Finite Group Databasebeta

← #25080504

Subgroups — #25080504

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145021C211yesmaximal, characteristic, complemented
2#19144746C211yesmaximal, characteristic, complemented
3#41×C43⋊C8C211yesmaximal, characteristic, complemented
4#19133963C211yesmaximal, characteristic, complemented
5#19133958C211yesmaximal, characteristic, complemented
6#19133953C211yesmaximal, characteristic, complemented
7#19133948C211yesmaximal, characteristic, complemented
8#19133945C211yesmaximal, characteristic, complemented
9#19133941C211yesmaximal, characteristic, complemented
10#19133938C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133356C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133300C211yesmaximal, characteristic, complemented
15C43×#3115C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17C2×#13063345—21no—
18#14583449C2211yescharacteristic
19#14583281—21no—
20#14583281—21no—
21#14583278C2211yescharacteristic
22#14583275C2211yescharacteristic
23#14583273C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583223—21no—
26#14583184C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583099C2211yescharacteristic
29#14583094C2211yescharacteristic
30#14583044—21no—
31Q8×C43⋊C8C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14583009—21no—
34#14582997—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582956C2211yescharacteristic
40#14582952—21no—
41#14582952C2211yescharacteristic
42C2×C4×C43⋊C8—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#442—21no—
65C43×#440—21no—
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68#13063345—44no—
69#13063345—44no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82C22×C43⋊C8D411yescharacteristic
83C22×C43⋊C8D411yescharacteristic
84#13063325C2311yescharacteristic
85#13063322C2311yescharacteristic
86#13063313—21no—
87#13063299—21no—
88#13063299—21no—
89C4×D172—21no—
90C4×D172—21no—
91#13063258—21no—
92#13063256—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063246—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107#13063236—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8D411yescharacteristic
112C4×C43⋊C8D411yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×#41×C43D411yescharacteristic
117C2×SD16×C43—21no—
118C2×D8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120#127×C43C2311yescharacteristic
121#124×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124C4×Q8×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43D411yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43D411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#107×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145#97×C43—21no—
146#41×C43—22no—
147#41×C43—22no—
148#41×C43—42no—
149#41×C43—42no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4111yescharacteristic
165C2×C22⋊D43—41no—
166#10621898—42no—
167#10621898—42no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×C4×D43—41no—
172C2×Dic86—21no—
173SD16×C43—42no—
174D8×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43#4111yescharacteristic
194C42×C43C2411yescharacteristic
195#10621885—42no—
196#10621885—42no—
197#10621884—42no—
198#10621884—42no—
199#10621884—42no—
200#10621883—42no—
201#10621883—42no—
202#10621882—42no—
203#10621882—42no—
204#10621882—42no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C2×C43⋊C8—22no—
210C2×C43⋊C8—22no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—42no—
216C2×C43⋊C8—42no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C23×C43—21no—
222C23×C43—41no—
223C23×C43#12111yescharacteristic
224C22×D43—41no—
225Q8×C43—21no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43#13512yescomplemented
229D4×C43—24no—
230D4×C43—21no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—81no—
236D4×C43—82no—
237D4×C43#13512yescomplemented
238C2×C4×C43—24no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—82no—
252C2×C4×C43#12111yescharacteristic
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C22⋊D43—82no—
259C2×Dic43—41no—
260D172—41no—
261D172—41no—
262D172—41no—
263D172—41no—
264D172—81no—
265C4×D43—82no—
266Dic86—41no—
267Dic86—41no—
268C8×C43—41no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8AGL(1,ℤ/8)12yes—
277C43⋊C8AGL(1,ℤ/8)12yes—
278#19269—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—22no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43C2×#12111yescharacteristic
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—22no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43C2×#13511yescharacteristic
301C4×C43C2×#13511yescharacteristic
302C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
304Dic43—81no—
305#3147—431no—
306#3115—431no—
307#3115D4311yescharacteristic, complemented
308C8×#41—431no—
309#1670—431no—
310#1669—431no—
311#1668—431no—
312#1667—431no—
313#1666—431no—
314#1666—431no—
315#1665—431no—
316#1665—431no—
317#1568—431no—
318#1553—431no—
319#1553—431no—
320C2×C43—41no—
321C2×C43—42no—
322C2×C43—161no—
323C2×C43#303811yescharacteristic
324C2×C43#305011yescharacteristic
325C2×C43#306711yescharacteristic
326D43—161no—
327C2×#135—861no—
328C2×#135—861no—
329#532—431no—
330#532C2×D4311yescharacteristic
331C4×#41C2×D4311yescharacteristic
332#495—861no—
333#495—861no—
334#494—431no—
335#493—431no—
336#492—431no—
337#492—431no—
338#482—21no—
339#482—861no—
340#475—431no—
341#475C2×D4311yescharacteristic
342#474—431no—
343#474C2×D4311yescharacteristic
344#460—431no—
345#460C2×D4311yescharacteristic
346#459—431no—
347#459C2×D4311yescharacteristic
348#449—21no—
349#449—861no—
350C8×Q8—431no—
351C8×Q8—431no—
352#442—21no—
353#442—861no—
354#440—21no—
355#440—861no—
356C8×D4—431no—
357C8×D4—431no—
358C8×D4—861no—
359C8×D4—861no—
360#432—431no—
361#432C2×D4311yescharacteristic
362#431—431no—
363#431—861no—
364C2×C4×C8—431no—
365C2×C4×C8—861no—
366#335—431no—
367#335—431no—
368#334—431no—
369#334—431no—
370#332—431no—
371#332—431no—
372#332—431no—
373#332—431no—
374#331—431no—
375#331—431no—
376#331—431no—
377#331—431no—
378C43#1926911yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C2×#41—861no—
381C2×#41C22⋊D4311yescharacteristic
382#135—1724no—
383#135—1724no—
384C2×Q16—861no—
385C2×Q16—861no—
386C2×SD16—21no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×D8—21no—
393C2×D8—861no—
394C2×D8—861no—
395C2×D8—861no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8—861no—
399C22×C8—861no—
400C4⋊Q8—431no—
401C4⋊Q8C22×D4311yescharacteristic
402#127—431no—
403#127C22×D4311yescharacteristic
404#124—21no—
405#124—861no—
406#121—21no—
407#121—21no—
408#121—861no—
409#121—861no—
410C4×Q8C22⋊D4311yescharacteristic
411C4×Q8C22×D4311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4C22⋊D4311yescharacteristic
419C4×D4C22×D4311yescharacteristic
420#117—21no—
421#117C22⋊D4311yescharacteristic
422C2×C42—21no—
423C2×C42C22×D4311yescharacteristic
424#107—21no—
425#107—861no—
426#106—21no—
427#106—861no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8C22×D4311yescharacteristic
435C4⋊C8C22×D4311yescharacteristic
436#103—21no—
437#103—861no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—861no—
442#102—861no—
443#102—861no—
444C22⋊C8—21no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C22⋊C8—861no—
449#97—21no—
450#97—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8—861no—
456C4×C8—861no—
457C4×C8—861no—
458#41—22no—
459#41—22no—
460#41—42no—
461#41—42no—
462#41—1722no—
463#41—1722no—
464C2×Q8—21no—
465C2×Q8—861no—
466C2×Q8C2×C22⋊D4311yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—1721no—
476C2×D4C2×C22⋊D4311yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—1721no—
482C22×C4D4×D4311yescharacteristic
483C22×C4#1062190011yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485Q16—1722no—
486Q16—1722no—
487SD16—42no—
488SD16—1722no—
489SD16—1722no—
490SD16—1722no—
491SD16—1722no—
492SD16—1722no—
493D8—42no—
494D8—1722no—
495D8—1722no—
496D8—1722no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—431no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—862no—
504C2×C8—862no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—1722no—
510C2×C8—1722no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—1721no—
525C22⋊C4—1721no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42D4×D4311yescharacteristic
530C42#1062190011yescharacteristic
531C42C2×C22⋊D4311yescharacteristic
532C42C23×D4311yescharacteristic
533C23—21no—
534C23—41no—
535C23—1721no—
536C23#1306329711yescharacteristic
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—1721no—
541Q8—1721no—
542Q8#1306334512yescomplemented
543D4—24no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—82no—
551D4—3441no—
552D4—3442no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4#1306334512yescomplemented
558C2×C4—24no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—3442no—
573C2×C4—1721no—
574C2×C4#1306329711yescharacteristic
575C2×C4#1306329711yescharacteristic
576C2×C4#1306329711yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C8—41no—
581C8—41no—
582C8—432no—
583C8—432no—
584C8—861no—
585C8—861no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C8—1721no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22C2×#1306329711yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—3441no—
612C4C2×#1306334511yescharacteristic
613C4C2×#1306334511yescharacteristic
614C4AGL(1,ℤ/8)×D4311yescharacteristic
615C4AGL(1,ℤ/8)×D4311yescharacteristic
616C2—41no—
617C2—42no—
618C2—161no—
619C2—6881no—
620C2#1914407311yescharacteristic
621C2#1914417311yescharacteristic
622C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3115C2
socleC22×C43C2×#121
hypercenter#3115D43
hypocenterC43#19269
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #19145021C2semidirect
2. #19144746C2semidirect
3. #41×C43⋊C8C2semidirect
4. #19133963C2semidirect
5. #19133958C2semidirect
6. #19133953C2semidirect
7. #19133948C2semidirect
8. #19133945C2semidirect
9. #19133941C2semidirect
10. #19133938C2semidirect
11. #19133934C2semidirect
12. #19133356C2semidirect
13. #19133301C2semidirect
14. #19133300C2semidirect
15. C43×#3115C2semidirect
228. Q8×C43#135semidirect
237. D4×C43#135semidirect
307. #3115D43semidirect
378. C43#19269semidirect
542. Q8#13063345semidirect
557. D4#13063345semidirect

Maximal subgroups

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

subgroupindex
#191450212
#191447462
#41×C43⋊C82
#191339632
#191339582
#191339532
#191339482
#191339452
#191339412
#191339382
#191339342
#191333562
#191333012
#191333002
C43×#31152
#1926943