Finite Group Databasebeta

← #25250371

Subgroups — #25250371

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#135×D43C211yesmaximal, characteristic, complemented
2C2×#14583329C211yesmaximal, characteristic, complemented
3#19144172C211yesmaximal, characteristic, complemented
4#19136534C211yesmaximal, characteristic, complemented
5#19136532C211yesmaximal, characteristic, complemented
6#19136527C211yesmaximal, characteristic, complemented
7#19136522C211yesmaximal, characteristic, complemented
8#19136517C211yesmaximal, characteristic, complemented
9#19136515C211yesmaximal, characteristic, complemented
10#19136510C211yesmaximal, characteristic, complemented
11#19136505C211yesmaximal, characteristic, complemented
12#19136303C211yesmaximal, characteristic, complemented
13#19136302C211yesmaximal, characteristic, complemented
14C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
15C2×C43×#508C211yesmaximal, characteristic, complemented
16C2×#41×D43—21no—
17C2×#13063348C2211yescharacteristic
18C2×#13063347C2211yescharacteristic
19C2×#13063346—21no—
20C2×#13063345—21no—
21C2×#13063344C2211yescharacteristic
22#135×D43—24no—
23#135×D43—24no—
24C2×Q16×D43C2211yescharacteristic
25C2×SD16×D43—21no—
26C2×D8×D43C2211yescharacteristic
27C22×C8×D43C2211yescharacteristic
28#14583406—21no—
29#14583329—24no—
30C2×#13063271C2211yescharacteristic, complemented
31C2×#13063269C2211yescharacteristic, complemented
32C2×#13063268C2211yescharacteristic, complemented
33C2×#13063266C2211yescharacteristic, complemented
34C22×C43⋊C16C2211yescharacteristic, complemented
35#14583137C2211yescharacteristic
36#14583137C2211yescharacteristic, complemented
37#14583132C2211yescharacteristic
38#14583132C2211yescharacteristic, complemented
39#14583125—21no—
40#14583125—21no—
41#14582937C2211yescharacteristic, complemented
42#14582895—21no—
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582703C2211yescharacteristic, complemented
47#14582701C2211yescharacteristic, complemented
48#14582701C2211yescharacteristic, complemented
49#14582700C2211yescharacteristic, complemented
50#14582700C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic
52(C2×D43)⋊C16C2211yescharacteristic
53(C2×D43)⋊C16C2211yescharacteristic, complemented
54(C2×D43)⋊C16C2211yescharacteristic, complemented
55C2×#135×C43C2211yescharacteristic
56C2×#135×C43C2211yescharacteristic, complemented
57C43×#508—24no—
58C2×Q32×C43C2211yescharacteristic, complemented
59C2×SD32×C43C2211yescharacteristic, complemented
60C2×SD32×C43C2211yescharacteristic, complemented
61C2×D16×C43C2211yescharacteristic, complemented
62C22×C16×C43C2211yescharacteristic, complemented
63C2×#10621902—21no—
64C2×#10621898—21no—
65C2×#10621898—41no—
66C2×#10621900—21no—
67C2×#10621900—41no—
68#41×D43—28no—
69#41×D43—44no—
70C2×Q8×D43—21no—
71C2×D4×D43—21no—
72C2×D4×D43—41no—
73C22×C4×D43—41no—
74C22×C4×D43D411yescharacteristic
75#13063348—22no—
76#13063348—22no—
77#13063347—22no—
78#13063347D414yescomplemented
79#13063346—28no—
80#13063345—28no—
81#13063344—22no—
82#13063344—22no—
83C2×Dic172C2311yescharacteristic
84C2×#10621885—21no—
85Q16×D43—22no—
86Q16×D43—22no—
87C2×#10621873—21no—
88C2×#10621883—21no—
89C2×#10621884—21no—
90SD16×D43—28no—
91C2×D344C2311yescharacteristic
92C2×#10621882—21no—
93D8×D43—22no—
94D8×D43—22no—
95C22×C43⋊C8D411yescharacteristic
96C2×C8×D43—22no—
97C2×C8×D43—22no—
98C2×C8×D43D411yescharacteristic
99C2×C8×D43D411yescharacteristic
100C2×C8×D43C2311yescharacteristic
101C2×C8×D43C2311yescharacteristic
102#13063306—41no—
103#13063301—21no—
104#13063301—21no—
105#13063296—21no—
106#13063296—21no—
107#13063293—41no—
108C4×C22⋊D43—41no—
109C4×C22⋊D43—41no—
110#13063284—21no—
111#13063271—22no—
112#13063269—22no—
113#13063268—22no—
114#13063266—22no—
115C2×C43⋊C16—22no—
116C2×C43⋊C16C2311yescharacteristic
117C2×C43⋊C16C2311yescharacteristic
118#13063259C2311yescharacteristic
119#13063259C2311yescharacteristic
120#13063257—21no—
121#13063249—21no—
122#13063249—21no—
123#13063246—21no—
124#13063246—21no—
125C2×#41×C43—21no—
126C2×#41×C43—21no—
127#135×C43—22no—
128#135×C43—22no—
129#135×C43—22no—
130#135×C43D414yescomplemented
131C2×Q16×C43C2311yescharacteristic
132C2×Q16×C43C2311yescharacteristic
133C2×SD16×C43—21no—
134C2×SD16×C43—21no—
135C2×D8×C43C2311yescharacteristic
136C2×D8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138Q32×C43—22no—
139SD32×C43—22no—
140SD32×C43—22no—
141D16×C43—22no—
142C2×C16×C43—22no—
143C2×C16×C43C2311yescharacteristic
144C2×C16×C43C2311yescharacteristic
145C23×D43—41no—
146C23×D43D811yescharacteristic
147#41×C43—24no—
148#41×C43—42no—
149#41×C43—42no—
150#41×C43—42no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165C22×Dic43—41no—
166C22×Dic43D811yescharacteristic
167#10621902—24no—
168#10621902—42no—
169Q8×D43—24no—
170Q8×D43—42no—
171#10621900—24no—
172#10621900—42no—
173#10621900—48no—
174D4×D43—24no—
175D4×D43—48no—
176D4×D43—42no—
177#10621898—24no—
178#10621898—48no—
179#10621898—42no—
180C2×D172—21no—
181C2×D172—41no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—48no—
185C2×C4×D43—41no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188C2×C4×D43D811yescharacteristic
189C2×C4×D43D811yescharacteristic
190C2×C4×D43C2×D411yescharacteristic
191C2×C4×D43C2×D411yescharacteristic
192C2×Dic86—21no—
193C2×Dic86—41no—
194Q16×C43—21no—
195Q16×C43—21no—
196Q16×C43—21no—
197Q16×C43C2×D412yes—
198SD16×C43—24no—
199SD16×C43—42no—
200D8×C43—21no—
201D8×C43—21no—
202D8×C43—21no—
203D8×C43C2×D412yes—
204C2×C8×C43C2×D411yescharacteristic
205C2×C8×C43C2×D412yes—
206C2×C8×C43C2×D412yes—
207C2×C8×C43C2411yescharacteristic
208C22⋊Dic43—41no—
209C22⋊Dic43—41no—
210C22⋊Dic43—41no—
211#10621885—24no—
212#10621884—24no—
213#10621883—24no—
214#10621882—24no—
215(C2×D43)⋊C4—41no—
216(C2×D43)⋊C4—41no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219Dic43⋊C4—41no—
220Dic43⋊C4—41no—
221C4×Dic43—41no—
222C2×C43⋊C8—22no—
223C2×C43⋊C8C2×D411yescharacteristic
224C2×C43⋊C8C2×D411yescharacteristic
225Dic172—21no—
226Dic172C2×D412yes—
227D344—21no—
228D344C2×D412yes—
229#10621873—24no—
230C8×D43—22no—
231C8×D43—22no—
232C8×D43—21no—
233C8×D43—21no—
234C8×D43—21no—
235C8×D43—21no—
236C16×C43—21no—
237C16×C43—21no—
238C43⋊C16—21no—
239C43⋊C16—21no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43C2×D811yescharacteristic
243C22×D43—22no—
244C22×D43—22no—
245C22×D43—41no—
246C22×D43—44no—
247C22×D43—41no—
248C22×D43—82no—
249C22×D43—82no—
250C22×D43C2×D811yescharacteristic
251C22×D43C2×D811yescharacteristic
252Q8×C43—22no—
253Q8×C43—41no—
254Q8×C43—41no—
255Q8×C43—41no—
256D4×C43—22no—
257D4×C43—44no—
258D4×C43—41no—
259D4×C43—41no—
260D4×C43—41no—
261D4×C43—82no—
262C2×C4×C43—41no—
263C2×C4×C43—44no—
264C2×C4×C43—41no—
265C2×C4×C43—82no—
266C2×C4×C43#12012yes—
267C2×C4×C43C2×D811yescharacteristic
268C2×C4×C43AGL(1,ℤ/8)12yes—
269C2×C4×C43C22×D411yescharacteristic
270C22⋊D43—44no—
271C22⋊D43—44no—
272C22⋊D43—44no—
273C22⋊D43—82no—
274C22⋊D43—82no—
275C2×Dic43—22no—
276C2×Dic43—44no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C2×D811yescharacteristic
281C2×Dic43C2×D811yescharacteristic
282D172—22no—
283D172—44no—
284D172—41no—
285C4×D43—21no—
286C4×D43—21no—
287C4×D43—21no—
288C4×D43—21no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—44no—
292C4×D43—44no—
293C4×D43—44no—
294Dic86—22no—
295Dic86—44no—
296Dic86—41no—
297C8×C43#12012yes—
298C8×C43C22×D411yescharacteristic
299C8×C43C22×D411yescharacteristic
300C43⋊C8—21no—
301C43⋊C8—21no—
302#33516—431nomaximal, Sylow
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—42no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43#44712yes—
312C22×C43C22×D811yescharacteristic
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—44no—
319C2×D43—42no—
320C2×D43—88no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43#50812yescomplemented
324C4×C43—42no—
325C4×C43—81no—
326C4×C43#44712yes—
327C4×C43C2×#12011yescharacteristic
328C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
329Dic43—21no—
330Dic43—21no—
331Dic43—42no—
332Dic43—81no—
333Dic43—81no—
334C22×#135—431no—
335C2×#508—431no—
336C2×#508D4311yescharacteristic, complemented
337#3050—431no—
338#2189—431no—
339#2189—431no—
340#2188—431no—
341#2187—431no—
342#2186—431no—
343#2186—431no—
344#2185—431no—
345#2184—431no—
346#2138—431no—
347#2138—431no—
348C2×C22⋊C16—431no—
349C2×C43—22no—
350C2×C43—82no—
351C2×C43—161no—
352C2×C43C2×#44711yescharacteristic
353C2×C43C2×#50811yescharacteristic
354C2×C43#341411yescharacteristic
355D43—22no—
356D43—41no—
357D43—82no—
358C22×#41—861no—
359C2×#135—431no—
360C2×#135—431no—
361C2×#135—431no—
362C2×#135—861no—
363C2×#135—861no—
364C2×#135—864no—
365C2×#135—864no—
366C2×#135C2×D4311yescharacteristic
367C2×#135C2×D4311yescharacteristic, complemented
368C22×Q16—431no—
369C22×SD16—861no—
370C22×D8—431no—
371C23×C8—431no—
372#525—861no—
373#508—24no—
374#508—864no—
375C2×Q32—431no—
376C2×Q32C2×D4311yescharacteristic, complemented
377C2×SD32—431no—
378C2×SD32—431no—
379C2×SD32C2×D4311yescharacteristic, complemented
380C2×SD32C2×D4311yescharacteristic, complemented
381C2×D16—431no—
382C2×D16C2×D4311yescharacteristic, complemented
383C22×C16—431no—
384C22×C16C2×D4311yescharacteristic, complemented
385#467—431no—
386#467—431no—
387#466—431no—
388#466—431no—
389#465—861no—
390#465—861no—
391#427—431no—
392#416—861no—
393#358—431no—
394#358—431no—
395#358—431no—
396#358—431no—
397#357—431no—
398#357—431no—
399#357—431no—
400#357—431no—
401C22⋊C16—431no—
402C22⋊C16—431no—
403C22⋊C16—431no—
404C22⋊C16—431no—
405C43#3351611yescharacteristic, complemented, Sylow
406C2×#41—21no—
407C2×#41—21no—
408C2×#41—861no—
409C2×#41—861no—
410C2×#41—868no—
411C2×#41—861no—
412C2×#41—1721no—
413C2×#41—1721no—
414C2×#41—1724no—
415C22×Q8—861no—
416C22×D4—861no—
417C22×D4—1721no—
418C23×C4—431no—
419C23×C4—1721no—
420#135—22no—
421#135—22no—
422#135—22no—
423#135—434no—
424#135—862no—
425#135—862no—
426#135—868no—
427#135—868no—
428#135—862no—
429#135—862no—
430#135—862no—
431#135C22⋊D4314yescomplemented
432C2×Q16—431no—
433C2×Q16—861no—
434C2×Q16—862no—
435C2×Q16—862no—
436C2×Q16C22×D4311yescharacteristic
437C2×Q16C22×D4311yescharacteristic
438C2×SD16—21no—
439C2×SD16—21no—
440C2×SD16—861no—
441C2×SD16—861no—
442C2×SD16—868no—
443C2×SD16—861no—
444C2×D8—431no—
445C2×D8—861no—
446C2×D8—862no—
447C2×D8—862no—
448C2×D8C22×D4311yescharacteristic
449C2×D8C22×D4311yescharacteristic
450C22×C8—431no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—862no—
456C22×C8—862no—
457C22×C8C22×D4311yescharacteristic
458#123—1721no—
459C22⋊Q8—861no—
460C22⋊Q8—861no—
461#121—861no—
462#121—861no—
463#120—1721no—
464C4×D4—1721no—
465C4×D4—1721no—
466#117—861no—
467Q32—22no—
468Q32—862no—
469SD32—22no—
470SD32—22no—
471SD32—862no—
472SD32—862no—
473D16—22no—
474D16—862no—
475C2×C16—22no—
476C2×C16—431no—
477C2×C16—431no—
478C2×C16—862no—
479C2×C16C22×D4311yescharacteristic
480C2×C16C22×D4311yescharacteristic
481#107—431no—
482#107—431no—
483#106—861no—
484#103—861no—
485#103—861no—
486#102—861no—
487#102—861no—
488C24—431no—
489C24—1721no—
490#41—24no—
491#41—42no—
492#41—42no—
493#41—42no—
494#41—864no—
495#41—864no—
496#41—864no—
497#41—1728no—
498#41—1728no—
499#41—1722no—
500#41—1722no—
501#41—1722no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—864no—
505C2×Q8—861no—
506C2×Q8—1721no—
507C2×Q8—1722no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—864no—
513C2×D4—861no—
514C2×D4—1721no—
515C2×D4—1721no—
516C2×D4—1722no—
517C2×D4—1728no—
518C2×D4—1721no—
519C2×D4—1721no—
520C2×D4—1721no—
521C2×D4—1721no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—1721no—
532C22×C4—1728no—
533C22×C4—1721no—
534C22×C4—1721no—
535C22×C4—1721no—
536C22×C4D4×D4311yescharacteristic
537Q16—21no—
538Q16—21no—
539Q16—21no—
540Q16—432no—
541Q16—864no—
542Q16—861no—
543Q16C2×C22⋊D4312yes—
544SD16—24no—
545SD16—42no—
546SD16—864no—
547SD16—864no—
548SD16—864no—
549D8—21no—
550D8—21no—
551D8—21no—
552D8—432no—
553D8—864no—
554D8—861no—
555D8C2×C22⋊D4312yes—
556C2×C8—431no—
557C2×C8—431no—
558C2×C8—862no—
559C2×C8—862no—
560C2×C8—862no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8D4×D4311yescharacteristic
566C2×C8D4×D4312yes—
567C2×C8C2×C22⋊D4312yes—
568C2×C8C23×D4311yescharacteristic
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—1721no—
572C4⋊C4—1721no—
573C22⋊C4—1721no—
574C22⋊C4—1721no—
575C22⋊C4—1721no—
576C22⋊C4—1721no—
577C22⋊C4—1721no—
578C42—1721no—
579C16—21no—
580C16—21no—
581C16—861no—
582C16—861no—
583C23—41no—
584C23—41no—
585C23—431no—
586C23—431no—
587C23—862no—
588C23—862no—
589C23—3442no—
590C23—3442no—
591C23—1721no—
592C23—1724no—
593C23—1721no—
594C23D8×D4311yescharacteristic
595Q8—22no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—862no—
600Q8—1724no—
601Q8—1721no—
602D4—22no—
603D4—44no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—82no—
608D4—862no—
609D4—3442no—
610D4—3442no—
611D4—1724no—
612D4—1724no—
613D4—1724no—
614D4—1724no—
615D4—1721no—
616C2×C4—41no—
617C2×C4—44no—
618C2×C4—41no—
619C2×C4—82no—
620C2×C4—431no—
621C2×C4—431no—
622C2×C4—862no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—1724no—
630C2×C4—1724no—
631C2×C4—1724no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1724no—
636C2×C4#1306329312yes—
637C2×C4D8×D4311yescharacteristic
638C2×C4#1306334912yes—
639C2×C4C2×D4×D4311yescharacteristic
640C8—861no—
641C8—861no—
642C8#1306329312yes—
643C8C2×D4×D4311yescharacteristic
644C8C22×C22⋊D4311yescharacteristic
645C22—21no—
646C22—21no—
647C22—42no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—432no—
654C22—861no—
655C22—861no—
656C22—861no—
657C22—861no—
658C22—861no—
659C22—3448no—
660C22—3441no—
661C22—3441no—
662C22—1724no—
663C22—1722no—
664C22#1458303112yes—
665C22C2×D8×D4311yescharacteristic
666C4—42no—
667C4—81no—
668C4—861no—
669C4—861no—
670C4—3441no—
671C4—3441no—
672C4—1722no—
673C4#1458303112yes—
674C4C2×#1306329311yescharacteristic
675C4C2×#1306334911yescharacteristic
676C2—22no—
677C2—82no—
678C2—161no—
679C2—862no—
680C2—3442no—
681C2—1721no—
682C2C2×#1458303111yescharacteristic
683C2#508×D4311yescharacteristic
684C2#1914772811yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#508C2
socleC22×C43C22×D8
hypercenterC2×#508D43
hypocenterC43#33516
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#135×D43C2semidirect
2. C2×#14583329C2semidirect
3. #19144172C2semidirect
4. #19136534C2semidirect
5. #19136532C2semidirect
6. #19136527C2semidirect
7. #19136522C2semidirect
8. #19136517C2semidirect
9. #19136515C2semidirect
10. #19136510C2semidirect
11. #19136505C2semidirect
12. #19136303C2semidirect
13. #19136302C2semidirect
14. C2×(C2×D43)⋊C16C2semidirect
15. C2×C43×#508C2semidirect
30. C2×#13063271C22semidirect
31. C2×#13063269C22semidirect
32. C2×#13063268C22semidirect
33. C2×#13063266C22semidirect
34. C22×C43⋊C16C22semidirect
36. #14583137C22semidirect
38. #14583132C22semidirect
41. #14582937C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582703C22semidirect
47. #14582701C22semidirect
48. #14582701C22semidirect
49. #14582700C22semidirect
50. #14582700C22semidirect
53. (C2×D43)⋊C16C22semidirect
54. (C2×D43)⋊C16C22semidirect
56. C2×#135×C43C22semidirect
58. C2×Q32×C43C22semidirect
59. C2×SD32×C43C22semidirect
60. C2×SD32×C43C22semidirect
61. C2×D16×C43C22semidirect
62. C22×C16×C43C22semidirect
78. #13063347D4semidirect
130. #135×C43D4semidirect
323. C2×D43#508semidirect
336. C2×#508D43semidirect
367. C2×#135C2×D43semidirect
376. C2×Q32C2×D43semidirect
379. C2×SD32C2×D43semidirect
380. C2×SD32C2×D43semidirect
382. C2×D16C2×D43semidirect
384. C22×C16C2×D43semidirect
405. C43#33516semidirect
431. #135C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#135×D432
C2×#145833292
#191441722
#191365342
#191365322
#191365272
#191365222
#191365172
#191365152
#191365102
#191365052
#191363032
#191363022
C2×(C2×D43)⋊C162
C2×C43×#5082
#3351643