Finite Group Databasebeta

← #25086058

Subgroups — #25086058

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#19146413C211yesmaximal, characteristic, complemented
2D4×#10621884C211yesmaximal, characteristic, complemented
3D8×D172C211yesmaximal, characteristic
4#19134224C211yesmaximal, characteristic, complemented
5#19134079C211yesmaximal, characteristic, complemented
6#19134006C211yesmaximal, characteristic, complemented
7#19133967C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133773C211yesmaximal, characteristic, complemented
10#19133710C211yesmaximal, characteristic, complemented
11#19133698C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133429C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3384C211yesmaximal, characteristic, complemented
16C22×#10621884—21no—
17C2×D8×D43—21no—
18D4×D172C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583276C2211yescharacteristic
21#14583273C2211yescharacteristic, complemented
22#14583273C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic, complemented
24#14583247C2211yescharacteristic, complemented
25#14583217—21no—
26#14583186C2211yescharacteristic
27#14583136—21no—
28#14583130—21no—
29#14583130—21no—
30#14583101C2211yescharacteristic
31#14583099C2211yescharacteristic, complemented
32#14583099C2211yescharacteristic, complemented
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583049—21no—
36#14583049—21no—
37#14583038—21no—
38#14583034—21no—
39#14583034—21no—
40C4×#10621884C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063245—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582642C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic, complemented
57D4×Q8×C43C2211yescharacteristic, complemented
58C43×#501—21no—
59C43×#498C2211yescharacteristic, complemented
60C43×#478—21no—
61C43×#476—21no—
62C43×#476C2211yescharacteristic, complemented
63C43×#474C2211yescharacteristic, complemented
64C43×#446C2211yescharacteristic, complemented
65C43×#442—21no—
66C4×D8×C43C2211yescharacteristic
67C22×D172—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—41no—
77C2×#10621884—44no—
78C2×#10621884D411yescharacteristic
79C2×D344—21no—
80C2×D344—21no—
81C2×#10621882—21no—
82C2×#10621882—21no—
83D8×D43—44no—
84C22×C43⋊C8—21no—
85C22×C43⋊C8—21no—
86C2×C8×D43—21no—
87#13063322C2311yescharacteristic
88#13063322C2311yescharacteristic
89#13063300—21no—
90#13063300—21no—
91#13063299—21no—
92#13063299—21no—
93#13063295—41no—
94#13063295—41no—
95C4×D172C2311yescharacteristic
96#13063256—21no—
97#13063256D411yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C22×Q8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144#97×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C23×D43—41no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162D4×D43—42no—
163D4×D43—42no—
164D4×D43—81no—
165D4×D43—81no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—41no—
173C2×D172—41no—
174C2×D172—42no—
175C2×D172—42no—
176C2×D172—81no—
177C2×D172—81no—
178C2×D172C2×D411yescharacteristic
179C2×C4×D43—21no—
180D8×C43SD1614yescomplemented
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43C2411yescharacteristic
201#10621884—22no—
202#10621884—42no—
203#10621884—42no—
204#10621884—42no—
205#10621884—81no—
206#10621884—81no—
207#10621884—82no—
208#10621882—42no—
209#10621882—42no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—41no—
212(C2×D43)⋊C4—41no—
213C4⋊Dic43C2×D411yescharacteristic
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—42no—
219C2×C43⋊C8—81no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222D344—42no—
223D344—81no—
224C8×D43—42no—
225C23×C43—21no—
226C23×C43—21no—
227C22×D43—21no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43—82no—
233C22×D43—82no—
234C22×D43—161no—
235C22×D43—161no—
236Q8×C43—21no—
237Q8×C43—21no—
238Q8×C43—41no—
239Q8×C43—41no—
240Q8×C43—81no—
241Q8×C43—82no—
242D4×C43—21no—
243D4×C43—21no—
244D4×C43C2×SD1612yes—
245D4×C43C2×SD1612yescomplemented
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—82no—
257C2×C4×C43—161no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C22⋊D43—82no—
262C22⋊D43—82no—
263C2×Dic43—21no—
264D172—21no—
265D172—41no—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—41no—
272D172—41no—
273D172—81no—
274D172—81no—
275D172—82no—
276D172—82no—
277D172AGL(1,ℤ/8)12yes—
278C4×D43—41no—
279C4×D43—41no—
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—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43D4211yescharacteristic
297C2×D43—22no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—164no—
307C2×D43—164no—
308C4×C43—21no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43C22×SD1611yescharacteristic
316C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
317C4×C43#57611yescharacteristic
318C4×C43#57711yescharacteristic
319Dic43—41no—
320#3384D4311yescharacteristic, complemented
321#3295—431no—
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#326411yescharacteristic
338C2×C43D4×SD1611yescharacteristic
339C2×C43#328811yescharacteristic
340D43—42no—
341D43—161no—
342D43—161no—
343C22×SD16—861no—
344C22×D8—861no—
345#554C2×D4311yescharacteristic, complemented
346D4×Q8C2×D4311yescharacteristic, complemented
347D42—431no—
348D42—431no—
349#501—21no—
350#498C2×D4311yescharacteristic, complemented
351#493—431no—
352#492—431no—
353#492—431no—
354#486—431no—
355#486—431no—
356#481—861no—
357#478—21no—
358#476—21no—
359#476—431no—
360#476C2×D4311yescharacteristic, complemented
361#474C2×D4311yescharacteristic, complemented
362#466—861no—
363#465—861no—
364#465—861no—
365#461—431no—
366#460—431no—
367#460—431no—
368#459—431no—
369#459—431no—
370#450—861no—
371#450—861no—
372#448—861no—
373#447—861no—
374#447—861no—
375#446C2×D4311yescharacteristic, complemented
376#442—21no—
377C4×SD16—431no—
378C4×D8C2×D4311yescharacteristic
379C8×D4—431no—
380C8×D4—431no—
381C8×D4—431no—
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—861no—
397C22×D4—861no—
398C22×D4—861no—
399C22×D4—861no—
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—861no—
409C2×D8—861no—
410C2×D8—861no—
411C2×D8—861no—
412C2×D8—1724no—
413C2×D8C22⋊D4311yescharacteristic
414C22×C8—861no—
415C22×C8—861no—
416C22×C8—861no—
417C4⋊Q8—21no—
418C4⋊Q8C22×D4311yescharacteristic
419C4⋊Q8C22×D4311yescharacteristic
420#127—431no—
421#127—431no—
422#125—21no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—41no—
426C22⋊Q8—41no—
427#121—861no—
428#121—861no—
429#121—861no—
430#121—861no—
431#120—1721no—
432#120—1721no—
433C4×Q8C22×D4311yescharacteristic
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—431no—
437C4×D4C22×D4311yescharacteristic
438C4×D4C22×D4311yescharacteristic
439C2×C4⋊C4—21no—
440#107—21no—
441#107C22⋊D4311yescharacteristic
442#106—21no—
443#106—21no—
444#106—21no—
445#106—431no—
446#106—861no—
447C4⋊C8—21no—
448C4⋊C8—431no—
449C4⋊C8—431no—
450C4⋊C8—431no—
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—861no—
468C22⋊C8—861no—
469C22⋊C8—861no—
470#97—21no—
471C4×C8—431no—
472C4×C8—431no—
473C4×C8C22×D4311yescharacteristic
474C24—1721no—
475C24—1721no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—41no—
479C2×Q8—42no—
480C2×Q8—81no—
481C2×Q8D4×D4311yescharacteristic
482C2×D4—431no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—3441no—
490C2×D4—3441no—
491C2×D4—3441no—
492C2×D4—3441no—
493C2×D4—1721no—
494C2×D4—1721no—
495C2×D4—1722no—
496C2×D4—1722no—
497C2×D4—1721no—
498C2×D4—1721no—
499C2×D4—1722no—
500C2×D4—1722no—
501C2×D4C2×C22⋊D4311yescharacteristic
502C2×D4C2×C22⋊D4311yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—861no—
508SD16—862no—
509SD16—3441no—
510SD16—3442no—
511SD16—3441no—
512SD16—1722no—
513SD16—1722no—
514SD16—1722no—
515D8—3441no—
516D8—1722no—
517D8—1722no—
518D8—1722no—
519D8#1062188414yescomplemented
520C2×C8—21no—
521C2×C8—431no—
522C2×C8—431no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—3441no—
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—21no—
536C4⋊C4—21no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—431no—
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—861no—
556C23—3442no—
557C23—3442no—
558C23—3442no—
559C23—3442no—
560C23—1721no—
561C23—1721no—
562C23—6881no—
563C23—6881no—
564Q8—21no—
565Q8—21no—
566Q8—41no—
567Q8—41no—
568Q8—81no—
569Q8—82no—
570D4—21no—
571D4—21no—
572D4—432no—
573D4—861no—
574D4—3441no—
575D4—3441no—
576D4—3442no—
577D4—3442no—
578D4—3442no—
579D4—3442no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583D4—1721no—
584D4—1721no—
585D4—1721no—
586D4—1721no—
587D4—1721no—
588D4C2×#1062188412yes—
589D4C2×#1062188412yescomplemented
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—41no—
600C2×C4—82no—
601C2×C4—161no—
602C2×C4—861no—
603C2×C4—1721no—
604C2×C4—1721no—
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×#1062188412yescomplemented
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—862no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—1721no—
631C22—1721no—
632C22—6884no—
633C22—6884no—
634C22D4×C22⋊D4311yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—1721no—
643C4C22×#1062188411yescharacteristic
644C4AGL(1,ℤ/8)×D4311yescharacteristic
645C4#1458370311yescharacteristic
646C4#1458370711yescharacteristic
647C2—42no—
648C2—42no—
649C2—1722no—
650C2—6881no—
651C2—6881no—
652C2#1914606911yescharacteristic
653C2D4×#1062188411yescharacteristic
654C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3384C2
socleC22×C43D42
prime radicalD8×D172C2
hypercenter#3384D43
hypocenterC43#19763
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #19146413C2semidirect
2. D4×#10621884C2semidirect
4. #19134224C2semidirect
5. #19134079C2semidirect
6. #19134006C2semidirect
7. #19133967C2semidirect
8. #19133938C2semidirect
9. #19133773C2semidirect
10. #19133710C2semidirect
11. #19133698C2semidirect
12. #19133667C2semidirect
13. #19133429C2semidirect
14. #19133419C2semidirect
15. C43×#3384C2semidirect
21. #14583273C22semidirect
22. #14583273C22semidirect
23. #14583247C22semidirect
24. #14583247C22semidirect
31. #14583099C22semidirect
32. #14583099C22semidirect
42. D4×C43⋊C8C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582645C22semidirect
49. #14582642C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
56. C43×#554C22semidirect
57. D4×Q8×C43C22semidirect
59. C43×#498C22semidirect
62. C43×#476C22semidirect
63. C43×#474C22semidirect
64. C43×#446C22semidirect
180. D8×C43SD16semidirect
245. D4×C43C2×SD16semidirect
282. C8×C43C2×SD16semidirect
320. #3384D43semidirect
345. #554C2×D43semidirect
346. D4×Q8C2×D43semidirect
350. #498C2×D43semidirect
360. #476C2×D43semidirect
361. #474C2×D43semidirect
375. #446C2×D43semidirect
394. C43#19763semidirect
519. D8#10621884semidirect
589. D4C2×#10621884semidirect
616. C8C2×#10621884semidirect

Maximal subgroups

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

subgroupindex
#191464132
D4×#106218842
D8×D1722
#191342242
#191340792
#191340062
#191339672
#191339382
#191337732
#191337102
#191336982
#191336672
#191334292
#191334192
C43×#33842
#1976343