Finite Group Databasebeta

← #25080042

Subgroups — #25080042

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145922C211yesmaximal, characteristic, complemented
2#19145915C211yesmaximal, characteristic, complemented
3#19145170C211yesmaximal, characteristic, complemented
4#19143564C211yesmaximal, characteristic, complemented
5#19134122C211yesmaximal, characteristic, complemented
6#19134117C211yesmaximal, characteristic, complemented
7#19134078C211yesmaximal, characteristic, complemented
8#19134073C211yesmaximal, characteristic, complemented
9#19134014C211yesmaximal, characteristic, complemented
10#19134010C211yesmaximal, characteristic, complemented
11#19134007C211yesmaximal, characteristic, complemented
12#19134003C211yesmaximal, characteristic, complemented
13C2×#14582649C211yesmaximal, characteristic, complemented
14#19133291C211yesmaximal, characteristic, complemented
15C43×#1551C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583275C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583200—21no—
23#14583199—21no—
24#14583195C2211yescharacteristic
25#14583191C2211yescharacteristic
26#14583190C2211yescharacteristic
27#14583186C2211yescharacteristic
28#14583135—21no—
29#14583133—21no—
30#14583133—21no—
31#14583133—21no—
32#14583128—21no—
33#14583126—21no—
34#14583115—21no—
35#14583114—21no—
36#14583100C2211yescharacteristic
37#14583096C2211yescharacteristic
38#14583095C2211yescharacteristic
39#14583091C2211yescharacteristic
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42C4×#10621882—21no—
43C4×#10621882—21no—
44#14582976C2211yescharacteristic
45#14582967—21no—
46#14582964C2211yescharacteristic
47(C22⋊D43)⋊C8—21no—
48#14582961—21no—
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50#14582856—21no—
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873—21no—
69C2×#10621883—21no—
70C2×D344—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8D411yescharacteristic
77C22×C43⋊C8D411yescharacteristic
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063319—21no—
82#13063317D411yescharacteristic
83#13063313—21no—
84#13063313D411yescharacteristic
85#13063308—21no—
86#13063304D411yescharacteristic
87#13063299—21no—
88#13063299—21no—
89#13063299D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×D172—21no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95#13063282—21no—
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063248—21no—
109#13063247—21no—
110#13063247—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122C4×C43⋊C8D411yescharacteristic
123C4×C43⋊C8D411yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130#127×C43C2311yescharacteristic
131#124×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155C2×C22⋊D43—41no—
156#10621898—82no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43#4111yescharacteristic
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621883—81no—
180#10621882—42no—
181#10621882—42no—
182#10621882—81no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207D344—81no—
208#10621873—81no—
209#10621872—42no—
210C8×D43—42no—
211C23×C43—41no—
212C23×C43#12111yescharacteristic
213C22×D43—21no—
214C22×D43—41no—
215Q8×C43—81no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—81no—
221D4×C43—82no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—42no—
236C22⋊D43—82no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241D172—21no—
242D172—21no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—81no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—82no—
251Dic86—21no—
252Dic86—21no—
253Dic86—81no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8#13512yes—
264#19227—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43#47212yes—
271C22×C43C2×#12111yescharacteristic
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—81no—
283C4×C43C2×#13511yescharacteristic
284C4×C43#57511yescharacteristic
285C4×C43#57711yescharacteristic
286C4×C43#57711yescharacteristic
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291#3247—431no—
292#3247—431no—
293#3169—431no—
294#2966—431no—
295#1696—431no—
296#1695—431no—
297#1688—431no—
298#1687—431no—
299#1678—431no—
300#1678—431no—
301#1677—431no—
302#1677—431no—
303C2×#334—431no—
304#1551—431no—
305#1551D4311yescharacteristic, complemented
306C2×C43—22no—
307C2×C43—161no—
308C2×C43#303511yescharacteristic
309C2×C43#306011yescharacteristic
310C2×C43C2×#47211yescharacteristic
311D43—81no—
312D43—161no—
313#532—431no—
314#532C2×D4311yescharacteristic
315#529—431no—
316#500—431no—
317#493—431no—
318#486—431no—
319#486—431no—
320#478—861no—
321#478—861no—
322#477—431no—
323#477—431no—
324#476—431no—
325#476—431no—
326#466—861no—
327#466—861no—
328#466—861no—
329#466—861no—
330#465—861no—
331#465—861no—
332#463—861no—
333#463—861no—
334#460—431no—
335#460—431no—
336#459—431no—
337#459—431no—
338#446—431no—
339C8×Q8—431no—
340C4×D8—861no—
341C4×D8—861no—
342#436—431no—
343#435—861no—
344C8×D4—431no—
345C8×D4—861no—
346#433—861no—
347#432C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349C2×C4⋊C8C2×D4311yescharacteristic
350#405—861no—
351C2×C4×C8—431no—
352#334—431no—
353#334—431no—
354#334—431no—
355#334—431no—
356#333—431no—
357#333—431no—
358#333C2×D4311yescharacteristic
359#333C2×D4311yescharacteristic
360#331—431no—
361#331—431no—
362#331C2×D4311yescharacteristic
363#331C2×D4311yescharacteristic
364C43#1922711yescharacteristic, complemented, Sylow
365C2×#41—21no—
366C2×#41—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8—861no—
370C2×D8—861no—
371C2×D8—861no—
372C2×D8—861no—
373C2×M16—861no—
374C22×C8—21no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—861no—
378C22×C8—861no—
379C4⋊Q8—431no—
380C4⋊Q8C22×D4311yescharacteristic
381#127—431no—
382#127C22×D4311yescharacteristic
383#126—861no—
384#125—431no—
385#124—21no—
386#124—431no—
387#124—861no—
388#123—861no—
389C22⋊Q8—431no—
390#121—21no—
391#121—21no—
392#121—431no—
393#121—861no—
394#121—861no—
395C4×Q8—431no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—861no—
402#117—861no—
403C2×C42C22×D4311yescharacteristic
404#107—861no—
405#107—861no—
406#107—861no—
407#107—861no—
408#106—861no—
409#106—861no—
410C4⋊C8—21no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419C4⋊C8C22×D4311yescharacteristic
420#103—861no—
421#103—861no—
422#102—861no—
423#102—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—
432C22⋊C8—21no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435#97—21no—
436#97—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442#41—82no—
443#41—3442no—
444C2×Q8—21no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—431no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—1721no—
457C22×C4—41no—
458C22×C4—861no—
459C22×C4—1721no—
460C22×C4#1062189811yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463SD16—3441no—
464SD16—3441no—
465D8—3441no—
466D8—3441no—
467D8—1722no—
468D8—1722no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—862no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—3441no—
483C2×C8—1722no—
484C2×C8—1721no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—431no—
488C4⋊C4—431no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—861no—
505C42#1062189811yescharacteristic
506C42D4×D4311yescharacteristic
507C42D4×D4311yescharacteristic
508C42C23×D4311yescharacteristic
509C23—41no—
510C23—861no—
511C23—1721no—
512C23#1306329811yescharacteristic
513Q8—81no—
514Q8—861no—
515Q8—861no—
516Q8—3441no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—81no—
522D4—82no—
523D4—861no—
524D4—861no—
525D4—3441no—
526D4—3442no—
527D4—1722no—
528D4—1721no—
529D4—1721no—
530D4—1721no—
531D4—1721no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—3442no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4#1306329811yescharacteristic
547C2×C4#1306329811yescharacteristic
548C2×C4#1306329811yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×D4×D4311yescharacteristic
551C2×C4C2×#1062189811yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—432no—
557C8—861no—
558C8—861no—
559C8—861no—
560C8—1721no—
561C8—1721no—
562C22—21no—
563C22—21no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—3441no—
568C22—3441no—
569C22—3441no—
570C22—1721no—
571C22—1721no—
572C22—1721no—
573C22#1458316812yes—
574C22C2×#1306329811yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—81no—
580C4—3441no—
581C4—1721no—
582C4—1721no—
583C4—1721no—
584C4#135×D4311yescharacteristic
585C4#1458369611yescharacteristic
586C4#1458370811yescharacteristic
587C4#1458370911yescharacteristic
588C2—22no—
589C2—161no—
590C2—3441no—
591C2—6881no—
592C2#1914404811yescharacteristic
593C2#1914425611yescharacteristic
594C2C2×#1458316811yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
hypercenter#1551D43
hypocenterC43#19227
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
1. #19145922C2semidirect
2. #19145915C2semidirect
3. #19145170C2semidirect
4. #19143564C2semidirect
5. #19134122C2semidirect
6. #19134117C2semidirect
7. #19134078C2semidirect
8. #19134073C2semidirect
9. #19134014C2semidirect
10. #19134010C2semidirect
11. #19134007C2semidirect
12. #19134003C2semidirect
13. C2×#14582649C2semidirect
14. #19133291C2semidirect
15. C43×#1551C2semidirect
305. #1551D43semidirect
364. C43#19227semidirect

Maximal subgroups

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

subgroupindex
#191459222
#191459152
#191451702
#191435642
#191341222
#191341172
#191340782
#191340732
#191340142
#191340102
#191340072
#191340032
C2×#145826492
#191332912
C43×#15512
#1922743