Finite Group Databasebeta

← #25115098

Subgroups — #25115098

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583019C211yesmaximal, characteristic
2#19143474C211yesmaximal, characteristic
3#19143466C211yesmaximal, characteristic
4#19143195C211yesmaximal, characteristic, complemented
5#19143186C211yesmaximal, characteristic, complemented
6#19135379C211yesmaximal, characteristic, complemented
7#19135374C211yesmaximal, characteristic, complemented
8#19134831C211yesmaximal, characteristic, complemented
9#19134826C211yesmaximal, characteristic, complemented
10#19134824C211yesmaximal, characteristic, complemented
11#19134819C211yesmaximal, characteristic, complemented
12#19134760C211yesmaximal, characteristic, complemented
13#19134656C211yesmaximal, characteristic, complemented
14#19134482C211yesmaximal, characteristic, complemented
15C43×#1815C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583380C2211yescharacteristic
21#14583380C2211yescharacteristic
22#14583019C418yescomplemented
23#14583008—21no—
24#14583003—21no—
25#14583002—21no—
26#14582996—21no—
27#14582991—21no—
28#14582990—21no—
29#14582984—21no—
30#14582979—21no—
31C2×#13063260C2211yescharacteristic
32#14582941—21no—
33#14582941—21no—
34#14582941C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582939C2211yescharacteristic
37#14582939C2211yescharacteristic
38#14582938—21no—
39#14582938—21no—
40#14582937—21no—
41#14582937C2211yescharacteristic
42#14582934—21no—
43C2×#13063259—21no—
44C2×#13063259C2211yescharacteristic
45C2×#13063258C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47#106×D43—21no—
48C2×#13063252C2211yescharacteristic
49C2×#13063251C2211yescharacteristic
50#14582901C2211yescharacteristic
51#14582901C2211yescharacteristic
52#14582857C2211yescharacteristic
53#14582857C2211yescharacteristic
54C2×#13063235C2211yescharacteristic
55#14582768C2211yescharacteristic
56#14582764C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582660C2211yescharacteristic
60#14582660C2211yescharacteristic
61C2×#131×C43C2211yescharacteristic
62C2×#108×C43C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063345C2×C414yes—
70#13063345Q814yes—
71C2×#10621885D411yescharacteristic
72C2×#10621883D411yescharacteristic
73C2×#10621884D411yescharacteristic
74C2×#10621882D411yescharacteristic
75#13063331—22no—
76#13063331C2×C414yescomplemented
77C2×#10621877C2311yescharacteristic
78C2×#10621872—21no—
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—21no—
81Q8×Dic43—21no—
82Q8×Dic43—21no—
83#13063290—21no—
84#13063290—21no—
85D4×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—41no—
88D4×Dic43—41no—
89#13063287—21no—
90#13063287—21no—
91C4×C22⋊D43—41no—
92C4×C22⋊D43—41no—
93#13063284—21no—
94#13063284—21no—
95#13063284C2311yescharacteristic
96#13063284C2311yescharacteristic
97#13063283—21no—
98#13063283—21no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—41no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43—21no—
106C2×C4×Dic43C2311yescharacteristic
107#13063260C2×C414yescomplemented
108#13063259—21no—
109#13063259—21no—
110#13063259—21no—
111#13063259—21no—
112#13063259D411yescharacteristic
113#13063259D411yescharacteristic
114#13063258—21no—
115#13063258—21no—
116#13063258—21no—
117#13063258—21no—
118#13063257—21no—
119#13063257—21no—
120#13063257D411yescharacteristic
121#13063257D411yescharacteristic
122#13063256—21no—
123#13063256—21no—
124#13063256—21no—
125#13063256—21no—
126#13063252C2×C414yescomplemented
127#13063251C2×C414yescomplemented
128#13063250—21no—
129#13063250—21no—
130#13063247—21no—
131#13063247—21no—
132#13063235—21no—
133#13063235—21no—
134#13063235C2×C414yescomplemented
135C8×Dic43—21no—
136C8×Dic43—21no—
137C43⋊#95—41no—
138C2×#41×C43C2311yescharacteristic
139#131×C43—22no—
140#131×C43C2×C414yescomplemented
141C2×M16×C43—21no—
142C2×M16×C43C2311yescharacteristic
143C2×M16×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C22×C8×C43—21no—
146C22×C8×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149#108×C43—22no—
150#106×C43—21no—
151#106×C43—21no—
152#103×C43—21no—
153#103×C43—21no—
154#102×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×C43C2411yescharacteristic
167C2×C22⋊D43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—41no—
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—24no—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43—21no—
187M16×C43—21no—
188M16×C43C22×C412yes—
189C2×C8×C43—21no—
190C2×C8×C43—24no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C22×C412yes—
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43#4112yes—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C22⋊Dic43—21no—
202C22⋊Dic43—21no—
203C22⋊Dic43—41no—
204C22⋊Dic43—41no—
205#10621885C4⋊C414yescomplemented
206#10621884C4⋊C414yescomplemented
207#10621883C4⋊C414yescomplemented
208#10621882C4⋊C414yescomplemented
209(C2×D43)⋊C4—41no—
210(C2×D43)⋊C4—41no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—41no—
216C4⋊Dic43—41no—
217C4⋊Dic43C2×D411yescharacteristic
218C4⋊Dic43C2×D411yescharacteristic
219C4⋊Dic43C2×D411yescharacteristic
220C4⋊Dic43C2×D411yescharacteristic
221Dic43⋊C4—41no—
222Dic43⋊C4—41no—
223Dic43⋊C4—82no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C4×Dic43—41no—
228C4×Dic43—41no—
229C4×Dic43—41no—
230C4×Dic43—41no—
231C4×Dic43C22×C412yes—
232#10621877—21no—
233#10621877C22×C412yes—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C22×C412yes—
236C2×C43⋊C8C2×D411yescharacteristic
237C2×C43⋊C8C2×D411yescharacteristic
238C2×C43⋊C8C2×Q812yes—
239#10621872—24no—
240C8×D43—24no—
241C23×C43—21no—
242C23×C43H(5,𝔽2)11yescharacteristic
243C22×D43—21no—
244Q8×C43—21no—
245Q8×C43C2×C4⋊C412yes—
246D4×C43—22no—
247D4×C43—22no—
248D4×C43—21no—
249D4×C43C2×C4⋊C412yes—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—81no—
256C2×C4×C43—81no—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×Q811yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C22⋊D43—22no—
264C22⋊D43—22no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—81no—
276C2×Dic43—81no—
277C2×Dic43—161no—
278C2×Dic43—161no—
279D172—21no—
280D172C2×C4⋊C412yes—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—161no—
284C4×D43—161no—
285Dic86—21no—
286Dic86C2×C4⋊C412yes—
287C8×C43—22no—
288C8×C43—41no—
289C8×C43—41no—
290C8×C43C4×D412yes—
291C8×C43C4×D412yes—
292C43⋊C8—22no—
293C43⋊C8C2×C4⋊C412yes—
294C43⋊C8C2×C4⋊C412yes—
295#22693—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—22no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43#52011yescharacteristic
302C22×C43D4211yescharacteristic
303C22×C43#55411yescharacteristic
304C2×D43—22no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—22no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43C22×C4⋊C411yescharacteristic
311C4×C43C2×C4×D411yescharacteristic
312C4×C43#54711yescharacteristic
313C4×C43D4×Q811yescharacteristic
314Dic43—22no—
315Dic43—42no—
316Dic43—41no—
317Dic43—41no—
318Dic43—41no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322C2×#444—431no—
323#2952—431no—
324#2951—431no—
325#2913—431no—
326#2912—431no—
327#1952—431no—
328#1951—431no—
329#1860—431no—
330#1860—431no—
331#1859—431no—
332#1859—431no—
333#1847—431no—
334#1816—431no—
335#1815D4311yescharacteristic, complemented
336#1773—431no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—42no—
340C2×C43D4×C4⋊C411yescharacteristic
341C2×C43#328811yescharacteristic
342C2×C43#328911yescharacteristic
343D43—42no—
344C2×#135—431no—
345C2×#131—431no—
346C2×#131C2×D4311yescharacteristic
347#520—431no—
348#520—431no—
349#520—431no—
350#520—431no—
351#444—438no—
352#442—861no—
353#441—861no—
354#440—861no—
355#440—861no—
356C4×Q16—861no—
357C4×SD16—861no—
358C4×SD16—861no—
359C4×D8—861no—
360C2×#108—431no—
361C2×#108C2×D4311yescharacteristic
362#428—431no—
363#428—431no—
364#428—431no—
365#428—431no—
366#428—861no—
367#428—861no—
368#428—861no—
369#428—861no—
370#427—431no—
371#427—861no—
372#427—861no—
373C2×#107—431no—
374C2×#107—431no—
375C2×#107—861no—
376C2×#106—431no—
377C2×#106—861no—
378C2×#106C2×D4311yescharacteristic
379C2×#104—431no—
380C2×#104—431no—
381#417—431no—
382#417—431no—
383#417C2×D4311yescharacteristic
384#417C2×D4311yescharacteristic
385#405—431no—
386#405—431no—
387C2×#97—431no—
388#384—431no—
389#382—431no—
390#343—431no—
391#343—431no—
392#343C2×D4311yescharacteristic
393#343C2×D4311yescharacteristic
394#339—431no—
395#339—431no—
396C43#2269311yescharacteristic, complemented, Sylow
397C2×#41—431no—
398C2×#41C22×D4311yescharacteristic
399#135—434no—
400#135—434no—
401C2×Q16—431no—
402C2×SD16—431no—
403C2×SD16—431no—
404C2×D8—431no—
405#131—22no—
406#131—434no—
407#131—862no—
408#131C4×D4314yescomplemented
409C2×M16—21no—
410C2×M16—431no—
411C2×M16—861no—
412C2×M16C22×D4311yescharacteristic
413C2×M16C22×D4311yescharacteristic
414C2×M16C22×D4311yescharacteristic
415C22×C8—21no—
416C22×C8—431no—
417C22×C8—861no—
418C22×C8C22×D4311yescharacteristic
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—1721no—
428C4×D4—1721no—
429C4×D4—1721no—
430C4×D4—1721no—
431#117—431no—
432#117—431no—
433#117—861no—
434#117—861no—
435#117—861no—
436#117—861no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—1721no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C42—431no—
447#108—22no—
448#108—434no—
449#107—431no—
450#107—431no—
451#107—861no—
452#107—861no—
453#107—861no—
454#107—861no—
455#107—861no—
456#107—861no—
457#107—861no—
458#107—861no—
459#106—21no—
460#106—21no—
461#106—431no—
462#106—431no—
463#106—861no—
464#106—861no—
465#106—861no—
466#106—861no—
467#106—861no—
468#106—861no—
469#104—434no—
470#104—434no—
471#103—21no—
472#103—21no—
473#103—861no—
474#103—861no—
475#102—21no—
476#102—21no—
477#102—861no—
478#102—861no—
479#97—434no—
480#97—861no—
481#97—861no—
482C4×C8—861no—
483C4×C8—861no—
484#95—1721no—
485#41—21no—
486#41—21no—
487#41—432no—
488#41—432no—
489#41—861no—
490#41—861no—
491#41C2×C4×D4312yes—
492#41Q8×D4312yes—
493C2×Q8—431no—
494C2×Q8D4×D4311yescharacteristic
495C2×D4—21no—
496C2×D4—431no—
497C2×D4—861no—
498C2×D4D4×D4311yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4C23×D4311yescharacteristic
511Q16—434no—
512SD16—434no—
513SD16—434no—
514D8—434no—
515M16—21no—
516M16—24no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—432no—
522M16—861no—
523M16—864no—
524M16C2×C4×D4312yes—
525C2×C8—21no—
526C2×C8—24no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—432no—
530C2×C8—431no—
531C2×C8—431no—
532C2×C8—432no—
533C2×C8—861no—
534C2×C8—864no—
535C2×C8C2×C4×D4312yes—
536C2×C8D4×D4311yescharacteristic
537C2×C8D4×D4311yescharacteristic
538C2×C8#1062190012yes—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—431no—
544C4⋊C4—431no—
545C4⋊C4—431no—
546C4⋊C4—431no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—3442no—
552C4⋊C4—1721no—
553C4⋊C4—1721no—
554C4⋊C4—1721no—
555C4⋊C4—1721no—
556C22⋊C4—861no—
557C22⋊C4—861no—
558C22⋊C4—1721no—
559C22⋊C4—1721no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C42—432no—
563C42—861no—
564C42—861no—
565C42—861no—
566C42—1721no—
567C42—1721no—
568C42—1721no—
569C42—1721no—
570C23—21no—
571C23—861no—
572C23#1306337111yescharacteristic
573Q8—21no—
574Q8—432no—
575Q8—861no—
576Q8C4⋊C4×D4312yes—
577D4—22no—
578D4—22no—
579D4—21no—
580D4—432no—
581D4—862no—
582D4—862no—
583D4—861no—
584D4C4⋊C4×D4312yes—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—3441no—
601C2×C4—3441no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—6881no—
607C2×C4—6881no—
608C2×C4—6881no—
609C2×C4—6881no—
610C2×C4C22×C4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4C2×D4×D4311yescharacteristic
613C2×C4C2×Q8×D4311yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4#1306337211yescharacteristic
616C8—22no—
617C8—41no—
618C8—41no—
619C8—432no—
620C8—432no—
621C8—862no—
622C8(C22⋊D43)⋊C412yes—
623C8(C22⋊D43)⋊C412yes—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—41no—
628C22—41no—
629C22—862no—
630C22—1721no—
631C22—1721no—
632C22#1458337911yescharacteristic
633C22#1458353311yescharacteristic
634C22#1458360711yescharacteristic
635C4—22no—
636C4—81no—
637C4—81no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4—1721no—
643C4—1721no—
644C4—1721no—
645C4—1721no—
646C4C2×C4⋊C4×D4311yescharacteristic
647C4C2×(C22⋊D43)⋊C411yescharacteristic
648C4#1458354911yescharacteristic
649C4#1458356211yescharacteristic
650C2—21no—
651C2—21no—
652C2—42no—
653C2—1722no—
654C2#1913749111yescharacteristic
655C2#1914636011yescharacteristic
656C2#1914636711yescharacteristic
subgroupG/H
centerC22#14583533
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1815C2
socleC22×C43D42
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1815D43
hypocenterC43#22693
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1815

Complements

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

NH ≅ G/Ntype
4. #19143195C2semidirect
5. #19143186C2semidirect
6. #19135379C2semidirect
7. #19135374C2semidirect
8. #19134831C2semidirect
9. #19134826C2semidirect
10. #19134824C2semidirect
11. #19134819C2semidirect
12. #19134760C2semidirect
13. #19134656C2semidirect
14. #19134482C2semidirect
15. C43×#1815C2semidirect
22. #14583019C4semidirect
76. #13063331C2×C4semidirect
107. #13063260C2×C4semidirect
126. #13063252C2×C4semidirect
127. #13063251C2×C4semidirect
134. #13063235C2×C4semidirect
140. #131×C43C2×C4semidirect
205. #10621885C4⋊C4semidirect
206. #10621884C4⋊C4semidirect
207. #10621883C4⋊C4semidirect
208. #10621882C4⋊C4semidirect
335. #1815D43semidirect
396. C43#22693semidirect
408. #131C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830192
#191434742
#191434662
#191431952
#191431862
#191353792
#191353742
#191348312
#191348262
#191348242
#191348192
#191347602
#191346562
#191344822
C43×#18152
#2269343