Finite Group Databasebeta

← #25080317

Subgroups — #25080317

Order 11008.

624 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145921C211yesmaximal, characteristic, complemented
2#19145567C211yesmaximal, characteristic, complemented
3#19145333C211yesmaximal, characteristic, complemented
4#19134163C211yesmaximal, characteristic, complemented
5#19134135C211yesmaximal, characteristic, complemented
6#19134094C211yesmaximal, characteristic, complemented
7#19134074C211yesmaximal, characteristic, complemented
8#19134032C211yesmaximal, characteristic, complemented
9#19134004C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133955C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133255C211yesmaximal, characteristic, complemented
14#19133242C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583281—21no—
20#14583276C2211yescharacteristic
21#14583256—21no—
22#14583246C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583196—21no—
25#14583194C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583152—21no—
28#14583152—21no—
29#14583133—21no—
30#14583130—21no—
31#14583111—21no—
32#14583109C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583094C2211yescharacteristic
37#14583094C2211yescharacteristic
38#14583059—21no—
39#14583042—21no—
40#14583012—21no—
41#14583012—21no—
42#14582952C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582642C2211yescharacteristic
53#14582642C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×D344—21no—
74C2×D344—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063313—21no—
83#13063313—21no—
84#13063299—21no—
85#13063299—21no—
86#13063299—21no—
87#13063299—21no—
88C4×D172—21no—
89C4×D172—21no—
90C4×D172—21no—
91C4×D172—21no—
92#13063258—21no—
93#13063257—21no—
94#13063257—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063248—21no—
103#13063248—21no—
104#13063247—21no—
105#13063247—21no—
106#13063247—21no—
107#13063247—21no—
108#13063246—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114C4×C43⋊C8—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153#10621898—81no—
154#10621898—81no—
155#10621898—82no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166M16×C43—22no—
167M16×C43—41no—
168M16×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—42no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43#4111yescharacteristic
191C42×C43C2411yescharacteristic
192#10621885—81no—
193#10621884—81no—
194#10621884—81no—
195#10621883—81no—
196#10621882—81no—
197#10621882—81no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—41no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211D344—42no—
212D344—42no—
213C23×C43—21no—
214C23×C43#12111yescharacteristic
215C22×D43—41no—
216C22×D43—41no—
217Q8×C43—21no—
218Q8×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—81no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—82no—
239C22⋊D43—82no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—81no—
251D172—81no—
252C4×D43—82no—
253C4×D43—82no—
254Dic86—41no—
255Dic86—41no—
256Dic86—81no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43#13512yes—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19250—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C2×#12111yescharacteristic
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43C2×#13511yescharacteristic
289C4×C43#57511yescharacteristic
290C4×C43#57611yescharacteristic
291C4×C43#57711yescharacteristic
292Dic43—81no—
293Dic43—81no—
294#3247—431no—
295#3212—431no—
296#3184—431no—
297#2969D4311yescharacteristic, complemented
298#1702—431no—
299#1698—431no—
300#1691—431no—
301#1687—431no—
302#1681—431no—
303#1677—431no—
304#1672—431no—
305#1668—431no—
306#1565—431no—
307#1543—431no—
308#1540—431no—
309C2×C43—41no—
310C2×C43—81no—
311C2×C43#303511yescharacteristic
312C2×C43#306211yescharacteristic
313C2×C43#306811yescharacteristic
314D43—161no—
315D43—161no—
316#532—431no—
317#532—431no—
318#529C2×D4311yescharacteristic
319#498—431no—
320#495—861no—
321#493—431no—
322#488—861no—
323#486—431no—
324#486—431no—
325#478—861no—
326#477—431no—
327#476—431no—
328#469—861no—
329#469—861no—
330#466—861no—
331#465—861no—
332#463—861no—
333#462—431no—
334#461—431no—
335#460—431no—
336#460—431no—
337#459—431no—
338#459—431no—
339#452—861no—
340#449—861no—
341#446C2×D4311yescharacteristic
342C8×Q8C2×D4311yescharacteristic
343#442—861no—
344#442—861no—
345#436—21no—
346#436C2×D4311yescharacteristic
347#435—21no—
348C8×D4C2×D4311yescharacteristic
349#433—21no—
350#431—431no—
351#431C2×D4311yescharacteristic
352C2×C4⋊C8—431no—
353#405—21no—
354C4×M16C2×D4311yescharacteristic
355#335—431no—
356#335—431no—
357#334—431no—
358#334—431no—
359#333—431no—
360#333—431no—
361#332—431no—
362#332—431no—
363#331—431no—
364#331—431no—
365#331—431no—
366#331—431no—
367C43#1925011yescharacteristic, complemented, Sylow
368C2×#41—861no—
369C2×#41—861no—
370C2×Q16—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×D8—861no—
375C2×D8—861no—
376C2×D8—861no—
377C2×D8—861no—
378C2×M16—21no—
379C2×M16C22⋊D4311yescharacteristic
380C2×M16C22⋊D4311yescharacteristic
381C22×C8—21no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385#127—431no—
386#127—431no—
387#126—21no—
388#125D17211yescharacteristic
389#124—861no—
390#124—861no—
391#124D17211yescharacteristic
392#123—21no—
393C22⋊Q8D17211yescharacteristic
394#121—861no—
395#121—861no—
396#121—861no—
397#121—861no—
398#121D17211yescharacteristic
399C4×Q8C22×D4311yescharacteristic
400C4×D4—21no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4C22×D4311yescharacteristic
406#117—21no—
407C2×C42C22×D4311yescharacteristic
408#107—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—861no—
422#103—861no—
423#103—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—861no—
437#97—21no—
438#97C22⋊D4311yescharacteristic
439#97C22⋊D4311yescharacteristic
440C4×C8—21no—
441C4×C8—21no—
442C4×C8—861no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445#41—3441no—
446#41—3441no—
447#41—3442no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8C2×D17211yescharacteristic
451C2×D4—21no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—1721no—
459C2×D4—1721no—
460C2×D4C2×D17211yescharacteristic
461C22×C4—21no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4C2×D17211yescharacteristic
465C22×C4#1062189811yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467Q16—3441no—
468SD16—3441no—
469SD16—3441no—
470SD16—3441no—
471D8—3441no—
472D8—3441no—
473D8—1722no—
474D8—1722no—
475M16—22no—
476M16—41no—
477M16—42no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—3441no—
486C2×C8C2×C22⋊D4311yescharacteristic
487C2×C8C2×C22⋊D4311yescharacteristic
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×D17211yescharacteristic
499C4⋊C4C2×D17211yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1721no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—21no—
510C42C2×D17211yescharacteristic
511C42#1062189811yescharacteristic
512C42C2×C22⋊D4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—1721no—
516C23—1721no—
517C23#1306329911yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—3441no—
521Q8—1721no—
522Q8—1721no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—3441no—
527D4—3441no—
528D4—3442no—
529D4—3442no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533D4—1721no—
534D4—1721no—
535D4—1721no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—3442no—
549C2×C4—3442no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4#1306329911yescharacteristic
553C2×C4#1306329911yescharacteristic
554C2×C4#1306329911yescharacteristic
555C2×C4C22×C22⋊D4311yescharacteristic
556C2×C4C22×D17211yescharacteristic
557C2×C4C2×#1062189811yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C8#1306334512yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22C2×#1306329911yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—3441no—
589C4—3441no—
590C4C2×#1306334511yescharacteristic
591C4#1458369711yescharacteristic
592C4#1458370411yescharacteristic
593C4#1458371111yescharacteristic
594C2—41no—
595C2—81no—
596C2—6881no—
597C2—6881no—
598C2#1914405011yescharacteristic
599C2#1914427511yescharacteristic
600C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×#121
hypercenter#2969D43
hypocenterC43#19250
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
1. #19145921C2semidirect
2. #19145567C2semidirect
3. #19145333C2semidirect
4. #19134163C2semidirect
5. #19134135C2semidirect
6. #19134094C2semidirect
7. #19134074C2semidirect
8. #19134032C2semidirect
9. #19134004C2semidirect
10. #19133977C2semidirect
11. #19133955C2semidirect
12. #19133347C2semidirect
13. #19133255C2semidirect
14. #19133242C2semidirect
15. C43×#2969C2semidirect
297. #2969D43semidirect
367. C43#19250semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191455672
#191453332
#191341632
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