Finite Group Databasebeta

← #25086064

Subgroups — #25086064

Order 11008.

756 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147492C211yesmaximal, characteristic, complemented
2#19146419C211yesmaximal, characteristic, complemented
3D4×#10621883C211yesmaximal, characteristic, complemented
4#19134221C211yesmaximal, characteristic, complemented
5#19134076C211yesmaximal, characteristic, complemented
6#19134002C211yesmaximal, characteristic, complemented
7#19133970C211yesmaximal, characteristic, complemented
8#19133934C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133697C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133431C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15D4×D8×C43C211yesmaximal, characteristic
16C22×#10621883—21no—
17#14583606C2211yescharacteristic, complemented
18D4×Dic86C2211yescharacteristic, complemented
19#14583307—21no—
20#14583297C2211yescharacteristic, complemented
21#14583271C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583215—21no—
26#14583201—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583187—21no—
30#14583179C2211yescharacteristic, complemented
31#14583126—21no—
32#14583126—21no—
33#14583104C2211yescharacteristic
34#14583096C2211yescharacteristic, complemented
35#14583096C2211yescharacteristic, complemented
36#14583050—21no—
37#14583050—21no—
38#14583037—21no—
39#14583029C2211yescharacteristic, complemented
40#14583011—21no—
41C4×#10621883C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063246—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582644C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic, complemented
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C22×D8×C43—21no—
57D42×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#466—21no—
61C43×#459C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C43×#447—21no—
65C4×D8×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—41no—
74C2×#10621883—44no—
75C2×#10621883D411yescharacteristic
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063316—21no—
82#13063304—21no—
83#13063304—21no—
84#13063302—41no—
85#13063302—41no—
86C4×Dic86C2311yescharacteristic
87D4×Dic43—21no—
88D4×Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063248—21no—
101#13063248D411yescharacteristic
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063235—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120C2×D8×C43—21no—
121C2×D8×C43—21no—
122C2×D8×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43—44no—
125C2×D8×C43D411yescharacteristic
126C22×C8×C43—21no—
127#127×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134#120×C43—41no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#107×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C24×C43—41no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C2×D4×C43C2×D411yescharacteristic
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—42no—
177C2×Dic86—41no—
178C2×Dic86—81no—
179C2×Dic86C2×D411yescharacteristic
180D8×C43—42no—
181D8×C43—42no—
182D8×C43—42no—
183D8×C43—81no—
184D8×C43SD1614yescomplemented
185C2×C8×C43—21no—
186C2×C8×C43—42no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—41no—
196C22⋊C4×C43—41no—
197C42×C43C2411yescharacteristic
198C22⋊Dic43—41no—
199C22⋊Dic43—41no—
200#10621883—22no—
201#10621883—42no—
202#10621883—42no—
203#10621883—42no—
204#10621883—81no—
205#10621883—81no—
206#10621883—82no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—41no—
212C4⋊Dic43C2×D411yescharacteristic
213Dic43⋊C4—21no—
214Dic43⋊C4—41no—
215Dic43⋊C4—41no—
216C4×Dic43—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C2×C43⋊C8—81no—
223C2×C43⋊C8C2×D411yescharacteristic
224C2×C43⋊C8C2×D411yescharacteristic
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—82no—
231C23×C43—82no—
232C23×C43—82no—
233C23×C43—82no—
234C23×C43—161no—
235C23×C43—161no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—81no—
248D4×C43—81no—
249D4×C43—82no—
250D4×C43—82no—
251D4×C43—82no—
252D4×C43—82no—
253D4×C43C2×SD1612yes—
254D4×C43C2×SD1612yescomplemented
255D4×C43AGL(1,ℤ/8)12yes—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—82no—
273C2×Dic43—161no—
274Dic86—21no—
275Dic86—21no—
276Dic86—41no—
277Dic86—41no—
278Dic86—82no—
279Dic86—81no—
280C8×C43—21no—
281C8×C43—41no—
282C8×C43C2×SD1612yescomplemented
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#19763—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—164no—
306C22×C43—164no—
307C22×C43D4211yescharacteristic
308C4×C43—21no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43C22×SD1611yescharacteristic
313C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C43#57611yescharacteristic
315C4×C43#57711yescharacteristic
316Dic43—41no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320#3384—431no—
321#3295—431no—
322D4×SD16—431no—
323D4×D8D4311yescharacteristic
324#1715—431no—
325#1688—431no—
326#1677—431no—
327#1671—431no—
328#1665—431no—
329#1639—431no—
330#1629—431no—
331#1627—431no—
332#1622—431no—
333#1582—431no—
334#1580—431no—
335C2×C43—42no—
336C2×C43—42no—
337C2×C43—42no—
338C2×C43—161no—
339C2×C43—161no—
340C2×C43#326411yescharacteristic
341C2×C43D4×SD1611yescharacteristic
342C2×C43#328811yescharacteristic
343C22×SD16—861no—
344C22×D8—21no—
345#554—431no—
346D4×Q8—431no—
347D42C2×D4311yescharacteristic
348D42C2×D4311yescharacteristic
349#501—861no—
350#498—431no—
351#493C2×D4311yescharacteristic
352#492—431no—
353#492—431no—
354#486—431no—
355#486—431no—
356#481—861no—
357#478—861no—
358#476—431no—
359#476—431no—
360#476—861no—
361#474—431no—
362#466—21no—
363#465—861no—
364#465—861no—
365#461—431no—
366#460—431no—
367#460—431no—
368#459C2×D4311yescharacteristic
369#459C2×D4311yescharacteristic
370#450—861no—
371#450—861no—
372#448—861no—
373#447—21no—
374#447—21no—
375#446—431no—
376#442—861no—
377C4×SD16—431no—
378C4×D8C2×D4311yescharacteristic
379C8×D4—431no—
380C8×D4—431no—
381C8×D4C2×D4311yescharacteristic
382C2×#102—861no—
383#334—431no—
384#334—431no—
385#333—431no—
386#332—431no—
387#331—431no—
388#331—431no—
389Q8⋊C8—431no—
390D4⋊C8—431no—
391D4⋊C8—431no—
392D4⋊C8—431no—
393#322—431no—
394C43#1976311yescharacteristic, complemented, Sylow
395C22×Q8—861no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—21no—
400C2×SD16—431no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16—861no—
405C2×SD16—861no—
406C2×SD16—1721no—
407C2×SD16—1724no—
408C2×D8—21no—
409C2×D8—21no—
410C2×D8—21no—
411C2×D8—21no—
412C2×D8—44no—
413C2×D8C22⋊D4311yescharacteristic
414C22×C8—21no—
415C22×C8—861no—
416C22×C8—861no—
417C4⋊Q8—431no—
418C4⋊Q8—431no—
419C4⋊Q8—861no—
420#127C22×D4311yescharacteristic
421#127C22×D4311yescharacteristic
422#125—861no—
423C22⋊Q8—861no—
424C22⋊Q8—861no—
425C22⋊Q8—1721no—
426C22⋊Q8—1721no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#120—41no—
432#120—41no—
433C4×Q8—431no—
434C4×D4—861no—
435C4×D4—861no—
436C4×D4C22×D4311yescharacteristic
437C4×D4C22×D4311yescharacteristic
438C4×D4C22×D4311yescharacteristic
439C2×C4⋊C4—861no—
440#107—861no—
441#107C22⋊D4311yescharacteristic
442#106—431no—
443#106—861no—
444#106—861no—
445#106—861no—
446#106—861no—
447C4⋊C8—431no—
448C4⋊C8—431no—
449C4⋊C8—431no—
450C4⋊C8—861no—
451C4⋊C8C22×D4311yescharacteristic
452#103—431no—
453#103—861no—
454#102—21no—
455#102—21no—
456#102—431no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—861no—
462#102—861no—
463#102—861no—
464#102—1721no—
465#102C22⋊D4311yescharacteristic
466#102C22⋊D4311yescharacteristic
467C22⋊C8—21no—
468C22⋊C8—861no—
469C22⋊C8—861no—
470#97—861no—
471C4×C8—431no—
472C4×C8—431no—
473C4×C8C22×D4311yescharacteristic
474C24—41no—
475C24—41no—
476C2×Q8—431no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—3441no—
480C2×Q8—1721no—
481C2×Q8—1722no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4D4×D4311yescharacteristic
501C2×D4C2×C22⋊D4311yescharacteristic
502C2×D4C2×C22⋊D4311yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—1721no—
507C22×C4—1721no—
508SD16—862no—
509SD16—3441no—
510SD16—3441no—
511SD16—3442no—
512SD16—1722no—
513SD16—1722no—
514SD16—1722no—
515D8—42no—
516D8—42no—
517D8—42no—
518D8—81no—
519D8#1062188314yescomplemented
520C2×C8—21no—
521C2×C8—42no—
522C2×C8—431no—
523C2×C8—431no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—3441no—
529C2×C8—1722no—
530C2×C8C2×C22⋊D4311yescharacteristic
531C2×C8C2×C22⋊D4311yescharacteristic
532C4⋊C4—431no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—1721no—
539C4⋊C4—1721no—
540C4⋊C4—1721no—
541C4⋊C4D4×D4311yescharacteristic
542C4⋊C4C2×C22⋊D4311yescharacteristic
543C4⋊C4C2×C22⋊D4311yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—1721no—
550C22⋊C4—1721no—
551C42—861no—
552C42C23×D4311yescharacteristic
553C23—21no—
554C23—21no—
555C23—21no—
556C23—41no—
557C23—41no—
558C23—82no—
559C23—82no—
560C23—82no—
561C23—82no—
562C23—161no—
563C23—161no—
564Q8—861no—
565Q8—861no—
566Q8—3441no—
567Q8—3442no—
568Q8—1721no—
569Q8—1721no—
570D4—21no—
571D4—21no—
572D4—21no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—81no—
582D4—81no—
583D4—82no—
584D4—82no—
585D4—82no—
586D4—82no—
587D4C2×#1062188312yes—
588D4C2×#1062188312yescomplemented
589D4#1306334912yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3442no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—6881no—
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4C22×C22⋊D4311yescharacteristic
607C2×C4#1306337011yescharacteristic
608C8—21no—
609C8—41no—
610C8—861no—
611C8—861no—
612C8—1721no—
613C8—1721no—
614C8—1721no—
615C8—1721no—
616C8C2×#1062188312yescomplemented
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—164no—
633C22—164no—
634C22D4×C22⋊D4311yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—3441no—
640C4—3441no—
641C4—1721no—
642C4—1721no—
643C4C22×#1062188311yescharacteristic
644C4C2×#1306334911yescharacteristic
645C4#1458370011yescharacteristic
646C4#1458371011yescharacteristic
647C2—42no—
648C2—42no—
649C2—42no—
650C2—161no—
651C2—161no—
652C2#1914607511yescharacteristic
653C2D4×#1062188311yescharacteristic
654C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalD4×D8×C43C2
socleC22×C43D42
hypercenterD4×D8D43
hypocenterC43#19763
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #19147492C2semidirect
2. #19146419C2semidirect
3. D4×#10621883C2semidirect
4. #19134221C2semidirect
5. #19134076C2semidirect
6. #19134002C2semidirect
7. #19133970C2semidirect
8. #19133934C2semidirect
9. #19133774C2semidirect
10. #19133711C2semidirect
11. #19133697C2semidirect
12. #19133665C2semidirect
13. #19133431C2semidirect
14. #19133419C2semidirect
17. #14583606C22semidirect
18. D4×Dic86C22semidirect
20. #14583297C22semidirect
21. #14583271C22semidirect
22. #14583271C22semidirect
23. #14583245C22semidirect
24. #14583245C22semidirect
28. #14583189C22semidirect
30. #14583179C22semidirect
34. #14583096C22semidirect
35. #14583096C22semidirect
39. #14583029C22semidirect
42. D4×C43⋊C8C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582644C22semidirect
49. #14582643C22semidirect
50. #14582643C22semidirect
51. #14582629C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
184. D8×C43SD16semidirect
254. D4×C43C2×SD16semidirect
282. C8×C43C2×SD16semidirect
394. C43#19763semidirect
519. D8#10621883semidirect
588. D4C2×#10621883semidirect
616. C8C2×#10621883semidirect

Maximal subgroups

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

subgroupindex
#191474922
#191464192
D4×#106218832
#191342212
#191340762
#191340022
#191339702
#191339342
#191337742
#191337112
#191336972
#191336652
#191334312
#191334192
D4×D8×C432
#1976343