Finite Group Databasebeta

← #25086320

Subgroups — #25086320

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
1D8×Dic86C211yesmaximal, characteristic, complemented
2#19146883C211yesmaximal, characteristic, complemented
3#19146454C211yesmaximal, characteristic, complemented
4#19134244C211yesmaximal, characteristic, complemented
5#19134144C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19134048C211yesmaximal, characteristic, complemented
8#19133984C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133856C211yesmaximal, characteristic, complemented
11#19133823C211yesmaximal, characteristic, complemented
12#19133759C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3303C211yesmaximal, characteristic
16D4×Dic86C2211yescharacteristic
17D4×Dic86C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583303—21no—
20#14583295C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583251C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583240—21no—
25#14583229—21no—
26#14583191C2211yescharacteristic
27#14583181C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583177—21no—
31#14583177—21no—
32#14583143—21no—
33#14583126—21no—
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583037—21no—
37#14583037—21no—
38C8×Dic86C2211yescharacteristic
39C4×#10621883C2211yescharacteristic
40D8×Dic43—21no—
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582907—21no—
44C2×#13063248—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582629C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#555C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#485—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#461C2211yescharacteristic
63C43×#449—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#416—21no—
67C22×Dic86—21no—
68C22×Dic86—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883D411yescharacteristic
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063304—21no—
79#13063304—21no—
80#13063302—41no—
81#13063302—41no—
82C4×Dic86C2311yescharacteristic
83D4×Dic43—21no—
84D4×Dic43—21no—
85#13063259—21no—
86#13063259—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063256—21no—
91#13063256—41no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—41no—
98#13063248—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#124×C43—41no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—41no—
149C2×D4×C43—41no—
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—42no—
162C2×Dic86—42no—
163C2×Dic86—41no—
164C2×Dic86—41no—
165C2×Dic86—81no—
166C2×Dic86—81no—
167C2×Dic86C2×D411yescharacteristic
168SD16×C43—81no—
169D8×C43—22no—
170C2×C8×C43—21no—
171C2×C8×C43—81no—
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—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—41no—
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191C22⋊Dic43—41no—
192#10621883—22no—
193#10621883—81no—
194#10621883—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204#10621877—81no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—82no—
224D4×C43—161no—
225D4×C43#13712yes—
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—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—82no—
246C2×Dic43—82no—
247Dic86—21no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—82no—
253Dic86—82no—
254Dic86#13512yes—
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×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43D4211yescharacteristic
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×#13711yescharacteristic
283C4×C43#57611yescharacteristic
284C4×C43#57711yescharacteristic
285Dic43—22no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Q8×D8—431no—
290#3329—431no—
291#3303D4311yescharacteristic
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—81no—
307C2×C43#326611yescharacteristic
308C2×C43#328011yescharacteristic
309C2×C43#328911yescharacteristic
310#555C2×D4311yescharacteristic
311D4×Q8—431no—
312D4×Q8—431no—
313#547C2×D4311yescharacteristic
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#477—431no—
325#476C2×D4311yescharacteristic
326#475—431no—
327#474—431no—
328#474—431no—
329#474—861no—
330#474—861no—
331#468—861no—
332#465—21no—
333#465—861no—
334#461—431no—
335#461—431no—
336#461C2×D4311yescharacteristic
337#449—21no—
338#448—861no—
339#448—861no—
340C8×Q8—431no—
341C4×SD16—431no—
342C4×D8—861no—
343C4×D8C2×D4311yescharacteristic
344#436—431no—
345C8×D4—431no—
346C8×D4C2×D4311yescharacteristic
347#419—861no—
348#416—21no—
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—21no—
363C22×Q8—861no—
364C22×Q8—861no—
365C2×SD16—21no—
366C2×SD16—431no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8C22⋊D4311yescharacteristic
370C2×M16—861no—
371C22×C8—21no—
372C22×C8—861no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377C4⋊Q8C22×D4311yescharacteristic
378C4⋊Q8C22×D4311yescharacteristic
379#124—41no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—861no—
383C22⋊Q8—861no—
384C22⋊Q8—1721no—
385C22⋊Q8—1721no—
386#121—21no—
387#121—21no—
388#121—21no—
389C4×Q8—431no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4C22×D4311yescharacteristic
393C4×D4C22×D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395#117—21no—
396#117—21no—
397C2×C4⋊C4—21no—
398#107—861no—
399#107—861no—
400#107—861no—
401#107—861no—
402#107—861no—
403#107C22⋊D4311yescharacteristic
404#106—21no—
405#106—431no—
406#106—861no—
407#106—1721no—
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—431no—
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—431no—
428#102—861no—
429#102—861no—
430#102C22⋊D4311yescharacteristic
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—42no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—431no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—3441no—
447C2×Q8—3441no—
448C2×Q8—1721no—
449C2×Q8—1721no—
450C2×Q8—1722no—
451C2×Q8—1722no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4D4×D4311yescharacteristic
455C2×D4C2×C22⋊D4311yescharacteristic
456C2×D4C2×C22⋊D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—1721no—
462C22×C4—1721no—
463SD16—81no—
464SD16—862no—
465SD16—3441no—
466SD16—3441no—
467D8—22no—
468M16—3441no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
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—41no—
485C4⋊C4—431no—
486C4⋊C4—861no—
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—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—41no—
505C42—861no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—432no—
514Q8—861no—
515Q8—3442no—
516Q8—3442no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—82no—
527D4—161no—
528D4#1306335512yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—3442no—
544C2×C4—3442no—
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—41no—
566C22—41no—
567C22—41no—
568C22D4×C22⋊D4311yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—862no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4#135×D4311yescharacteristic
580C4C2×#1306335511yescharacteristic
581C4#1458370111yescharacteristic
582C4#1458371011yescharacteristic
583C2—42no—
584C2—81no—
585C2—81no—
586C2#1914610111yescharacteristic
587C2#1914627411yescharacteristic
588C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3303C2
socleC22×C43D42
hypercenter#3303D43
hypocenterC43#19780
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. D8×Dic86C2semidirect
2. #19146883C2semidirect
3. #19146454C2semidirect
4. #19134244C2semidirect
5. #19134144C2semidirect
6. #19134050C2semidirect
7. #19134048C2semidirect
8. #19133984C2semidirect
9. #19133879C2semidirect
10. #19133856C2semidirect
11. #19133823C2semidirect
12. #19133759C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
361. C43#19780semidirect

Maximal subgroups

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

subgroupindex
D8×Dic862
#191468832
#191464542
#191342442
#191341442
#191340502
#191340482
#191339842
#191338792
#191338562
#191338232
#191337592
#191334252
#191334072
C43×#33032
#1978043