Finite Group Databasebeta

← #25102566

Subgroups — #25102566

Order 11008.

1282 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149306C211yesmaximal, characteristic, complemented
2#19143941C211yesmaximal, characteristic
3#19143496C211yesmaximal, characteristic, complemented
4#19143311C211yesmaximal, characteristic, complemented
5#19134975C211yesmaximal, characteristic, complemented
6#19134959C211yesmaximal, characteristic, complemented
7#19134954C211yesmaximal, characteristic, complemented
8#19134833C211yesmaximal, characteristic, complemented
9#19134832C211yesmaximal, characteristic, complemented
10#19134813C211yesmaximal, characteristic, complemented
11#19134557C211yesmaximal, characteristic, complemented
12#19134441C211yesmaximal, characteristic, complemented
13#19134437C211yesmaximal, characteristic, complemented
14#19134396C211yesmaximal, characteristic, complemented
15C43×#2955C211yesmaximal, characteristic, complemented
16#14583735C2211yescharacteristic
17#14583697C2211yescharacteristic
18#14583666C2211yescharacteristic
19#14583665—22no—
20#14583665C2211yescharacteristic
21#14583665C2211yescharacteristic
22#14583664—22no—
23#14583664—22no—
24C2×#13063331—22no—
25C2×#13063331C2211yescharacteristic
26C2×#13063331C2211yescharacteristic
27#131×D43—22no—
28#131×D43—22no—
29#14583445C2211yescharacteristic
30#14583080C412yescomplemented
31#14583075C412yescomplemented
32#14583070C412yescomplemented
33#14583065C412yescomplemented
34#14583019—22no—
35#14583014—22no—
36#14582970—22no—
37#14582968—22no—
38#14582947C2211yescharacteristic, complemented
39#14582922C2211yescharacteristic, complemented
40#14582916C2211yescharacteristic, complemented
41#14582915C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44#14582895C2211yescharacteristic
45#14582893C2211yescharacteristic
46#14582881C2211yescharacteristic
47#14582872C2211yescharacteristic
48#14582867C2211yescharacteristic
49#14582866C2211yescharacteristic, complemented
50#14582854C2211yescharacteristic, complemented
51C2×#13063235C2211yescharacteristic, complemented
52#14582671C2211yescharacteristic, complemented
53#14582669C2211yescharacteristic, complemented
54#14582663C2211yescharacteristic, complemented
55#14582663C2211yescharacteristic, complemented
56#14582660C2211yescharacteristic, complemented
57#14582658C2211yescharacteristic, complemented
58C43×#575C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic, complemented
61C43×#444—22no—
62C43×#443—22no—
63C43×#430C2211yescharacteristic, complemented
64C43×#421C2211yescharacteristic
65C43×#421C2211yescharacteristic, complemented
66C43×#405C2211yescharacteristic, complemented
67#13063373—21no—
68#13063372—21no—
69#13063372C2×C412yes—
70#13063371—21no—
71#13063371C2×C412yes—
72#13063370—21no—
73#13063370—22no—
74C2×#10621898—22no—
75C2×#10621898C2311yescharacteristic
76C2×#10621898C2311yescharacteristic
77#41×D43—22no—
78#41×D43—22no—
79#13063356C2×C412yes—
80#13063355—21no—
81#13063351C2×C412yes—
82#13063350—21no—
83#13063345—22no—
84#13063333—24no—
85#13063333—24no—
86#13063333—22no—
87#13063333—22no—
88#13063332—22no—
89#13063332—22no—
90#13063331—24no—
91#13063331—24no—
92#13063331—22no—
93#13063331—21no—
94#13063331—21no—
95#13063331—21no—
96#13063331—21no—
97#13063331—21no—
98#13063331—21no—
99#13063331—22no—
100#13063331D412yescomplemented
101#13063331D412yescomplemented
102C2×#10621877—22no—
103C2×#10621877C2311yescharacteristic
104C2×#10621877C2311yescharacteristic
105C2×#10621877C2311yescharacteristic
106C2×#10621872—24no—
107C2×#10621872—21no—
108C2×#10621872D412yes—
109M16×D43—24no—
110M16×D43—24no—
111M16×D43—22no—
112M16×D43—22no—
113C22×C43⋊C8C2311yescharacteristic
114C2×C8×D43—24no—
115C2×C8×D43—21no—
116C2×C8×D43D412yes—
117#13063323C2×C411yescharacteristic
118#13063321C2×C411yescharacteristic
119#13063314C2×C411yescharacteristic
120#13063312C2×C411yescharacteristic
121#13063297—22no—
122C4×C22⋊D43—22no—
123#13063284C2311yescharacteristic
124C2×C4×Dic43C2311yescharacteristic
125#13063260—22no—
126Dic43⋊C8—22no—
127#13063252—22no—
128#13063252C2×C412yes—
129#13063252C2×C412yes—
130#13063251—22no—
131#13063251C2×C412yes—
132#13063251C2×C412yes—
133#13063249—21no—
134#13063248—21no—
135#13063246—21no—
136#13063245—21no—
137#13063243C2×C412yes—
138#13063241C2×C412yes—
139#13063239—22no—
140C22⋊(C43⋊C8)—22no—
141(C2×D43)⋊C8—22no—
142#13063235—21no—
143#13063235—21no—
144#13063235—21no—
145C8×Dic43—21no—
146C2×#41×C43C2311yescharacteristic
147C2×#41×C43C2311yescharacteristic
148#137×C43—21no—
149#137×C43C2×C412yes—
150AGL(1,ℤ/8)×C43—21no—
151AGL(1,ℤ/8)×C43C2×C412yes—
152#135×C43—22no—
153#131×C43—21no—
154#131×C43—21no—
155#131×C43—21no—
156#131×C43—21no—
157#131×C43—21no—
158#131×C43—21no—
159#131×C43D412yescomplemented
160#131×C43D412yescomplemented
161C2×M16×C43—21no—
162C2×M16×C43—21no—
163C2×M16×C43C2311yescharacteristic
164C2×M16×C43C2311yescharacteristic
165C2×M16×C43C2311yescharacteristic
166C22×C8×C43—21no—
167C22×C8×C43—21no—
168C22×C8×C43C2311yescharacteristic
169#117×C43C2311yescharacteristic
170#108×C43—22no—
171#104×C43—22no—
172#104×C43—22no—
173#97×C43—21no—
174C4×C8×C43—21no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43C22×C412yes—
182#41×C43C2×D412yes—
183C2×Q8×C43C22×C411yescharacteristic
184C2×Q8×C43#4111yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43C22×C411yescharacteristic
188C2×D4×C43#4111yescharacteristic
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C2411yescharacteristic
192C2×C22⋊D43—24no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43#4112yes—
196C22×Dic43—21no—
197#10621902—22no—
198#10621902—22no—
199Q8×D43—22no—
200Q8×D43—22no—
201#10621900—24no—
202#10621900—22no—
203#10621900—22no—
204#10621900—24no—
205D4×D43—22no—
206D4×D43—24no—
207D4×D43—22no—
208D4×D43—24no—
209#10621898—24no—
210#10621898—24no—
211#10621898—21no—
212#10621898—21no—
213#10621898—21no—
214#10621898—21no—
215#10621898—21no—
216#10621898—21no—
217#10621898—22no—
218#10621898—22no—
219#10621898C22×C412yes—
220#10621898C2×D412yes—
221C2×D172—22no—
222C2×D172C22×C411yescharacteristic
223C2×D172#4111yescharacteristic
224C2×C4×D43—24no—
225C2×C4×D43—21no—
226C2×C4×D43C2×D412yes—
227C2×Dic86—22no—
228C2×Dic86C22×C411yescharacteristic
229C2×Dic86#4111yescharacteristic
230Q16×C43—22no—
231SD16×C43—22no—
232SD16×C43—22no—
233D8×C43—22no—
234M16×C43—21no—
235M16×C43—21no—
236M16×C43—22no—
237M16×C43—22no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—41no—
241M16×C43—41no—
242M16×C43C22×C412yes—
243M16×C43C2×D412yes—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—22no—
247C2×C8×C43—22no—
248C2×C8×C43—21no—
249C2×C8×C43—41no—
250C2×C8×C43—41no—
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C2×C8×C43C2×D411yescharacteristic
254C2×C8×C43C2×D411yescharacteristic
255C2×C8×C43C2×D411yescharacteristic
256C2×C8×C43C2×D411yescharacteristic
257C4⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C42×C43—21no—
260C22⋊Dic43—22no—
261C22⋊Dic43—21no—
262#10621885—22no—
263#10621884—22no—
264#10621883—22no—
265#10621882—22no—
266(C2×D43)⋊C4—22no—
267C4⋊Dic43—21no—
268Dic43⋊C4—22no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43C22×C411yescharacteristic
272C4×Dic43C22×C411yescharacteristic
273#10621877—24no—
274#10621877—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877—21no—
278#10621877C22×C412yes—
279#10621877C2×D412yes—
280C2×C43⋊C8—24no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8C2×D412yes—
287#10621872—24no—
288#10621872—24no—
289#10621872—22no—
290#10621872—22no—
291#10621872—22no—
292#10621872—22no—
293C8×D43—24no—
294C8×D43—24no—
295C8×D43—22no—
296C8×D43—22no—
297C8×D43—22no—
298C8×D43—22no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43C2×#4111yescharacteristic
302C22×D43—24no—
303C22×D43—21no—
304C22×D43C4×D412yes—
305Q8×C43—21no—
306Q8×C43—21no—
307Q8×C43—21no—
308Q8×C43C4×D412yes—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—21no—
312D4×C43—21no—
313D4×C43—21no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43C4×D412yes—
317C2×C4×C43—21no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C22⋊D43—24no—
331C22⋊D43—24no—
332C22⋊D43—22no—
333C22⋊D43—22no—
334C22⋊D43—22no—
335C22⋊D43—22no—
336C22⋊D43—82no—
337C2×Dic43—24no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—41no—
342C2×Dic43—81no—
343C2×Dic43C4×D412yes—
344D172—24no—
345D172—21no—
346D172—21no—
347D172—21no—
348D172C4×D412yes—
349C4×D43—24no—
350C4×D43—24no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355Dic86—24no—
356Dic86—21no—
357Dic86—21no—
358Dic86—21no—
359Dic86C4×D412yes—
360C8×C43—22no—
361C8×C43—22no—
362C8×C43—41no—
363C8×C43#12011yescharacteristic
364C8×C43#12011yescharacteristic
365C8×C43#12011yescharacteristic
366C8×C43#12011yescharacteristic
367C43⋊C8—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C43⋊C8—41no—
371#21478—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—41no—
376C22×C43—81no—
377C22×C43C2×C4×D411yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43#52511yescharacteristic
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—42no—
383C2×D43—81no—
384C2×D43—84no—
385C4×C43—22no—
386C4×C43—41no—
387C4×C43—81no—
388C4×C43C2×C4×D411yescharacteristic
389C4×C43C2×C4×D411yescharacteristic
390C4×C43C2×#12011yescharacteristic
391C4×C43#52511yescharacteristic
392Dic43—22no—
393Dic43—22no—
394Dic43—41no—
395Dic43—41no—
396Dic43—81no—
397#3573—431no—
398#3018—431no—
399#2955—431no—
400#2955D4311yescharacteristic, complemented
401#2932—431no—
402#1884—431no—
403#1881—431no—
404#1881—431no—
405#1861—431no—
406#1861—431no—
407#1858—431no—
408#1794—431no—
409#1765—431no—
410#1765—431no—
411#1757—431no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—42no—
416C2×C43—81no—
417C2×C43C4×#12011yescharacteristic
418D43—42no—
419D43—42no—
420#585—431no—
421#575—431no—
422#575C2×D4311yescharacteristic
423#568—431no—
424#568—431no—
425#568—431no—
426#568—862no—
427#568—862no—
428#568—862no—
429C2×#131—431no—
430C2×#131—431no—
431C2×#131—862no—
432C2×#131—862no—
433C2×#131—862no—
434C2×#131C2×D4311yescharacteristic
435C2×#131C2×D4311yescharacteristic, complemented
436#532—431no—
437#456—432no—
438#455—432no—
439#454—432no—
440#453—432no—
441#444—22no—
442#444—862no—
443#443—22no—
444#443—862no—
445#435—862no—
446#435—862no—
447#430—431no—
448#430C2×D4311yescharacteristic, complemented
449#423—431no—
450#421—431no—
451#421—431no—
452#421C2×D4311yescharacteristic
453#421C2×D4311yescharacteristic, complemented
454C2×#104—431no—
455C2×#104—431no—
456#416—431no—
457#416—431no—
458#413—431no—
459#410—431no—
460#408—431no—
461#408—431no—
462#405—431no—
463#405C2×D4311yescharacteristic, complemented
464C2×#97—431no—
465#344—431no—
466#344—431no—
467#341—431no—
468#341—431no—
469#339—431no—
470#339—431no—
471C43#2147811yescharacteristic, complemented, Sylow
4722−1+4—432no—
4732−1+4—861no—
4742−1+4—861no—
475H(5,𝔽2)—432no—
476H(5,𝔽2)—862no—
477H(5,𝔽2)—861no—
478H(5,𝔽2)—861no—
479C2×#41—431no—
480C2×#41—431no—
481C2×#41—862no—
482C2×#41—862no—
483C2×#41—862no—
484C2×#41C22×D4311yescharacteristic
485C2×#41C22×D4311yescharacteristic
486#137—21no—
487#137—432no—
488#137—861no—
489#137C4×D4312yes—
490AGL(1,ℤ/8)—21no—
491AGL(1,ℤ/8)—432no—
492AGL(1,ℤ/8)—861no—
493AGL(1,ℤ/8)C4×D4312yes—
494#135—22no—
495#135—862no—
496#131—21no—
497#131—21no—
498#131—21no—
499#131—21no—
500#131—21no—
501#131—21no—
502#131—432no—
503#131—432no—
504#131—862no—
505#131—862no—
506#131—864no—
507#131—864no—
508#131—862no—
509#131—862no—
510#131—864no—
511#131—864no—
512#131—862no—
513#131—862no—
514#131—861no—
515#131—861no—
516#131—861no—
517#131—861no—
518#131—861no—
519#131—861no—
520#131C22⋊D4312yescomplemented
521#131C22⋊D4312yescomplemented
522C2×M16—21no—
523C2×M16—21no—
524C2×M16—431no—
525C2×M16—432no—
526C2×M16—431no—
527C2×M16—431no—
528C2×M16—864no—
529C2×M16—862no—
530C2×M16—864no—
531C2×M16—864no—
532C2×M16—862no—
533C2×M16—862no—
534C2×M16—861no—
535C2×M16C22×D4311yescharacteristic
536C2×M16C22×D4311yescharacteristic
537C2×M16C22×D4311yescharacteristic
538C22×C8—21no—
539C22×C8—21no—
540C22×C8—432no—
541C22×C8—431no—
542C22×C8—864no—
543C22×C8—861no—
544C22×C8C22×D4311yescharacteristic
545C4⋊Q8—431no—
546#127—431no—
547#124—431no—
548#124—431no—
549#121—862no—
550C4×D4—862no—
551#117—431no—
552#117C22×D4311yescharacteristic
553C2×C42—431no—
554#108—22no—
555#108—862no—
556C4⋊C8—862no—
557#104—22no—
558#104—22no—
559#104—432no—
560#104—432no—
561#104—432no—
562#104—432no—
563#104—862no—
564#104—862no—
565#103—861no—
566#103—861no—
567#102—861no—
568#102—861no—
569#101—432no—
570#100—432no—
571#99—862no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574#97—21no—
575#97—861no—
576#97—861no—
577#97—861no—
578C4×C8—21no—
579C4×C8—861no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—21no—
586#41—432no—
587#41—432no—
588#41—862no—
589#41—862no—
590#41—864no—
591#41—864no—
592#41—864no—
593#41—864no—
594#41—862no—
595#41—862no—
596#41—862no—
597#41—862no—
598#41—861no—
599#41—861no—
600#41—861no—
601#41—861no—
602#41—861no—
603#41—861no—
604#41C2×C4×D4312yes—
605#41C2×C22⋊D4312yes—
606C2×Q8—431no—
607C2×Q8—431no—
608C2×Q8—862no—
609C2×Q8—862no—
610C2×Q8—862no—
611C2×Q8C2×C4×D4311yescharacteristic
612C2×Q8#1062189811yescharacteristic
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—432no—
616C2×D4—431no—
617C2×D4—431no—
618C2×D4—862no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—862no—
622C2×D4—864no—
623C2×D4—861no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4C2×C4×D4311yescharacteristic
627C2×D4#1062189811yescharacteristic
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—432no—
631C22×C4—864no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4C23×D4311yescharacteristic
635Q16—22no—
636Q16—862no—
637SD16—22no—
638SD16—22no—
639SD16—862no—
640SD16—862no—
641D8—22no—
642D8—862no—
643M16—21no—
644M16—21no—
645M16—22no—
646M16—22no—
647M16—21no—
648M16—21no—
649M16—41no—
650M16—41no—
651M16—432no—
652M16—432no—
653M16—864no—
654M16—864no—
655M16—864no—
656M16—861no—
657M16—861no—
658M16—861no—
659M16—861no—
660M16—862no—
661M16—862no—
662M16—862no—
663M16—862no—
664M16C2×C4×D4312yes—
665M16C2×C22⋊D4312yes—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—21no—
671C2×C8—41no—
672C2×C8—41no—
673C2×C8—432no—
674C2×C8—864no—
675C2×C8—864no—
676C2×C8—864no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—862no—
680C2×C8—862no—
681C2×C8—862no—
682C2×C8—862no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8D4×D4311yescharacteristic
687C2×C8D4×D4311yescharacteristic
688C2×C8D4×D4311yescharacteristic
689C2×C8D4×D4311yescharacteristic
690C2×C8C2×C22⋊D4311yescharacteristic
691C2×C8C2×C22⋊D4311yescharacteristic
692C4⋊C4—21no—
693C4⋊C4—862no—
694C4⋊C4—861no—
695C22⋊C4—21no—
696C22⋊C4—862no—
697C22⋊C4—862no—
698C22⋊C4—861no—
699C42—21no—
700C42—431no—
701C42—431no—
702C42—861no—
703C42—861no—
704C23—21no—
705C23—21no—
706C23—432no—
707C23—864no—
708C23—861no—
709C23#41×D4311yescharacteristic
710Q8—21no—
711Q8—21no—
712Q8—21no—
713Q8—432no—
714Q8—864no—
715Q8—861no—
716Q8—861no—
717Q8—861no—
718Q8C4×C22⋊D4312yes—
719D4—22no—
720D4—22no—
721D4—21no—
722D4—21no—
723D4—21no—
724D4—41no—
725D4—41no—
726D4—432no—
727D4—864no—
728D4—864no—
729D4—864no—
730D4—862no—
731D4—862no—
732D4—862no—
733D4—862no—
734D4—861no—
735D4—861no—
736D4—861no—
737D4—3442no—
738D4C4×C22⋊D4312yes—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—432no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—864no—
750C2×C4—861no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—3441no—
758C2×C4—1721no—
759C2×C4C22×C4×D4311yescharacteristic
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4C2×D4×D4311yescharacteristic
762C2×C4C22×C22⋊D4311yescharacteristic
763C2×C4#41×D4311yescharacteristic
764C2×C4C2×#1062189811yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—862no—
769C8—862no—
770C8—862no—
771C8—1721no—
772C8#1306329311yescharacteristic
773C8#1306329311yescharacteristic
774C8#1306329311yescharacteristic
775C8#1306329311yescharacteristic
776C22—22no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—81no—
781C22—862no—
782C22—862no—
783C22—3441no—
784C22—3444no—
785C22—1722no—
786C22C4×D4×D4311yescharacteristic
787C22#1458340611yescharacteristic
788C22#1458340811yescharacteristic
789C4—22no—
790C4—41no—
791C4—81no—
792C4—862no—
793C4—862no—
794C4—3441no—
795C4—1721no—
796C4—1721no—
797C4C4×D4×D4311yescharacteristic
798C4C2×C4×C22⋊D4311yescharacteristic
799C4C2×#1306329311yescharacteristic
800C4#1458340811yescharacteristic
801C2—21no—
802C2—21no—
803C2—21no—
804C2—42no—
805C2—81no—
806C2—1722no—
807C2—1722no—
808C2C4×#1306329311yescharacteristic
subgroupG/H
centerC4C2×#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2955C2
socleC2×C43C4×#120
prime radical#19143941C2
cosocleC22×C4×C43C24
hypercenter#2955D43
hypocenterC43#21478
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2955

Complements

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

NH ≅ G/Ntype
1. #19149306C2semidirect
3. #19143496C2semidirect
4. #19143311C2semidirect
5. #19134975C2semidirect
6. #19134959C2semidirect
7. #19134954C2semidirect
8. #19134833C2semidirect
9. #19134832C2semidirect
10. #19134813C2semidirect
11. #19134557C2semidirect
12. #19134441C2semidirect
13. #19134437C2semidirect
14. #19134396C2semidirect
15. C43×#2955C2semidirect
30. #14583080C4semidirect
31. #14583075C4semidirect
32. #14583070C4semidirect
33. #14583065C4semidirect
38. #14582947C22semidirect
39. #14582922C22semidirect
40. #14582916C22semidirect
49. #14582866C22semidirect
50. #14582854C22semidirect
51. C2×#13063235C22semidirect
52. #14582671C22semidirect
53. #14582669C22semidirect
54. #14582663C22semidirect
55. #14582663C22semidirect
56. #14582660C22semidirect
57. #14582658C22semidirect
60. C2×#131×C43C22semidirect
63. C43×#430C22semidirect
65. C43×#421C22semidirect
66. C43×#405C22semidirect
100. #13063331D4semidirect
101. #13063331D4semidirect
159. #131×C43D4semidirect
160. #131×C43D4semidirect
400. #2955D43semidirect
435. C2×#131C2×D43semidirect
448. #430C2×D43semidirect
453. #421C2×D43semidirect
463. #405C2×D43semidirect
471. C43#21478semidirect
520. #131C22⋊D43semidirect
521. #131C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191493062
#191439412
#191434962
#191433112
#191349752
#191349592
#191349542
#191348332
#191348322
#191348132
#191345572
#191344412
#191344372
#191343962
C43×#29552
#2147843