Finite Group Databasebeta

← #25086065

Subgroups — #25086065

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#19147494C211yesmaximal, characteristic, complemented
2SD16×D172C211yesmaximal, characteristic, complemented
3D4×#10621882C211yesmaximal, characteristic
4#19134225C211yesmaximal, characteristic, complemented
5#19134077C211yesmaximal, characteristic, complemented
6#19134001C211yesmaximal, characteristic, complemented
7#19133972C211yesmaximal, characteristic, complemented
8#19133936C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133710C211yesmaximal, characteristic, complemented
11#19133696C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C22×#10621882—21no—
18Q8×D172C2211yescharacteristic, complemented
19D4×D172C2211yescharacteristic
20#14583309—21no—
21#14583295C2211yescharacteristic, complemented
22#14583275C2211yescharacteristic
23#14583273C2211yescharacteristic, complemented
24#14583272C2211yescharacteristic, complemented
25#14583245C2211yescharacteristic, complemented
26#14583196—21no—
27#14583189—21no—
28#14583186C2211yescharacteristic, complemented
29#14583179C2211yescharacteristic, complemented
30#14583133—21no—
31#14583129—21no—
32#14583104C2211yescharacteristic
33#14583099C2211yescharacteristic, complemented
34#14583094C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583051—21no—
37#14583039—21no—
38#14583033—21no—
39#14583032—21no—
40#14583030C2211yescharacteristic, complemented
41#14583009—21no—
42C4×#10621882C2211yescharacteristic
43C8×D172C2211yescharacteristic, complemented
44D4×C43⋊C8C2211yescharacteristic
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55#14582621C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic, complemented
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic, complemented
59C43×#481—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#460C2211yescharacteristic, complemented
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C2×#102×C43—21no—
67C2×Q8×D43—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621884—41no—
75SD16×D43—44no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80C2×#10621882—44no—
81C2×#10621882D411yescharacteristic
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84#13063325—21no—
85#13063325C2311yescharacteristic
86#13063322C2311yescharacteristic
87#13063305—21no—
88#13063305—41no—
89#13063300—21no—
90#13063299—21no—
91#13063295—41no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94#13063258—21no—
95#13063258D411yescharacteristic
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103#13063248—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—41no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114#13063236—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43D411yescharacteristic
121C22×C8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43C2311yescharacteristic
124#125×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—41no—
127#121×C43—21no—
128#121×C43—21no—
129#120×C43—41no—
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43D411yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C23×D43—41no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—41no—
164C2×C22⋊D43—41no—
165Q8×D43—42no—
166Q8×D43—81no—
167D4×D43—42no—
168D4×D43—81no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—41no—
173C2×D172—42no—
174C2×D172—81no—
175C2×D172C2×D411yescharacteristic
176C2×C4×D43—21no—
177C2×C4×D43—41no—
178C2×Dic86—21no—
179C2×Dic86—41no—
180SD16×C43—22no—
181SD16×C43—81no—
182C2×C8×C43—21no—
183C2×C8×C43—81no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43C2411yescharacteristic
200#10621884—42no—
201#10621884—82no—
202#10621883—42no—
203#10621882—42no—
204#10621882—42no—
205#10621882—42no—
206#10621882—81no—
207#10621882SD1614yescomplemented
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—41no—
210(C2×D43)⋊C4—41no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—41no—
214C4⋊Dic43C2×D411yescharacteristic
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—42no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222#10621873—42no—
223#10621873—81no—
224C8×D43—42no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—41no—
228C23×C43—82no—
229C23×C43—82no—
230C23×C43—161no—
231C22×D43—21no—
232C22×D43—41no—
233C22×D43—82no—
234C22×D43—82no—
235C22×D43—161no—
236Q8×C43—21no—
237Q8×C43—21no—
238Q8×C43—81no—
239D4×C43—21no—
240D4×C43—21no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—81no—
246D4×C43—82no—
247D4×C43—82no—
248D4×C43C2×SD1612yescomplemented
249D4×C43AGL(1,ℤ/8)12yes—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—161no—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C22⋊D43—82no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266D172—21no—
267D172—41no—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—81no—
272D172—82no—
273D172C2×SD1612yes—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—82no—
277Dic86—41no—
278Dic86—41no—
279Dic86—82no—
280C8×C43—21no—
281C8×C43—21no—
282C8×C43—41no—
283C43⋊C8—21no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288C43⋊C8C2×SD1612yescomplemented
289#19763—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—164no—
300C22×C43D4211yescharacteristic
301C2×D43—22no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—164no—
308C4×C43—21no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43C22×SD1611yescharacteristic
315C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
316C4×C43#57611yescharacteristic
317C4×C43#57711yescharacteristic
318Dic43—41no—
319Dic43—81no—
320#3384—431no—
321#3295D4311yescharacteristic, complemented
322D4×SD16—431no—
323D4×D8—431no—
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—161no—
338C2×C43#326411yescharacteristic
339C2×C43D4×SD1611yescharacteristic
340C2×C43#328811yescharacteristic
341D43—42no—
342D43—161no—
343C22×SD16—861no—
344C22×D8—861no—
345#554C2×D4311yescharacteristic, complemented
346D4×Q8—431no—
347D42—431no—
348D42C2×D4311yescharacteristic
349#501—861no—
350#498—431no—
351#493—431no—
352#492—431no—
353#492—431no—
354#486—431no—
355#486C2×D4311yescharacteristic, complemented
356#481—21no—
357#478—861no—
358#476—431no—
359#476—861no—
360#476C2×D4311yescharacteristic
361#474—431no—
362#466—861no—
363#465—21no—
364#465—861no—
365#461—431no—
366#460—431no—
367#460C2×D4311yescharacteristic, complemented
368#459—431no—
369#459—431no—
370#450—21no—
371#450—861no—
372#448—861no—
373#447—861no—
374#447—861no—
375#446—431no—
376#442—861no—
377C4×SD16C2×D4311yescharacteristic
378C4×D8—431no—
379C8×D4—431no—
380C8×D4—431no—
381C8×D4C2×D4311yescharacteristic, complemented
382C2×#102—21no—
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—861no—
399C22×D4—861no—
400C2×SD16—21no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16—861no—
405C2×SD16—1721no—
406C2×SD16—1724no—
407C2×SD16C22⋊D4311yescharacteristic
408C2×D8—431no—
409C2×D8—861no—
410C2×D8—861no—
411C2×D8—861no—
412C2×D8—861no—
413C2×D8—1724no—
414C22×C8—21no—
415C22×C8—861no—
416C22×C8—861no—
417C4⋊Q8—431no—
418C4⋊Q8—861no—
419C4⋊Q8C22×D4311yescharacteristic
420#127—431no—
421#127C22×D4311yescharacteristic
422#125—21no—
423C22⋊Q8—21no—
424C22⋊Q8—41no—
425C22⋊Q8—861no—
426C22⋊Q8—1721no—
427#121—21no—
428#121—21no—
429#121—861no—
430#121—861no—
431#120—41no—
432#120—1721no—
433C4×Q8C22×D4311yescharacteristic
434C4×D4—21no—
435C4×D4—431no—
436C4×D4—861no—
437C4×D4C22×D4311yescharacteristic
438C4×D4C22×D4311yescharacteristic
439C2×C4⋊C4—21no—
440#107—431no—
441#107—861no—
442#106—21no—
443#106—861no—
444#106—861no—
445#106—861no—
446#106C22⋊D4311yescharacteristic
447C4⋊C8—431no—
448C4⋊C8—431no—
449C4⋊C8—431no—
450C4⋊C8—861no—
451C4⋊C8C22×D4311yescharacteristic
452#103—861no—
453#103C22⋊D4311yescharacteristic
454#102—21no—
455#102—21no—
456#102—21no—
457#102—21no—
458#102—431no—
459#102—431no—
460#102—861no—
461#102—861no—
462#102—861no—
463#102—861no—
464#102—861no—
465#102—1721no—
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—1721no—
476C2×Q8—21no—
477C2×Q8—861no—
478C2×Q8—3441no—
479C2×Q8—1721no—
480C2×Q8—1722no—
481C2×Q8C2×C22⋊D4311yescharacteristic
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4—431no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—3441no—
496C2×D4—3441no—
497C2×D4—1721no—
498C2×D4—1722no—
499C2×D4—1721no—
500C2×D4—1722no—
501C2×D4D4×D4311yescharacteristic
502C2×D4C2×C22⋊D4311yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—41no—
506C22×C4—861no—
507C22×C4—1721no—
508SD16—22no—
509SD16—81no—
510SD16—3441no—
511SD16—3442no—
512SD16—1722no—
513SD16—1722no—
514SD16—1722no—
515D8—434no—
516D8—3441no—
517D8—1722no—
518D8—1722no—
519D8—1722no—
520C2×C8—21no—
521C2×C8—81no—
522C2×C8—431no—
523C2×C8—431no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—1722no—
529C2×C8—1722no—
530C2×C8C2×C22⋊D4311yescharacteristic
531C2×C8C2×C22⋊D4311yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—431no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—1721no—
541C4⋊C4D4×D4311yescharacteristic
542C4⋊C4C2×C22⋊D4311yescharacteristic
543C4⋊C4C2×C22⋊D4311yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—861no—
549C22⋊C4—1721no—
550C22⋊C4—1721no—
551C42—21no—
552C42C23×D4311yescharacteristic
553C23—21no—
554C23—21no—
555C23—41no—
556C23—82no—
557C23—82no—
558C23—161no—
559C23—861no—
560C23—3442no—
561C23—3442no—
562C23—1721no—
563C23—6881no—
564Q8—21no—
565Q8—21no—
566Q8—81no—
567Q8—3442no—
568Q8—1721no—
569Q8—1721no—
570D4—21no—
571D4—21no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—81no—
577D4—82no—
578D4—82no—
579D4—432no—
580D4—861no—
581D4—3441no—
582D4—3442no—
583D4—3442no—
584D4—1721no—
585D4—1721no—
586D4—1721no—
587D4—1721no—
588D4SD16×D4312yescomplemented
589D4#1306335012yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—161no—
600C2×C4—861no—
601C2×C4—3442no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4C22×C22⋊D4311yescharacteristic
607C2×C4#1306337011yescharacteristic
608C8—21no—
609C8—21no—
610C8—41no—
611C8—432no—
612C8—861no—
613C8—1721no—
614C8—1721no—
615C8—1721no—
616C8—1721no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—164no—
627C22—862no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—1721no—
632C22—1721no—
633C22—6884no—
634C22D4×C22⋊D4311yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—3441no—
642C4—1721no—
643C4C2×SD16×D4311yescharacteristic
644C4C2×#1306335011yescharacteristic
645C4#1458370211yescharacteristic
646C4#1458370511yescharacteristic
647C2—42no—
648C2—42no—
649C2—161no—
650C2—1722no—
651C2—6881no—
652C2#1914607611yescharacteristic
653C2SD16×C22⋊D4311yescharacteristic
654C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
prime radicalD4×#10621882C2
hypercenter#3295D43
hypocenterC43#19763
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #19147494C2semidirect
2. SD16×D172C2semidirect
4. #19134225C2semidirect
5. #19134077C2semidirect
6. #19134001C2semidirect
7. #19133972C2semidirect
8. #19133936C2semidirect
9. #19133774C2semidirect
10. #19133710C2semidirect
11. #19133696C2semidirect
12. #19133667C2semidirect
13. #19133432C2semidirect
14. #19133417C2semidirect
15. C43×#3295C2semidirect
18. Q8×D172C22semidirect
21. #14583295C22semidirect
23. #14583273C22semidirect
24. #14583272C22semidirect
25. #14583245C22semidirect
28. #14583186C22semidirect
29. #14583179C22semidirect
33. #14583099C22semidirect
40. #14583030C22semidirect
43. C8×D172C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582621C22semidirect
56. C43×#554C22semidirect
58. C43×#486C22semidirect
62. C43×#460C22semidirect
65. C8×D4×C43C22semidirect
207. #10621882SD16semidirect
248. D4×C43C2×SD16semidirect
288. C43⋊C8C2×SD16semidirect
321. #3295D43semidirect
345. #554C2×D43semidirect
355. #486C2×D43semidirect
367. #460C2×D43semidirect
381. C8×D4C2×D43semidirect
394. C43#19763semidirect
588. D4SD16×D43semidirect

Maximal subgroups

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

subgroupindex
#191474942
SD16×D1722
D4×#106218822
#191342252
#191340772
#191340012
#191339722
#191339362
#191337742
#191337102
#191336962
#191336672
#191334322
#191334172
C43×#32952
#1976343