Finite Group Databasebeta

← #25974032

Subgroups — #25974032

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148302C211yesmaximal, characteristic, complemented
2#19148238C211yesmaximal, characteristic, complemented
3#19146906C212yesmaximal, complemented
4#19146895C212yesmaximal, complemented
5#19146817C212yesmaximal, complemented
6#19146802C212yesmaximal, complemented
7#19146697C212yesmaximal, complemented
8#19146682C212yesmaximal, complemented
9#19146577C212yesmaximal, complemented
10#19146562C212yesmaximal, complemented
11#19144958C211yesmaximal, characteristic, complemented
12#19144558C211yesmaximal, characteristic, complemented
13#19144521C211yesmaximal, characteristic, complemented
14#19144424C211yesmaximal, characteristic, complemented
15#19144203C211yesmaximal, characteristic, complemented
16#19144149C211yesmaximal, characteristic, complemented
17#19143896C211yesmaximal, characteristic, complemented
18#19143836C211yesmaximal, characteristic, complemented
19#19143430C211yesmaximal, characteristic, complemented
20#19143296C211yesmaximal, characteristic, complemented
21#19143122C211yesmaximal, characteristic, complemented
22C2×#14582899C211yesmaximal, characteristic, complemented
23C43×#3063C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C22×#10621902C2211yescharacteristic
26C2×#13063350C2211yescharacteristic
27C2×#13063345C2211yescharacteristic
28C22×#10621872C2211yescharacteristic, complemented
29#14583607—21no—
30#14583607C2212yescomplemented
31#14583596—21no—
32#14583596C2212yescomplemented
33#14583583—21no—
34#14583583C2212yescomplemented
35#14583552—21no—
36#14583552—21no—
37#14583551C2212yes—
38#14583551C2212yes—
39#14583549—21no—
40#14583549C2212yescomplemented
41#14583542—21no—
42#14583542—21no—
43#14583540C2212yes—
44#14583540C2212yes—
45#14583530C2211yescharacteristic, complemented
46#14583494—22no—
47#14583473C2211yescharacteristic
48#14583460—22no—
49#14583411C2211yescharacteristic
50#14583409—22no—
51#14583406C2211yescharacteristic
52#14583406C2211yescharacteristic, complemented
53#123×D43—22no—
54#14583382C2211yescharacteristic
55#14583382C2211yescharacteristic, complemented
56#14583373C2211yescharacteristic
57C2×C4⋊C4×D43C2211yescharacteristic, complemented
58#14583266C2212yescomplemented
59#14583260C2212yescomplemented
60#14583255C2212yescomplemented
61#14583248C2212yescomplemented
62#14583237C2212yescomplemented
63#14583237C2212yescomplemented
64#14583236C2212yescomplemented
65#14583232C2212yescomplemented
66#14583231C2212yescomplemented
67#14583227C2212yescomplemented
68#14583219C2212yescomplemented
69#14583214C2212yescomplemented
70#14583202C2212yescomplemented
71#14583198C2212yescomplemented
72#14583188C2212yescomplemented
73#14583178C2212yescomplemented
74#14583156C2211yescharacteristic, complemented
75#14583156C2211yescharacteristic, complemented
76#14583151C2211yescharacteristic, complemented
77#14583151C2211yescharacteristic, complemented
78#14583148C2211yescharacteristic, complemented
79#14583148C2211yescharacteristic, complemented
80#14583144C2211yescharacteristic, complemented
81#14583144C2211yescharacteristic, complemented
82#14583123C2212yescomplemented
83#14583116C2212yescomplemented
84#14583107C2212yescomplemented
85#14583102C2212yescomplemented
86#14583060C2212yescomplemented
87#14583060C2212yescomplemented
88#14583059C2212yescomplemented
89#14583049C2212yescomplemented
90#14583043C2212yescomplemented
91#14583043C2212yescomplemented
92#14583042C2212yescomplemented
93#14583032C2212yescomplemented
94#14583008C2212yescomplemented
95#14583002C2212yescomplemented
96#14582984C2212yescomplemented
97#14582979C2212yescomplemented
98#14582975C2212yescomplemented
99#14582975C2212yescomplemented
100#14582970C2212yescomplemented
101#14582970C2212yescomplemented
102#14582942C2211yescharacteristic, complemented
103#14582935C2211yescharacteristic, complemented
104#14582927C2211yescharacteristic, complemented
105#14582908C2211yescharacteristic, complemented
106#14582905C2211yescharacteristic
107#14582905C2212yescomplemented
108#14582901C2211yescharacteristic
109#14582901C2212yescomplemented
110#14582899C2212yescomplemented
111#14582899C2212yescomplemented
112#14582899C2212yescomplemented
113#14582899C2212yescomplemented
114#14582898C2211yescharacteristic
115#14582896C2211yescharacteristic
116#14582896C2212yescomplemented
117C2×#13063249C2211yescharacteristic, complemented
118C2×#13063247C2211yescharacteristic
119C2×#13063247C2212yescomplemented
120C2×#13063245C2211yescharacteristic
121#14582866C2211yescharacteristic
122#14582862C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C2×#137×C43C2211yescharacteristic, complemented
125C2×#131×C43C2211yescharacteristic
126C43×#537C2211yescharacteristic
127C43×#536C2211yescharacteristic
128C43×#470C2212yescomplemented
129C43×#468C2212yescomplemented
130C43×#467C2212yescomplemented
131C43×#465C2212yescomplemented
132C43×#428C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C2×#103×C43C2211yescharacteristic, complemented
135#13063371—24no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621902—21no—
139C2×#10621902—21no—
140C2×#10621902—24no—
141C2×#10621902—42no—
142C2×#10621902C2312yes—
143C2×#10621902C2312yes—
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2312yes—
146C2×#10621900—22no—
147C22×D172—21no—
148C22×D172C2312yes—
149C22×D172C2311yescharacteristic
150C2×D4×D43—22no—
151C2×D4×D43—21no—
152C22×C4×D43—21no—
153C22×C4×D43—21no—
154C22×C4×D43C2311yescharacteristic
155#13063350—24no—
156#13063345—42no—
157C2×#10621885C2311yescharacteristic
158C2×#10621883C2311yescharacteristic
159C2×#10621884C2312yes—
160C2×#10621884C2311yescharacteristic
161C2×#10621882C2312yes—
162C2×#10621882C2311yescharacteristic
163C2×#10621877C2311yescharacteristic
164C2×#10621872—42no—
165C2×#10621872C2311yescharacteristic
166C2×#10621872C2311yescharacteristic
167C2×#10621872C2311yescharacteristic
168C2×#10621872C2311yescharacteristic
169C22×C43⋊C8C2311yescharacteristic
170#13063324—21no—
171#13063324C2312yes—
172#13063323C2312yes—
173#13063318—22no—
174#13063318—22no—
175#13063316—21no—
176#13063316C2312yes—
177#13063315—22no—
178#13063315—22no—
179#13063314C2312yes—
180#13063310—22no—
181#13063310—22no—
182#13063310—22no—
183#13063310—22no—
184#13063309—21no—
185#13063308—22no—
186#13063307—22no—
187#13063307—22no—
188#13063307—22no—
189#13063307—22no—
190#13063306—21no—
191#13063306—22no—
192#13063306—22no—
193#13063306D412yes—
194#13063305—22no—
195#13063305C2311yescharacteristic
196#13063305C2311yescharacteristic
197#13063304—22no—
198#13063302—22no—
199#13063302—22no—
200#13063301—21no—
201#13063301—21no—
202#13063301D411yescharacteristic
203#13063301D411yescharacteristic
204#13063301C2311yescharacteristic
205#13063301C2311yescharacteristic
206#13063300—22no—
207#13063300—22no—
208#13063300C2311yescharacteristic
209#13063300C2311yescharacteristic
210#13063298—22no—
211#13063298—22no—
212#13063296—22no—
213#13063296D411yescharacteristic
214#13063296D411yescharacteristic
215#13063296C2311yescharacteristic
216#13063296C2311yescharacteristic
217#13063295—21no—
218#13063295—22no—
219#13063295—22no—
220#13063293—21no—
221#13063293D412yes—
222Q8×Dic43—21no—
223Q8×Dic43C2312yes—
224C4×D172—21no—
225C4×D172—21no—
226C4×D172—21no—
227C4×D172—21no—
228D4×Dic43—21no—
229D4×Dic43—22no—
230D4×Dic43—22no—
231D4×Dic43C2312yes—
232#13063287C2312yes—
233#13063287C2312yes—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—21no—
236C4×C22⋊D43C2312yes—
237C4×C22⋊D43C2312yes—
238(C22⋊D43)⋊C4—22no—
239(C22⋊D43)⋊C4—22no—
240#13063284—21no—
241#13063284C2312yes—
242#13063284C2311yescharacteristic
243#13063284C2311yescharacteristic
244#13063283—22no—
245C2×C4⋊Dic43—21no—
246C2×C4⋊Dic43C2311yescharacteristic
247C2×C4⋊Dic43C2312yes—
248C2×Dic43⋊C4—21no—
249C4⋊C4×D43—21no—
250C4⋊C4×D43—21no—
251C4⋊C4×D43—22no—
252C4⋊C4×D43—22no—
253C4⋊C4×D43C2312yes—
254C4⋊C4×D43C2312yes—
255C22⋊C4×D43—22no—
256C22⋊C4×D43—22no—
257C22⋊C4×D43—22no—
258#13063258C2311yescharacteristic
259#13063258C2311yescharacteristic
260#13063258C2312yes—
261#13063256C2311yescharacteristic
262#13063256C2311yescharacteristic
263#13063256C2312yes—
264Dic43⋊C8C2312yes—
265Dic43⋊C8C2312yes—
266#13063250C2312yes—
267#13063250C2311yescharacteristic
268#13063250C2311yescharacteristic
269#13063249C2312yes—
270#13063249C2312yes—
271#13063249C2312yes—
272#13063249C2312yes—
273#13063248C2312yes—
274#13063247C2312yes—
275#13063247C2312yes—
276#13063247C2312yes—
277#13063247C2312yes—
278#13063247C2312yes—
279#13063247C2311yescharacteristic
280#13063247C2311yescharacteristic
281#13063245C2312yes—
282#13063245C2312yes—
283#13063245C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285C22⋊(C43⋊C8)C2312yes—
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2312yes—
288#13063235C2312yes—
289C8×Dic43C2312yes—
290C2×#41×C43C2311yescharacteristic
291C2×#41×C43C2311yescharacteristic
292C22×Q8×C43C2311yescharacteristic
293#137×C43—42no—
294C2×Q16×C43C2312yes—
295C2×SD16×C43C2312yes—
296#131×C43—42no—
297C2×M16×C43C2311yescharacteristic
298C2×M16×C43C2312yes—
299C22×C8×C43C2311yescharacteristic
300C22×C8×C43C2312yes—
301C4⋊Q8×C43—21no—
302#124×C43—21no—
303#123×C43—22no—
304C22⋊Q8×C43—21no—
305C22⋊Q8×C43C2312yes—
306C22⋊Q8×C43C2312yes—
307C22⋊Q8×C43C2312yes—
308#121×C43—21no—
309#121×C43—22no—
310#121×C43C2312yes—
311#117×C43C2311yescharacteristic
312C2×C4⋊C4×C43C2311yescharacteristic
313#107×C43C2312yes—
314#106×C43C2312yes—
315#103×C43C2311yescharacteristic
316#103×C43C2311yescharacteristic
317#103×C43C2312yes—
318#103×C43C2312yes—
319#102×C43C2311yescharacteristic
320#102×C43C2311yescharacteristic
321C23×D43—21no—
322C23×D43—22no—
323C23×D43C2×D411yescharacteristic
324#41×C43—22no—
325#41×C43—22no—
326#41×C43—22no—
327#41×C43—22no—
328C2×Q8×C43—21no—
329C2×Q8×C43—22no—
330C2×Q8×C43—22no—
331C2×Q8×C43C2×D411yescharacteristic
332C2×Q8×C43C2412yes—
333C2×Q8×C43C2411yescharacteristic
334C2×D4×C43—21no—
335C2×D4×C43—22no—
336C2×D4×C43C2×D412yes—
337C2×D4×C43C2×D411yescharacteristic
338C2×D4×C43C2411yescharacteristic
339C22×C4×C43—21no—
340C22×C4×C43—21no—
341C22×C4×C43—21no—
342C22×C4×C43C2412yes—
343C22×C4×C43C2411yescharacteristic
344C2×C22⋊D43—21no—
345C2×C22⋊D43—22no—
346C2×C22⋊D43—21no—
347C2×C22⋊D43—21no—
348C2×C22⋊D43C2×D412yes—
349C2×C22⋊D43C2×D412yes—
350C22×Dic43—22no—
351C22×Dic43—21no—
352C22×Dic43—22no—
353C22×Dic43C2×D411yescharacteristic
354#10621902—24no—
355#10621902—24no—
356#10621902—42no—
357#10621902—42no—
358#10621902—44no—
359#10621902—44no—
360#10621902—44no—
361#10621900—84no—
362D4×D43—48no—
363D4×D43—44no—
364#10621898—22no—
365#10621898—22no—
366#10621898—24no—
367#10621898—42no—
368C2×D172—21no—
369C2×D172—22no—
370C2×D172—22no—
371C2×D172—22no—
372C2×D172—22no—
373C2×D172—21no—
374C2×D172—21no—
375C2×D172—24no—
376C2×D172—44no—
377C2×D172—42no—
378C2×D172#4114yescomplemented
379C2×D172C2411yescharacteristic
380C2×D172C2412yes—
381C2×C4×D43—22no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—21no—
385C2×C4×D43—22no—
386C2×C4×D43—22no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—22no—
391C2×C4×D43—44no—
392C2×C4×D43—82no—
393C2×C4×D43C2×D411yescharacteristic
394C2×C4×D43C2×D411yescharacteristic
395C2×C4×D43C2411yescharacteristic
396C2×C4×D43C2411yescharacteristic
397C2×Dic86—22no—
398C2×Dic86C2411yescharacteristic
399Q16×C43—42no—
400SD16×C43—42no—
401M16×C43—22no—
402M16×C43—42no—
403C2×C8×C43—22no—
404C2×C8×C43—42no—
405C2×C8×C43C2411yescharacteristic
406C2×C8×C43C2411yescharacteristic
407C2×C8×C43C2412yes—
408C4⋊C4×C43—21no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43—22no—
411C4⋊C4×C43—22no—
412C4⋊C4×C43C2411yescharacteristic
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2412yes—
415C22⋊C4×C43—22no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—22no—
418C22⋊C4×C43—22no—
419C22⋊C4×C43—22no—
420C42×C43—21no—
421C22⋊Dic43—22no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425C22⋊Dic43—22no—
426C22⋊Dic43C2×D412yes—
427C22⋊Dic43C2×D412yes—
428C22⋊Dic43C2×D412yes—
429#10621885—41no—
430#10621884—24no—
431#10621884—41no—
432#10621883—41no—
433#10621882—24no—
434#10621882—41no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—21no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4C2×D412yes—
446(C2×D43)⋊C4C2×D412yes—
447C4⋊Dic43—21no—
448C4⋊Dic43—22no—
449C4⋊Dic43—21no—
450C4⋊Dic43—21no—
451C4⋊Dic43—22no—
452C4⋊Dic43—22no—
453C4⋊Dic43C2×D411yescharacteristic
454C4⋊Dic43C2×D411yescharacteristic
455C4⋊Dic43C2412yes—
456C4⋊Dic43C2411yescharacteristic
457C4⋊Dic43C2411yescharacteristic
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—21no—
465Dic43⋊C4—21no—
466Dic43⋊C4C2×D412yes—
467Dic43⋊C4C2×D412yes—
468C4×Dic43—22no—
469C4×Dic43—21no—
470C4×Dic43—22no—
471C4×Dic43C2412yes—
472#10621877—22no—
473C2×C43⋊C8—22no—
474C2×C43⋊C8C2412yes—
475C2×C43⋊C8C2411yescharacteristic
476C2×C43⋊C8C2411yescharacteristic
477#10621872—41no—
478#10621872—41no—
479#10621872—41no—
480#10621872—41no—
481C23×C43—21no—
482C23×C43C22×D412yes—
483C23×C43C22×D411yescharacteristic
484C22×D43—22no—
485C22×D43—22no—
486C22×D43—24no—
487C22×D43—21no—
488C22×D43—41no—
489C22×D43—41no—
490C22×D43—44no—
491C22×D43—81no—
492C22×D43—81no—
493C22×D43—82no—
494C22×D43—82no—
495C22×D43C22×D411yescharacteristic
496C22×D43C22×D411yescharacteristic
497Q8×C43—22no—
498Q8×C43—21no—
499Q8×C43—22no—
500Q8×C43—21no—
501Q8×C43—22no—
502Q8×C43—42no—
503D4×C43—24no—
504D4×C43—22no—
505D4×C43—21no—
506D4×C43—21no—
507D4×C43—42no—
508D4×C43—82no—
509C2×C4×C43—22no—
510C2×C4×C43—22no—
511C2×C4×C43—21no—
512C2×C4×C43—22no—
513C2×C4×C43—22no—
514C2×C4×C43—21no—
515C2×C4×C43—21no—
516C2×C4×C43—42no—
517C2×C4×C43—42no—
518C2×C4×C43—81no—
519C2×C4×C43C22×D412yes—
520C2×C4×C43C22×D411yescharacteristic
521C2×C4×C43C2×#4112yes—
522C2×C4×C43H(5,𝔽2)12yes—
523C2×C4×C43C2511yescharacteristic
524C22⋊D43—42no—
525C22⋊D43—42no—
526C22⋊D43—44no—
527C22⋊D43—42no—
528C22⋊D43—42no—
529C22⋊D43—42no—
530C2×Dic43—22no—
531C2×Dic43—21no—
532C2×Dic43—22no—
533C2×Dic43—21no—
534C2×Dic43—21no—
535C2×Dic43—82no—
536C2×Dic43—81no—
537C2×Dic43—82no—
538C2×Dic43C22×D412yes—
539C2×Dic43C22×D412yes—
540C2×Dic43C22×D411yescharacteristic
541C2×Dic43C22×D411yescharacteristic
542D172—24no—
543D172—21no—
544D172—22no—
545D172—21no—
546D172—44no—
547D172—44no—
548D172—44no—
549D172—81no—
550D172—81no—
551D172C2×#4114yes—
552C4×D43—22no—
553C4×D43—22no—
554C4×D43—21no—
555C4×D43—21no—
556C4×D43—21no—
557C4×D43—21no—
558C4×D43—44no—
559C4×D43—44no—
560C4×D43—44no—
561C4×D43—44no—
562C4×D43—42no—
563C4×D43—82no—
564C4×D43—82no—
565C4×D43—82no—
566Dic86—21no—
567Dic86—21no—
568Dic86—82no—
569C8×C43—21no—
570C8×C43—21no—
571C8×C43—22no—
572C43⋊C8—22no—
573C43⋊C8—21no—
574C43⋊C8—21no—
575#61177—431nomaximal, Sylow
576C22×C43—21no—
577C22×C43—21no—
578C22×C43—22no—
579C22×C43—22no—
580C22×C43—22no—
581C22×C43—41no—
582C22×C43—41no—
583C22×C43—41no—
584C22×C43#54612yes—
585C22×C43C23×D411yescharacteristic
586C2×D43—21no—
587C2×D43—21no—
588C2×D43—21no—
589C2×D43—21no—
590C2×D43—24no—
591C2×D43—21no—
592C2×D43—21no—
593C2×D43—44no—
594C2×D43—42no—
595C2×D43—42no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—41no—
599C2×D43—84no—
600C2×D43—164no—
601C4×C43—22no—
602C4×C43—42no—
603C4×C43—41no—
604C4×C43—41no—
605C4×C43—42no—
606C4×C43—41no—
607C4×C43#54612yes—
608C4×C43C22×#4111yescharacteristic
609C4×C43C2×H(5,𝔽2)11yescharacteristic
610Dic43—22no—
611Dic43—22no—
612Dic43—21no—
613Dic43—21no—
614Dic43—41no—
615Dic43—42no—
616Dic43—41no—
617Dic43—41no—
618#3492—431no—
619#3485—431no—
620#3331—432no—
621#3330—432no—
622#3323—432no—
623#3322—432no—
624#3315—432no—
625#3314—432no—
626#3307—432no—
627#3306—432no—
628#3137—431no—
629#3097—431no—
630#3092—431no—
631#3081—431no—
632#3063D4311yescharacteristic, complemented
633#3054—431no—
634#3046—431no—
635#3012—431no—
636#3005—431no—
637#2946—431no—
638#2930—431no—
639#2897—431no—
640C2×#417—431no—
641C2×C43—22no—
642C2×C43—42no—
643C2×C43—81no—
644C2×C43C2×#54611yescharacteristic
645C2×C43#358511yescharacteristic
646C2×C43#358611yescharacteristic
647D43—41no—
648D43—41no—
649D43—44no—
650D43—81no—
651C2×H(5,𝔽2)—431no—
652C22×#41—431no—
653C2×#137C2×D4311yescharacteristic, complemented
654C2×AGL(1,ℤ/8)—431no—
655C2×#135—431no—
656C2×#131C2×D4311yescharacteristic
657C22×M16—431no—
658#554—432no—
659#554—861no—
660#553—432no—
661#553—861no—
662#552—432no—
663#552—861no—
664#547—432no—
665#547—432no—
666#547—432no—
667#547—861no—
668#547—861no—
669#547—861no—
670#546—432no—
671#546—432no—
672#546—861no—
673#546—861no—
674#544—431no—
675#539—862no—
676#537C2×D4311yescharacteristic
677#536—431no—
678#536C2×D4311yescharacteristic
679#534—862no—
680#525—431no—
681#525—431no—
682#525—431no—
683#525—862no—
684C2×#123—862no—
685#520—431no—
686#520—431no—
687#518—431no—
688C22×C4⋊C4—431no—
689#491—432no—
690#489—432no—
691#488—432no—
692#487—432no—
693#485—432no—
694#485—432no—
695#484—432no—
696#484—432no—
697#483—432no—
698#483—432no—
699#481—432no—
700#480—432no—
701#478—432no—
702#478—432no—
703#476—432no—
704#474—432no—
705#470—431no—
706#470—431no—
707#470C2×D4312yescomplemented
708#469—431no—
709#469—431no—
710#468—431no—
711#468—431no—
712#468—431no—
713#468—431no—
714#468C2×D4312yescomplemented
715#467C2×D4312yescomplemented
716#465C2×D4312yescomplemented
717#464—432no—
718#463—432no—
719#462—432no—
720#461—432no—
721#452—432no—
722#452—432no—
723#452—432no—
724#450—432no—
725#449—432no—
726#449—432no—
727#449—432no—
728#447—432no—
729#442—432no—
730#440—432no—
731C4×SD16—432no—
732C4×D8—432no—
733#436—432no—
734#436—432no—
735#435—432no—
736#435—432no—
737#428—431no—
738#428C2×D4311yescharacteristic, complemented
739#427—431no—
740#424—431no—
741#419—431no—
742#418—431no—
743#418—432no—
744#417—432no—
745#417—431no—
746#417—431no—
747#417—432no—
748#417—432no—
749#417—432no—
750#417—432no—
751#416—431no—
752#416—432no—
753#416C2×D4311yescharacteristic, complemented
754C2×#103—431no—
755C2×#103C2×D4311yescharacteristic, complemented
756C2×#102—431no—
757C2×#102—432no—
758C2×#102—431no—
759#408—431no—
760#407—431no—
761#405—431no—
762C43#6117711yescharacteristic, complemented, Sylow
763H(5,𝔽2)—864no—
764H(5,𝔽2)—1722no—
765C2×#41—432no—
766C2×#41—432no—
767C2×#41—431no—
768C2×#41—432no—
769C2×#41—861no—
770C2×#41—861no—
771C2×#41—862no—
772C2×#41—861no—
773C2×#41—864no—
774C2×#41—1722no—
775C2×#41C22×D4311yescharacteristic
776C2×#41C22×D4311yescharacteristic
777C22×Q8C22×D4311yescharacteristic
778C22×D4—431no—
779C22×D4—432no—
780C22×D4—861no—
781C22×D4—862no—
782C22×D4—861no—
783C23×C4—431no—
784C23×C4—861no—
785C23×C4—861no—
786#137—42no—
787AGL(1,ℤ/8)—864no—
788#135—1722no—
789C2×Q16—431no—
790C2×Q16C22×D4312yes—
791C2×SD16—432no—
792C2×SD16—431no—
793C2×SD16—431no—
794C2×SD16C22×D4312yes—
795C2×D8—432no—
796C2×D8—431no—
797#131—42no—
798C2×M16—431no—
799C2×M16—431no—
800C2×M16—431no—
801C2×M16—431no—
802C2×M16—431no—
803C2×M16—1722no—
804C2×M16C22×D4311yescharacteristic
805C2×M16C22×D4312yes—
806C22×C8—431no—
807C22×C8C22×D4311yescharacteristic
808C22×C8C22×D4312yes—
809C4⋊Q8—21no—
810C4⋊Q8—432no—
811C4⋊Q8—432no—
812C4⋊Q8—861no—
813#126—862no—
814#126—862no—
815#125—432no—
816#125—862no—
817#125—862no—
818#125—861no—
819#124—21no—
820#124—432no—
821#123—22no—
822#123—432no—
823#123—862no—
824#123—862no—
825#123—862no—
826#123—861no—
827#123—862no—
828#123—862no—
829#123—862no—
830#123—862no—
831#123—862no—
832#123—862no—
833#123—862no—
834#123—862no—
835#123—861no—
836C22⋊Q8—21no—
837C22⋊Q8—431no—
838C22⋊Q8—431no—
839C22⋊Q8—431no—
840C22⋊Q8—431no—
841C22⋊Q8—431no—
842C22⋊Q8—431no—
843C22⋊Q8—862no—
844C22⋊Q8—862no—
845C22⋊Q8—862no—
846C22⋊Q8—862no—
847C22⋊Q8—861no—
848C22⋊Q8—861no—
849C22⋊Q8C22×D4312yes—
850C22⋊Q8C22×D4312yes—
851C22⋊Q8C22×D4312yes—
852#121—22no—
853#121—21no—
854#121—431no—
855#121—431no—
856#121—431no—
857#121—431no—
858#121—431no—
859#121—431no—
860#121—862no—
861#121—862no—
862#121—862no—
863#121—862no—
864#121—862no—
865#121C22×D4312yes—
866#120—432no—
867#120—862no—
868#120—862no—
869#120—861no—
870#120—861no—
871C4×Q8—432no—
872C4×Q8—861no—
873C4×D4—432no—
874C4×D4—432no—
875C4×D4—432no—
876C4×D4—432no—
877C4×D4—432no—
878C4×D4—861no—
879C4×D4—861no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—862no—
883C4×D4—862no—
884C4×D4—862no—
885C4×D4—861no—
886C4×D4—861no—
887C4×D4—862no—
888C4×D4—861no—
889#117—431no—
890#117—431no—
891#117—432no—
892#117—862no—
893#117—861no—
894#117C22×D4311yescharacteristic
895C2×C4⋊C4—431no—
896C2×C4⋊C4—432no—
897C2×C4⋊C4—432no—
898C2×C4⋊C4—432no—
899C2×C4⋊C4—862no—
900C2×C4⋊C4—862no—
901C2×C4⋊C4—861no—
902C2×C4⋊C4—861no—
903C2×C4⋊C4—861no—
904C2×C4⋊C4—861no—
905C2×C4⋊C4C22×D4311yescharacteristic
906C2×C22⋊C4—862no—
907C2×C22⋊C4—862no—
908C2×C22⋊C4—862no—
909#107—431no—
910#107—431no—
911#107—432no—
912#107C22×D4312yes—
913#106—431no—
914#106—431no—
915#106—432no—
916#106C22×D4312yes—
917C4⋊C8—432no—
918C4⋊C8—432no—
919#103—432no—
920#103—432no—
921#103—432no—
922#103—432no—
923#103—431no—
924#103—432no—
925#103—431no—
926#103—432no—
927#103C22×D4312yes—
928#103C22×D4312yes—
929#103C22×D4311yescharacteristic
930#103C22×D4311yescharacteristic
931#102—432no—
932#102—431no—
933#102—432no—
934#102—432no—
935#102—432no—
936#102—432no—
937#102—431no—
938#102—432no—
939#102—432no—
940#102—432no—
941#102C22×D4311yescharacteristic
942#102C22×D4311yescharacteristic
943C22⋊C8—432no—
944C22⋊C8—432no—
945C22⋊C8—432no—
946C22⋊C8—432no—
947#97—432no—
948C4×C8—432no—
949C24—431no—
950C24—861no—
951C24—862no—
952#41—22no—
953#41—22no—
954#41—22no—
955#41—22no—
956#41—864no—
957#41—864no—
958#41—864no—
959#41—862no—
960#41—862no—
961#41—3444no—
962#41—1722no—
963#41—1722no—
964#41—1722no—
965#41—1724no—
966#41—1724no—
967#41—1724no—
968C2×Q8—21no—
969C2×Q8—22no—
970C2×Q8—22no—
971C2×Q8—431no—
972C2×Q8—862no—
973C2×Q8D4×D4311yescharacteristic
974C2×Q8C23×D4312yes—
975C2×Q8C23×D4311yescharacteristic
976C2×D4—21no—
977C2×D4—22no—
978C2×D4—432no—
979C2×D4—432no—
980C2×D4—434no—
981C2×D4—432no—
982C2×D4—431no—
983C2×D4—864no—
984C2×D4—861no—
985C2×D4—861no—
986C2×D4—862no—
987C2×D4—862no—
988C2×D4—861no—
989C2×D4—861no—
990C2×D4—861no—
991C2×D4—862no—
992C2×D4—861no—
993C2×D4—862no—
994C2×D4—862no—
995C2×D4—1722no—
996C2×D4—1724no—
997C2×D4—1724no—
998C2×D4—1728no—
999C2×D4D4×D4312yes—
1000C2×D4D4×D4311yescharacteristic
1001C2×D4C23×D4311yescharacteristic
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—431no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—862no—
1011C22×C4—862no—
1012C22×C4—862no—
1013C22×C4—862no—
1014C22×C4—862no—
1015C22×C4—862no—
1016C22×C4—862no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—861no—
1020C22×C4—862no—
1021C22×C4—862no—
1022C22×C4—861no—
1023C22×C4—3442no—
1024C22×C4—1724no—
1025C22×C4C23×D4312yes—
1026C22×C4C23×D4311yescharacteristic
1027Q16—42no—
1028Q16—1721no—
1029SD16—42no—
1030SD16—864no—
1031SD16—1721no—
1032SD16—1721no—
1033D8—864no—
1034D8—1721no—
1035M16—22no—
1036M16—42no—
1037M16—862no—
1038M16—1721no—
1039M16—1721no—
1040M16—1721no—
1041M16—1721no—
1042C2×C8—22no—
1043C2×C8—42no—
1044C2×C8—432no—
1045C2×C8—431no—
1046C2×C8—431no—
1047C2×C8—862no—
1048C2×C8C23×D4311yescharacteristic
1049C2×C8C23×D4311yescharacteristic
1050C2×C8C23×D4312yes—
1051C4⋊C4—21no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—431no—
1056C4⋊C4—432no—
1057C4⋊C4—432no—
1058C4⋊C4—431no—
1059C4⋊C4—432no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—862no—
1063C4⋊C4—862no—
1064C4⋊C4—861no—
1065C4⋊C4—861no—
1066C4⋊C4—862no—
1067C4⋊C4—862no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—862no—
1073C4⋊C4—862no—
1074C4⋊C4—861no—
1075C4⋊C4—862no—
1076C4⋊C4C23×D4312yes—
1077C4⋊C4C23×D4311yescharacteristic
1078C4⋊C4C23×D4311yescharacteristic
1079C22⋊C4—21no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—432no—
1085C22⋊C4—432no—
1086C22⋊C4—432no—
1087C22⋊C4—432no—
1088C22⋊C4—432no—
1089C22⋊C4—861no—
1090C22⋊C4—861no—
1091C22⋊C4—862no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—862no—
1095C22⋊C4—861no—
1096C22⋊C4—861no—
1097C22⋊C4—861no—
1098C22⋊C4—861no—
1099C22⋊C4—862no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—861no—
1103C22⋊C4—862no—
1104C42—21no—
1105C42—432no—
1106C42—862no—
1107C42—862no—
1108C42—861no—
1109C23—21no—
1110C23—431no—
1111C23—431no—
1112C23—864no—
1113C23—862no—
1114C23—862no—
1115C23—861no—
1116C23—3441no—
1117C23—3441no—
1118C23—3442no—
1119C23—3442no—
1120C23—1721no—
1121C23—1721no—
1122C23—1724no—
1123C23C2×D4×D4312yes—
1124C23C2×D4×D4311yescharacteristic
1125Q8—22no—
1126Q8—21no—
1127Q8—22no—
1128Q8—22no—
1129Q8—21no—
1130Q8—42no—
1131Q8—861no—
1132Q8—861no—
1133Q8—3442no—
1134D4—24no—
1135D4—21no—
1136D4—21no—
1137D4—22no—
1138D4—42no—
1139D4—82no—
1140D4—434no—
1141D4—861no—
1142D4—862no—
1143D4—861no—
1144D4—864no—
1145D4—3441no—
1146D4—3441no—
1147D4—1724no—
1148D4—1724no—
1149D4—1724no—
1150D4—1722no—
1151D4—1722no—
1152D4—1724no—
1153D4—1722no—
1154D4—1722no—
1155D4—1722no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—81no—
1166C2×C4—432no—
1167C2×C4—432no—
1168C2×C4—431no—
1169C2×C4—431no—
1170C2×C4—862no—
1171C2×C4—861no—
1172C2×C4—861no—
1173C2×C4—861no—
1174C2×C4—861no—
1175C2×C4—862no—
1176C2×C4—862no—
1177C2×C4—861no—
1178C2×C4—862no—
1179C2×C4—861no—
1180C2×C4—861no—
1181C2×C4—3442no—
1182C2×C4—3442no—
1183C2×C4—3442no—
1184C2×C4—3442no—
1185C2×C4—3441no—
1186C2×C4—3442no—
1187C2×C4—1724no—
1188C2×C4—1724no—
1189C2×C4—1724no—
1190C2×C4—1724no—
1191C2×C4—1722no—
1192C2×C4C2×D4×D4312yes—
1193C2×C4C2×D4×D4311yescharacteristic
1194C2×C4#41×D4312yes—
1195C2×C4#1306337012yes—
1196C2×C4C24×D4311yescharacteristic
1197C8—21no—
1198C8—21no—
1199C8—22no—
1200C8—862no—
1201C8—861no—
1202C8—861no—
1203C22—21no—
1204C22—21no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—861no—
1212C22—861no—
1213C22—864no—
1214C22—861no—
1215C22—861no—
1216C22—861no—
1217C22—861no—
1218C22—3444no—
1219C22—1724no—
1220C22—1721no—
1221C22—1721no—
1222C22—1721no—
1223C22—1722no—
1224C22—1722no—
1225C22—6884no—
1226C22#1458353812yes—
1227C22C22×D4×D4311yescharacteristic
1228C4—22no—
1229C4—42no—
1230C4—41no—
1231C4—42no—
1232C4—41no—
1233C4—41no—
1234C4—861no—
1235C4—861no—
1236C4—862no—
1237C4—862no—
1238C4—1721no—
1239C4—1722no—
1240C4—1721no—
1241C4—1721no—
1242C4#1458353812yes—
1243C4C2×#41×D4311yescharacteristic
1244C4C2×#1306337011yescharacteristic
1245C2—22no—
1246C2—42no—
1247C2—81no—
1248C2—3441no—
1249C2—1721no—
1250C2—1721no—
1251C2—1724no—
1252C2C2×#1458353811yescharacteristic
1253C2#1914937311yescharacteristic
1254C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3063C2
socleC22×C43C23×D4
hypercenter#3063D43
hypocenterC43#61177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3063

Complements

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

NH ≅ G/Ntype
1. #19148302C2semidirect
2. #19148238C2semidirect
3. #19146906C2semidirect
4. #19146895C2semidirect
5. #19146817C2semidirect
6. #19146802C2semidirect
7. #19146697C2semidirect
8. #19146682C2semidirect
9. #19146577C2semidirect
10. #19146562C2semidirect
11. #19144958C2semidirect
12. #19144558C2semidirect
13. #19144521C2semidirect
14. #19144424C2semidirect
15. #19144203C2semidirect
16. #19144149C2semidirect
17. #19143896C2semidirect
18. #19143836C2semidirect
19. #19143430C2semidirect
20. #19143296C2semidirect
21. #19143122C2semidirect
22. C2×#14582899C2semidirect
23. C43×#3063C2semidirect
28. C22×#10621872C22semidirect
30. #14583607C22semidirect
32. #14583596C22semidirect
34. #14583583C22semidirect
40. #14583549C22semidirect
45. #14583530C22semidirect
52. #14583406C22semidirect
55. #14583382C22semidirect
57. C2×C4⋊C4×D43C22semidirect
58. #14583266C22semidirect
59. #14583260C22semidirect
60. #14583255C22semidirect
61. #14583248C22semidirect
62. #14583237C22semidirect
63. #14583237C22semidirect
64. #14583236C22semidirect
65. #14583232C22semidirect
66. #14583231C22semidirect
67. #14583227C22semidirect
68. #14583219C22semidirect
69. #14583214C22semidirect
70. #14583202C22semidirect
71. #14583198C22semidirect
72. #14583188C22semidirect
73. #14583178C22semidirect
74. #14583156C22semidirect
75. #14583156C22semidirect
76. #14583151C22semidirect
77. #14583151C22semidirect
78. #14583148C22semidirect
79. #14583148C22semidirect
80. #14583144C22semidirect
81. #14583144C22semidirect
82. #14583123C22semidirect
83. #14583116C22semidirect
84. #14583107C22semidirect
85. #14583102C22semidirect
86. #14583060C22semidirect
87. #14583060C22semidirect
88. #14583059C22semidirect
89. #14583049C22semidirect
90. #14583043C22semidirect
91. #14583043C22semidirect
92. #14583042C22semidirect
93. #14583032C22semidirect
94. #14583008C22semidirect
95. #14583002C22semidirect
96. #14582984C22semidirect
97. #14582979C22semidirect
98. #14582975C22semidirect
99. #14582975C22semidirect
100. #14582970C22semidirect
101. #14582970C22semidirect
102. #14582942C22semidirect
103. #14582935C22semidirect
104. #14582927C22semidirect
105. #14582908C22semidirect
107. #14582905C22semidirect
109. #14582901C22semidirect
110. #14582899C22semidirect
111. #14582899C22semidirect
112. #14582899C22semidirect
113. #14582899C22semidirect
116. #14582896C22semidirect
117. C2×#13063249C22semidirect
119. C2×#13063247C22semidirect
122. #14582862C22semidirect
123. #14582854C22semidirect
124. C2×#137×C43C22semidirect
128. C43×#470C22semidirect
129. C43×#468C22semidirect
130. C43×#467C22semidirect
131. C43×#465C22semidirect
132. C43×#428C22semidirect
133. C43×#416C22semidirect
134. C2×#103×C43C22semidirect
378. C2×D172#41semidirect
632. #3063D43semidirect
653. C2×#137C2×D43semidirect
707. #470C2×D43semidirect
714. #468C2×D43semidirect
715. #467C2×D43semidirect
716. #465C2×D43semidirect
738. #428C2×D43semidirect
753. #416C2×D43semidirect
755. C2×#103C2×D43semidirect
762. C43#61177semidirect

Maximal subgroups

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

subgroupindex
#191483022
#191482382
#191469062
#191468952
#191468172
#191468022
#191466972
#191466822
#191465772
#191465622
#191449582
#191445582
#191445212
#191444242
#191442032
#191441492
#191438962
#191438362
#191434302
#191432962
#191431222
C2×#145828992
C43×#30632
#6117743