Finite Group Databasebeta

← #25115068

Subgroups — #25115068

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583013C211yesmaximal, characteristic
2#19143476C211yesmaximal, characteristic
3#19143474C211yesmaximal, characteristic
4#19143189C211yesmaximal, characteristic, complemented
5#19143188C211yesmaximal, characteristic, complemented
6#19135374C211yesmaximal, characteristic, complemented
7#19135372C211yesmaximal, characteristic, complemented
8#19134823C211yesmaximal, characteristic, complemented
9#19134822C211yesmaximal, characteristic, complemented
10#19134820C211yesmaximal, characteristic, complemented
11#19134751C211yesmaximal, characteristic, complemented
12#19134653C211yesmaximal, characteristic, complemented
13#19134652C211yesmaximal, characteristic, complemented
14#19134473C211yesmaximal, characteristic, complemented
15C43×#1859C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583380C2211yescharacteristic
21#14583379C2211yescharacteristic
22#14583013C418yescomplemented
23#14583009—21no—
24#14583008—21no—
25#14583004—21no—
26#14583003—21no—
27#14582990—21no—
28C4×#10621884—21no—
29C4×#10621883—21no—
30#14582984—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582942—21no—
34#14582942C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582940—21no—
37#14582939—21no—
38#14582939C2211yescharacteristic
39#14582938—21no—
40#14582936—21no—
41#14582935—21no—
42#14582935C2211yescharacteristic
43C2×#13063256—21no—
44C2×#13063256C2211yescharacteristic
45C2×#13063256C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48#106×D43—21no—
49C2×#13063253C2211yescharacteristic
50#14582901C2211yescharacteristic
51#14582900C2211yescharacteristic
52#14582898C2211yescharacteristic
53#14582857C2211yescharacteristic
54#14582855C2211yescharacteristic
55C2×C4×C43⋊C8C2211yescharacteristic
56#14582769C2211yescharacteristic
57#14582668C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582659C2211yescharacteristic
61C43×#520C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#384C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#339C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063345C2×C414yes—
70#13063345Q814yes—
71C2×#10621885D411yescharacteristic
72C2×#10621883D411yescharacteristic
73C2×#10621884D411yescharacteristic
74C2×#10621882D411yescharacteristic
75#13063333—22no—
76#13063333C2×C414yescomplemented
77#13063332—22no—
78#13063332C2×C414yescomplemented
79C2×#10621877—21no—
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621872—21no—
83C22×C43⋊C8—21no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C2×C8×D43—21no—
87Q8×Dic43—21no—
88C4×Dic86—21no—
89#13063290—21no—
90C4×D172—21no—
91D4×Dic43—21no—
92D4×Dic43—41no—
93#13063287—21no—
94C4×C22⋊D43—41no—
95(C22⋊D43)⋊C4—41no—
96#13063284—21no—
97#13063284C2311yescharacteristic
98#13063283—21no—
99#13063283—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—41no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C4⋊C4×D43—21no—
105C4⋊C4×D43—21no—
106#13063260—22no—
107#13063260C2×C414yescomplemented
108#13063259—21no—
109#13063258—21no—
110#13063258—21no—
111#13063258D411yescharacteristic
112#13063258D411yescharacteristic
113#13063257—21no—
114#13063256—21no—
115#13063256—21no—
116#13063256—21no—
117#13063256—21no—
118#13063256—21no—
119#13063256—21no—
120#13063256—21no—
121#13063256—21no—
122#13063256—21no—
123#13063256—21no—
124#13063256D411yescharacteristic
125#13063256D411yescharacteristic
126#13063253C2×C414yescomplemented
127#13063250—21no—
128#13063249—21no—
129#13063248—21no—
130#13063247—21no—
131#13063246—21no—
132#13063245—21no—
133#13063236—21no—
134#13063235—21no—
135C4×C43⋊C8—21no—
136C4×C43⋊C8C2×C414yescomplemented
137C8×Dic43—21no—
138C2×#41×C43C2311yescharacteristic
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C4×Q8×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—41no—
144#117×C43—21no—
145#117×C43C2311yescharacteristic
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43—41no—
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C42×C43C2311yescharacteristic
151#107×C43—21no—
152#106×C43—21no—
153#104×C43C2×C414yescomplemented
154#103×C43—21no—
155#102×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43C22×C412yes—
159#41×C43C2×Q812yes—
160C2×Q8×C43C2×D411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—41no—
173#10621898—21no—
174#10621898—21no—
175#10621898C22×C412yes—
176#10621898C2×Q812yes—
177C2×D172C2×D411yescharacteristic
178C2×C4×D43—21no—
179C2×C4×D43—41no—
180C2×C4×D43—41no—
181C2×Dic86C2×D411yescharacteristic
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43C22×C412yes—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—82no—
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—41no—
201C42×C43C22×C412yes—
202C22⋊Dic43—21no—
203C22⋊Dic43—41no—
204#10621885C4⋊C414yescomplemented
205#10621884C4⋊C414yescomplemented
206#10621883C4⋊C414yescomplemented
207#10621882C4⋊C414yescomplemented
208(C2×D43)⋊C4—41no—
209(C2×D43)⋊C4—41no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—41no—
215C4⋊Dic43—82no—
216C4⋊Dic43C2×D411yescharacteristic
217C4⋊Dic43C2×D411yescharacteristic
218Dic43⋊C4—41no—
219Dic43⋊C4—41no—
220C4×Dic43—21no—
221C4×Dic43—41no—
222C4×Dic43—41no—
223C4×Dic43—41no—
224#10621877—21no—
225#10621877—24no—
226#10621877—21no—
227#10621877—21no—
228#10621877C22×C412yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—24no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8C22×C412yes—
233C2×C43⋊C8C22×C412yes—
234C2×C43⋊C8C2×D411yescharacteristic
235C2×C43⋊C8C2×D411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C2×C43⋊C8C2×D411yescharacteristic
238C2×C43⋊C8C2×Q812yes—
239C2×C43⋊C8#4112yes—
240#10621872—24no—
241C8×D43—24no—
242C23×C43—21no—
243C23×C43H(5,𝔽2)11yescharacteristic
244C22×D43—21no—
245Q8×C43—21no—
246Q8×C43C2×C4⋊C412yes—
247D4×C43—22no—
248D4×C43—22no—
249D4×C43—21no—
250D4×C43C2×C4⋊C412yes—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—81no—
262C2×C4×C43—81no—
263C2×C4×C43—161no—
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×Q811yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C432−1+411yescharacteristic
270C22⋊D43—22no—
271C22⋊D43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—81no—
278C2×Dic43—81no—
279C2×Dic43—161no—
280D172—21no—
281D172C2×C4⋊C412yes—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—161no—
285C4×D43—161no—
286Dic86—21no—
287Dic86C2×C4⋊C412yes—
288C8×C43—22no—
289C8×C43—41no—
290C43⋊C8—22no—
291C43⋊C8—41no—
292C43⋊C8C2×C4⋊C412yes—
293C43⋊C8C2×C4⋊C412yes—
294C43⋊C8C4×D412yes—
295C43⋊C8C4×D412yes—
296#22689—431nomaximal, Sylow
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—22no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43#52011yescharacteristic
303C22×C43D4211yescharacteristic
304C22×C43#55411yescharacteristic
305C2×D43—22no—
306C2×D43—41no—
307C2×D43—41no—
308C4×C43—24no—
309C4×C43—22no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43C22×C4⋊C411yescharacteristic
315C4×C43C2×C4×D411yescharacteristic
316C4×C43#54711yescharacteristic
317C4×C43D4×Q811yescharacteristic
318Dic43—22no—
319Dic43—41no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C2×#443—431no—
324#2952—431no—
325#2952—431no—
326#2912—431no—
327#2912—431no—
328#1951—431no—
329#1951—431no—
330#1859—431no—
331#1859—431no—
332#1859—431no—
333#1859D4311yescharacteristic, complemented
334#1844—431no—
335#1815—431no—
336#1815—431no—
337#1772—431no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—42no—
341C2×C43D4×C4⋊C411yescharacteristic
342C2×C43#329111yescharacteristic
343C2×C43#329111yescharacteristic
344D43—42no—
345C2×#135—431no—
346C2×#131—431no—
347C2×#131—431no—
348#520—431no—
349#520—431no—
350#520—431no—
351#520C2×D4311yescharacteristic
352#443—438no—
353#442—861no—
354#442—861no—
355#441—861no—
356#441—861no—
357C4×SD16—861no—
358C4×SD16—861no—
359C4×SD16—861no—
360C4×SD16—861no—
361C2×#108—431no—
362C2×#108—431no—
363#428—431no—
364#428—431no—
365#428—431no—
366#428—861no—
367#428—861no—
368#428—861no—
369#428—861no—
370#428C2×D4311yescharacteristic
371#427—431no—
372#427—861no—
373#427—861no—
374C2×#106—431no—
375C2×#106—431no—
376C2×#106—431no—
377C2×#106—431no—
378C2×#106—861no—
379C2×#106—861no—
380C2×#104—431no—
381C2×#104C2×D4311yescharacteristic
382#417—431no—
383#417—431no—
384#417—431no—
385#417C2×D4311yescharacteristic
386#405—431no—
387#405—431no—
388C2×C4×C8—431no—
389#384—431no—
390#384C2×D4311yescharacteristic
391#343—431no—
392#343—431no—
393#343—431no—
394#343C2×D4311yescharacteristic
395#339—431no—
396#339C2×D4311yescharacteristic
397C43#2268911yescharacteristic, complemented, Sylow
398C2×#41—431no—
399C2×#41C22×D4311yescharacteristic
400#135—434no—
401#135—434no—
402C2×Q16—431no—
403C2×SD16—431no—
404C2×SD16—431no—
405C2×D8—431no—
406#131—434no—
407#131—434no—
408#131—862no—
409#131—862no—
410C2×M16—431no—
411C2×M16—431no—
412C2×M16—861no—
413C2×M16—861no—
414C2×M16C22×D4311yescharacteristic
415C2×M16C22×D4311yescharacteristic
416C22×C8—431no—
417C22×C8—431no—
418C22×C8—861no—
419C22×C8—861no—
420C4×Q8—21no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×D4—21no—
425C4×D4—41no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4—1721no—
430C4×D4—1721no—
431C4×D4—1721no—
432#117—21no—
433#117—431no—
434#117—861no—
435#117—861no—
436#117—861no—
437#117C22×D4311yescharacteristic
438C2×C4⋊C4—21no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—1721no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C42C22×D4311yescharacteristic
449#108—434no—
450#108—862no—
451#107—21no—
452#107—431no—
453#107—431no—
454#107—861no—
455#107—861no—
456#107—861no—
457#106—21no—
458#106—431no—
459#106—431no—
460#106—861no—
461#106—861no—
462#106—861no—
463#106—861no—
464#106—861no—
465#106—861no—
466#106—861no—
467#106—861no—
468#106—861no—
469#106—861no—
470#106—861no—
471#104—434no—
472#104C4×D4314yescomplemented
473#103—21no—
474#103—861no—
475#103—861no—
476#103—861no—
477#102—21no—
478#102—861no—
479#102—861no—
480#102—861no—
481#97—861no—
482#97—861no—
483C4×C8—434no—
484C4×C8—861no—
485C4×C8—861no—
486#41—21no—
487#41—21no—
488#41—432no—
489#41—432no—
490#41—861no—
491#41—861no—
492#41C2×C4×D4312yes—
493#41Q8×D4312yes—
494C2×Q8—431no—
495C2×Q8D4×D4311yescharacteristic
496C2×D4—21no—
497C2×D4—431no—
498C2×D4—861no—
499C2×D4D4×D4311yescharacteristic
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4—1721no—
511C22×C4C23×D4311yescharacteristic
512Q16—434no—
513SD16—434no—
514SD16—434no—
515D8—434no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—432no—
520M16—864no—
521M16—864no—
522M16—861no—
523M16—861no—
524M16—861no—
525M16C2×C4×D4312yes—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—432no—
529C2×C8—432no—
530C2×C8—431no—
531C2×C8—431no—
532C2×C8—431no—
533C2×C8—431no—
534C2×C8—432no—
535C2×C8—432no—
536C2×C8—864no—
537C2×C8—864no—
538C2×C8—861no—
539C2×C8—861no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—41no—
545C4⋊C4—82no—
546C4⋊C4—431no—
547C4⋊C4—431no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—3442no—
553C4⋊C4—1721no—
554C4⋊C4—1721no—
555C4⋊C4—1721no—
556C4⋊C4D4×D4311yescharacteristic
557C4⋊C4D4×D4311yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—41no—
560C22⋊C4—861no—
561C22⋊C4—1721no—
562C22⋊C4—1721no—
563C22⋊C4—1721no—
564C42—21no—
565C42—21no—
566C42—41no—
567C42—861no—
568C42—1721no—
569C42—1721no—
570C42—1721no—
571C42C2×C4×D4312yes—
572C23—21no—
573C23—861no—
574C23#1306337011yescharacteristic
575Q8—21no—
576Q8—432no—
577Q8—861no—
578Q8C4⋊C4×D4312yes—
579D4—22no—
580D4—22no—
581D4—21no—
582D4—432no—
583D4—862no—
584D4—862no—
585D4—861no—
586D4C4⋊C4×D4312yes—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—161no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—3441no—
606C2×C4—3441no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—6881no—
610C2×C4—6881no—
611C2×C4—6881no—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C2×C4C2×Q8×D4311yescharacteristic
616C2×C4#41×D4311yescharacteristic
617C2×C4#1306337211yescharacteristic
618C8—22no—
619C8—41no—
620C8—432no—
621C8—432no—
622C8—432no—
623C8—432no—
624C8—862no—
625C8—1721no—
626C22—21no—
627C22—21no—
628C22—22no—
629C22—41no—
630C22—41no—
631C22—862no—
632C22—1721no—
633C22—1721no—
634C22#1458337811yescharacteristic
635C22#1458353111yescharacteristic
636C22#1458360311yescharacteristic
637C4—24no—
638C4—22no—
639C4—41no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—1721no—
647C4—1721no—
648C4C2×C4⋊C4×D4311yescharacteristic
649C4C4×D4×D4311yescharacteristic
650C4#1458354711yescharacteristic
651C4#1458356211yescharacteristic
652C2—21no—
653C2—21no—
654C2—42no—
655C2—1722no—
656C2#1913749311yescharacteristic
657C2#1914638511yescharacteristic
658C2#1914639011yescharacteristic
subgroupG/H
centerC22#14583531
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1859C2
socleC22×C43D42
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1859D43
hypocenterC43#22689
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
4. #19143189C2semidirect
5. #19143188C2semidirect
6. #19135374C2semidirect
7. #19135372C2semidirect
8. #19134823C2semidirect
9. #19134822C2semidirect
10. #19134820C2semidirect
11. #19134751C2semidirect
12. #19134653C2semidirect
13. #19134652C2semidirect
14. #19134473C2semidirect
15. C43×#1859C2semidirect
22. #14583013C4semidirect
76. #13063333C2×C4semidirect
78. #13063332C2×C4semidirect
107. #13063260C2×C4semidirect
126. #13063253C2×C4semidirect
136. C4×C43⋊C8C2×C4semidirect
153. #104×C43C2×C4semidirect
204. #10621885C4⋊C4semidirect
205. #10621884C4⋊C4semidirect
206. #10621883C4⋊C4semidirect
207. #10621882C4⋊C4semidirect
333. #1859D43semidirect
397. C43#22689semidirect
472. #104C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830132
#191434762
#191434742
#191431892
#191431882
#191353742
#191353722
#191348232
#191348222
#191348202
#191347512
#191346532
#191346522
#191344732
C43×#18592
#2268943