Finite Group Databasebeta

← #25102451

Subgroups — #25102451

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×#14583666C211yesmaximal, characteristic, complemented
2#19143813C211yesmaximal, characteristic
3C2×#14583018C211yesmaximal, characteristic, complemented
4C2×#14583013C211yesmaximal, characteristic, complemented
5#19143294C211yesmaximal, characteristic, complemented
6#19134920C211yesmaximal, characteristic, complemented
7#19134920C211yesmaximal, characteristic, complemented
8#19134895C211yesmaximal, characteristic, complemented
9#19134868C211yesmaximal, characteristic, complemented
10#19134868C211yesmaximal, characteristic, complemented
11#19134799C211yesmaximal, characteristic, complemented
12#19134440C211yesmaximal, characteristic, complemented
13#19134433C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1789C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18#14583666—24no—
19#14583666—24no—
20C2×#13063333C2211yescharacteristic, complemented
21C2×#13063332—21no—
22C2×#13063332—21no—
23C2×#13063332C2211yescharacteristic
24C2×#13063332C2211yescharacteristic
25C2×#13063332C2211yescharacteristic
26C2×#13063332C2211yescharacteristic
27C22×#10621877—21no—
28C22×#10621877—21no—
29C22×#10621877C2211yescharacteristic
30C22×#10621877C2211yescharacteristic
31#14583410C2211yescharacteristic
32#14583061C411yescharacteristic, complemented
33#14583061C411yescharacteristic, complemented
34#14583055C411yescharacteristic, complemented
35#14583050C411yescharacteristic, complemented
36#14583044C411yescharacteristic, complemented
37#14583044C411yescharacteristic, complemented
38#14583038C411yescharacteristic, complemented
39#14583033C411yescharacteristic, complemented
40#14583018—24no—
41#14583013—24no—
42#14582974—21no—
43#14582974—21no—
44#14582973—21no—
45#14582973—21no—
46C2×#13063260C2211yescharacteristic, complemented
47C2×#13063260C2211yescharacteristic, complemented
48#14582927C2211yescharacteristic, complemented
49C2×#13063253C2211yescharacteristic, complemented
50C2×#13063253C2211yescharacteristic, complemented
51#14582895C2211yescharacteristic
52#14582895C2211yescharacteristic
53#14582867C2211yescharacteristic, complemented
54C2×C22⋊(C43⋊C8)C2211yescharacteristic
55#14582857C2211yescharacteristic, complemented
56C2×#13063236C2211yescharacteristic, complemented
57C2×C4×C43⋊C8C2211yescharacteristic, complemented
58#14582663C2211yescharacteristic, complemented
59#14582663C2211yescharacteristic, complemented
60#14582659C2211yescharacteristic, complemented
61#14582659C2211yescharacteristic, complemented
62#14582654C2211yescharacteristic, complemented
63#14582654C2211yescharacteristic, complemented
64C22×#41×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic
68C2×#104×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C4×C22⋊C4×C43C2211yescharacteristic
71C2×#10621898C2311yescharacteristic
72#13063345—22no—
73#13063345—22no—
74#13063345—22no—
75#13063345—22no—
76C2×#10621885C2×C411yescharacteristic
77C2×#10621885C2×C411yescharacteristic
78C2×#10621883C2×C411yescharacteristic
79C2×#10621883C2×C411yescharacteristic
80C2×#10621884C2×C411yescharacteristic
81C2×#10621884C2×C411yescharacteristic
82C2×#10621882C2×C411yescharacteristic
83C2×#10621882C2×C411yescharacteristic
84#13063333—22no—
85#13063333—22no—
86#13063332—28no—
87#13063332—28no—
88#13063332—22no—
89#13063332—22no—
90#13063332—22no—
91#13063332—22no—
92#13063332—22no—
93#13063332—22no—
94#13063332D414yescomplemented
95#13063332D414yescomplemented
96C2×#10621877—28no—
97C2×#10621877—28no—
98C2×#10621877—21no—
99C2×#10621877—22no—
100C2×#10621877—22no—
101C2×#10621877—21no—
102C2×#10621877—21no—
103C2×#10621877—21no—
104C2×#10621877—21no—
105C2×#10621877—22no—
106C2×#10621877—22no—
107C2×#10621877D411yescharacteristic
108C2×#10621877D411yescharacteristic
109C2×#10621877D411yescharacteristic
110C2×#10621877D411yescharacteristic
111C2×#10621877C2311yescharacteristic
112C2×#10621877C2311yescharacteristic
113C2×#10621872—21no—
114C22×C43⋊C8—21no—
115C22×C43⋊C8—21no—
116C22×C43⋊C8—21no—
117C22×C43⋊C8—21no—
118C22×C43⋊C8—21no—
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2311yescharacteristic
122C22×C43⋊C8C2311yescharacteristic
123C2×C8×D43—21no—
124#13063308—21no—
125#13063304C2×C411yescharacteristic
126#13063304C2×C411yescharacteristic
127#13063299C2×C411yescharacteristic
128#13063299C2×C411yescharacteristic
129#13063294—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132#13063284C2311yescharacteristic
133#13063260—22no—
134#13063260—22no—
135Dic43⋊C8—21no—
136Dic43⋊C8—21no—
137#13063253—22no—
138#13063253—22no—
139#13063249C2×C411yescharacteristic
140#13063249C2×C411yescharacteristic
141#13063249C2×C411yescharacteristic
142#13063249C2×C411yescharacteristic
143#13063246C2×C411yescharacteristic
144#13063246C2×C411yescharacteristic
145#13063246C2×C411yescharacteristic
146#13063246C2×C411yescharacteristic
147C22⋊(C43⋊C8)C2×C411yescharacteristic
148C22⋊(C43⋊C8)C2×C411yescharacteristic
149C22⋊(C43⋊C8)C2×C411yescharacteristic
150C22⋊(C43⋊C8)C2×C411yescharacteristic
151(C2×D43)⋊C8—21no—
152(C2×D43)⋊C8—21no—
153#13063236—22no—
154#13063235—21no—
155C4×C43⋊C8—22no—
156C8×Dic43—21no—
157C2×#41×C43—22no—
158C2×#41×C43—22no—
159C2×#41×C43—22no—
160C2×#41×C43—22no—
161C2×#41×C43—21no—
162C2×#41×C43—21no—
163C2×#41×C43C2×C411yescharacteristic
164C2×#41×C43C2×C411yescharacteristic
165C2×#41×C43C2311yescharacteristic
166C2×#41×C43C2311yescharacteristic
167C22×Q8×C43C2×C411yescharacteristic
168C22×D4×C43—21no—
169C22×D4×C43C2×C411yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177#104×C43—22no—
178#104×C43—22no—
179#104×C43—22no—
180#104×C43—22no—
181C22⋊C8×C43—21no—
182C22⋊C8×C43—21no—
183#95×C43—21no—
184C24×C43—21no—
185C24×C43#4111yescharacteristic
186#41×C43—24no—
187#41×C43—24no—
188#41×C43—24no—
189#41×C43—24no—
190#41×C43—22no—
191#41×C43—22no—
192#41×C43—22no—
193#41×C43—22no—
194#41×C43—21no—
195#41×C43—21no—
196#41×C43—21no—
197#41×C43—21no—
198#41×C43C2×D412yes—
199#41×C43C2×D412yes—
200#41×C43#4112yes—
201#41×C43#4112yes—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43—21no—
205C2×Q8×C43C22×C411yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—24no—
208C2×D4×C43—24no—
209C2×D4×C43—22no—
210C2×D4×C43—22no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43C22×C411yescharacteristic
217C2×D4×C43C22×C411yescharacteristic
218C22×C4×C43—24no—
219C22×C4×C43—24no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43C22×C411yescharacteristic
232C22×C4×C43C22×C411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43#4111yescharacteristic
236C22×C4×C43C2411yescharacteristic
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240#10621898—21no—
241#10621898—21no—
242#10621898—21no—
243#10621898—21no—
244C2×D172C22×C411yescharacteristic
245C2×C4×D43—21no—
246C2×Dic86C22×C411yescharacteristic
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C22⋊C4×C43—42no—
254C42×C43—21no—
255C42×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261#10621885—22no—
262#10621885—22no—
263#10621884—22no—
264#10621884—22no—
265#10621883—22no—
266#10621883—22no—
267#10621882—22no—
268#10621882—22no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271C4⋊Dic43C22×C411yescharacteristic
272C4⋊Dic43C22×C411yescharacteristic
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—21no—
276#10621877—24no—
277#10621877—24no—
278#10621877—24no—
279#10621877—21no—
280#10621877—21no—
281#10621877—22no—
282#10621877—22no—
283#10621877—24no—
284#10621877—24no—
285#10621877—22no—
286#10621877—22no—
287#10621877C2×D412yes—
288#10621877C2×D412yes—
289C2×C43⋊C8—24no—
290C2×C43⋊C8—24no—
291C2×C43⋊C8—24no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—24no—
301C2×C43⋊C8—24no—
302C2×C43⋊C8C22×C411yescharacteristic
303C2×C43⋊C8C22×C411yescharacteristic
304C2×C43⋊C8C22×C411yescharacteristic
305C2×C43⋊C8C22×C411yescharacteristic
306C2×C43⋊C8C2×D411yescharacteristic
307C2×C43⋊C8C2×D411yescharacteristic
308C2×C43⋊C8C2×D411yescharacteristic
309C2×C43⋊C8C2×D412yes—
310C2×C43⋊C8C2×D411yescharacteristic
311C2×C43⋊C8C2×D412yes—
312#10621872—42no—
313C8×D43—42no—
314C23×C43—24no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—81no—
322C23×C43—81no—
323C23×C43C4×D411yescharacteristic
324C23×C43C4×D411yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C22×D43—21no—
327Q8×C43—24no—
328Q8×C43—21no—
329Q8×C43—21no—
330Q8×C43C4×D412yes—
331Q8×C43C4×D412yes—
332D4×C43—24no—
333D4×C43—24no—
334D4×C43—24no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—21no—
340D4×C43—21no—
341D4×C43C4×D412yes—
342D4×C43C4×D412yes—
343C2×C4×C43—24no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—22no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43C4×D411yescharacteristic
369C2×C4×C43C4×D411yescharacteristic
370C2×C4×C43C23×C411yescharacteristic
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C2×#4111yescharacteristic
375C2×C4×C43C2×#4111yescharacteristic
376C22⋊D43—41no—
377C22⋊D43—41no—
378C22⋊D43—81no—
379C22⋊D43—81no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383D172—21no—
384D172—21no—
385C4×D43—41no—
386C4×D43—41no—
387Dic86—21no—
388Dic86—21no—
389C8×C43—41no—
390C8×C43—41no—
391C43⋊C8—21no—
392C43⋊C8—21no—
393C43⋊C8—21no—
394C43⋊C8—21no—
395C43⋊C8—22no—
396C43⋊C8—22no—
397C43⋊C8—21no—
398C43⋊C8—21no—
399C43⋊C8#12012yes—
400C43⋊C8#12012yes—
401#21468—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—22no—
410C22×C43—22no—
411C22×C43—21no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—84no—
419C22×C43C2×C4×D411yescharacteristic
420C22×C43#52511yescharacteristic
421C22×C43#52511yescharacteristic
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—41no—
425C4×C43—21no—
426C4×C43—22no—
427C4×C43—22no—
428C4×C43—21no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43C2×C4×D411yescharacteristic
432C4×C43C2×C4×D411yescharacteristic
433C4×C43C2×#12011yescharacteristic
434C4×C43#52511yescharacteristic
435Dic43—41no—
436Dic43—41no—
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#1789D4311yescharacteristic, complemented
450#1765—431no—
451#1764—431no—
452#1753—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—41no—
456C2×C43—41no—
457C2×C43—42no—
458C2×C43—42no—
459C2×C43C4×#12011yescharacteristic
460C2×C43#295611yescharacteristic
461C2×C43#295711yescharacteristic
462D43—81no—
463C22×#41C2×D4311yescharacteristic
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—431no—
473C2×#131—861no—
474C2×#131—861no—
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×#104C2×D4311yescharacteristic
500C2×#104C2×D4311yescharacteristic
501C2×#104C2×D4311yescharacteristic
502C2×#104C2×D4311yescharacteristic
503#416—431no—
504#416—431no—
505#408—431no—
506#407C2×D4311yescharacteristic
507C2×C22⋊C8—431no—
508#405—431no—
509C2×#97—431no—
510C2×C4×C8—431no—
511C4×C22⋊C4C2×D4311yescharacteristic
512#341—431no—
513#341—431no—
514#339—431no—
515#339—431no—
516#336—431no—
517#336—431no—
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41—431no—
526C2×#41C4×D4311yescharacteristic
527C2×#41C4×D4311yescharacteristic
528C2×#41C22×D4311yescharacteristic
529C2×#41C22×D4311yescharacteristic
530C22×Q8C4×D4311yescharacteristic
531C22×D4—21no—
532C22×D4C4×D4311yescharacteristic
533C23×C4—21no—
534C23×C4C22×D4311yescharacteristic
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—434no—
548#131—434no—
549#131—862no—
550#131—862no—
551#131—862no—
552#131—862no—
553#131—862no—
554#131—862no—
555#131—868no—
556#131—868no—
557#131—862no—
558#131—862no—
559C2×M16—431no—
560C2×M16—431no—
561C2×M16—431no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—861no—
566C2×M16—862no—
567C2×M16—862no—
568C2×M16—861no—
569C2×M16—861no—
570C2×M16—861no—
571C2×M16—861no—
572C2×M16—862no—
573C2×M16—862no—
574C2×M16—868no—
575C2×M16—868no—
576C2×M16—861no—
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—431no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—431no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8—861no—
586C22×C8—861no—
587C22×C8—861no—
588C22×C8—861no—
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#117—431no—
598C2×C22⋊C4—21no—
599C2×C42C22×D4311yescharacteristic
600C2×C42C22×D4311yescharacteristic
601#108—862no—
602#108—862no—
603C4⋊C8—861no—
604C4⋊C8—861no—
605#104—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—862no—
610#104—862no—
611#103—431no—
612#103—431no—
613#103—431no—
614#103—431no—
615#102—431no—
616#102—431no—
617#102—431no—
618#102—431no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—431no—
622C22⋊C8—431no—
623C22⋊C8—431no—
624C22⋊C8—431no—
625C22⋊C8—861no—
626C22⋊C8—861no—
627#97—862no—
628#97—861no—
629C4×C8—862no—
630C4×C8—861no—
631#95—21no—
632C24—21no—
633C24#1062190011yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—22no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—861no—
647#41—861no—
648#41—861no—
649#41—861no—
650#41D4×D4312yes—
651#41D4×D4312yes—
652#41#1062190012yes—
653#41#1062190012yes—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—431no—
658C2×Q8C2×C4×D4311yescharacteristic
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—431no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4C2×C4×D4311yescharacteristic
674C2×D4C2×C4×D4311yescharacteristic
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—861no—
689C22×C4C2×C4×D4311yescharacteristic
690C22×C4C2×C4×D4311yescharacteristic
691C22×C4D4×D4311yescharacteristic
692C22×C4D4×D4311yescharacteristic
693C22×C4#1062190011yescharacteristic
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—21no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—432no—
708M16—432no—
709M16—862no—
710M16—862no—
711M16—862no—
712M16—862no—
713M16—864no—
714M16—864no—
715M16—864no—
716M16—864no—
717M16—864no—
718M16—861no—
719M16—861no—
720M16—1722no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—432no—
724C2×C8—432no—
725C2×C8—431no—
726C2×C8—431no—
727C2×C8—431no—
728C2×C8—431no—
729C2×C8—431no—
730C2×C8—431no—
731C2×C8—431no—
732C2×C8—431no—
733C2×C8—864no—
734C2×C8—864no—
735C2×C8—864no—
736C2×C8—864no—
737C2×C8—864no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—861no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—1722no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C22⋊C4—42no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—861no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—81no—
770C23—81no—
771C23—861no—
772C23(C22⋊D43)⋊C411yescharacteristic
773C23(C22⋊D43)⋊C411yescharacteristic
774C23C2×#1062190011yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—861no—
779Q8—861no—
780Q8(C22⋊D43)⋊C412yes—
781Q8(C22⋊D43)⋊C412yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—861no—
792D4—861no—
793D4—3441no—
794D4—3441no—
795D4—1721no—
796D4—1721no—
797D4(C22⋊D43)⋊C412yes—
798D4(C22⋊D43)⋊C412yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4(C22⋊D43)⋊C411yescharacteristic
830C2×C4(C22⋊D43)⋊C411yescharacteristic
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4C2×#1062190011yescharacteristic
836C2×C4C2×#1062190011yescharacteristic
837C8—41no—
838C8—41no—
839C8—432no—
840C8—432no—
841C8—861no—
842C8—861no—
843C8—861no—
844C8—861no—
845C8—861no—
846C8—861no—
847C8—862no—
848C8—862no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—81no—
864C22—81no—
865C22—84no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C2×(C22⋊D43)⋊C411yescharacteristic
870C22#1458340511yescharacteristic
871C22#1458340511yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—42no—
877C4—81no—
878C4—1721no—
879C4—1721no—
880C4—1721no—
881C4C2×(C22⋊D43)⋊C411yescharacteristic
882C4C2×(C22⋊D43)⋊C411yescharacteristic
883C4#120×D4311yescharacteristic
884C4#1458340511yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—3441no—
892C2#1913709411yescharacteristic
893C2#1914350111yescharacteristic
894C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1789C2
socleC22×C43C2×C4×D4
prime radical#19143813C2
cosocleC22×C4×C43C24
hypercenter#1789D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. C2×#14583666C2semidirect
3. C2×#14583018C2semidirect
4. C2×#14583013C2semidirect
5. #19143294C2semidirect
6. #19134920C2semidirect
7. #19134920C2semidirect
8. #19134895C2semidirect
9. #19134868C2semidirect
10. #19134868C2semidirect
11. #19134799C2semidirect
12. #19134440C2semidirect
13. #19134433C2semidirect
14. #19134379C2semidirect
15. C43×#1789C2semidirect
20. C2×#13063333C22semidirect
32. #14583061C4semidirect
33. #14583061C4semidirect
34. #14583055C4semidirect
35. #14583050C4semidirect
36. #14583044C4semidirect
37. #14583044C4semidirect
38. #14583038C4semidirect
39. #14583033C4semidirect
46. C2×#13063260C22semidirect
47. C2×#13063260C22semidirect
48. #14582927C22semidirect
49. C2×#13063253C22semidirect
50. C2×#13063253C22semidirect
53. #14582867C22semidirect
55. #14582857C22semidirect
56. C2×#13063236C22semidirect
57. C2×C4×C43⋊C8C22semidirect
58. #14582663C22semidirect
59. #14582663C22semidirect
60. #14582659C22semidirect
61. #14582659C22semidirect
62. #14582654C22semidirect
63. #14582654C22semidirect
94. #13063332D4semidirect
95. #13063332D4semidirect
449. #1789D43semidirect
518. C43#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#145836662
#191438132
C2×#145830182
C2×#145830132
#191432942
#191349202
#191348952
#191348682
#191347992
#191344402
#191344332
#191343792
C43×#17892
#2146843