Finite Group Databasebeta

← #25097667

Subgroups — #25097667

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583664C211yesmaximal, characteristic
2C2×#108×D43C211yesmaximal, characteristic, complemented
3#19143156C211yesmaximal, characteristic, complemented
4C2×#14582914C211yesmaximal, characteristic
5#416×D43C211yesmaximal, characteristic
6#19134873C211yesmaximal, characteristic, complemented
7#19134872C211yesmaximal, characteristic, complemented
8#19134871C211yesmaximal, characteristic, complemented
9#19134870C211yesmaximal, characteristic, complemented
10#19134869C211yesmaximal, characteristic, complemented
11#19134868C211yesmaximal, characteristic, complemented
12#19134867C211yesmaximal, characteristic, complemented
13#19134303C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583664—24no—
18#14583664—24no—
19C2×#13063333—21no—
20C2×#13063333C2211yescharacteristic
21C2×#13063332C2211yescharacteristic
22C2×#13063331—21no—
23C2×#13063331C2211yescharacteristic
24C22×#10621872—21no—
25C22×#10621872C2211yescharacteristic
26C2×M16×D43—21no—
27C2×M16×D43C2211yescharacteristic
28C2×M16×D43C2211yescharacteristic
29C22×C8×D43C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31#117×D43C2211yescharacteristic
32C2×#13063261C2211yescharacteristic, complemented
33C2×#13063260C2211yescharacteristic, complemented
34C2×#13063260C2211yescharacteristic, complemented
35#108×D43—24no—
36#14582927C2211yescharacteristic, complemented
37#14582926C2211yescharacteristic, complemented
38#14582925C2211yescharacteristic, complemented
39#14582924—21no—
40#14582924—21no—
41#14582921—21no—
42#14582921—21no—
43#14582914—24no—
44C2×#13063253C2211yescharacteristic
45C2×#13063252C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47#14582896C2211yescharacteristic
48#14582895C2211yescharacteristic
49#14582894C411yescharacteristic, complemented
50#14582894C411yescharacteristic, complemented
51#14582893C2211yescharacteristic
52#14582892C411yescharacteristic, complemented
53#14582892C411yescharacteristic, complemented
54#103×D43C411yescharacteristic, complemented
55#103×D43C411yescharacteristic, complemented
56#102×D43C411yescharacteristic, complemented
57#102×D43C411yescharacteristic, complemented
58#14582660C2211yescharacteristic, complemented
59#14582659C2211yescharacteristic, complemented
60#14582658C2211yescharacteristic, complemented
61#14582654C2211yescharacteristic, complemented
62#14582653C2211yescharacteristic, complemented
63#14582653C2211yescharacteristic, complemented
64C2×#131×C43C2211yescharacteristic
65C2×#108×C43C2211yescharacteristic, complemented
66C43×#424C2211yescharacteristic, complemented
67C2×#104×C43C2211yescharacteristic
68C43×#416C2211yescharacteristic
69C43×#339C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
71C2×#10621902C2×C411yescharacteristic
72C2×#10621898—21no—
73C2×#10621898C2311yescharacteristic
74C2×#10621900—21no—
75C2×#10621900C2×C411yescharacteristic
76#41×D43—22no—
77#41×D43—22no—
78#41×D43D414yes—
79#41×D43Q814yes—
80C2×Q8×D43C2×C411yescharacteristic
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85#13063333—28no—
86#13063333—22no—
87#13063333—22no—
88#13063332—22no—
89#13063332—22no—
90#13063331—28no—
91#13063331—22no—
92#13063331—22no—
93C2×#10621877—21no—
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96C2×#10621872—28no—
97C2×#10621872—21no—
98C2×#10621872—22no—
99C2×#10621872—22no—
100C2×#10621872—21no—
101C2×#10621872—21no—
102C2×#10621872—21no—
103C2×#10621872D411yescharacteristic
104C2×#10621872D411yescharacteristic
105C2×#10621872D411yescharacteristic
106C2×#10621872D411yescharacteristic
107M16×D43—28no—
108M16×D43—22no—
109M16×D43—22no—
110M16×D43—22no—
111M16×D43D414yes—
112C22×C43⋊C8—21no—
113C22×C43⋊C8C2311yescharacteristic
114C22×C43⋊C8C2311yescharacteristic
115C2×C8×D43—22no—
116C2×C8×D43—21no—
117C2×C8×D43—22no—
118C2×C8×D43—21no—
119C2×C8×D43—21no—
120C2×C8×D43—21no—
121C2×C8×D43C2×C411yescharacteristic
122C2×C8×D43C2×C411yescharacteristic
123C2×C8×D43C2×C411yescharacteristic
124C2×C8×D43C2×C411yescharacteristic
125#13063284C2311yescharacteristic
126#13063283C2×C411yescharacteristic
127#13063283C2×C411yescharacteristic
128#13063282—21no—
129#13063282—22no—
130#13063282—22no—
131#13063281—21no—
132C2×Dic43⋊C4—21no—
133C4⋊C4×D43C2×C411yescharacteristic
134C4⋊C4×D43C2×C411yescharacteristic
135C2×(C2×D43)⋊C4—21no—
136C22⋊C4×D43—21no—
137C2×C4×Dic43C2311yescharacteristic
138C42×D43—21no—
139#13063261—22no—
140#13063260—22no—
141#13063260—22no—
142C4⋊(C43⋊C8)—21no—
143C4⋊(C43⋊C8)—21no—
144Dic43⋊C8—21no—
145Dic43⋊C8—21no—
146Dic43⋊C8—21no—
147Dic43⋊C8—21no—
148#13063253—22no—
149#13063252—22no—
150#13063251—22no—
151#13063250C2×C411yescharacteristic
152#13063250C2×C411yescharacteristic
153#13063249C2×C411yescharacteristic
154#13063249C2×C411yescharacteristic
155#13063248C2×C411yescharacteristic
156#13063248C2×C411yescharacteristic
157#13063247C2×C411yescharacteristic
158#13063247C2×C411yescharacteristic
159#13063246C2×C411yescharacteristic
160#13063246C2×C411yescharacteristic
161#13063245C2×C411yescharacteristic
162#13063245C2×C411yescharacteristic
163C2×#41×C43C2311yescharacteristic
164#131×C43—22no—
165#131×C43—22no—
166C2×M16×C43—21no—
167C2×M16×C43C2311yescharacteristic
168C2×M16×C43C2311yescharacteristic
169C22×C8×C43—21no—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#117×C43C2311yescharacteristic
173C2×C42×C43C2311yescharacteristic
174#108×C43—22no—
175C4⋊C8×C43—21no—
176C4⋊C8×C43—21no—
177#104×C43—22no—
178#103×C43C2×C411yescharacteristic
179#103×C43C2×C411yescharacteristic
180#102×C43C2×C411yescharacteristic
181#102×C43C2×C411yescharacteristic
182C23×D43—21no—
183C23×D43#4111yescharacteristic
184#41×C43—21no—
185#41×C43—21no—
186#41×C43C2×D412yes—
187#41×C43C2×Q812yes—
188C2×Q8×C43C22×C411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43C22×C411yescharacteristic
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43#4111yescharacteristic
200#10621902—22no—
201#10621902C4⋊C414yes—
202Q8×D43—22no—
203Q8×D43C4⋊C414yes—
204#10621900—24no—
205#10621900—24no—
206#10621900—22no—
207#10621900C4⋊C414yes—
208D4×D43—22no—
209D4×D43—24no—
210D4×D43—24no—
211D4×D43C4⋊C414yes—
212#10621898—21no—
213#10621898—21no—
214#10621898—24no—
215#10621898—24no—
216#10621898C2×D412yes—
217#10621898C2×Q812yes—
218C2×D172—21no—
219C2×D172C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43C22×C411yescharacteristic
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2×Q812yes—
234C2×C4×D43#4112yes—
235C2×Dic86—21no—
236C2×Dic86C22×C411yescharacteristic
237M16×C43—24no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43C2×D412yes—
242C2×C8×C43—24no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43C22×C411yescharacteristic
250C2×C8×C43C22×C411yescharacteristic
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C4⋊C4×C43C22×C411yescharacteristic
254C4⋊C4×C43C22×C411yescharacteristic
255C22⋊C4×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—21no—
259C22⋊Dic43—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4—21no—
262(C2×D43)⋊C4—42no—
263C4⋊Dic43C22×C411yescharacteristic
264C4⋊Dic43C22×C411yescharacteristic
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—42no—
268C4×Dic43—21no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273#10621877—24no—
274#10621877—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877C2×D412yes—
278C2×C43⋊C8—24no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8C22×C411yescharacteristic
286C2×C43⋊C8C22×C411yescharacteristic
287C2×C43⋊C8C2×D411yescharacteristic
288C2×C43⋊C8C2×D411yescharacteristic
289#10621872—24no—
290#10621872—24no—
291#10621872—22no—
292#10621872—24no—
293#10621872—22no—
294#10621872—22no—
295#10621872—22no—
296#10621872—42no—
297C8×D43—24no—
298C8×D43—24no—
299C8×D43—22no—
300C8×D43—22no—
301C8×D43—22no—
302C8×D43—22no—
303C8×D43—24no—
304C8×D43—42no—
305C23×C43—21no—
306C23×C43C2×#4111yescharacteristic
307C22×D43—21no—
308C22×D43—24no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—81no—
312C22×D43—81no—
313C22×D43C4×D411yescharacteristic
314C22×D43C4×D411yescharacteristic
315C22×D43C22⋊Q812yes—
316C22×D43#12312yes—
317Q8×C43—21no—
318Q8×C43C2×C4⋊C412yes—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—21no—
322D4×C43C2×C4⋊C412yes—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43C23×C411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×Q811yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C22⋊D43—22no—
338C22⋊D43—22no—
339C22⋊D43—24no—
340C22⋊D43—24no—
341C2×Dic43—21no—
342C2×Dic43—24no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43C4×D411yescharacteristic
349C2×Dic43C4×D411yescharacteristic
350C2×Dic43C22⋊Q812yes—
351C2×Dic43#12312yes—
352D172—24no—
353D172—21no—
354D172C2×C4⋊C412yes—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—24no—
359C4×D43—81no—
360C4×D43—81no—
361C4×D43C2×C4⋊C412yes—
362C4×D43C2×C4⋊C412yes—
363C4×D43C4×D412yes—
364C4×D43C4×D412yes—
365C4×D43#12012yes—
366C4×D43#12012yes—
367C4×D43C22⋊Q812yes—
368C4×D43C22⋊Q812yes—
369Dic86—21no—
370Dic86—24no—
371Dic86C2×C4⋊C412yes—
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—22no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—41no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—22no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—41no—
384#20886—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43C2×C4×D411yescharacteristic
391C22×C43C2×C22⋊Q811yescharacteristic
392C22×C43C2×#12311yescharacteristic
393C2×D43—21no—
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—21no—
397C2×D43—22no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—84no—
403C2×D43#38512yes—
404C2×D43#38512yes—
405C4×C43—22no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—81no—
409C4×C43C22×C4⋊C411yescharacteristic
410C4×C43C2×C4×D411yescharacteristic
411C4×C43C2×#12011yescharacteristic
412C4×C43C2×C22⋊Q811yescharacteristic
413Dic43—22no—
414Dic43—41no—
415Dic43—41no—
416Dic43—81no—
417Dic43#38512yes—
418Dic43#38512yes—
419C2×#568—431no—
420C22×#108—431no—
421#2905—431no—
422C2×#421—431no—
423C2×#416—431no—
424#1866—431no—
425#1866—431no—
426#1866—431no—
427#1866—431no—
428#1866—431no—
429#1866—431no—
430#1866—431no—
431#1866D4311yescharacteristic, complemented
432#1733—431no—
433#1729—431no—
434C2×C43—21no—
435C2×C43—21no—
436C2×C43—42no—
437C2×C43C2×#38511yescharacteristic
438C2×C43#295711yescharacteristic
439C2×C43#295711yescharacteristic
440D43—22no—
441D43—22no—
442D43—42no—
443C22×#41—431no—
444#568—864no—
445#568—864no—
446C2×#131—431no—
447C2×#131—431no—
448C2×#131—431no—
449C2×#131—861no—
450C2×#131—861no—
451C2×#131C2×D4311yescharacteristic
452C22×M16—431no—
453C22×M16—431no—
454C22×M16—431no—
455C22×M16—861no—
456C22×M16—861no—
457C23×C8—431no—
458C2×#117—431no—
459C2×#117—431no—
460C2×#108—431no—
461C2×#108—431no—
462C2×#108—431no—
463C2×#108—864no—
464C2×#108C2×D4311yescharacteristic, complemented
465#424—431no—
466#424—431no—
467#424—431no—
468#424—861no—
469#424—861no—
470#424C2×D4311yescharacteristic, complemented
471#423—861no—
472#423—861no—
473#421—864no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104C2×D4311yescharacteristic
478#416—431no—
479#416—431no—
480#416—431no—
481#416—431no—
482#416—431no—
483#416—431no—
484#416—431no—
485#416C2×D4311yescharacteristic
486C2×#103—431no—
487C2×#103—431no—
488C2×#102—431no—
489C2×#102—431no—
490#339—431no—
491#339—431no—
492#339—431no—
493#339C2×D4311yescharacteristic, complemented
494#336—431no—
495#336—431no—
496#336—431no—
497#336C2×D4311yescharacteristic, complemented
498C43#2088611yescharacteristic, complemented, Sylow
499C2×#41—434no—
500C2×#41—434no—
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—431no—
504C2×#41—861no—
505C2×#41—861no—
506C2×#41—862no—
507C2×#41—862no—
508C2×#41C22×D4311yescharacteristic
509C22×Q8—431no—
510C22×D4—431no—
511C22×D4—861no—
512C23×C4—431no—
513C23×C4—861no—
514#131—22no—
515#131—22no—
516#131—862no—
517#131—862no—
518#131—868no—
519#131—862no—
520#131—868no—
521#131—862no—
522#131—862no—
523#131—862no—
524C2×M16—21no—
525C2×M16—431no—
526C2×M16—431no—
527C2×M16—431no—
528C2×M16—431no—
529C2×M16—431no—
530C2×M16—434no—
531C2×M16—431no—
532C2×M16—861no—
533C2×M16—861no—
534C2×M16—862no—
535C2×M16—862no—
536C2×M16—868no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—862no—
540C2×M16—868no—
541C2×M16—861no—
542C2×M16—862no—
543C2×M16—862no—
544C2×M16C22×D4311yescharacteristic
545C2×M16C22×D4311yescharacteristic
546C22×C8—21no—
547C22×C8—431no—
548C22×C8—431no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—431no—
553C22×C8—861no—
554C22×C8—862no—
555C22×C8—862no—
556C22×C8—861no—
557C22×C8—861no—
558C22×C8—861no—
559C22×C8—861no—
560C22×C8C22×D4311yescharacteristic
561C22×C8C22×D4311yescharacteristic
562#117—431no—
563#117—431no—
564#117—431no—
565#117—861no—
566#117—862no—
567#117—862no—
568#117—861no—
569#117C22×D4311yescharacteristic
570C2×C4⋊C4—431no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—861no—
577C2×C42C22×D4311yescharacteristic
578#108—22no—
579#108—862no—
580#108—862no—
581#108—862no—
582C4⋊C8—21no—
583C4⋊C8—21no—
584C4⋊C8—861no—
585C4⋊C8—861no—
586C4⋊C8—861no—
587C4⋊C8—861no—
588C4⋊C8—861no—
589C4⋊C8—861no—
590#104—22no—
591#104—862no—
592#104—862no—
593#104—862no—
594#103—431no—
595#103—431no—
596#103—431no—
597#103—431no—
598#103—431no—
599#103—431no—
600#103C4×D4311yescharacteristic
601#103C4×D4311yescharacteristic
602#102—431no—
603#102—431no—
604#102—431no—
605#102—431no—
606#102—431no—
607#102—431no—
608#102C4×D4311yescharacteristic
609#102C4×D4311yescharacteristic
610C24—431no—
611C24—861no—
612#41—21no—
613#41—21no—
614#41—434no—
615#41—434no—
616#41—432no—
617#41—432no—
618#41—864no—
619#41—864no—
620#41—864no—
621#41—864no—
622#41—862no—
623#41—862no—
624#41—861no—
625#41—861no—
626#41D4×D4312yes—
627#41Q8×D4312yes—
628C2×Q8—434no—
629C2×Q8—431no—
630C2×Q8—861no—
631C2×Q8—862no—
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—434no—
635C2×D4—431no—
636C2×D4—861no—
637C2×D4—862no—
638C2×D4—861no—
639C2×D4—864no—
640C2×D4—864no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4C2×C4×D4311yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—864no—
656C22×C4—861no—
657C22×C4—864no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4C23×D4311yescharacteristic
665M16—24no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—432no—
670M16—862no—
671M16—864no—
672M16—862no—
673M16—862no—
674M16—862no—
675M16—864no—
676M16—864no—
677M16—864no—
678M16—861no—
679M16—861no—
680M16—861no—
681M16—1722no—
682M16D4×D4312yes—
683C2×C8—24no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—431no—
691C2×C8—431no—
692C2×C8—431no—
693C2×C8—431no—
694C2×C8—862no—
695C2×C8—862no—
696C2×C8—862no—
697C2×C8—862no—
698C2×C8—864no—
699C2×C8—864no—
700C2×C8—864no—
701C2×C8—864no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—1722no—
709C2×C8C2×C4×D4311yescharacteristic
710C2×C8C2×C4×D4311yescharacteristic
711C2×C8D4×D4311yescharacteristic
712C2×C8D4×D4311yescharacteristic
713C4⋊C4—431no—
714C4⋊C4—431no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—1722no—
718C4⋊C4C2×C4×D4311yescharacteristic
719C4⋊C4C2×C4×D4311yescharacteristic
720C22⋊C4—21no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—1722no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—861no—
729C42—861no—
730C42—861no—
731C42—861no—
732C42—861no—
733C23—21no—
734C23—431no—
735C23—431no—
736C23—432no—
737C23—432no—
738C23—864no—
739C23—861no—
740C23—3441no—
741C23—3441no—
742C23—1721no—
743C23—1721no—
744C23#41×D4311yescharacteristic
745Q8—21no—
746Q8—432no—
747Q8—864no—
748Q8—861no—
749Q8C4⋊C4×D4312yes—
750D4—22no—
751D4—22no—
752D4—21no—
753D4—432no—
754D4—864no—
755D4—864no—
756D4—864no—
757D4—862no—
758D4—862no—
759D4—861no—
760D4C4⋊C4×D4312yes—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—432no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—432no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—432no—
779C2×C4—432no—
780C2×C4—432no—
781C2×C4—864no—
782C2×C4—864no—
783C2×C4—864no—
784C2×C4—861no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—3441no—
790C2×C4—3441no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4C22×C4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4C2×D4×D4311yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4C2×Q8×D4311yescharacteristic
799C2×C4#41×D4311yescharacteristic
800C8—21no—
801C8—21no—
802C8—21no—
803C8—22no—
804C8—21no—
805C8—41no—
806C8—861no—
807C8—861no—
808C8—861no—
809C8—861no—
810C8—862no—
811C8—1721no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—432no—
818C22—432no—
819C22—861no—
820C22—861no—
821C22—861no—
822C22—861no—
823C22—862no—
824C22—3444no—
825C22—1722no—
826C22—1722no—
827C22—1721no—
828C22—1721no—
829C22C4×D4×D4311yescharacteristic
830C22C22⋊Q8×D4311yescharacteristic
831C22#123×D4311yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—81no—
836C4—432no—
837C4—432no—
838C4—862no—
839C4—3441no—
840C4—1721no—
841C4—1721no—
842C4C2×C4⋊C4×D4311yescharacteristic
843C4C4×D4×D4311yescharacteristic
844C4#120×D4311yescharacteristic
845C4C22⋊Q8×D4311yescharacteristic
846C2—21no—
847C2—21no—
848C2—42no—
849C2—862no—
850C2—862no—
851C2—1722no—
852C2#385×D4311yescharacteristic
853C2#1914350711yescharacteristic
854C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#20886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#108×D43C2semidirect
3. #19143156C2semidirect
6. #19134873C2semidirect
7. #19134872C2semidirect
8. #19134871C2semidirect
9. #19134870C2semidirect
10. #19134869C2semidirect
11. #19134868C2semidirect
12. #19134867C2semidirect
13. #19134303C2semidirect
14. #19134290C2semidirect
15. C43×#1866C2semidirect
32. C2×#13063261C22semidirect
33. C2×#13063260C22semidirect
34. C2×#13063260C22semidirect
36. #14582927C22semidirect
37. #14582926C22semidirect
38. #14582925C22semidirect
49. #14582894C4semidirect
50. #14582894C4semidirect
52. #14582892C4semidirect
53. #14582892C4semidirect
54. #103×D43C4semidirect
55. #103×D43C4semidirect
56. #102×D43C4semidirect
57. #102×D43C4semidirect
58. #14582660C22semidirect
59. #14582659C22semidirect
60. #14582658C22semidirect
61. #14582654C22semidirect
62. #14582653C22semidirect
63. #14582653C22semidirect
65. C2×#108×C43C22semidirect
66. C43×#424C22semidirect
69. C43×#339C22semidirect
70. C43×#336C22semidirect
431. #1866D43semidirect
464. C2×#108C2×D43semidirect
470. #424C2×D43semidirect
493. #339C2×D43semidirect
497. #336C2×D43semidirect
498. C43#20886semidirect

Maximal subgroups

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

subgroupindex
C2×#145836642
C2×#108×D432
#191431562
C2×#145829142
#416×D432
#191348732
#191348722
#191348712
#191348702
#191348692
#191348682
#191348672
#191343032
#191342902
C43×#18662
#2088643