—21no—
515Dic43—41no—
516Dic43—44no—
517Dic43—41no—
518Dic43—41no—
519Dic43#53612yes—
520C2×#533—431no—
521C2×#529—431no—
522#3240—432no—
523#3240—432no—
524#3239—431no—
525#3239D4311yescharacteristic, complemented
526#3238—431no—
527#3238—431no—
528#3233—432no—
529#3233—432no—
530#3232—432no—
531#3232—432no—
532#3166—432no—
533#3140—432no—
534#3095—432no—
535#3094—432no—
536#3078—432no—
537#3077—432no—
538#2920—431no—
539C2×C43—22no—
540C2×C43—81no—
541C2×C43C2×#53611yescharacteristic
542C2×C43C2×#57511yescharacteristic
543C2×C43C2×#57511yescharacteristic
544D43—22no—
545D43—41no—
546D43—81no—
547#533—432no—
548#533—432no—
549#533—432no—
550#533—432no—
551#533—861no—
552#533—861no—
553#533—861no—
554#533—861no—
555C2×C4⋊Q8—431no—
556C2×C4⋊Q8C2×D4311yescharacteristic, complemented
557#529—431no—
558#529—431no—
559#529—431no—
560#529—431no—
561#529—431no—
562#529—431no—
563#529—431no—
564#529—861no—
565#529—861no—
566#529—861no—
567#529—861no—
568#529C2×D4311yescharacteristic
569C2×#126—861no—
570C2×#125—431no—
571C2×#125—432no—
572C2×#124—431no—
573C2×#123—861no—
574C2×C22⋊Q8—431no—
575C2×C22⋊Q8—861no—
576C2×C22⋊Q8—861no—
577C2×#121—431no—
578C2×C4×Q8—431no—
579C2×C4×Q8—861no—
580C2×C4×Q8—861no—
581C2×C4×D4—431no—
582C2×C4×D4—861no—
583C2×#117—432no—
584C2×#117—861no—
585C22×C42—431no—
586#501—432no—
587#501—432no—
588#501—432no—
589#501C2×D4312yescomplemented
590#499—434no—
591#499—434no—
592#489—432no—
593#489—432no—
594#489—432no—
595#489C2×D4312yescomplemented
596#488—434no—
597#488—434no—
598#485—434no—
599#485—434no—
600#484—432no—
601#484C2×D4312yescomplemented
602#483—432no—
603#483—432no—
604#482—434no—
605#482—434no—
606#481—432no—
607#481C2×D4312yes—
608#480—432no—
609#480—432no—
610#479—434no—
611#479—434no—
612#478—434no—
613#478—434no—
614#477—432no—
615#477—432no—
616#476—432no—
617#476—432no—
618#475—432no—
619#475C2×D4312yescomplemented
620#474—432no—
621#474C2×D4312yescomplemented
622#432—431no—
623#432—432no—
624#432C2×D4311yescharacteristic, complemented
625#431—432no—
626#431—432no—
627#428—434no—
628#428—434no—
629#423—432no—
630#419—434no—
631#418—434no—
632#407—432no—
633C4×M16—432no—
634C43#6086611yescharacteristic, complemented, Sylow
635C22×Q8—21no—
636C22×Q8—431no—
637C22×Q8—861no—
638C22×D4—431no—
639C22×D4—861no—
640C23×C4—431no—
641C23×C4—431no—
642C23×C4—431no—
643C23×C4—861no—
644C2×M16—434no—
645C4⋊Q8—21no—
646C4⋊Q8—21no—
647C4⋊Q8—432no—
648C4⋊Q8—432no—
649C4⋊Q8—861no—
650C4⋊Q8—861no—
651C4⋊Q8C22×D4312yes—
652C4⋊Q8C22×D4312yes—
653#126—21no—
654#126—861no—
655#126—861no—
656#126—861no—
657#126—861no—
658#126—861no—
659#126—861no—
660#126—861no—
661#125—431no—
662#125—431no—
663#125—434no—
664#125—434no—
665#125—431no—
666#125—861no—
667#125—861no—
668#125—862no—
669#125—862no—
670#125C22×D4311yescharacteristic
671#124—431no—
672#124—431no—
673#124—431no—
674#124—861no—
675#124—861no—
676#124C22×D4311yescharacteristic
677#123—21no—
678#123—861no—
679#123—861no—
680#123—861no—
681#123—861no—
682#123—861no—
683#123—861no—
684#123—861no—
685C22⋊Q8—431no—
686C22⋊Q8—431no—
687C22⋊Q8—431no—
688C22⋊Q8—861no—
689C22⋊Q8—861no—
690C22⋊Q8—862no—
691C22⋊Q8—862no—
692C22⋊Q8—862no—
693C22⋊Q8—862no—
694C22⋊Q8—862no—
695C22⋊Q8—862no—
696C22⋊Q8—862no—
697C22⋊Q8—862no—
698C22⋊Q8C22×D4311yescharacteristic
699#121—431no—
700#121—431no—
701#121—431no—
702#121—861no—
703#121—861no—
704#121C22×D4311yescharacteristic
705C4×Q8—431no—
706C4×Q8—431no—
707C4×Q8—431no—
708C4×Q8—861no—
709C4×Q8—861no—
710C4×Q8—862no—
711C4×Q8—862no—
712C4×Q8—862no—
713C4×Q8—862no—
714C4×Q8—862no—
715C4×Q8—862no—
716C4×Q8—862no—
717C4×Q8—862no—
718C4×Q8C22×D4311yescharacteristic
719C4×D4—21no—
720C4×D4—431no—
721C4×D4—431no—
722C4×D4—431no—
723C4×D4—861no—
724C4×D4—861no—
725C4×D4—861no—
726C4×D4—861no—
727C4×D4—861no—
728C4×D4—861no—
729C4×D4—861no—
730C4×D4—861no—
731C4×D4—861no—
732C4×D4C22×D4311yescharacteristic
733#117—21no—
734#117—434no—
735#117—434no—
736#117—861no—
737#117—861no—
738#117—861no—
739#117—861no—
740#117—861no—
741#117—861no—
742#117—862no—
743#117—862no—
744#117—861no—
745C2×C4⋊C4—21no—
746C2×C4⋊C4—432no—
747C2×C4⋊C4—431no—
748C2×C4⋊C4—431no—
749C2×C4⋊C4—861no—
750C2×C4⋊C4—861no—
751C2×C4⋊C4—861no—
752C2×C4⋊C4—861no—
753C2×C4⋊C4—862no—
754C2×C4⋊C4—862no—
755C2×C4⋊C4—861no—
756C2×C4⋊C4C22×D4312yes—
757C2×C22⋊C4—861no—
758C2×C22⋊C4—861no—
759C2×C22⋊C4—861no—
760C2×C22⋊C4—861no—
761C2×C22⋊C4—861no—
762C2×C22⋊C4—862no—
763C2×C42—431no—
764C2×C42—431no—
765C2×C42—431no—
766C2×C42—431no—
767C2×C42—431no—
768C2×C42—431no—
769C2×C42—431no—
770C2×C42—431no—
771C2×C42—431no—
772C2×C42—431no—
773C2×C42—431no—
774C2×C42—861no—
775C2×C42—862no—
776C2×C42C22×D4311yescharacteristic
777#107—434no—
778#107—434no—
779#107—434no—
780#107C22×D4314yes—
781#106—434no—
782#106—434no—
783#106—434no—
784#106C22×D4314yes—
785C4⋊C8—434no—
786C4⋊C8—432no—
787C4⋊C8C22×D4312yes—
788#103—434no—
789#103—434no—
790#103—434no—
791#103C22×D4314yes—
792#102—434no—
793#102—434no—
794#102—434no—
795#102C22×D4314yes—
796C22⋊C8—432no—
797C22⋊C8—434no—
798C22⋊C8C22×D4312yes—
799#97—432no—
800#97C22×D4312yes—
801C4×C8—434no—
802C24—431no—
803C24—861no—
804C2×Q8—22no—
805C2×Q8—22no—
806C2×Q8—44no—
807C2×Q8—431no—
808C2×Q8—861no—
809C2×Q8—864no—
810C2×Q8—862no—
811C2×Q8—862no—
812C2×Q8—1724no—
813C2×Q8C23×D4311yescharacteristic
814C2×D4—21no—
815C2×D4—431no—
816C2×D4—861no—
817C2×D4—864no—
818C2×D4—861no—
819C2×D4—861no—
820C2×D4—861no—
821C2×D4—1724no—
822C2×D4C23×D4311yescharacteristic
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—431no—
826C22×C4—431no—
827C22×C4—431no—
828C22×C4—431no—
829C22×C4—431no—
830C22×C4—431no—
831C22×C4—431no—
832C22×C4—431no—
833C22×C4—431no—
834C22×C4—431no—
835C22×C4—431no—
836C22×C4—431no—
837C22×C4—431no—
838C22×C4—431no—
839C22×C4—431no—
840C22×C4—864no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—862no—
847C22×C4—861no—
848C22×C4—1722no—
849C22×C4—1722no—
850C22×C4—1724no—
851C22×C4D4×D4311yescharacteristic
852C22×C4D4×D4311yescharacteristic
853C22×C4C23×D4311yescharacteristic
854M16—868no—
855C2×C8—434no—
856C2×C8C23×D4314yes—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—22no—
864C4⋊C4—434no—
865C4⋊C4—431no—
866C4⋊C4—431no—
867C4⋊C4—861no—
868C4⋊C4—861no—
869C4⋊C4—861no—
870C4⋊C4—861no—
871C4⋊C4—861no—
872C4⋊C4—861no—
873C4⋊C4—861no—
874C4⋊C4—861no—
875C4⋊C4—861no—
876C4⋊C4—861no—
877C4⋊C4—864no—
878C4⋊C4—864no—
879C4⋊C4—864no—
880C4⋊C4—864no—
881C4⋊C4—862no—
882C4⋊C4—861no—
883C4⋊C4—861no—
884C4⋊C4—861no—
885C4⋊C4—861no—
886C4⋊C4—862no—
887C4⋊C4—862no—
888C4⋊C4C23×D4314yes—
889C4⋊C4C23×D4311yescharacteristic
890C4⋊C4C23×D4311yescharacteristic
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—861no—
897C22⋊C4—861no—
898C22⋊C4—861no—
899C22⋊C4—861no—
900C22⋊C4—864no—
901C22⋊C4—864no—
902C22⋊C4—861no—
903C22⋊C4—861no—
904C22⋊C4—861no—
905C22⋊C4—861no—
906C22⋊C4—861no—
907C22⋊C4—861no—
908C22⋊C4—861no—
909C22⋊C4—861no—
910C22⋊C4—861no—
911C22⋊C4—861no—
912C22⋊C4—861no—
913C42—21no—
914C42—431no—
915C42—431no—
916C42—431no—
917C42—431no—
918C42—431no—
919C42—431no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—431no—
924C42—431no—
925C42—431no—
926C42—864no—
927C42—864no—
928C42—861no—
929C42—861no—
930C42—861no—
931C42D4×D4311yescharacteristic
932C42D4×D4311yescharacteristic
933C42C23×D4311yescharacteristic
934C42C23×D4311yescharacteristic
935C23—21no—
936C23—431no—
937C23—431no—
938C23—862no—
939C23—862no—
940C23—861no—
941C23—1721no—
942C23—1722no—
943C23—1722no—
944C23—1722no—
945C23C2×D4×D4311yescharacteristic
946Q8—22no—
947Q8—44no—
948Q8—44no—
949Q8—862no—
950Q8—1724no—
951Q8—1724no—
952Q8—1722no—
953D4—22no—
954D4—42no—
955D4—862no—
956D4—1722no—
957D4—1722no—
958D4—1722no—
959D4—1722no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—24no—
966C2×C4—21no—
967C2×C4—44no—
968C2×C4—42no—
969C2×C4—431no—
970C2×C4—434no—
971C2×C4—431no—
972C2×C4—431no—
973C2×C4—431no—
974C2×C4—431no—
975C2×C4—431no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—862no—
979C2×C4—862no—
980C2×C4—862no—
981C2×C4—862no—
982C2×C4—862no—
983C2×C4—861no—
984C2×C4—861no—
985C2×C4—864no—
986C2×C4—861no—
987C2×C4—1721no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1721no—
993C2×C4—1722no—
994C2×C4—1722no—
995C2×C4—1722no—
996C2×C4—1722no—
997C2×C4—1721no—
998C2×C4—1722no—
999C2×C4—1724no—
1000C2×C4—1722no—
1001C2×C4C2×D4×D4311yescharacteristic
1002C2×C4C2×D4×D4311yescharacteristic
1003C2×C4C2×D4×D4311yescharacteristic
1004C2×C4C2×D4×D4311yescharacteristic
1005C2×C4C2×D4×D4311yescharacteristic
1006C2×C4C24×D4311yescharacteristic
1007C8—24no—
1008C8—864no—
1009C22—21no—
1010C22—21no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—432no—
1015C22—861no—
1016C22—861no—
1017C22—861no—
1018C22—861no—
1019C22—861no—
1020C22—3444no—
1021C22—1724no—
1022C22—1721no—
1023C22—1721no—
1024C22—1721no—
1025C22#1458369812yes—
1026C22C22×D4×D4311yescharacteristic
1027C4—21no—
1028C4—21no—
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—44no—
1033C4—41no—
1034C4—41no—
1035C4—432no—
1036C4—861no—
1037C4—861no—
1038C4—861no—
1039C4—861no—
1040C4—861no—
1041C4—1721no—
1042C4—1721no—
1043C4—1724no—
1044C4—1721no—
1045C4#1458369512yes—
1046C42−1+4×D4312yes—
1047C2—22no—
1048C2—81no—
1049C2—862no—
1050C2—3441no—
1051C2—1721no—
1052C2#536×D4311yescharacteristic
1053C2C2×#1458369511yescharacteristic
1054C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3239C2
socleC22×C43C23×D4
prime radical#121×D43C22
hypercenter#3239D43
hypocenterC43#60866
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3239

Complements

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

NH ≅ G/Ntype
1. C2×#14583454C2semidirect
3. #19145836C2semidirect
4. #19145830C2semidirect
5. #19145825C2semidirect
6. #19145818C2semidirect
7. #19145813C2semidirect
8. #19145778C2semidirect
9. #19145772C2semidirect
10. #19145768C2semidirect
11. #19145762C2semidirect
12. #19145146C2semidirect
13. #19144980C2semidirect
14. #19144540C2semidirect
16. #19144395C2semidirect
17. #19144387C2semidirect
18. #19143225C2semidirect
19. C43×#3239C2semidirect
26. #14583454C22semidirect
27. #14583454C22semidirect
28. C2×#13063325C22semidirect
41. C2×#13063316C22semidirect
57. #14583309C22semidirect
58. #14583308C22semidirect
59. #14583305C22semidirect
60. #14583300C22semidirect
61. #14583299C22semidirect
62. #14583261C22semidirect
63. #14583259C22semidirect
64. #14583258C22semidirect
65. #14583255C22semidirect
66. #14583252C22semidirect
67. #14583242C22semidirect
68. #14583238C22semidirect
69. #14583234C22semidirect
70. #14583230C22semidirect
71. #14583227C22semidirect
77. #14583209C22semidirect
78. #14583208C22semidirect
79. #14583202C22semidirect
80. #14583201C22semidirect
81. #14583195C22semidirect
82. #14583194C22semidirect
83. #14583190C22semidirect
84. #14583189C22semidirect
85. #14583181C22semidirect
86. #14583176C22semidirect
87. #14582956C22semidirect
88. #14582954C22semidirect
89. #14582951C22semidirect
90. #14582949C22semidirect
98. C2×C4⋊Q8×C43C22semidirect
100. C43×#501C22semidirect
101. C43×#489C22semidirect
102. C43×#484C22semidirect
104. C43×#475C22semidirect
105. C43×#474C22semidirect
106. C43×#432C22semidirect
525. #3239D43semidirect
556. C2×C4⋊Q8C2×D43semidirect
589. #501C2×D43semidirect
595. #489C2×D43semidirect
601. #484C2×D43semidirect
619. #475C2×D43semidirect
621. #474C2×D43semidirect
624. #432C2×D43semidirect
634. C43#60866semidirect

Maximal subgroups

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

subgroupindex
C2×#145834542
#529×D432
#191458362
#191458302
#191458252
#191458182
#191458132
#191457782
#191457722
#191457682
#191457622
#191451462
#191449802
#191445402
#191445322
#191443952
#191443872
#191432252
C43×#32392
#6086643