Finite Group Databasebeta

← #25974471

Subgroups — #25974471

Order 11008.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148315C211yesmaximal, characteristic, complemented
2#19148264C211yesmaximal, characteristic, complemented
3#19146844C212yesmaximal, complemented
4#19146822C212yesmaximal, complemented
5#19146747C212yesmaximal, complemented
6#19146737C212yesmaximal, complemented
7#19146717C212yesmaximal, complemented
8#19146662C212yesmaximal, complemented
9#19146541C212yesmaximal, complemented
10#19146431C212yesmaximal, complemented
11#19144952C211yesmaximal, characteristic, complemented
12#19144583C211yesmaximal, characteristic, complemented
13C2×#14583223C211yesmaximal, characteristic, complemented
14#19144450C211yesmaximal, characteristic, complemented
15#19144264C211yesmaximal, characteristic, complemented
16#19144214C211yesmaximal, characteristic, complemented
17#19144133C211yesmaximal, characteristic, complemented
18#19143901C211yesmaximal, characteristic, complemented
19#19143813C211yesmaximal, characteristic, complemented
20#19143474C211yesmaximal, characteristic, complemented
21#19143320C211yesmaximal, characteristic, complemented
22#19143119C211yesmaximal, characteristic, complemented
23C43×#2896C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#13063353C2211yescharacteristic, complemented
26C2×#13063345C2211yescharacteristic
27C2×#13063345C2211yescharacteristic, complemented
28C2×#13063333C2211yescharacteristic, complemented
29#14583617—21no—
30#14583617C2212yescomplemented
31#14583612—21no—
32#14583612C2212yescomplemented
33#14583593—21no—
34#14583593C2212yescomplemented
35#14583588—21no—
36#14583588C2212yescomplemented
37#14583568C2212yes—
38#14583560C2212yes—
39#14583537—22no—
40#14583537C2212yes—
41D4×C22⋊D43—22no—
42D4×C22⋊D43C2212yes—
43#14583530C2211yescharacteristic, complemented
44#14583487—22no—
45#14583480C2211yescharacteristic, complemented
46#14583477—21no—
47#14583477C2211yescharacteristic
48#14583463—21no—
49#14583463C2211yescharacteristic
50#14583433—22no—
51#14583410—21no—
52#14583410C2211yescharacteristic
53#14583410C2211yescharacteristic, complemented
54C2×#13063299—21no—
55C2×#13063299C2211yescharacteristic
56#14583382C2211yescharacteristic
57#14583380C2211yescharacteristic, complemented
58#14583380C2211yescharacteristic, complemented
59#14583262C2212yescomplemented
60#14583260C2212yescomplemented
61#14583255C2212yescomplemented
62#14583244C2212yescomplemented
63#14583239C2212yescomplemented
64#14583228C2212yescomplemented
65#14583223C2212yescomplemented
66#14583223C2212yescomplemented
67#14583223C2212yescomplemented
68#14583223C2212yescomplemented
69#14583221C2212yescomplemented
70#14583216C2212yescomplemented
71#14583204C2212yescomplemented
72#14583201C2212yescomplemented
73#14583192C2212yescomplemented
74#14583177C2212yescomplemented
75#14583152C2212yescomplemented
76#14583148C2212yescomplemented
77#14583145C2212yescomplemented
78#14583144C2212yescomplemented
79#14583139C2212yescomplemented
80#14583135C2212yescomplemented
81#14583134C2212yescomplemented
82#14583128C2212yescomplemented
83#14583124C2212yescomplemented
84#14583117C2212yescomplemented
85#14583098C2212yescomplemented
86#14583093C2212yescomplemented
87#14583064C2212yescomplemented
88#14583061C2211yescharacteristic, complemented
89#14583061C2211yescharacteristic, complemented
90#14583055C2211yescharacteristic, complemented
91#14583051C2212yescomplemented
92#14583050C2211yescharacteristic, complemented
93#14583047C2212yescomplemented
94#14583044C2211yescharacteristic, complemented
95#14583044C2211yescharacteristic, complemented
96#14583038C2211yescharacteristic, complemented
97#14583034C2212yescomplemented
98#14583033C2211yescharacteristic, complemented
99#14583008C2212yescomplemented
100#14583003C2212yescomplemented
101#14582990C2212yescomplemented
102#14582984C2212yescomplemented
103#14582975C2212yescomplemented
104#14582970C2212yescomplemented
105#14582968C2212yescomplemented
106C8×C22⋊D43C2212yescomplemented
107#14582941C2211yescharacteristic, complemented
108C2×#13063258C2211yescharacteristic, complemented
109C2×#13063256C2211yescharacteristic, complemented
110#14582927C2211yescharacteristic, complemented
111#14582905C2211yescharacteristic, complemented
112#14582902C2212yescomplemented
113#14582901C2211yescharacteristic, complemented
114#14582899C2212yescomplemented
115#14582895C2211yescharacteristic
116#14582895C2211yescharacteristic, complemented
117#14582894C2212yescomplemented
118C2×#13063245C2211yescharacteristic, complemented
119C2×#13063245C2211yescharacteristic, complemented
120#102×D43C2212yescomplemented
121#14582867C2211yescharacteristic, complemented
122C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
123#14582857C2211yescharacteristic, complemented
124C22×#41×C43C2211yescharacteristic
125C22×M16×C43C2211yescharacteristic, complemented
126C2×#117×C43C2211yescharacteristic, complemented
127C43×#419C2212yescomplemented
128C43×#418C2212yescomplemented
129C43×#417C2211yescharacteristic
130C43×#417C2211yescharacteristic
131C43×#417C2211yescharacteristic, complemented
132C43×#417C2211yescharacteristic, complemented
133C43×#416C2212yescomplemented
134C43×#416C2212yescomplemented
135#13063371—24no—
136#13063371—42no—
137C2×#10621902C2312yes—
138C2×#10621898—21no—
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2311yescharacteristic
141C22×D172—21no—
142C22×D172C2311yescharacteristic
143C22×C22⋊D43—21no—
144C22×C22⋊D43—22no—
145C2×D4×D43—22no—
146C2×D4×D43C2312yes—
147#13063353—42no—
148#13063345—24no—
149#13063345—42no—
150C2×#10621885C2311yescharacteristic
151C2×#10621885C2311yescharacteristic
152C2×#10621873C2312yes—
153C2×#10621883C2311yescharacteristic
154C2×#10621883C2311yescharacteristic
155C2×#10621884C2311yescharacteristic
156C2×#10621884C2311yescharacteristic
157C2×D344C2312yes—
158C2×#10621882C2311yescharacteristic
159C2×#10621882C2311yescharacteristic
160#13063333—42no—
161C2×#10621872C2312yes—
162C22×C43⋊C8C2311yescharacteristic
163C22×C43⋊C8C2311yescharacteristic
164C2×C8×D43C2312yes—
165#13063324—21no—
166#13063324C2312yes—
167#13063321—22no—
168#13063321C2312yes—
169#13063319—22no—
170#13063319—22no—
171#13063318—22no—
172#13063318—22no—
173#13063317—22no—
174#13063316—21no—
175#13063316C2312yes—
176#13063314—22no—
177#13063314C2312yes—
178#13063313—22no—
179#13063311—22no—
180#13063311—22no—
181#13063308—21no—
182#13063308—22no—
183#13063308D412yes—
184#13063307—22no—
185#13063307—22no—
186#13063305—21no—
187#13063305C2312yes—
188#13063304—21no—
189#13063304—22no—
190#13063304D411yescharacteristic
191#13063304D411yescharacteristic
192#13063304C2311yescharacteristic
193#13063304C2311yescharacteristic
194#13063301—22no—
195#13063301C2312yes—
196#13063300—21no—
197#13063300C2312yes—
198#13063299—21no—
199#13063299—21no—
200#13063299—22no—
201#13063299—22no—
202#13063299—21no—
203#13063299—22no—
204#13063299—21no—
205#13063299—21no—
206#13063299D411yescharacteristic
207#13063299D411yescharacteristic
208#13063299C2311yescharacteristic
209#13063299C2312yes—
210#13063299C2312yes—
211#13063299C2311yescharacteristic
212#13063298—22no—
213#13063298—22no—
214#13063297—22no—
215#13063297—22no—
216#13063297—22no—
217#13063296—22no—
218#13063296C2312yes—
219#13063294—21no—
220#13063294—22no—
221#13063294D412yes—
222#13063293—22no—
223#13063293—22no—
224#13063293—22no—
225Q8×Dic43C2312yes—
226C4×Dic86—22no—
227#13063290—21no—
228#13063290C2312yes—
229C4×D172—22no—
230D4×Dic43—22no—
231D4×Dic43C2312yes—
232#13063287—21no—
233#13063287C2312yes—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—21no—
236C4×C22⋊D43—22no—
237C4×C22⋊D43—22no—
238C4×C22⋊D43—22no—
239C4×C22⋊D43—22no—
240C4×C22⋊D43C2312yes—
241C4×C22⋊D43C2312yes—
242#13063284—21no—
243#13063284C2311yescharacteristic
244#13063284C2311yescharacteristic
245#13063283—21no—
246#13063283C2312yes—
247#13063282—22no—
248#13063282—22no—
249C2×C4⋊Dic43—21no—
250C2×C4⋊Dic43C2311yescharacteristic
251C4⋊C4×D43—21no—
252C4⋊C4×D43C2312yes—
253C2×(C2×D43)⋊C4—21no—
254C2×(C2×D43)⋊C4—22no—
255#13063259C2312yes—
256#13063258C2312yes—
257#13063258C2312yes—
258#13063257C2312yes—
259#13063256C2312yes—
260#13063256C2312yes—
261Dic43⋊C8C2312yes—
262Dic43⋊C8C2312yes—
263#13063250C2312yes—
264#13063249C2311yescharacteristic
265#13063249C2311yescharacteristic
266#13063249C2311yescharacteristic
267#13063249C2311yescharacteristic
268#13063247C2312yes—
269#13063247C2312yes—
270#13063247C2312yes—
271#13063246C2311yescharacteristic
272#13063246C2311yescharacteristic
273#13063246C2311yescharacteristic
274#13063246C2311yescharacteristic
275#13063245C2312yes—
276#13063245C2312yes—
277#13063245C2312yes—
278#13063245C2312yes—
279C22⋊(C43⋊C8)C2311yescharacteristic
280C22⋊(C43⋊C8)C2311yescharacteristic
281C22⋊(C43⋊C8)C2311yescharacteristic
282C22⋊(C43⋊C8)C2311yescharacteristic
283(C2×D43)⋊C8C2312yes—
284(C2×D43)⋊C8C2312yes—
285#13063235C2312yes—
286C8×Dic43C2312yes—
287C2×#41×C43—21no—
288C2×#41×C43—21no—
289C2×#41×C43—24no—
290C2×#41×C43—42no—
291C2×#41×C43C2311yescharacteristic
292C2×#41×C43C2311yescharacteristic
293C2×#41×C43C2311yescharacteristic
294C2×#41×C43C2311yescharacteristic
295C22×Q8×C43C2311yescharacteristic
296C22×D4×C43—21no—
297C22×D4×C43C2311yescharacteristic
298C23×C4×C43—21no—
299C23×C4×C43C2311yescharacteristic
300C2×M16×C43—42no—
301C2×M16×C43C2311yescharacteristic
302C2×M16×C43C2311yescharacteristic
303C2×M16×C43C2312yes—
304C22×C8×C43C2312yes—
305#117×C43—21no—
306#117×C43—21no—
307#117×C43C2312yes—
308#117×C43C2312yes—
309C2×C4⋊C4×C43C2311yescharacteristic
310C2×C4⋊C4×C43C2311yescharacteristic
311C2×C22⋊C4×C43—21no—
312C2×C42×C43—21no—
313#103×C43C2312yes—
314#103×C43C2312yes—
315#103×C43C2312yes—
316#103×C43C2312yes—
317#102×C43C2312yes—
318#102×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321C24×C43—21no—
322C24×C43C2×D411yescharacteristic
323C23×D43—21no—
324C23×D43—22no—
325#41×C43—22no—
326#41×C43—22no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—44no—
331#41×C43—41no—
332#41×C43—41no—
333#41×C43—44no—
334#41×C43#4114yes—
335C2×Q8×C43—21no—
336C2×Q8×C43—22no—
337C2×Q8×C43—41no—
338C2×Q8×C43C2411yescharacteristic
339C2×Q8×C43C2411yescharacteristic
340C2×D4×C43—21no—
341C2×D4×C43—21no—
342C2×D4×C43—21no—
343C2×D4×C43—21no—
344C2×D4×C43—21no—
345C2×D4×C43—22no—
346C2×D4×C43—44no—
347C2×D4×C43—41no—
348C2×D4×C43C2411yescharacteristic
349C2×D4×C43C2411yescharacteristic
350C22×C4×C43—21no—
351C22×C4×C43—22no—
352C22×C4×C43—22no—
353C22×C4×C43—21no—
354C22×C4×C43—21no—
355C22×C4×C43—21no—
356C22×C4×C43—21no—
357C22×C4×C43—21no—
358C22×C4×C43—21no—
359C22×C4×C43—44no—
360C22×C4×C43C2×D411yescharacteristic
361C22×C4×C43C2×D411yescharacteristic
362C22×C4×C43C2×D411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C22×C4×C43C2411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C2×C22⋊D43—22no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—22no—
369C2×C22⋊D43—21no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—21no—
372C2×C22⋊D43—21no—
373C2×C22⋊D43—22no—
374C2×C22⋊D43—22no—
375C2×C22⋊D43—84no—
376C2×C22⋊D43—82no—
377C2×C22⋊D43C2×D412yes—
378C2×C22⋊D43C2×D412yes—
379C2×C22⋊D43C2×D412yes—
380C22×Dic43—22no—
381C22×Dic43—21no—
382#10621902—24no—
383#10621902—42no—
384D4×D43—24no—
385D4×D43—42no—
386D4×D43—48no—
387#10621898—22no—
388#10621898—22no—
389#10621898—22no—
390#10621898—22no—
391#10621898—44no—
392C2×D172—21no—
393C2×D172—22no—
394C2×D172—22no—
395C2×D172—22no—
396C2×D172—22no—
397C2×D172—44no—
398C2×D172C2×D411yescharacteristic
399C2×D172C2412yes—
400C2×D172C2411yescharacteristic
401C2×C4×D43—21no—
402C2×C4×D43—22no—
403C2×C4×D43—22no—
404C2×C4×D43—22no—
405C2×C4×D43C2412yes—
406C2×Dic86—22no—
407C2×Dic86C2×D411yescharacteristic
408C2×Dic86C2411yescharacteristic
409M16×C43—22no—
410M16×C43—22no—
411M16×C43—42no—
412C2×C8×C43—42no—
413C2×C8×C43C2412yes—
414C2×C8×C43C2412yes—
415C4⋊C4×C43—21no—
416C4⋊C4×C43—21no—
417C4⋊C4×C43C2412yes—
418C4⋊C4×C43C2412yes—
419C22⋊C4×C43—22no—
420C22⋊C4×C43—22no—
421C42×C43—22no—
422C42×C43—22no—
423C22⋊Dic43—22no—
424C22⋊Dic43—22no—
425C22⋊Dic43—21no—
426C22⋊Dic43—21no—
427C22⋊Dic43—21no—
428C22⋊Dic43C2×D412yes—
429C22⋊Dic43C2×D412yes—
430C22⋊Dic43C2×D412yes—
431#10621885—22no—
432#10621885—41no—
433#10621884—22no—
434#10621884—41no—
435#10621883—22no—
436#10621883—41no—
437#10621882—22no—
438#10621882—41no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—21no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4—22no—
444(C2×D43)⋊C4—22no—
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)⋊C4C2×D412yes—
451(C2×D43)⋊C4C2×D412yes—
452C4⋊Dic43—21no—
453C4⋊Dic43—22no—
454C4⋊Dic43—22no—
455C4⋊Dic43—22no—
456C4⋊Dic43C2×D411yescharacteristic
457C4⋊Dic43C2×D411yescharacteristic
458C4⋊Dic43C2411yescharacteristic
459C4⋊Dic43C2411yescharacteristic
460C4⋊Dic43C2412yes—
461Dic43⋊C4—21no—
462Dic43⋊C4—21no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4C2×D412yes—
469Dic43⋊C4C2×D412yes—
470C4×Dic43—21no—
471C4×Dic43—22no—
472C4×Dic43—22no—
473C4×Dic43—22no—
474C4×Dic43C2412yes—
475C2×C43⋊C8—22no—
476C2×C43⋊C8—22no—
477C2×C43⋊C8C2411yescharacteristic
478C2×C43⋊C8C2411yescharacteristic
479C2×C43⋊C8C2411yescharacteristic
480C2×C43⋊C8C2411yescharacteristic
481D344—42no—
482#10621873—42no—
483#10621872—42no—
484C8×D43—42no—
485C23×C43—21no—
486C23×C43—22no—
487C23×C43—21no—
488C23×C43—41no—
489C23×C43—41no—
490C23×C43—42no—
491C23×C43—42no—
492C23×C43—81no—
493C23×C43C22×D411yescharacteristic
494C23×C43C22×D411yescharacteristic
495C23×C43C22×D411yescharacteristic
496C22×D43—21no—
497C22×D43—22no—
498C22×D43—44no—
499C22×D43—42no—
500C22×D43—82no—
501C22×D43—82no—
502C22×D43—81no—
503C22×D43—81no—
504C22×D43C22×D412yes—
505Q8×C43—21no—
506Q8×C43—21no—
507Q8×C43—21no—
508Q8×C43—42no—
509Q8×C43C2×#4112yes—
510D4×C43—24no—
511D4×C43—21no—
512D4×C43—21no—
513D4×C43—21no—
514D4×C43—42no—
515D4×C43—42no—
516D4×C43—42no—
517D4×C43—42no—
518D4×C43C2×#4112yes—
519C2×C4×C43—22no—
520C2×C4×C43—21no—
521C2×C4×C43—24no—
522C2×C4×C43—22no—
523C2×C4×C43—22no—
524C2×C4×C43—21no—
525C2×C4×C43—21no—
526C2×C4×C43—21no—
527C2×C4×C43—21no—
528C2×C4×C43—22no—
529C2×C4×C43—22no—
530C2×C4×C43—21no—
531C2×C4×C43—42no—
532C2×C4×C43—42no—
533C2×C4×C43—42no—
534C2×C4×C43—42no—
535C2×C4×C43—81no—
536C2×C4×C43—81no—
537C2×C4×C43C22×D411yescharacteristic
538C2×C4×C43C22×D411yescharacteristic
539C2×C4×C43C22×D411yescharacteristic
540C2×C4×C43C2×#4112yes—
541C2×C4×C43H(5,𝔽2)12yes—
542C2×C4×C43C2511yescharacteristic
543C22⋊D43—24no—
544C22⋊D43—42no—
545C22⋊D43—42no—
546C22⋊D43—44no—
547C22⋊D43—44no—
548C22⋊D43—42no—
549C22⋊D43—82no—
550C22⋊D43—82no—
551C22⋊D43—82no—
552C22⋊D43—81no—
553C22⋊D43—81no—
554C22⋊D43—82no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—22no—
559C2×Dic43—82no—
560C2×Dic43—81no—
561C2×Dic43C22×D412yes—
562C2×Dic43C22×D412yes—
563C2×Dic43C22×D412yes—
564D172—22no—
565D172—21no—
566D172—22no—
567D172—22no—
568D172—21no—
569D172—44no—
570D172—42no—
571D172—82no—
572C4×D43—22no—
573C4×D43—22no—
574C4×D43—44no—
575C4×D43—42no—
576C4×D43—82no—
577C4×D43—82no—
578Dic86—22no—
579Dic86—21no—
580Dic86—21no—
581Dic86—82no—
582C8×C43—22no—
583C8×C43—22no—
584C43⋊C8—21no—
585C43⋊C8—21no—
586C43⋊C8—21no—
587C43⋊C8—21no—
588#61196—431nomaximal, Sylow
589C22×C43—21no—
590C22×C43—21no—
591C22×C43—21no—
592C22×C43—21no—
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—22no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—41no—
601C22×C43—41no—
602C22×C43—41no—
603C22×C43—82no—
604C22×C43—84no—
605C22×C43#54612yes—
606C22×C43C23×D411yescharacteristic
607C2×D43—22no—
608C2×D43—22no—
609C2×D43—22no—
610C2×D43—42no—
611C2×D43—41no—
612C2×D43—42no—
613C2×D43—41no—
614C2×D43—42no—
615C2×D43—41no—
616C2×D43—164no—
617C2×D43—162no—
618C4×C43—22no—
619C4×C43—21no—
620C4×C43—21no—
621C4×C43—42no—
622C4×C43—42no—
623C4×C43—41no—
624C4×C43#54612yes—
625C4×C43C22×#4111yescharacteristic
626C4×C43C2×H(5,𝔽2)11yescharacteristic
627Dic43—22no—
628Dic43—22no—
629Dic43—22no—
630Dic43—41no—
631Dic43—41no—
632Dic43—42no—
633Dic43—41no—
634#3493—431no—
635#3488—431no—
636#3326—432no—
637#3324—432no—
638#3319—432no—
639#3318—432no—
640#3317—432no—
641#3313—432no—
642#3305—432no—
643#3296—432no—
644#3136—431no—
645#3099—431no—
646C2×#482—431no—
647#3083—431no—
648#3061—431no—
649#3055—431no—
650#3045—431no—
651#3012—431no—
652#3002—431no—
653#2952—431no—
654#2933—431no—
655#2897—431no—
656#2896D4311yescharacteristic, complemented
657C2×C43—22no—
658C2×C43—42no—
659C2×C43—41no—
660C2×C43—41no—
661C2×C43—81no—
662C2×C43C2×#54611yescharacteristic
663C2×C43#358411yescharacteristic
664C2×C43#358511yescharacteristic
665D43—42no—
666D43—81no—
667D43—82no—
668C2×H(5,𝔽2)—431no—
669C22×#41C2×D4311yescharacteristic
670C2×AGL(1,ℤ/8)—431no—
671C2×#135—431no—
672C2×#135—431no—
673C2×#131—431no—
674C22×M16C2×D4311yescharacteristic, complemented
675#556—432no—
676#556—861no—
677#555—432no—
678#555—861no—
679#553—432no—
680#553—861no—
681#552—432no—
682#552—861no—
683#550—432no—
684#548—432no—
685#546—432no—
686#546—862no—
687D42—432no—
688D42—862no—
689#544—431no—
690#538—862no—
691#537—431no—
692#537—431no—
693#537—861no—
694#535—431no—
695#535—861no—
696#529—862no—
697#525—431no—
698#525—431no—
699#525—861no—
700C2×#121—431no—
701C2×#121—861no—
702#520—431no—
703#520—431no—
704#520—431no—
705C2×#117C2×D4311yescharacteristic, complemented
706#490—432no—
707#489—432no—
708#488—432no—
709#486—432no—
710#485—432no—
711#483—432no—
712#482—432no—
713#482—432no—
714#482—432no—
715#482—432no—
716#482—432no—
717#481—432no—
718#479—432no—
719#478—432no—
720#477—432no—
721#474—432no—
722#469—432no—
723#468—432no—
724#468—432no—
725#468—432no—
726#467—432no—
727#466—432no—
728#466—432no—
729#465—432no—
730#464—432no—
731#463—432no—
732#460—432no—
733#459—432no—
734#452—431no—
735#452—431no—
736#452—432no—
737#451—431no—
738#450—431no—
739#450—432no—
740#449—431no—
741#449—431no—
742#449—432no—
743#448—431no—
744#447—431no—
745#447—432no—
746#442—432no—
747#441—432no—
748C4×SD16—432no—
749C4×SD16—432no—
750#436—432no—
751#435—432no—
752#435—432no—
753C8×D4—432no—
754#428—431no—
755C2×#107—431no—
756C2×#106—431no—
757#424—431no—
758#419C2×D4312yescomplemented
759#418—431no—
760#418—432no—
761#418C2×D4312yescomplemented
762#417—431no—
763#417—432no—
764#417C2×D4311yescharacteristic
765#417C2×D4311yescharacteristic
766#417C2×D4311yescharacteristic, complemented
767#417C2×D4311yescharacteristic, complemented
768#416—431no—
769#416—431no—
770#416—432no—
771#416C2×D4312yescomplemented
772#416C2×D4312yescomplemented
773C2×#102—431no—
774C2×#102—431no—
775C2×#102—432no—
776#408—431no—
777C2×C22⋊C8—431no—
778#405—431no—
779C43#6119611yescharacteristic, complemented, Sylow
780H(5,𝔽2)—864no—
781H(5,𝔽2)—1722no—
782C2×#41—21no—
783C2×#41—21no—
784C2×#41—24no—
785C2×#41—42no—
786C2×#41—431no—
787C2×#41—432no—
788C2×#41—431no—
789C2×#41—861no—
790C2×#41C22×D4311yescharacteristic
791C2×#41C22×D4311yescharacteristic
792C2×#41C22×D4311yescharacteristic
793C2×#41C22×D4311yescharacteristic
794C22×Q8C22×D4311yescharacteristic
795C22×D4—21no—
796C22×D4—432no—
797C22×D4—431no—
798C22×D4—861no—
799C22×D4—862no—
800C22×D4—862no—
801C22×D4—861no—
802C22×D4C22×D4311yescharacteristic
803C23×C4—21no—
804C23×C4C22×D4311yescharacteristic
805AGL(1,ℤ/8)—1722no—
806#135—864no—
807#135—1722no—
808C2×Q16—431no—
809C2×Q16—431no—
810C2×SD16—431no—
811C2×SD16—431no—
812C2×SD16—431no—
813C2×SD16—431no—
814C2×SD16—432no—
815C2×D8—431no—
816C2×D8—431no—
817C2×D8—432no—
818#131—1722no—
819C2×M16—42no—
820C2×M16—432no—
821C2×M16C22×D4311yescharacteristic
822C2×M16C22×D4311yescharacteristic
823C2×M16C22×D4312yes—
824C22×C8—431no—
825C22×C8—431no—
826C22×C8—432no—
827C22×C8C22×D4312yes—
828C4⋊Q8—432no—
829C4⋊Q8—861no—
830#127—432no—
831#127—862no—
832#126—862no—
833#126—862no—
834#126—862no—
835#126—862no—
836#125—432no—
837#125—862no—
838#125—861no—
839#124—432no—
840#124—862no—
841#124—862no—
842#124—862no—
843#124—862no—
844#123—432no—
845#123—862no—
846#123—862no—
847#123—862no—
848#123—861no—
849C22⋊Q8—431no—
850C22⋊Q8—431no—
851C22⋊Q8—432no—
852C22⋊Q8—431no—
853C22⋊Q8—431no—
854C22⋊Q8—432no—
855C22⋊Q8—862no—
856C22⋊Q8—861no—
857C22⋊Q8—862no—
858C22⋊Q8—861no—
859#121—431no—
860#121—431no—
861#121—432no—
862#121—432no—
863#121—432no—
864#121—431no—
865#121—431no—
866#121—432no—
867#121—862no—
868#121—862no—
869#121—862no—
870#121—862no—
871#121—862no—
872#121—861no—
873#121—861no—
874#121—861no—
875#121—862no—
876#121—861no—
877#121—862no—
878#121—862no—
879#121—862no—
880#121—861no—
881#121—861no—
882#120—432no—
883#120—862no—
884#120—862no—
885#120—862no—
886#120—862no—
887#120—861no—
888C4×Q8—432no—
889C4×Q8—432no—
890C4×Q8—862no—
891C4×Q8—861no—
892C4×D4—432no—
893C4×D4—432no—
894C4×D4—432no—
895C4×D4—432no—
896C4×D4—862no—
897C4×D4—862no—
898C4×D4—862no—
899C4×D4—862no—
900C4×D4—861no—
901C4×D4—862no—
902C4×D4—862no—
903C4×D4—861no—
904C4×D4—861no—
905#117—21no—
906#117—21no—
907#117—431no—
908#117—431no—
909#117—432no—
910#117—862no—
911#117—862no—
912#117—861no—
913#117—861no—
914#117C22×D4312yes—
915#117C22×D4312yes—
916C2×C4⋊C4—431no—
917C2×C4⋊C4—432no—
918C2×C4⋊C4—861no—
919C2×C4⋊C4—861no—
920C2×C4⋊C4C22×D4311yescharacteristic
921C2×C4⋊C4C22×D4311yescharacteristic
922C2×C22⋊C4—21no—
923C2×C22⋊C4—862no—
924C2×C22⋊C4—861no—
925C2×C42—21no—
926#107—432no—
927#107—432no—
928#107—432no—
929#106—432no—
930#106—432no—
931#106—432no—
932C4⋊C8—432no—
933C4⋊C8—432no—
934#103—431no—
935#103—431no—
936#103—431no—
937#103—431no—
938#103—432no—
939#103C22×D4312yes—
940#103C22×D4312yes—
941#103C22×D4312yes—
942#103C22×D4312yes—
943#102—431no—
944#102—431no—
945#102—431no—
946#102—431no—
947#102—432no—
948#102—432no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102C22×D4312yes—
955#102C22×D4312yes—
956#102C22×D4312yes—
957#102C22×D4312yes—
958C22⋊C8—431no—
959C22⋊C8—431no—
960C22⋊C8—431no—
961C22⋊C8—431no—
962C22⋊C8—432no—
963C22⋊C8—432no—
964#97—432no—
965C4×C8—432no—
966C24—21no—
967C24—862no—
968C24—861no—
969C24D4×D4311yescharacteristic
970#41—22no—
971#41—22no—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—44no—
976#41—41no—
977#41—41no—
978#41—44no—
979#41—862no—
980#41—862no—
981#41—864no—
982#41—862no—
983#41—862no—
984#41—1724no—
985#41—1722no—
986#41#1062189814yes—
987C2×Q8—21no—
988C2×Q8—22no—
989C2×Q8—41no—
990C2×Q8—431no—
991C2×Q8—431no—
992C2×Q8—862no—
993C2×Q8C23×D4311yescharacteristic
994C2×Q8C23×D4311yescharacteristic
995C2×D4—21no—
996C2×D4—22no—
997C2×D4—21no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—21no—
1001C2×D4—41no—
1002C2×D4—44no—
1003C2×D4—432no—
1004C2×D4—432no—
1005C2×D4—432no—
1006C2×D4—431no—
1007C2×D4—432no—
1008C2×D4—431no—
1009C2×D4—862no—
1010C2×D4—862no—
1011C2×D4—862no—
1012C2×D4—862no—
1013C2×D4—862no—
1014C2×D4—864no—
1015C2×D4—862no—
1016C2×D4—861no—
1017C2×D4—861no—
1018C2×D4—862no—
1019C2×D4—861no—
1020C2×D4—862no—
1021C2×D4—861no—
1022C2×D4—862no—
1023C2×D4—862no—
1024C2×D4—3444no—
1025C2×D4—3442no—
1026C2×D4—1724no—
1027C2×D4—1722no—
1028C2×D4—1728no—
1029C2×D4C23×D4311yescharacteristic
1030C2×D4C23×D4311yescharacteristic
1031C22×C4—21no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—21no—
1035C22×C4—21no—
1036C22×C4—21no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—44no—
1041C22×C4—432no—
1042C22×C4—862no—
1043C22×C4—862no—
1044C22×C4—862no—
1045C22×C4—862no—
1046C22×C4—861no—
1047C22×C4—861no—
1048C22×C4D4×D4311yescharacteristic
1049C22×C4D4×D4311yescharacteristic
1050C22×C4D4×D4311yescharacteristic
1051C22×C4C23×D4311yescharacteristic
1052C22×C4C23×D4311yescharacteristic
1053C22×C4C23×D4311yescharacteristic
1054Q16—862no—
1055Q16—1721no—
1056SD16—862no—
1057SD16—862no—
1058SD16—1722no—
1059SD16—1721no—
1060SD16—1721no—
1061D8—862no—
1062D8—1722no—
1063D8—1721no—
1064M16—22no—
1065M16—22no—
1066M16—42no—
1067M16—1722no—
1068C2×C8—42no—
1069C2×C8—431no—
1070C2×C8—431no—
1071C2×C8—431no—
1072C2×C8—431no—
1073C2×C8—862no—
1074C2×C8—862no—
1075C2×C8—1722no—
1076C2×C8C23×D4312yes—
1077C2×C8C23×D4312yes—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—431no—
1081C4⋊C4—431no—
1082C4⋊C4—432no—
1083C4⋊C4—432no—
1084C4⋊C4—431no—
1085C4⋊C4—431no—
1086C4⋊C4—432no—
1087C4⋊C4—862no—
1088C4⋊C4—862no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—861no—
1096C4⋊C4—861no—
1097C4⋊C4—861no—
1098C4⋊C4C23×D4312yes—
1099C4⋊C4C23×D4312yes—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—432no—
1103C22⋊C4—432no—
1104C22⋊C4—432no—
1105C22⋊C4—432no—
1106C22⋊C4—432no—
1107C22⋊C4—862no—
1108C22⋊C4—862no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—861no—
1117C22⋊C4—861no—
1118C22⋊C4—861no—
1119C22⋊C4—862no—
1120C22⋊C4—862no—
1121C22⋊C4—861no—
1122C22⋊C4—861no—
1123C42—22no—
1124C42—22no—
1125C42—432no—
1126C42—862no—
1127C42—862no—
1128C42—862no—
1129C42—861no—
1130C23—21no—
1131C23—22no—
1132C23—21no—
1133C23—41no—
1134C23—41no—
1135C23—42no—
1136C23—42no—
1137C23—81no—
1138C23—432no—
1139C23—861no—
1140C23—862no—
1141C23—3441no—
1142C23—3441no—
1143C23—3442no—
1144C23—3442no—
1145C23—1724no—
1146C23—1722no—
1147C23C2×D4×D4311yescharacteristic
1148C23C2×D4×D4311yescharacteristic
1149C23C2×D4×D4311yescharacteristic
1150Q8—21no—
1151Q8—21no—
1152Q8—21no—
1153Q8—42no—
1154Q8—862no—
1155Q8—861no—
1156Q8—861no—
1157Q8—3442no—
1158Q8C2×#1062189812yes—
1159D4—24no—
1160D4—21no—
1161D4—21no—
1162D4—21no—
1163D4—42no—
1164D4—42no—
1165D4—42no—
1166D4—42no—
1167D4—864no—
1168D4—861no—
1169D4—862no—
1170D4—861no—
1171D4—862no—
1172D4—862no—
1173D4—3442no—
1174D4—3442no—
1175D4—3442no—
1176D4—3442no—
1177D4—3441no—
1178D4—3441no—
1179D4—3442no—
1180D4—1724no—
1181D4—1722no—
1182D4—1722no—
1183D4—1724no—
1184D4—1724no—
1185D4—1722no—
1186D4—1722no—
1187D4C2×#1062189812yes—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—81no—
1205C2×C4—81no—
1206C2×C4—432no—
1207C2×C4—432no—
1208C2×C4—432no—
1209C2×C4—862no—
1210C2×C4—862no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—862no—
1214C2×C4—861no—
1215C2×C4—3442no—
1216C2×C4—3442no—
1217C2×C4—3442no—
1218C2×C4—3441no—
1219C2×C4—1724no—
1220C2×C4—1722no—
1221C2×C4C2×D4×D4311yescharacteristic
1222C2×C4C2×D4×D4311yescharacteristic
1223C2×C4C2×D4×D4311yescharacteristic
1224C2×C4C2×#1062189812yes—
1225C2×C4#1306337012yes—
1226C2×C4C24×D4311yescharacteristic
1227C8—22no—
1228C8—22no—
1229C8—861no—
1230C8—861no—
1231C8—861no—
1232C8—861no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—22no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—82no—
1248C22—84no—
1249C22—862no—
1250C22—862no—
1251C22—862no—
1252C22—1722no—
1253C22—1721no—
1254C22—1721no—
1255C22—1722no—
1256C22—1721no—
1257C22—1722no—
1258C22—6882no—
1259C22—6884no—
1260C22#1458353912yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—41no—
1266C4—42no—
1267C4—42no—
1268C4—862no—
1269C4—862no—
1270C4—862no—
1271C4—1721no—
1272C4—1721no—
1273C4—1722no—
1274C4—1721no—
1275C4#1458353912yes—
1276C4C22×#1062189811yescharacteristic
1277C4C2×#1306337011yescharacteristic
1278C2—22no—
1279C2—41no—
1280C2—41no—
1281C2—42no—
1282C2—81no—
1283C2—3442no—
1284C2—3441no—
1285C2—1722no—
1286C2C2×#1458353911yescharacteristic
1287C2#1914936811yescharacteristic
1288C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2896C2
socleC22×C43C23×D4
hypercenter#2896D43
hypocenterC43#61196
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #19148315C2semidirect
2. #19148264C2semidirect
3. #19146844C2semidirect
4. #19146822C2semidirect
5. #19146747C2semidirect
6. #19146737C2semidirect
7. #19146717C2semidirect
8. #19146662C2semidirect
9. #19146541C2semidirect
10. #19146431C2semidirect
11. #19144952C2semidirect
12. #19144583C2semidirect
13. C2×#14583223C2semidirect
14. #19144450C2semidirect
15. #19144264C2semidirect
16. #19144214C2semidirect
17. #19144133C2semidirect
18. #19143901C2semidirect
19. #19143813C2semidirect
20. #19143474C2semidirect
21. #19143320C2semidirect
22. #19143119C2semidirect
23. C43×#2896C2semidirect
25. C2×#13063353C22semidirect
27. C2×#13063345C22semidirect
28. C2×#13063333C22semidirect
30. #14583617C22semidirect
32. #14583612C22semidirect
34. #14583593C22semidirect
36. #14583588C22semidirect
43. #14583530C22semidirect
45. #14583480C22semidirect
53. #14583410C22semidirect
57. #14583380C22semidirect
58. #14583380C22semidirect
59. #14583262C22semidirect
60. #14583260C22semidirect
61. #14583255C22semidirect
62. #14583244C22semidirect
63. #14583239C22semidirect
64. #14583228C22semidirect
65. #14583223C22semidirect
66. #14583223C22semidirect
67. #14583223C22semidirect
68. #14583223C22semidirect
69. #14583221C22semidirect
70. #14583216C22semidirect
71. #14583204C22semidirect
72. #14583201C22semidirect
73. #14583192C22semidirect
74. #14583177C22semidirect
75. #14583152C22semidirect
76. #14583148C22semidirect
77. #14583145C22semidirect
78. #14583144C22semidirect
79. #14583139C22semidirect
80. #14583135C22semidirect
81. #14583134C22semidirect
82. #14583128C22semidirect
83. #14583124C22semidirect
84. #14583117C22semidirect
85. #14583098C22semidirect
86. #14583093C22semidirect
87. #14583064C22semidirect
88. #14583061C22semidirect
89. #14583061C22semidirect
90. #14583055C22semidirect
91. #14583051C22semidirect
92. #14583050C22semidirect
93. #14583047C22semidirect
94. #14583044C22semidirect
95. #14583044C22semidirect
96. #14583038C22semidirect
97. #14583034C22semidirect
98. #14583033C22semidirect
99. #14583008C22semidirect
100. #14583003C22semidirect
101. #14582990C22semidirect
102. #14582984C22semidirect
103. #14582975C22semidirect
104. #14582970C22semidirect
105. #14582968C22semidirect
106. C8×C22⋊D43C22semidirect
107. #14582941C22semidirect
108. C2×#13063258C22semidirect
109. C2×#13063256C22semidirect
110. #14582927C22semidirect
111. #14582905C22semidirect
112. #14582902C22semidirect
113. #14582901C22semidirect
114. #14582899C22semidirect
116. #14582895C22semidirect
117. #14582894C22semidirect
118. C2×#13063245C22semidirect
119. C2×#13063245C22semidirect
120. #102×D43C22semidirect
121. #14582867C22semidirect
122. C2×C22⋊(C43⋊C8)C22semidirect
123. #14582857C22semidirect
125. C22×M16×C43C22semidirect
126. C2×#117×C43C22semidirect
127. C43×#419C22semidirect
128. C43×#418C22semidirect
131. C43×#417C22semidirect
132. C43×#417C22semidirect
133. C43×#416C22semidirect
134. C43×#416C22semidirect
656. #2896D43semidirect
674. C22×M16C2×D43semidirect
705. C2×#117C2×D43semidirect
758. #419C2×D43semidirect
761. #418C2×D43semidirect
766. #417C2×D43semidirect
767. #417C2×D43semidirect
771. #416C2×D43semidirect
772. #416C2×D43semidirect
779. C43#61196semidirect

Maximal subgroups

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

subgroupindex
#191483152
#191482642
#191468442
#191468222
#191467472
#191467372
#191467172
#191466622
#191465412
#191464312
#191449522
#191445832
C2×#145832232
#191444502
#191442642
#191442142
#191441332
#191439012
#191438132
#191434742
#191433202
#191431192
C43×#28962
#6119643