Finite Group Databasebeta

← #25968367

Subgroups — #25968367

Order 11008.

2054 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148516C211yesmaximal, characteristic, complemented
2#19148389C211yesmaximal, characteristic, complemented
3#19145674C212yesmaximal, complemented
4#19145665C212yesmaximal, complemented
5#19145652C212yesmaximal, complemented
6#19145643C212yesmaximal, complemented
7#19145574C212yesmaximal, complemented
8#19145568C212yesmaximal, complemented
9#19145565C212yesmaximal, complemented
10#19145559C212yesmaximal, complemented
11#19145062C211yesmaximal, characteristic, complemented
12#19145019C211yesmaximal, characteristic, complemented
13#19144993C211yesmaximal, characteristic, complemented
14C2×#14583255C211yesmaximal, characteristic, complemented
15#19144150C211yesmaximal, characteristic, complemented
16#19144149C211yesmaximal, characteristic, complemented
17#19144133C211yesmaximal, characteristic, complemented
18#19144132C211yesmaximal, characteristic, complemented
19#19143910C211yesmaximal, characteristic, complemented
20#19143902C211yesmaximal, characteristic, complemented
21#19143896C211yesmaximal, characteristic, complemented
22#19143235C211yesmaximal, characteristic, complemented
23C43×#3013C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#13063356C2211yescharacteristic, complemented
26C2×#13063353C2211yescharacteristic
27C2×#13063350C2211yescharacteristic
28C2×#13063347C2211yescharacteristic
29C2×#13063345C2211yescharacteristic
30C2×#13063345C2211yescharacteristic, complemented
31#14583601—22no—
32#14583601—21no—
33#14583596—21no—
34#14583592—22no—
35#14583591—21no—
36#14583583—21no—
37#14583560—21no—
38#14583560—21no—
39#14583537—22no—
40#14583537—21no—
41#14583537—21no—
42#14583537—22no—
43#14583509C2212yescomplemented
44#14583502C2212yescomplemented
45#14583477C2211yescharacteristic
46#14583473C2212yes—
47#14583473C2211yescharacteristic
48#14583463C2212yes—
49#14583463C2211yescharacteristic
50#14583445C2211yescharacteristic
51#14583445C2212yes—
52#14583445C2211yescharacteristic, complemented
53#14583435C2212yescomplemented
54#14583430C2212yescomplemented
55C2×#13063316C2211yescharacteristic, complemented
56C2×#13063314C2212yes—
57C2×#13063314C2211yescharacteristic
58#14583382C2211yescharacteristic, complemented
59#14583380C2211yescharacteristic, complemented
60#41×Dic43C2211yescharacteristic
61#14583292C2212yescomplemented
62#14583285C2212yescomplemented
63#14583284C2211yescharacteristic, complemented
64#14583284C2212yescomplemented
65#14583282C2211yescharacteristic, complemented
66#14583280C2211yescharacteristic, complemented
67#14583280C2211yescharacteristic, complemented
68#14583280C2212yescomplemented
69#14583277C2211yescharacteristic, complemented
70#14583274C2211yescharacteristic, complemented
71#14583270C2211yescharacteristic, complemented
72#14583270C2211yescharacteristic, complemented
73#14583266C2212yescomplemented
74#14583262C2212yescomplemented
75#14583255C2212yescomplemented
76#14583255C2212yescomplemented
77#14583255C2212yescomplemented
78#14583255C2212yescomplemented
79#14583255C2212yescomplemented
80#14583252C2212yescomplemented
81#14583124C2212yescomplemented
82#14583124C2212yescomplemented
83#14583123C2212yescomplemented
84#14583123C2212yescomplemented
85#14583117C2212yescomplemented
86#14583117C2212yescomplemented
87#14583116C2212yescomplemented
88#14583116C2212yescomplemented
89#14583108C2212yescomplemented
90#14583107C2212yescomplemented
91#14583103C2212yescomplemented
92#14583102C2212yescomplemented
93#14583098C2212yescomplemented
94#14583097C2212yescomplemented
95#14583093C2212yescomplemented
96#14583092C2212yescomplemented
97#14583063C2212yes—
98#14583061C2212yescomplemented
99#14583059C2212yes—
100#14583055C2212yescomplemented
101#14583052C2212yes—
102#14583049C2212yes—
103#14583046C2212yes—
104#14583044C2212yescomplemented
105#14583042C2212yes—
106#14583038C2212yescomplemented
107#14583035C2212yes—
108#14583032C2212yes—
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582949C2212yescomplemented
112#14582949C2212yescomplemented
113#14582927C2211yescharacteristic, complemented
114#14582925C2211yescharacteristic, complemented
115#14582901C2211yescharacteristic
116#14582900C2211yescharacteristic, complemented
117#14582898C2211yescharacteristic
118C2×#13063249C2211yescharacteristic, complemented
119C2×#13063247C2211yescharacteristic
120C2×#13063245C2211yescharacteristic
121#14582866C2211yescharacteristic
122M16×Dic43C2211yescharacteristic, complemented
123C2×C8×Dic43C2211yescharacteristic, complemented
124C2×2−1+4×C43C2211yescharacteristic
125C2×#137×C43C2211yescharacteristic, complemented
126C2×#135×C43C2211yescharacteristic, complemented
127C43×#537C2211yescharacteristic
128C43×#452C2212yescomplemented
129C43×#451C2212yescomplemented
130C43×#449C2212yescomplemented
131C43×#448C2212yescomplemented
132C43×#417C2211yescharacteristic, complemented
133C2×#103×C43C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic
135#13063371—42no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2312yes—
141C22×D172C2311yescharacteristic
142C22×D172C2312yes—
143C2×D4×D43—21no—
144C2×D4×D43—22no—
145#13063356—42no—
146#13063353—42no—
147#13063350—42no—
148#13063347—42no—
149#13063345—42no—
150#13063345—42no—
151C2×Dic172C2311yescharacteristic
152C2×#10621885C2311yescharacteristic
153C2×#10621885C2312yes—
154C2×#10621885C2311yescharacteristic
155C2×#10621873C2311yescharacteristic
156C2×#10621873C2311yescharacteristic
157C2×#10621873C2312yes—
158C2×#10621883C2311yescharacteristic
159C2×#10621883C2311yescharacteristic
160C2×#10621884C2312yes—
161C2×#10621884C2311yescharacteristic
162C2×#10621884C2312yes—
163C2×#10621884C2311yescharacteristic
164C2×D344C2312yes—
165C2×D344C2311yescharacteristic
166C2×#10621882C2312yes—
167C2×#10621882C2311yescharacteristic
168C2×#10621882C2311yescharacteristic
169C2×#10621877C2311yescharacteristic
170C22×C43⋊C8C2311yescharacteristic
171#13063323C2312yes—
172#13063323C2311yescharacteristic
173#13063323C2311yescharacteristic
174#13063321C2312yes—
175#13063321C2311yescharacteristic
176#13063321C2311yescharacteristic
177#13063320—22no—
178#13063318—22no—
179#13063318—22no—
180#13063318—22no—
181#13063316—22no—
182#13063316—21no—
183#13063316—21no—
184#13063316C2312yes—
185#13063316C2312yes—
186#13063315—22no—
187#13063314—22no—
188#13063314—22no—
189#13063314—21no—
190#13063314—21no—
191#13063314C2312yes—
192#13063314C2312yes—
193#13063314C2311yescharacteristic
194#13063314C2312yes—
195#13063314C2312yes—
196#13063314C2311yescharacteristic
197#13063312C2311yescharacteristic
198#13063312C2311yescharacteristic
199#13063309—22no—
200#13063309—22no—
201#13063308—22no—
202#13063308—22no—
203#13063308—22no—
204#13063307—22no—
205#13063306—22no—
206#13063304C2312yes—
207#13063301—21no—
208#13063301—21no—
209#13063301—21no—
210#13063301—22no—
211#13063301—22no—
212#13063299—21no—
213#13063299—21no—
214#13063299—22no—
215#13063299—22no—
216#13063299C2312yes—
217#13063297—22no—
218#13063297—21no—
219#13063297—21no—
220#13063297—21no—
221#13063297—21no—
222#13063297—22no—
223#13063297—22no—
224#13063297—22no—
225#13063296—21no—
226#13063296—22no—
227#13063293—22no—
228#13063293—22no—
229#13063293—22no—
230Q8×Dic43D411yescharacteristic
231Q8×Dic43D411yescharacteristic
232Q8×Dic43C2312yes—
233#13063290C2312yes—
234D4×Dic43—22no—
235D4×Dic43—22no—
236D4×Dic43D412yes—
237D4×Dic43D411yescharacteristic
238D4×Dic43D412yes—
239D4×Dic43D411yescharacteristic
240D4×Dic43C2312yes—
241#13063287C2312yes—
242C4×C22⋊D43—22no—
243C4×C22⋊D43—22no—
244C4×C22⋊D43—22no—
245C4×C22⋊D43—21no—
246C4×C22⋊D43—21no—
247C4×C22⋊D43—21no—
248C4×C22⋊D43—21no—
249(C22⋊D43)⋊C4—22no—
250#13063284—21no—
251#13063284C2311yescharacteristic
252#13063284C2312yes—
253#13063283—21no—
254#13063283—22no—
255#13063281—22no—
256C2×C4⋊Dic43—21no—
257C2×C4⋊Dic43—21no—
258C2×C4⋊Dic43C2311yescharacteristic
259C2×Dic43⋊C4—21no—
260C4⋊C4×D43—21no—
261C2×(C2×D43)⋊C4—21no—
262C2×(C2×D43)⋊C4—21no—
263C2×(C2×D43)⋊C4—22no—
264C2×(C2×D43)⋊C4—22no—
265C2×C4×Dic43C2311yescharacteristic
266C2×C4×Dic43C2312yes—
267Dic43⋊C8C2312yes—
268Dic43⋊C8C2312yes—
269Dic43⋊C8C2312yes—
270Dic43⋊C8C2312yes—
271#13063250C2312yes—
272#13063249C2312yes—
273#13063249C2312yes—
274#13063249C2312yes—
275#13063248C2312yes—
276#13063247C2312yes—
277#13063247C2312yes—
278#13063247C2312yes—
279#13063246C2312yes—
280#13063245C2312yes—
281#13063245C2312yes—
282#13063245C2312yes—
283C22⋊(C43⋊C8)C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285#13063235C2312yes—
286C8×Dic43C2311yescharacteristic
287C8×Dic43C2311yescharacteristic
288C8×Dic43C2311yescharacteristic
289C8×Dic43C2311yescharacteristic
290C8×Dic43C2312yes—
2912−1+4×C43—42no—
2922−1+4×C43—42no—
293C2×#41×C43—21no—
294C2×#41×C43—22no—
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2311yescharacteristic
297C2×#41×C43C2312yes—
298C2×#41×C43C2311yescharacteristic
299C22×Q8×C43—21no—
300C22×Q8×C43C2311yescharacteristic
301C22×Q8×C43C2312yes—
302#137×C43—42no—
303#135×C43—42no—
304C2×Q16×C43C2312yes—
305C2×Q16×C43C2311yescharacteristic
306C2×SD16×C43C2311yescharacteristic
307C2×SD16×C43C2312yes—
308C2×SD16×C43C2311yescharacteristic
309C2×D8×C43C2311yescharacteristic
310C2×M16×C43C2311yescharacteristic
311C22×C8×C43C2311yescharacteristic
312C22⋊Q8×C43—21no—
313C22⋊Q8×C43C2312yes—
314#121×C43—22no—
315#121×C43—21no—
316#121×C43C2312yes—
317C2×C4⋊C4×C43C2311yescharacteristic
318#103×C43C2312yes—
319#103×C43C2312yes—
320#103×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C23×D43—22no—
325C23×D43—21no—
326#41×C43—22no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—42no—
333#41×C43—42no—
334#41×C43—48no—
335#41×C43—44no—
336C2×Q8×C43—22no—
337C2×Q8×C43—21no—
338C2×Q8×C43—22no—
339C2×Q8×C43—22no—
340C2×Q8×C43—42no—
341C2×Q8×C43—42no—
342C2×Q8×C43—44no—
343C2×Q8×C43C2×D411yescharacteristic
344C2×Q8×C43C2412yes—
345C2×Q8×C43C2411yescharacteristic
346C2×Q8×C43C2411yescharacteristic
347C2×D4×C43—21no—
348C2×D4×C43—22no—
349C2×D4×C43—21no—
350C2×D4×C43—22no—
351C2×D4×C43C2×D411yescharacteristic
352C2×D4×C43C2×D412yes—
353C2×D4×C43C2411yescharacteristic
354C2×D4×C43C2411yescharacteristic
355C22×C4×C43—21no—
356C22×C4×C43—22no—
357C22×C4×C43—21no—
358C22×C4×C43—22no—
359C22×C4×C43—21no—
360C22×C4×C43—21no—
361C22×C4×C43C2412yes—
362C22×C4×C43C2411yescharacteristic
363C2×C22⋊D43—22no—
364C2×C22⋊D43—22no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43—21no—
367C2×C22⋊D43—21no—
368C2×C22⋊D43—21no—
369C2×C22⋊D43—21no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—21no—
372C2×C22⋊D43—22no—
373C22×Dic43—22no—
374C22×Dic43—21no—
375C22×Dic43C2×D411yescharacteristic
376C22×Dic43C2×D411yescharacteristic
377C22×Dic43C2×D412yes—
378C22×Dic43C2×D412yes—
379#10621902—44no—
380D4×D43—44no—
381D4×D43—48no—
382#10621898—22no—
383#10621898—22no—
384#10621898—22no—
385#10621898—22no—
386#10621898—42no—
387#10621898—42no—
388C2×D172—22no—
389C2×D172—21no—
390C2×D172—22no—
391C2×D172—22no—
392C2×D172—42no—
393C2×D172—42no—
394C2×D172C2412yes—
395C2×D172C2411yescharacteristic
396C2×D172C2411yescharacteristic
397C2×C4×D43—21no—
398C2×C4×D43—22no—
399C2×C4×D43—21no—
400C2×C4×D43—22no—
401C2×Dic86C2411yescharacteristic
402C2×Dic86C2411yescharacteristic
403Q16×C43—41no—
404Q16×C43—42no—
405SD16×C43—41no—
406SD16×C43—41no—
407SD16×C43—42no—
408D8×C43—41no—
409M16×C43—22no—
410C2×C8×C43—22no—
411C2×C8×C43C2412yes—
412C2×C8×C43C2411yescharacteristic
413C2×C8×C43C2411yescharacteristic
414C4⋊C4×C43—21no—
415C4⋊C4×C43—22no—
416C4⋊C4×C43C2412yes—
417C22⋊C4×C43—22no—
418C22⋊C4×C43—22no—
419C22⋊Dic43—21no—
420C22⋊Dic43—22no—
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43—22no—
425C22⋊Dic43C2×D412yes—
426C22⋊Dic43C2×D412yes—
427C22⋊Dic43C2×D412yes—
428#10621885—41no—
429#10621885—41no—
430#10621885—42no—
431#10621884—41no—
432#10621884—41no—
433#10621884—42no—
434#10621884—42no—
435#10621883—41no—
436#10621883—41no—
437#10621882—41no—
438#10621882—41no—
439#10621882—42no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4—22no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—22no—
450(C2×D43)⋊C4—22no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4—22no—
453(C2×D43)⋊C4—21no—
454C4⋊Dic43—21no—
455C4⋊Dic43—22no—
456C4⋊Dic43—22no—
457C4⋊Dic43—22no—
458C4⋊Dic43C2×D411yescharacteristic
459C4⋊Dic43C2×D411yescharacteristic
460C4⋊Dic43C2×D412yes—
461C4⋊Dic43C2×D412yes—
462C4⋊Dic43C2412yes—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—22no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473C4×Dic43—22no—
474C4×Dic43—22no—
475C4×Dic43C2×D412yes—
476C4×Dic43C2×D412yes—
477C4×Dic43C2×D411yescharacteristic
478C4×Dic43C2×D411yescharacteristic
479C4×Dic43C2411yescharacteristic
480C4×Dic43C2411yescharacteristic
481C4×Dic43C2412yes—
482#10621877—22no—
483C2×C43⋊C8—22no—
484C2×C43⋊C8C2411yescharacteristic
485C2×C43⋊C8C2411yescharacteristic
486C2×C43⋊C8C2412yes—
487Dic172—41no—
488D344—41no—
489D344—42no—
490#10621873—41no—
491#10621873—41no—
492#10621873—42no—
493C23×C43—21no—
494C23×C43—21no—
495C23×C43C22×D412yes—
496C23×C43C22×D411yescharacteristic
497C22×D43—21no—
498C22×D43—21no—
499C22×D43—22no—
500C22×D43—44no—
501C22×D43—42no—
502C22×D43—81no—
503C22×D43—81no—
504C22×D43—82no—
505C22×D43—82no—
506Q8×C43—22no—
507Q8×C43—21no—
508Q8×C43—21no—
509Q8×C43—22no—
510Q8×C43—21no—
511Q8×C43—22no—
512Q8×C43—21no—
513Q8×C43—44no—
514Q8×C43—42no—
515D4×C43—24no—
516D4×C43—22no—
517D4×C43—21no—
518D4×C43—21no—
519D4×C43—21no—
520D4×C43—21no—
521D4×C43—44no—
522D4×C43—42no—
523D4×C43—42no—
524D4×C43—82no—
525C2×C4×C43—22no—
526C2×C4×C43—22no—
527C2×C4×C43—21no—
528C2×C4×C43—22no—
529C2×C4×C43—22no—
530C2×C4×C43—21no—
531C2×C4×C43—44no—
532C2×C4×C43—44no—
533C2×C4×C43—42no—
534C2×C4×C43—42no—
535C2×C4×C43—42no—
536C2×C4×C43—81no—
537C2×C4×C43C22×D412yes—
538C2×C4×C43C22×D411yescharacteristic
539C2×C4×C43H(5,𝔽2)12yes—
540C2×C4×C43H(5,𝔽2)12yes—
541C2×C4×C43C2511yescharacteristic
542C22⋊D43—44no—
543C22⋊D43—42no—
544C22⋊D43—42no—
545C22⋊D43—82no—
546C22⋊D43—82no—
547C22⋊D43—81no—
548C22⋊D43—81no—
549C22⋊D43—81no—
550C22⋊D43—81no—
551C22⋊D43—82no—
552C2×Dic43—21no—
553C2×Dic43—22no—
554C2×Dic43—21no—
555C2×Dic43—42no—
556C2×Dic43—42no—
557C2×Dic43—41no—
558C2×Dic43—41no—
559C2×Dic43—82no—
560C2×Dic43—81no—
561C2×Dic43C22×D412yes—
562C2×Dic43C22×D412yes—
563C2×Dic43C22×D411yescharacteristic
564C2×Dic43C22×D411yescharacteristic
565C2×Dic43C22×D411yescharacteristic
566C2×Dic43C22×D411yescharacteristic
567D172—21no—
568D172—22no—
569D172—21no—
570D172—21no—
571D172—22no—
572D172—21no—
573D172—44no—
574D172—42no—
575C4×D43—44no—
576C4×D43—42no—
577C4×D43—42no—
578C4×D43—82no—
579Dic86—21no—
580Dic86—21no—
581Dic86—21no—
582Dic86—21no—
583C8×C43—21no—
584C8×C43—22no—
585C8×C43—21no—
586C43⋊C8—21no—
587C43⋊C8—21no—
588C43⋊C8—22no—
589#60823—431nomaximal, Sylow
590C22×C43—21no—
591C22×C43—21no—
592C22×C43—22no—
593C22×C43—22no—
594C22×C43—22no—
595C22×C43—41no—
596C22×C43—41no—
597C22×C43—41no—
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—41no—
601C22×C43#53512yes—
602C22×C43C23×D411yescharacteristic
603C2×D43—42no—
604C2×D43—41no—
605C2×D43—42no—
606C2×D43—41no—
607C2×D43—41no—
608C2×D43—41no—
609C2×D43—41no—
610C2×D43—42no—
611C2×D43—41no—
612C2×D43—162no—
613C2×D43—164no—
614C4×C43—22no—
615C4×C43—42no—
616C4×C43—42no—
617C4×C43—41no—
618C4×C43—41no—
619C4×C43#53512yes—
620C4×C43C2×H(5,𝔽2)11yescharacteristic
621C4×C43C2×H(5,𝔽2)11yescharacteristic
622Dic43—22no—
623Dic43—21no—
624Dic43—21no—
625Dic43—22no—
626Dic43—21no—
627Dic43—21no—
628Dic43—42no—
629Dic43—41no—
630Dic43—41no—
631#3512—431no—
632#3500—431no—
633#3223—432no—
634#3222—432no—
635#3221—432no—
636#3220—432no—
637#3212—432no—
638#3212—432no—
639#3211—432no—
640#3211—432no—
641#3153—431no—
642#3147—431no—
643#3142—431no—
644C2×#488—431no—
645#3046—431no—
646#3046—431no—
647#3045—431no—
648#3045—431no—
649#3013—431no—
650#3013D4311yescharacteristic, complemented
651#3012—431no—
652#3012—431no—
653#2922—431no—
654C2×C43—22no—
655C2×C43—42no—
656C2×C43—81no—
657C2×C43—81no—
658C2×C43C2×#53511yescharacteristic
659C2×C43#358411yescharacteristic
660C2×C43#358411yescharacteristic
661D43—81no—
662D43—82no—
663D43—81no—
664C2×2−1+4C2×D4311yescharacteristic
665C2×H(5,𝔽2)—431no—
666C2×#137—431no—
667C2×#137C2×D4311yescharacteristic, complemented
668C2×AGL(1,ℤ/8)—431no—
669C2×AGL(1,ℤ/8)—431no—
670C2×#135—431no—
671C2×#135—431no—
672C2×#135—431no—
673C2×#135C2×D4311yescharacteristic, complemented
674#553—862no—
675#553—861no—
676#553—861no—
677#553—862no—
678#552—861no—
679#552—861no—
680#548—861no—
681#548—861no—
682#546—862no—
683#546—862no—
684#546—861no—
685#546—861no—
686#541—432no—
687#540—432no—
688#537—431no—
689#537C2×D4311yescharacteristic
690#536—432no—
691#536—431no—
692#535—432no—
693#535—431no—
694#532—431no—
695#532—431no—
696#532—432no—
697#529—432no—
698#529—432no—
699C2×#125—431no—
700C2×#124—431no—
701C2×#124—432no—
702#520—431no—
703#520—431no—
704C4×#41—431no—
705#497—432no—
706#496—432no—
707#495—431no—
708#495—432no—
709#495—431no—
710#495—431no—
711#495—432no—
712#495—431no—
713#494—431no—
714#493—431no—
715#492—431no—
716#492—431no—
717#491—432no—
718#490—432no—
719#488—432no—
720#488—432no—
721#488—432no—
722#488—432no—
723#488—432no—
724#488—432no—
725#464—432no—
726#464—432no—
727#464—432no—
728#464—432no—
729#463—432no—
730#463—432no—
731#463—432no—
732#463—432no—
733#462—432no—
734#462—432no—
735#461—432no—
736#461—432no—
737#460—432no—
738#460—432no—
739#459—432no—
740#459—432no—
741#452—432no—
742#452—432no—
743#452—432no—
744#452C2×D4312yescomplemented
745#451—432no—
746#451C2×D4312yescomplemented
747#450—432no—
748#450—432no—
749#449—432no—
750#449—432no—
751#449—432no—
752#449C2×D4312yescomplemented
753#448—432no—
754#448C2×D4312yescomplemented
755#447—432no—
756#447—432no—
757#433—432no—
758#433—432no—
759#431—432no—
760#431—432no—
761#424—431no—
762#424—431no—
763#417—431no—
764#417—431no—
765#417—431no—
766#417C2×D4311yescharacteristic, complemented
767C2×#103—431no—
768C2×#103C2×D4311yescharacteristic, complemented
769C2×#102—431no—
770C2×#102—431no—
771#408—431no—
772#408C2×D4311yescharacteristic
773C4×M16—431no—
774C2×C4×C8—431no—
775C43#6082311yescharacteristic, complemented, Sylow
7762−1+4—42no—
7772−1+4—42no—
778H(5,𝔽2)—1722no—
779H(5,𝔽2)—1722no—
780C2×#41—21no—
781C2×#41—22no—
782C2×#41—431no—
783C2×#41—431no—
784C2×#41—432no—
785C2×#41—861no—
786C2×#41C22×D4311yescharacteristic
787C2×#41C22×D4311yescharacteristic
788C2×#41C22×D4312yes—
789C2×#41C22×D4311yescharacteristic
790C22×Q8—21no—
791C22×Q8C22×D4311yescharacteristic
792C22×Q8C22×D4312yes—
793C22×D4—431no—
794C22×D4—432no—
795C22×D4—862no—
796C22×D4—861no—
797#137—42no—
798#137—1722no—
799AGL(1,ℤ/8)—1722no—
800AGL(1,ℤ/8)—1722no—
801#135—42no—
802#135—1722no—
803#135—1722no—
804#135—1722no—
805C2×Q16—431no—
806C2×Q16—431no—
807C2×Q16—432no—
808C2×Q16—431no—
809C2×Q16C22×D4311yescharacteristic
810C2×Q16C22×D4312yes—
811C2×SD16—431no—
812C2×SD16—431no—
813C2×SD16—432no—
814C2×SD16—432no—
815C2×SD16—431no—
816C2×SD16—431no—
817C2×SD16—431no—
818C2×SD16—431no—
819C2×SD16—432no—
820C2×SD16C22×D4311yescharacteristic
821C2×SD16C22×D4311yescharacteristic
822C2×SD16C22×D4312yes—
823C2×D8—431no—
824C2×D8—431no—
825C2×D8—432no—
826C2×D8—431no—
827C2×D8—432no—
828C2×D8C22×D4311yescharacteristic
829C2×M16—431no—
830C2×M16C22×D4311yescharacteristic
831C22×C8—431no—
832C22×C8C22×D4311yescharacteristic
833C4⋊Q8—432no—
834C4⋊Q8—431no—
835C4⋊Q8—431no—
836#127—432no—
837#127—431no—
838#127—431no—
839#126—862no—
840#126—862no—
841#126—862no—
842#126—862no—
843#125—432no—
844#125—432no—
845#125—861no—
846#125—861no—
847#125—862no—
848#125—862no—
849#124—432no—
850#124—431no—
851#124—432no—
852#124—432no—
853#124—432no—
854#124—431no—
855#124—431no—
856#124—431no—
857#124—862no—
858#124—862no—
859#124—861no—
860#124—861no—
861#123—862no—
862#123—862no—
863#123—862no—
864#123—862no—
865#123—862no—
866#123—862no—
867#123—862no—
868C22⋊Q8—21no—
869C22⋊Q8—432no—
870C22⋊Q8—861no—
871C22⋊Q8—861no—
872C22⋊Q8—862no—
873C22⋊Q8—862no—
874C22⋊Q8—861no—
875C22⋊Q8C22×D4312yes—
876#121—21no—
877#121—22no—
878#121—432no—
879#121—862no—
880#121—862no—
881#121—861no—
882#121—861no—
883#121—862no—
884#121—862no—
885#121—861no—
886#121—861no—
887#121—862no—
888#121—862no—
889#121—861no—
890#121—861no—
891#121—861no—
892#121—862no—
893#121C22×D4312yes—
894#120—862no—
895#120—862no—
896#120—862no—
897C4×Q8—431no—
898C4×Q8—431no—
899C4×Q8—432no—
900C4×Q8—432no—
901C4×D4—432no—
902C4×D4—432no—
903C4×D4—431no—
904C4×D4—431no—
905C4×D4—432no—
906C4×D4—432no—
907C4×D4—862no—
908C4×D4—862no—
909C4×D4—861no—
910C4×D4—861no—
911C4×D4—861no—
912C4×D4—861no—
913C4×D4—862no—
914C4×D4—862no—
915C4×D4—862no—
916C4×D4—862no—
917#117—431no—
918#117—432no—
919#117—862no—
920#117—862no—
921#117—861no—
922#117—861no—
923C2×C4⋊C4—431no—
924C2×C4⋊C4—861no—
925C2×C4⋊C4—861no—
926C2×C4⋊C4—861no—
927C2×C4⋊C4—861no—
928C2×C4⋊C4C22×D4311yescharacteristic
929C2×C22⋊C4—861no—
930C2×C22⋊C4—861no—
931C2×C22⋊C4—862no—
932C2×C22⋊C4—862no—
933C2×C42—431no—
934C2×C42—432no—
935C4⋊C8—432no—
936C4⋊C8—432no—
937C4⋊C8—432no—
938C4⋊C8—432no—
939#103—432no—
940#103—432no—
941#103—432no—
942#103—432no—
943#103—432no—
944#103C22×D4312yes—
945#103C22×D4312yes—
946#103C22×D4312yes—
947#102—432no—
948#102—432no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102C22×D4312yes—
955C22⋊C8—432no—
956C22⋊C8—432no—
957C22⋊C8C22×D4312yes—
958C22⋊C8C22×D4312yes—
959#97—432no—
960C4×C8—431no—
961C4×C8—431no—
962C4×C8—431no—
963C4×C8—431no—
964C4×C8—432no—
965C24—862no—
966C24—861no—
967#41—22no—
968#41—22no—
969#41—22no—
970#41—22no—
971#41—22no—
972#41—22no—
973#41—42no—
974#41—42no—
975#41—48no—
976#41—44no—
977#41—862no—
978#41—862no—
979#41—862no—
980#41—862no—
981#41—1722no—
982#41—1722no—
983#41—1724no—
984C2×Q8—22no—
985C2×Q8—21no—
986C2×Q8—22no—
987C2×Q8—22no—
988C2×Q8—42no—
989C2×Q8—42no—
990C2×Q8—44no—
991C2×Q8—431no—
992C2×Q8—431no—
993C2×Q8D4×D4311yescharacteristic
994C2×Q8C23×D4312yes—
995C2×Q8C23×D4311yescharacteristic
996C2×Q8C23×D4311yescharacteristic
997C2×D4—21no—
998C2×D4—22no—
999C2×D4—21no—
1000C2×D4—22no—
1001C2×D4—432no—
1002C2×D4—431no—
1003C2×D4—431no—
1004C2×D4—862no—
1005C2×D4—862no—
1006C2×D4—861no—
1007C2×D4—861no—
1008C2×D4—861no—
1009C2×D4—861no—
1010C2×D4—862no—
1011C2×D4—861no—
1012C2×D4—862no—
1013C2×D4—861no—
1014C2×D4—862no—
1015C2×D4—861no—
1016C2×D4—862no—
1017C2×D4—862no—
1018C2×D4—1722no—
1019C2×D4—1722no—
1020C2×D4—1728no—
1021C2×D4—1724no—
1022C2×D4D4×D4312yes—
1023C2×D4D4×D4311yescharacteristic
1024C2×D4C23×D4311yescharacteristic
1025C2×D4C23×D4311yescharacteristic
1026C22×C4—22no—
1027C22×C4—21no—
1028C22×C4—21no—
1029C22×C4—21no—
1030C22×C4—22no—
1031C22×C4—21no—
1032C22×C4—431no—
1033C22×C4—431no—
1034C22×C4—432no—
1035C22×C4—432no—
1036C22×C4—862no—
1037C22×C4—862no—
1038C22×C4—861no—
1039C22×C4—861no—
1040C22×C4—862no—
1041C22×C4—861no—
1042C22×C4C23×D4312yes—
1043C22×C4C23×D4311yescharacteristic
1044Q16—41no—
1045Q16—42no—
1046Q16—1721no—
1047Q16—1721no—
1048Q16—1721no—
1049Q16—1722no—
1050SD16—41no—
1051SD16—41no—
1052SD16—42no—
1053SD16—1721no—
1054SD16—1721no—
1055SD16—1722no—
1056SD16—1721no—
1057SD16—1721no—
1058SD16—1721no—
1059SD16—1721no—
1060SD16—1722no—
1061SD16—1722no—
1062D8—41no—
1063D8—1721no—
1064D8—1722no—
1065D8—1721no—
1066D8—1721no—
1067D8—1722no—
1068M16—22no—
1069M16—862no—
1070C2×C8—22no—
1071C2×C8—431no—
1072C2×C8—431no—
1073C2×C8—432no—
1074C2×C8—862no—
1075C2×C8C23×D4311yescharacteristic
1076C2×C8C23×D4311yescharacteristic
1077C2×C8C23×D4312yes—
1078C4⋊C4—21no—
1079C4⋊C4—22no—
1080C4⋊C4—431no—
1081C4⋊C4—431no—
1082C4⋊C4—432no—
1083C4⋊C4—432no—
1084C4⋊C4—432no—
1085C4⋊C4—862no—
1086C4⋊C4—862no—
1087C4⋊C4—862no—
1088C4⋊C4—862no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—861no—
1094C4⋊C4—861no—
1095C4⋊C4—861no—
1096C4⋊C4—861no—
1097C4⋊C4—861no—
1098C4⋊C4—862no—
1099C4⋊C4C23×D4312yes—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—432no—
1103C22⋊C4—432no—
1104C22⋊C4—432no—
1105C22⋊C4—862no—
1106C22⋊C4—861no—
1107C22⋊C4—862no—
1108C22⋊C4—861no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—861no—
1116C22⋊C4—862no—
1117C22⋊C4—861no—
1118C22⋊C4—861no—
1119C22⋊C4—862no—
1120C22⋊C4—861no—
1121C22⋊C4—861no—
1122C22⋊C4—861no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C42—432no—
1126C42—432no—
1127C42—431no—
1128C42—431no—
1129C42—431no—
1130C42—431no—
1131C42—432no—
1132C42—862no—
1133C42—862no—
1134C23—21no—
1135C23—21no—
1136C23—861no—
1137C23—862no—
1138C23—861no—
1139C23—3441no—
1140C23—3441no—
1141C23—3442no—
1142C23—3442no—
1143C23—1724no—
1144C23—1722no—
1145C23C2×D4×D4312yes—
1146C23C2×D4×D4311yescharacteristic
1147Q8—22no—
1148Q8—21no—
1149Q8—22no—
1150Q8—21no—
1151Q8—21no—
1152Q8—22no—
1153Q8—21no—
1154Q8—44no—
1155Q8—42no—
1156Q8—861no—
1157Q8—861no—
1158Q8—861no—
1159Q8—861no—
1160D4—24no—
1161D4—22no—
1162D4—21no—
1163D4—21no—
1164D4—21no—
1165D4—21no—
1166D4—44no—
1167D4—42no—
1168D4—42no—
1169D4—82no—
1170D4—861no—
1171D4—861no—
1172D4—862no—
1173D4—862no—
1174D4—861no—
1175D4—861no—
1176D4—3442no—
1177D4—3441no—
1178D4—3441no—
1179D4—3442no—
1180D4—3441no—
1181D4—3441no—
1182D4—3442no—
1183D4—1724no—
1184D4—1724no—
1185D4—1722no—
1186D4—1722no—
1187D4—1722no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—44no—
1195C2×C4—44no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—81no—
1200C2×C4—431no—
1201C2×C4—431no—
1202C2×C4—432no—
1203C2×C4—432no—
1204C2×C4—431no—
1205C2×C4—431no—
1206C2×C4—861no—
1207C2×C4—862no—
1208C2×C4—861no—
1209C2×C4—3442no—
1210C2×C4—3442no—
1211C2×C4—3441no—
1212C2×C4—1724no—
1213C2×C4—1722no—
1214C2×C4—1721no—
1215C2×C4—1722no—
1216C2×C4—1721no—
1217C2×C4—1722no—
1218C2×C4—1722no—
1219C2×C4C2×D4×D4312yes—
1220C2×C4C2×D4×D4311yescharacteristic
1221C2×C4#1306337012yes—
1222C2×C4#1306337012yes—
1223C2×C4C24×D4311yescharacteristic
1224C8—21no—
1225C8—21no—
1226C8—22no—
1227C8—861no—
1228C8—861no—
1229C8—862no—
1230C22—21no—
1231C22—21no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—1721no—
1242C22—1722no—
1243C22—1721no—
1244C22—1721no—
1245C22—1722no—
1246C22—1721no—
1247C22—1722no—
1248C22—1721no—
1249C22—1721no—
1250C22—6882no—
1251C22—6884no—
1252C22#1458346412yes—
1253C22C22×D4×D4311yescharacteristic
1254C4—22no—
1255C4—42no—
1256C4—42no—
1257C4—41no—
1258C4—41no—
1259C4—862no—
1260C4—861no—
1261C4—861no—
1262C4—862no—
1263C4—861no—
1264C4—861no—
1265C4—1722no—
1266C4—1721no—
1267C4—1721no—
1268C4#1458346412yes—
1269C4C2×#1306337011yescharacteristic
1270C4C2×#1306337011yescharacteristic
1271C2—22no—
1272C2—42no—
1273C2—81no—
1274C2—81no—
1275C2—3442no—
1276C2—3441no—
1277C2—3441no—
1278C2C2×#1458346411yescharacteristic
1279C2#1914936511yescharacteristic
1280C2#1914936711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3013C2
socleC22×C43C23×D4
hypercenter#3013D43
hypocenterC43#60823
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3013

Complements

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

NH ≅ G/Ntype
1. #19148516C2semidirect
2. #19148389C2semidirect
3. #19145674C2semidirect
4. #19145665C2semidirect
5. #19145652C2semidirect
6. #19145643C2semidirect
7. #19145574C2semidirect
8. #19145568C2semidirect
9. #19145565C2semidirect
10. #19145559C2semidirect
11. #19145062C2semidirect
12. #19145019C2semidirect
13. #19144993C2semidirect
14. C2×#14583255C2semidirect
15. #19144150C2semidirect
16. #19144149C2semidirect
17. #19144133C2semidirect
18. #19144132C2semidirect
19. #19143910C2semidirect
20. #19143902C2semidirect
21. #19143896C2semidirect
22. #19143235C2semidirect
23. C43×#3013C2semidirect
25. C2×#13063356C22semidirect
30. C2×#13063345C22semidirect
43. #14583509C22semidirect
44. #14583502C22semidirect
52. #14583445C22semidirect
53. #14583435C22semidirect
54. #14583430C22semidirect
55. C2×#13063316C22semidirect
58. #14583382C22semidirect
59. #14583380C22semidirect
61. #14583292C22semidirect
62. #14583285C22semidirect
63. #14583284C22semidirect
64. #14583284C22semidirect
65. #14583282C22semidirect
66. #14583280C22semidirect
67. #14583280C22semidirect
68. #14583280C22semidirect
69. #14583277C22semidirect
70. #14583274C22semidirect
71. #14583270C22semidirect
72. #14583270C22semidirect
73. #14583266C22semidirect
74. #14583262C22semidirect
75. #14583255C22semidirect
76. #14583255C22semidirect
77. #14583255C22semidirect
78. #14583255C22semidirect
79. #14583255C22semidirect
80. #14583252C22semidirect
81. #14583124C22semidirect
82. #14583124C22semidirect
83. #14583123C22semidirect
84. #14583123C22semidirect
85. #14583117C22semidirect
86. #14583117C22semidirect
87. #14583116C22semidirect
88. #14583116C22semidirect
89. #14583108C22semidirect
90. #14583107C22semidirect
91. #14583103C22semidirect
92. #14583102C22semidirect
93. #14583098C22semidirect
94. #14583097C22semidirect
95. #14583093C22semidirect
96. #14583092C22semidirect
98. #14583061C22semidirect
100. #14583055C22semidirect
104. #14583044C22semidirect
106. #14583038C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582949C22semidirect
112. #14582949C22semidirect
113. #14582927C22semidirect
114. #14582925C22semidirect
116. #14582900C22semidirect
118. C2×#13063249C22semidirect
122. M16×Dic43C22semidirect
123. C2×C8×Dic43C22semidirect
125. C2×#137×C43C22semidirect
126. C2×#135×C43C22semidirect
128. C43×#452C22semidirect
129. C43×#451C22semidirect
130. C43×#449C22semidirect
131. C43×#448C22semidirect
132. C43×#417C22semidirect
133. C2×#103×C43C22semidirect
650. #3013D43semidirect
667. C2×#137C2×D43semidirect
673. C2×#135C2×D43semidirect
744. #452C2×D43semidirect
746. #451C2×D43semidirect
752. #449C2×D43semidirect
754. #448C2×D43semidirect
766. #417C2×D43semidirect
768. C2×#103C2×D43semidirect
775. C43#60823semidirect

Maximal subgroups

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

subgroupindex
#191485162
#191483892
#191456742
#191456652
#191456522
#191456432
#191455742
#191455682
#191455652
#191455592
#191450622
#191450192
#191449932
C2×#145832552
#191441502
#191441492
#191441332
#191441322
#191439102
#191439022
#191438962
#191432352
C43×#30132
#6082343