Finite Group Databasebeta

← #25102460

Subgroups — #25102460

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583664C211yesmaximal, characteristic, complemented
2#19143815C211yesmaximal, characteristic
3C2×#14583022C211yesmaximal, characteristic, complemented
4C2×#14583014C211yesmaximal, characteristic, complemented
5#19143300C211yesmaximal, characteristic, complemented
6#19134923C211yesmaximal, characteristic, complemented
7#19134920C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic, complemented
9#19134872C211yesmaximal, characteristic, complemented
10#19134871C211yesmaximal, characteristic, complemented
11#19134801C211yesmaximal, characteristic, complemented
12#19134537C211yesmaximal, characteristic, complemented
13#19134434C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C43×#1765C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19#14583664—24no—
20#14583664—24no—
21C2×#13063333—21no—
22C2×#13063333C2211yescharacteristic
23C2×#13063332C2211yescharacteristic
24C2×#13063331—21no—
25C2×#13063331C2211yescharacteristic
26C2×#13063331C2211yescharacteristic, complemented
27C22×#10621872—21no—
28C22×#10621872C2211yescharacteristic
29C2×M16×D43—21no—
30C2×M16×D43C2211yescharacteristic
31#14583411C2211yescharacteristic
32#14583064C411yescharacteristic, complemented
33#14583062C411yescharacteristic, complemented
34#14583056C411yescharacteristic, complemented
35#14583051C411yescharacteristic, complemented
36#14583047C411yescharacteristic, complemented
37#14583045C411yescharacteristic, complemented
38#14583039C411yescharacteristic, complemented
39#14583034C411yescharacteristic, complemented
40#14583022—24no—
41#14583014—24no—
42#14582978—21no—
43#14582978—21no—
44#14582972—21no—
45#14582972—21no—
46C2×#13063261C2211yescharacteristic, complemented
47C2×#13063260C2211yescharacteristic, complemented
48#14582926C2211yescharacteristic, complemented
49C2×#13063253C2211yescharacteristic
50C2×#13063253C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic
52C2×#13063251C2211yescharacteristic
53C2×#13063251C2211yescharacteristic, complemented
54#14582893C2211yescharacteristic
55#14582867C2211yescharacteristic, complemented
56#14582862C2211yescharacteristic
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C2×C8×Dic43C2211yescharacteristic, complemented
59C4×(C2×D43)⋊C4C2211yescharacteristic
60#14582663C2211yescharacteristic, complemented
61#14582658C2211yescharacteristic, complemented
62#14582654C2211yescharacteristic, complemented
63#14582653C2211yescharacteristic, complemented
64C2×#131×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic
66C43×#416C2211yescharacteristic
67C43×#405C2211yescharacteristic, complemented
68C2×#97×C43C2211yescharacteristic, complemented
69C43×#341C2211yescharacteristic, complemented
70C43×#339C2211yescharacteristic, complemented
71C2×#10621902C2×C411yescharacteristic
72C2×#10621898—21no—
73C2×#10621898C2311yescharacteristic
74C2×#10621898C2311yescharacteristic
75C2×#10621900—21no—
76C2×#10621900C2×C411yescharacteristic
77#41×D43—22no—
78#41×D43—22no—
79#41×D43—22no—
80#41×D43—22no—
81C2×Q8×D43C2×C411yescharacteristic
82C2×D4×D43—21no—
83C2×D4×D43C2×C411yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86#13063347—22no—
87#13063347—22no—
88#13063345—22no—
89#13063345—22no—
90C2×Dic172C2×C411yescharacteristic
91C2×#10621885C2×C411yescharacteristic
92C2×#10621873C2×C411yescharacteristic
93C2×#10621873C2×C411yescharacteristic
94C2×#10621883C2×C411yescharacteristic
95C2×#10621884C2×C411yescharacteristic
96C2×D344C2×C411yescharacteristic
97C2×#10621882C2×C411yescharacteristic
98#13063333—28no—
99#13063333—22no—
100#13063333—22no—
101#13063332—22no—
102#13063332—22no—
103#13063331—28no—
104#13063331—22no—
105#13063331—22no—
106#13063331—22no—
107#13063331D414yescomplemented
108C2×#10621877—21no—
109C2×#10621877C2311yescharacteristic
110C2×#10621877C2311yescharacteristic
111C2×#10621872—28no—
112C2×#10621872—21no—
113C2×#10621872—21no—
114C2×#10621872—22no—
115C2×#10621872—22no—
116C2×#10621872—21no—
117C2×#10621872—21no—
118C2×#10621872D411yescharacteristic
119C2×#10621872D411yescharacteristic
120C2×#10621872D411yescharacteristic
121C2×#10621872D411yescharacteristic
122M16×D43—28no—
123M16×D43—22no—
124M16×D43—22no—
125C22×C43⋊C8—21no—
126C22×C43⋊C8C2311yescharacteristic
127C22×C43⋊C8C2311yescharacteristic
128C2×C8×D43—21no—
129C2×C8×D43—21no—
130C2×C8×D43—21no—
131C2×C8×D43—21no—
132#13063309—21no—
133#13063305C2×C411yescharacteristic
134#13063305C2×C411yescharacteristic
135#13063300C2×C411yescharacteristic
136#13063300C2×C411yescharacteristic
137#13063295—21no—
138C4×D172—21no—
139C4×D172—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×C4×Dic43C2311yescharacteristic
142#13063261—22no—
143#13063260—22no—
144C4⋊(C43⋊C8)—21no—
145C4⋊(C43⋊C8)—21no—
146#13063253—22no—
147#13063253—22no—
148#13063252—22no—
149#13063251—22no—
150#13063251—22no—
151#13063248C2×C411yescharacteristic
152#13063248C2×C411yescharacteristic
153#13063245C2×C411yescharacteristic
154#13063245C2×C411yescharacteristic
155(C2×D43)⋊C8—21no—
156(C2×D43)⋊C8—21no—
157(C2×D43)⋊C8—21no—
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8C2×C411yescharacteristic
160(C2×D43)⋊C8C2×C411yescharacteristic
161(C2×D43)⋊C8C2×C411yescharacteristic
162(C2×D43)⋊C8C2×C411yescharacteristic
163C8×Dic43—22no—
164C43⋊#95—21no—
165C2×#41×C43C2311yescharacteristic
166#131×C43—22no—
167#131×C43D414yescomplemented
168C2×M16×C43—21no—
169C2×M16×C43C2311yescharacteristic
170C2×M16×C43C2311yescharacteristic
171C22×C8×C43—21no—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#117×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176#104×C43—22no—
177#103×C43C2×C411yescharacteristic
178#103×C43C2×C411yescharacteristic
179#102×C43C2×C411yescharacteristic
180#102×C43C2×C411yescharacteristic
181#97×C43—22no—
182#97×C43—21no—
183C4×C8×C43—21no—
184C23×D43—21no—
185C23×D43#4111yescharacteristic
186#41×C43—21no—
187#41×C43—21no—
188#41×C43C2×D412yes—
189#41×C43#4112yes—
190C2×Q8×C43C22×C411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43C22×C411yescharacteristic
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43#4111yescharacteristic
203#10621902—22no—
204#10621902—22no—
205Q8×D43—22no—
206Q8×D43—22no—
207#10621900—24no—
208#10621900—24no—
209#10621900—22no—
210#10621900—22no—
211D4×D43—24no—
212D4×D43—24no—
213D4×D43—22no—
214D4×D43—22no—
215#10621898—24no—
216#10621898—24no—
217#10621898—21no—
218#10621898—21no—
219#10621898—21no—
220#10621898—21no—
221#10621898—21no—
222#10621898—21no—
223#10621898C2×D412yes—
224#10621898#4112yes—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172C22×C411yescharacteristic
229C2×D172C22×C411yescharacteristic
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43C22×C411yescharacteristic
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C2×D411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×Dic86—21no—
245C2×Dic86C22×C411yescharacteristic
246C2×Dic86C22×C411yescharacteristic
247M16×C43—21no—
248M16×C43—24no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43C2×D412yes—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—24no—
256C2×C8×C43—21no—
257C2×C8×C43C22×C411yescharacteristic
258C2×C8×C43C22×C411yescharacteristic
259C2×C8×C43C2×D412yes—
260C2×C8×C43C2×D411yescharacteristic
261C2×C8×C43C2×D411yescharacteristic
262C2×C8×C43C2×D412yes—
263C4⋊C4×C43C22×C411yescharacteristic
264C4⋊C4×C43C22×C411yescharacteristic
265C22⋊C4×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43—21no—
269#10621885—22no—
270#10621884—22no—
271#10621883—22no—
272#10621882—22no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—42no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282#10621877—24no—
283#10621877—21no—
284#10621877—21no—
285#10621877—21no—
286#10621877C2×D412yes—
287C2×C43⋊C8—24no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8C22×C411yescharacteristic
295C2×C43⋊C8C22×C411yescharacteristic
296C2×C43⋊C8C2×D411yescharacteristic
297C2×C43⋊C8C2×D411yescharacteristic
298Dic172—22no—
299D344—22no—
300#10621873—22no—
301#10621873—22no—
302#10621872—24no—
303#10621872—24no—
304#10621872—22no—
305#10621872—22no—
306#10621872—24no—
307#10621872—22no—
308#10621872—22no—
309#10621872—42no—
310C8×D43—24no—
311C8×D43—24no—
312C8×D43—24no—
313C8×D43—42no—
314C23×C43—21no—
315C23×C43C2×#4111yescharacteristic
316C22×D43—21no—
317C22×D43—24no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—81no—
324C22×D43—81no—
325C22×D43C4×D411yescharacteristic
326C22×D43C4×D411yescharacteristic
327Q8×C43—21no—
328Q8×C43C4×D412yes—
329D4×C43—22no—
330D4×C43—22no—
331D4×C43—21no—
332D4×C43C4×D412yes—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C22⋊D43—24no—
348C22⋊D43—24no—
349C22⋊D43—22no—
350C22⋊D43—22no—
351C22⋊D43—41no—
352C22⋊D43—41no—
353C2×Dic43—24no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—22no—
358C2×Dic43—21no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43C4×D411yescharacteristic
362C2×Dic43C4×D411yescharacteristic
363D172—24no—
364D172—21no—
365D172—21no—
366D172—21no—
367D172—81no—
368D172—81no—
369D172C4×D412yes—
370C4×D43—24no—
371C4×D43—24no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—22no—
377C4×D43—21no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—22no—
381C4×D43—21no—
382C4×D43—41no—
383C4×D43—41no—
384Dic86—24no—
385Dic86—21no—
386Dic86—21no—
387Dic86—21no—
388Dic86C4×D412yes—
389C8×C43—21no—
390C8×C43—21no—
391C8×C43—22no—
392C8×C43—41no—
393C8×C43#12012yes—
394C8×C43#12012yes—
395C43⋊C8—21no—
396C43⋊C8—21no—
397C43⋊C8—22no—
398C43⋊C8—21no—
399C43⋊C8—21no—
400C43⋊C8—41no—
401#21468—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—22no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43C2×C4×D411yescharacteristic
408C22×C43#52511yescharacteristic
409C22×C43#52511yescharacteristic
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—21no—
414C2×D43—21no—
415C2×D43—22no—
416C2×D43—21no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—81no—
423C2×D43—81no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—41no—
427C4×C43—41no—
428C4×C43—81no—
429C4×C43C2×C4×D411yescharacteristic
430C4×C43C2×C4×D411yescharacteristic
431C4×C43C2×#12011yescharacteristic
432C4×C43#52511yescharacteristic
433Dic43—21no—
434Dic43—22no—
435Dic43—21no—
436Dic43—42no—
437Dic43—41no—
438C2×#568—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#443—431no—
442#2930—431no—
443#1876—431no—
444#1876—431no—
445#1871—431no—
446#1866—431no—
447#1866—431no—
448#1855—431no—
449#1789—431no—
450#1765D4311yescharacteristic, complemented
451#1764—431no—
452#1753—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—42no—
456C2×C43C4×#12011yescharacteristic
457C2×C43#295611yescharacteristic
458C2×C43#295711yescharacteristic
459D43—41no—
460D43—41no—
461D43—42no—
462D43—81no—
463C22×#41—431no—
464C2×#135—431no—
465C2×#135—431no—
466#568—864no—
467#568—864no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131—431no—
471C2×#131—431no—
472C2×#131—861no—
473C2×#131—861no—
474C2×#131C2×D4311yescharacteristic
475C22×M16—431no—
476C22×M16—431no—
477C22×M16—861no—
478C22×M16—861no—
479#525—431no—
480#452—431no—
481#452—431no—
482#451—431no—
483#450—431no—
484#449—431no—
485#449—431no—
486#448—431no—
487#447—431no—
488#444—864no—
489#443—864no—
490#436—861no—
491#436—861no—
492#435—861no—
493#435—861no—
494C2×#108—431no—
495C2×#108—431no—
496#424—431no—
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500C2×#104—431no—
501C2×#104—431no—
502C2×#104C2×D4311yescharacteristic
503#416—431no—
504#416C2×D4311yescharacteristic
505#408—431no—
506#407—431no—
507C2×C22⋊C8—431no—
508#405C2×D4311yescharacteristic, complemented
509C2×#97C2×D4311yescharacteristic, complemented
510C2×C4×C8—431no—
511C4×C22⋊C4—431no—
512#341—431no—
513#341C2×D4311yescharacteristic, complemented
514#339—431no—
515#339C2×D4311yescharacteristic, complemented
516#336—431no—
517#336—431no—
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—431no—
523C2×#41—861no—
524C2×#41—861no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—862no—
529C2×#41C22×D4311yescharacteristic
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C23×C4—431no—
534C23×C4—861no—
535#135—862no—
536#135—862no—
537#135—862no—
538#135—862no—
539C2×Q16—431no—
540C2×Q16—431no—
541C2×SD16—431no—
542C2×SD16—431no—
543C2×SD16—431no—
544C2×SD16—431no—
545C2×D8—431no—
546C2×D8—431no—
547#131—22no—
548#131—434no—
549#131—868no—
550#131—862no—
551#131—868no—
552#131—862no—
553#131—862no—
554#131—862no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131D17214yescomplemented
559C2×M16—21no—
560C2×M16—431no—
561C2×M16—431no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—431no—
566C2×M16—861no—
567C2×M16—861no—
568C2×M16—868no—
569C2×M16—861no—
570C2×M16—862no—
571C2×M16—868no—
572C2×M16—862no—
573C2×M16—862no—
574C2×M16—862no—
575C2×M16—861no—
576C2×M16—861no—
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—21no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—861no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8—861no—
586C22×C8—861no—
587C22×C8C22×D4311yescharacteristic
588C22×C8C22×D4311yescharacteristic
589#123—861no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592#121—431no—
593#121—431no—
594#120—861no—
595C4×D4—861no—
596C4×D4—861no—
597#117C22×D4311yescharacteristic
598C2×C22⋊C4—861no—
599C2×C42—431no—
600C2×C42C22×D4311yescharacteristic
601#108—862no—
602#108—862no—
603C4⋊C8—861no—
604C4⋊C8—861no—
605#104—22no—
606#104—862no—
607#104—862no—
608#104—862no—
609#104—862no—
610#104—862no—
611#103—431no—
612#103—431no—
613#103C4×D4311yescharacteristic
614#103C4×D4311yescharacteristic
615#102—431no—
616#102—431no—
617#102C4×D4311yescharacteristic
618#102C4×D4311yescharacteristic
619C22⋊C8—431no—
620C22⋊C8—431no—
621C22⋊C8—431no—
622C22⋊C8—431no—
623C22⋊C8—861no—
624C22⋊C8—861no—
625C22⋊C8—861no—
626C22⋊C8—861no—
627#97—22no—
628#97—21no—
629C4×C8—21no—
630C4×C8—862no—
631#95—861no—
632C24—431no—
633C24—861no—
634#41—21no—
635#41—21no—
636#41—432no—
637#41—432no—
638#41—864no—
639#41—864no—
640#41—862no—
641#41—864no—
642#41—864no—
643#41—862no—
644#41—862no—
645#41—862no—
646#41—861no—
647#41—861no—
648#41—861no—
649#41—861no—
650#41—861no—
651#41—861no—
652#41C2×D17212yes—
653#41#1062189812yes—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—861no—
657C2×Q8—862no—
658C2×Q8—862no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—21no—
661C2×D4—431no—
662C2×D4—431no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—862no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—862no—
673C2×D4—861no—
674C2×D4C2×C4×D4311yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—864no—
685C22×C4—864no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—21no—
704M16—24no—
705M16—21no—
706M16—21no—
707M16—432no—
708M16—864no—
709M16—864no—
710M16—864no—
711M16—861no—
712M16—862no—
713M16—862no—
714M16—862no—
715M16—862no—
716M16—864no—
717M16—861no—
718M16—861no—
719M16—1722no—
720M16C2×D17212yes—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—24no—
725C2×C8—21no—
726C2×C8—431no—
727C2×C8—431no—
728C2×C8—431no—
729C2×C8—431no—
730C2×C8—864no—
731C2×C8—864no—
732C2×C8—864no—
733C2×C8—861no—
734C2×C8—861no—
735C2×C8—861no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—864no—
739C2×C8—861no—
740C2×C8—1722no—
741C2×C8C2×C4×D4311yescharacteristic
742C2×C8C2×C4×D4311yescharacteristic
743C2×C8C2×D17212yes—
744C2×C8D4×D4312yes—
745C2×C8D4×D4311yescharacteristic
746C2×C8D4×D4311yescharacteristic
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4C2×C4×D4311yescharacteristic
750C4⋊C4C2×C4×D4311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—1722no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—861no—
761C42—861no—
762C23—21no—
763C23—431no—
764C23—431no—
765C23—864no—
766C23—861no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—3441no—
771C23—3441no—
772C23—1721no—
773C23—1721no—
774C23#41×D4311yescharacteristic
775Q8—21no—
776Q8—432no—
777Q8—864no—
778Q8—861no—
779Q8—861no—
780Q8—861no—
781Q8C4×D17212yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—432no—
786D4—864no—
787D4—864no—
788D4—864no—
789D4—862no—
790D4—862no—
791D4—861no—
792D4—861no—
793D4—861no—
794D4—3441no—
795D4—3441no—
796D4—1721no—
797D4—1721no—
798D4C4×D17212yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—431no—
808C2×C4—431no—
809C2×C4—864no—
810C2×C4—864no—
811C2×C4—864no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—862no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—861no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×D17211yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4C2×#1062189811yescharacteristic
837C8—21no—
838C8—21no—
839C8—22no—
840C8—41no—
841C8—861no—
842C8—861no—
843C8—861no—
844C8—861no—
845C8—862no—
846C8—1721no—
847C8#1306329512yes—
848C8#1306329512yes—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—861no—
855C22—862no—
856C22—861no—
857C22—861no—
858C22—861no—
859C22—861no—
860C22—861no—
861C22—3441no—
862C22—3441no—
863C22—3444no—
864C22—1721no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C4×D4×D4311yescharacteristic
870C22#1458340811yescharacteristic
871C22#1458341111yescharacteristic
872C4—22no—
873C4—41no—
874C4—41no—
875C4—81no—
876C4—861no—
877C4—861no—
878C4—862no—
879C4—1722no—
880C4—1721no—
881C4C4×D4×D4311yescharacteristic
882C4C2×C4×D17211yescharacteristic
883C4C2×#1306329511yescharacteristic
884C4#1458340811yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—3441no—
889C2—1721no—
890C2—1721no—
891C2—1722no—
892C2C4×#1306329511yescharacteristic
893C2#1914350311yescharacteristic
894C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1765C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1765D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
1. C2×#14583664C2semidirect
3. C2×#14583022C2semidirect
4. C2×#14583014C2semidirect
5. #19143300C2semidirect
6. #19134923C2semidirect
7. #19134920C2semidirect
8. #19134896C2semidirect
9. #19134872C2semidirect
10. #19134871C2semidirect
11. #19134801C2semidirect
12. #19134537C2semidirect
13. #19134434C2semidirect
14. #19134380C2semidirect
15. C43×#1765C2semidirect
26. C2×#13063331C22semidirect
32. #14583064C4semidirect
33. #14583062C4semidirect
34. #14583056C4semidirect
35. #14583051C4semidirect
36. #14583047C4semidirect
37. #14583045C4semidirect
38. #14583039C4semidirect
39. #14583034C4semidirect
46. C2×#13063261C22semidirect
47. C2×#13063260C22semidirect
48. #14582926C22semidirect
50. C2×#13063253C22semidirect
53. C2×#13063251C22semidirect
55. #14582867C22semidirect
58. C2×C8×Dic43C22semidirect
60. #14582663C22semidirect
61. #14582658C22semidirect
62. #14582654C22semidirect
63. #14582653C22semidirect
67. C43×#405C22semidirect
68. C2×#97×C43C22semidirect
69. C43×#341C22semidirect
70. C43×#339C22semidirect
107. #13063331D4semidirect
167. #131×C43D4semidirect
450. #1765D43semidirect
508. #405C2×D43semidirect
509. C2×#97C2×D43semidirect
513. #341C2×D43semidirect
515. #339C2×D43semidirect
518. C43#21468semidirect
558. #131D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836642
#191438152
C2×#145830222
C2×#145830142
#191433002
#191349232
#191349202
#191348962
#191348722
#191348712
#191348012
#191345372
#191344342
#191343802
C43×#17652
#2146843