Finite Group Databasebeta

← #25086313

Subgroups — #25086313

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
1Q8×#10621882C211yesmaximal, characteristic, complemented
2#19146517C211yesmaximal, characteristic
3#19146462C211yesmaximal, characteristic, complemented
4#19134238C211yesmaximal, characteristic, complemented
5#19134142C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19134043C211yesmaximal, characteristic, complemented
8#19133982C211yesmaximal, characteristic, complemented
9#19133877C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133823C211yesmaximal, characteristic, complemented
12#19133758C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3329C211yesmaximal, characteristic, complemented
16Q8×D172C2211yescharacteristic
17#14583554C2211yescharacteristic
18#14583302—21no—
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583240—21no—
25#14583231—21no—
26#14583186C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583179—21no—
29#14583179C2211yescharacteristic
30#14583176—21no—
31#14583176C2211yescharacteristic
32#14583127—21no—
33#14583126—21no—
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583042—21no—
37#14583036—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C4×#10621882—21no—
40C4×#10621882C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582893—21no—
44#103×D43—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#555C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#485—21no—
60C43×#477C2211yescharacteristic
61C43×#468—21no—
62C43×#461C2211yescharacteristic
63C43×#448—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#419—21no—
67C2×#10621898—21no—
68C2×Q8×D43—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621882D411yescharacteristic
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063307—41no—
78#13063305—21no—
79#13063305—41no—
80#13063304—21no—
81#13063296—21no—
82C4×D172—21no—
83C4×D172C2311yescharacteristic
84C4⋊C4×D43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—21no—
92#13063256—41no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—41no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C2×M16×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#124×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125#121×C43—21no—
126#121×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43—21no—
133#107×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—41no—
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C2×C22⋊D43—41no—
157Q8×D43—42no—
158Q8×D43—81no—
159#10621898—42no—
160#10621898—81no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—41no—
168SD16×C43—22no—
169SD16×C43—81no—
170M16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—21no—
189C42×C43—41no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—41no—
192#10621883—81no—
193#10621883—81no—
194#10621882—22no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—41no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—41no—
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—82no—
219Q8×C43—81no—
220Q8×C43#13512yes—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—161no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—21no—
245D172#13712yes—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—82no—
249C4×D43—82no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—82no—
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—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43D4211yescharacteristic
272C2×D43—22no—
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×D8—431no—
290#3329D4311yescharacteristic, complemented
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—81no—
305C2×C43—81no—
306C2×C43#326611yescharacteristic
307C2×C43#328011yescharacteristic
308C2×C43#328911yescharacteristic
309D43—42no—
310#555C2×D4311yescharacteristic
311D4×Q8—431no—
312D4×Q8C2×D4311yescharacteristic
313#547—431no—
314#500—431no—
315#500—861no—
316#498—431no—
317#487—431no—
318#487—431no—
319#487—431no—
320#487C2×D4311yescharacteristic
321#485—21no—
322#485—861no—
323#483—861no—
324#477C2×D4311yescharacteristic
325#476—431no—
326#475—431no—
327#474—431no—
328#474—431no—
329#474—861no—
330#474—861no—
331#468—21no—
332#465—861no—
333#465—861no—
334#461—431no—
335#461—431no—
336#461C2×D4311yescharacteristic
337#449—861no—
338#448—21no—
339#448—861no—
340C8×Q8—431no—
341C4×SD16C2×D4311yescharacteristic
342C4×D8—431no—
343C4×D8—861no—
344#436C2×D4311yescharacteristic
345C8×D4—431no—
346C8×D4—431no—
347#419—21no—
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—861no—
365C2×SD16—21no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16C22⋊D4311yescharacteristic
369C2×D8—431no—
370C2×M16—21no—
371C22×C8—861no—
372C22×C8—861no—
373C4⋊Q8—21no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8—861no—
377C4⋊Q8C22×D4311yescharacteristic
378C4⋊Q8C22×D4311yescharacteristic
379#124—41no—
380#123—1721no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383C22⋊Q8—861no—
384C22⋊Q8—861no—
385C22⋊Q8—1721no—
386#121—21no—
387#121—21no—
388#121—861no—
389C4×Q8C22×D4311yescharacteristic
390C4×D4—21no—
391C4×D4—431no—
392C4×D4—861no—
393C4×D4C22×D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395#117—21no—
396#117—21no—
397C2×C4⋊C4—861no—
398#107—21no—
399#107—431no—
400#107—861no—
401#107—861no—
402#107—861no—
403#107—861no—
404#106—861no—
405#106—861no—
406#106—1721no—
407#106C22⋊D4311yescharacteristic
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—1721no—
425#103C22⋊D4311yescharacteristic
426#102—431no—
427#102—431no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102C22⋊D4311yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—861no—
438C4×C8C22×D4311yescharacteristic
439#41—3441no—
440#41—1722no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—42no—
445C2×Q8—81no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—3441no—
449C2×Q8—1721no—
450C2×Q8—1722no—
451C2×Q8C2×C22⋊D4311yescharacteristic
452C2×D4—41no—
453C2×D4—431no—
454C2×D4—1721no—
455C2×D4D4×D4311yescharacteristic
456C2×D4C2×C22⋊D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—861no—
461C22×C4—1721no—
462C22×C4—1721no—
463SD16—22no—
464SD16—81no—
465SD16—3441no—
466SD16—3441no—
467D8—862no—
468M16—81no—
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—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—1721no—
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—41no—
501C22⋊C4—861no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—41no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—21no—
509C23—861no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—81no—
515Q8—3442no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8#1306334512yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—161no—
526D4—432no—
527D4—861no—
528D4—3442no—
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—861no—
541C2×C4—3442no—
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—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—862no—
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×#1306334511yescharacteristic
580C4#137×D4311yescharacteristic
581C4#1458370211yescharacteristic
582C4#1458370811yescharacteristic
583C2—81no—
584C2—81no—
585C2—1722no—
586C2#1914609911yescharacteristic
587C2#1914627611yescharacteristic
588C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3329C2
socleC22×C43D42
prime radical#19146517C2
hypercenter#3329D43
hypocenterC43#19780
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3329

Complements

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

NH ≅ G/Ntype
1. Q8×#10621882C2semidirect
3. #19146462C2semidirect
4. #19134238C2semidirect
5. #19134142C2semidirect
6. #19134055C2semidirect
7. #19134043C2semidirect
8. #19133982C2semidirect
9. #19133877C2semidirect
10. #19133858C2semidirect
11. #19133823C2semidirect
12. #19133758C2semidirect
13. #19133422C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3329C2semidirect
290. #3329D43semidirect
361. C43#19780semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191465172
#191464622
#191342382
#191341422
#191340552
#191340432
#191339822
#191338772
#191338582
#191338232
#191337582
#191334222
SD16⋊(C43⋊C8)2
C43×#33292
#1978043