Finite Group Databasebeta

← #25086315

Subgroups — #25086315

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146889C211yesmaximal, characteristic, complemented
2#19146525C211yesmaximal, characteristic
3#19146460C211yesmaximal, characteristic, complemented
4#19134240C211yesmaximal, characteristic, complemented
5#19134140C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic, complemented
8#19133981C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133822C211yesmaximal, characteristic, complemented
12#19133760C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15Q8×D8×C43C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583242—21no—
24#14583237—21no—
25#14583227—21no—
26#14583194C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583147—21no—
30#14583130—21no—
31#14583127—21no—
32#14583104C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583101C2211yescharacteristic
35#14583041—21no—
36#14583038—21no—
37#14583038—21no—
38C4×#10621884C2211yescharacteristic
39#14582977C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582908—21no—
43#14582892—21no—
44C2×#13063249—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56D4×Q8×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#500—21no—
59C43×#500C2211yescharacteristic
60C43×#474—21no—
61C43×#474—21no—
62C43×#474C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621883—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621884D411yescharacteristic
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063311—41no—
78#13063309—41no—
79#13063305—21no—
80#13063299—21no—
81#13063299—21no—
82#13063296—21no—
83C4×D172C2311yescharacteristic
84#13063284—21no—
85#13063283—21no—
86C2×C4⋊Dic43—21no—
87#13063258—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—41no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—41no—
108#13063246—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C22×Q8×C43—21no—
117C2×D8×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#107×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C2×C22⋊D43—41no—
160C2×C22⋊D43—41no—
161C22×Dic43—41no—
162#10621900—42no—
163#10621900—81no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168D8×C43—22no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—41no—
189#10621884—22no—
190#10621884—81no—
191#10621884—81no—
192#10621883—81no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43C2×D411yescharacteristic
202C4×Dic43—41no—
203#10621877—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C8×D43—81no—
212C23×C43—21no—
213C23×C43—21no—
214C22×D43—21no—
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—82no—
221Q8×C43—82no—
222Q8×C43#13512yes—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43#13712yes—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43—82no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C22⋊D43—82no—
243C22⋊D43—161no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—82no—
248D172—21no—
249D172—21no—
250C4×D43—41no—
251C4×D43—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—81no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19780—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43D4211yescharacteristic
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×#13511yescharacteristic
283C4×C43C2×#13711yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Q8×D8D4311yescharacteristic, complemented
290#3329—431no—
291#3303—431no—
292#3298—431no—
293#1718—431no—
294#1699—431no—
295#1684—431no—
296#1683—431no—
297#1673—431no—
298#1654—431no—
299#1651—431no—
300#1646—431no—
301#1637—431no—
302#1581—431no—
303SD16⋊C8—431no—
304C2×C43—42no—
305C2×C43—81no—
306C2×C43#326611yescharacteristic
307C2×C43#328011yescharacteristic
308C2×C43#328911yescharacteristic
309D43—81no—
310#555—431no—
311D4×Q8C2×D4311yescharacteristic
312D4×Q8C2×D4311yescharacteristic
313#547—431no—
314#500—21no—
315#500C2×D4311yescharacteristic
316#498—431no—
317#487—431no—
318#487—431no—
319#487—431no—
320#487—431no—
321#485—861no—
322#485—861no—
323#483—861no—
324#477—431no—
325#476—431no—
326#475—431no—
327#474—21no—
328#474—21no—
329#474C2×D4311yescharacteristic
330#474C2×D4311yescharacteristic
331#468—861no—
332#465—861no—
333#465—861no—
334#461—431no—
335#461—431no—
336#461—431no—
337#449—861no—
338#448—861no—
339#448—861no—
340C8×Q8C2×D4311yescharacteristic
341C4×SD16—431no—
342C4×D8—21no—
343C4×D8C2×D4311yescharacteristic
344#436—431no—
345C8×D4—431no—
346C8×D4—431no—
347#419—861no—
348#416—861no—
349C2×#103—861no—
350#335—431no—
351#335—431no—
352#333—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360#322—431no—
361C43#1978011yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C22×Q8—21no—
364C22×Q8—21no—
365C2×SD16—431no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8C22⋊D4311yescharacteristic
370C2×M16—861no—
371C22×C8—861no—
372C22×C8—861no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8C22×D4311yescharacteristic
378C4⋊Q8C22×D4311yescharacteristic
379#124—1721no—
380#123—1721no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385C22⋊Q8—861no—
386#121—861no—
387#121—861no—
388#121—861no—
389C4×Q8C22×D4311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—431no—
393C4×D4C22×D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395#117—861no—
396#117—861no—
397C2×C4⋊C4—861no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—861no—
403#107C22⋊D4311yescharacteristic
404#106—431no—
405#106—861no—
406#106—861no—
407#106—1721no—
408C4⋊C8—21no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8C22×D4311yescharacteristic
413#103—431no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—1721no—
426#102—21no—
427#102—21no—
428#102—431no—
429#102—861no—
430#102C22⋊D4311yescharacteristic
431#102C22⋊D4311yescharacteristic
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C4×C8—21no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8C22×D4311yescharacteristic
439#41—3441no—
440#41—1722no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—81no—
448C2×Q8—81no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8D4×D4311yescharacteristic
452C2×D4—431no—
453C2×D4—1721no—
454C2×D4—1721no—
455C2×D4C2×C22⋊D4311yescharacteristic
456C2×D4C2×C22⋊D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—861no—
462C22×C4—1721no—
463SD16—862no—
464SD16—3441no—
465SD16—3441no—
466SD16—3441no—
467D8—22no—
468M16—3441no—
469C2×C8—21no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—3441no—
477C2×C8—3441no—
478C2×C8C2×C22⋊D4311yescharacteristic
479C2×C8C2×C22⋊D4311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—431no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4D4×D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—861no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—1721no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—21no—
509C23—861no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—82no—
516Q8—82no—
517Q8—3441no—
518Q8—1721no—
519Q8—1721no—
520Q8#1306334412yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—861no—
525D4—861no—
526D4—3442no—
527D4—6881no—
528D4#1306335612yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—861no—
542C2×C4—3442no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C22×C22⋊D4311yescharacteristic
549C2×C4#1306337011yescharacteristic
550C8—21no—
551C8—21no—
552C8—41no—
553C8—861no—
554C8—861no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—1721no—
566C22—1721no—
567C22—1721no—
568C22D4×C22⋊D4311yescharacteristic
569C4—22no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4C2×#1306334411yescharacteristic
580C4C2×#1306335611yescharacteristic
581C4#1458370011yescharacteristic
582C4#1458370711yescharacteristic
583C2—42no—
584C2—81no—
585C2—3441no—
586C2#1914610611yescharacteristic
587C2#1914628011yescharacteristic
588C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×D8×C43C2
socleC22×C43D42
prime radical#19146525C2
hypercenterQ8×D8D43
hypocenterC43#19780
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
1. #19146889C2semidirect
3. #19146460C2semidirect
4. #19134240C2semidirect
5. #19134140C2semidirect
6. #19134053C2semidirect
7. #19134044C2semidirect
8. #19133981C2semidirect
9. #19133878C2semidirect
10. #19133858C2semidirect
11. #19133822C2semidirect
12. #19133760C2semidirect
13. #19133425C2semidirect
14. #19133405C2semidirect
15. Q8×D8×C43C2semidirect
289. Q8×D8D43semidirect
361. C43#19780semidirect

Maximal subgroups

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

subgroupindex
#191468892
#191465252
#191464602
#191342402
#191341402
#191340532
#191340442
#191339812
#191338782
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