Finite Group Databasebeta

← #25086060

Subgroups — #25086060

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#19147490C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3D4×#10621882C211yesmaximal, characteristic
4#19134222C211yesmaximal, characteristic, complemented
5#19134077C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19133968C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133772C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133698C211yesmaximal, characteristic, complemented
12#19133666C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16C22×#10621882—21no—
17#14583609C2211yescharacteristic, complemented
18D4×D172C2211yescharacteristic
19#14583305—21no—
20#14583295C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583271C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic, complemented
25#14583219—21no—
26#14583199—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583186—21no—
30#14583176C2211yescharacteristic, complemented
31#14583133—21no—
32#14583131—21no—
33#14583099C2211yescharacteristic, complemented
34#14583094C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583033—21no—
38#14583032—21no—
39#14583030C2211yescharacteristic, complemented
40#14583009—21no—
41C4×#10621882C2211yescharacteristic
42C8×D172C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic
44#102×D43—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, 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
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic, complemented
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic, complemented
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic, complemented
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic, complemented
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621883—41no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621882—44no—
76C2×#10621882D411yescharacteristic
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063303—41no—
83#13063301—21no—
84#13063300—21no—
85#13063299—21no—
86#13063295—41no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4⋊C4×D43—21no—
90#13063258—21no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063247—21no—
101#13063247—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246D411yescharacteristic
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—44no—
124C2×SD16×C43D411yescharacteristic
125C22×C8×C43—21no—
126C4⋊Q8×C43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
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×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C2×C22⋊D43—41no—
168D4×D43—42no—
169D4×D43—81no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—41no—
174C2×D172—42no—
175C2×D172—81no—
176C2×D172C2×D411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—41no—
179C2×Dic86—21no—
180SD16×C43—22no—
181SD16×C43—42no—
182SD16×C43—42no—
183SD16×C43—42no—
184SD16×C43—81no—
185C2×C8×C43—21no—
186C2×C8×C43—42no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C42×C43—21no—
201C42×C43C2411yescharacteristic
202#10621884—81no—
203#10621883—82no—
204#10621882—42no—
205#10621882—42no—
206#10621882—42no—
207#10621882—81no—
208#10621882SD1614yescomplemented
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—41no—
211(C2×D43)⋊C4—41no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C2×D411yescharacteristic
215Dic43⋊C4—41no—
216Dic43⋊C4—41no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×D411yescharacteristic
224C8×D43—81no—
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—41no—
239Q8×C43—41no—
240Q8×C43—82no—
241D4×C43—21no—
242D4×C43—21no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—81no—
248D4×C43—82no—
249D4×C43—82no—
250D4×C43C2×SD1612yes—
251D4×C43AGL(1,ℤ/8)12yes—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—82no—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C22⋊D43—82no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268D172—21no—
269D172—41no—
270D172—41no—
271D172—41no—
272D172—41no—
273D172—81no—
274D172—82no—
275D172C2×SD1612yescomplemented
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—161no—
279Dic86—81no—
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#3295—431no—
322D4×SD16D4311yescharacteristic, complemented
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—21no—
344C22×D8—861no—
345#554—431no—
346D4×Q8C2×D4311yescharacteristic, complemented
347D42—431no—
348D42C2×D4311yescharacteristic
349#501—861no—
350#498—431no—
351#493—431no—
352#492—431no—
353#492C2×D4311yescharacteristic, complemented
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—861no—
363#465—21no—
364#465—861no—
365#461C2×D4311yescharacteristic
366#460—431no—
367#460C2×D4311yescharacteristic, complemented
368#459—431no—
369#459—431no—
370#450—21no—
371#450—861no—
372#448—21no—
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—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—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—861no—
399C22×D4—861no—
400C2×SD16—21no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—44no—
405C2×SD16—861no—
406C2×SD16—1721no—
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—21no—
418C4⋊Q8—431no—
419C4⋊Q8C22×D4311yescharacteristic
420#127—431no—
421#127C22×D4311yescharacteristic
422#125—861no—
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—861no—
440#107—431no—
441#107—861no—
442#106—861no—
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—21no—
453#103C22⋊D4311yescharacteristic
454#102—21no—
455#102—431no—
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—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—41no—
478C2×Q8—42no—
479C2×Q8—81no—
480C2×Q8—861no—
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—42no—
510SD16—42no—
511SD16—42no—
512SD16—81no—
513SD16—3442no—
514SD16—3441no—
515D8—434no—
516D8—3441no—
517D8—1722no—
518D8—1722no—
519D8—1722no—
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—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—41no—
536C4⋊C4—431no—
537C4⋊C4—861no—
538C4⋊C4—861no—
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—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—41no—
567Q8—41no—
568Q8—82no—
569Q8—3441no—
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×D4312yes—
589D4#1306335112yes—
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—82no—
600C2×C4—861no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—6881no—
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×#1306335111yescharacteristic
645C4#1458370211yescharacteristic
646C4#1458370511yescharacteristic
647C2—42no—
648C2—42no—
649C2—161no—
650C2—1722no—
651C2—6881no—
652C2#1914607111yescharacteristic
653C2SD16×C22⋊D4311yescharacteristic
654C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radicalD4×#10621882C2
hypercenterD4×SD16D43
hypocenterC43#19763
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #19147490C2semidirect
2. #19146421C2semidirect
4. #19134222C2semidirect
5. #19134077C2semidirect
6. #19134004C2semidirect
7. #19133968C2semidirect
8. #19133933C2semidirect
9. #19133772C2semidirect
10. #19133711C2semidirect
11. #19133698C2semidirect
12. #19133666C2semidirect
13. #19133432C2semidirect
14. #19133417C2semidirect
15. D4×SD16×C43C2semidirect
17. #14583609C22semidirect
20. #14583295C22semidirect
22. #14583271C22semidirect
23. #14583247C22semidirect
24. #14583246C22semidirect
28. #14583189C22semidirect
30. #14583176C22semidirect
33. #14583099C22semidirect
39. #14583030C22semidirect
42. C8×D172C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582621C22semidirect
57. D4×Q8×C43C22semidirect
59. C43×#492C22semidirect
62. C43×#460C22semidirect
66. C8×D4×C43C22semidirect
208. #10621882SD16semidirect
275. D172C2×SD16semidirect
288. C43⋊C8C2×SD16semidirect
322. D4×SD16D43semidirect
346. D4×Q8C2×D43semidirect
353. #492C2×D43semidirect
367. #460C2×D43semidirect
381. C8×D4C2×D43semidirect
394. C43#19763semidirect

Maximal subgroups

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

subgroupindex
#191474902
#191464212
D4×#106218822
#191342222
#191340772
#191340042
#191339682
#191339332
#191337722
#191337112
#191336982
#191336662
#191334322
#191334172
D4×SD16×C432
#1976343