Finite Group Databasebeta

← #25088144

Subgroups — #25088144

Order 11008.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621882C211yesmaximal, characteristic, complemented
2#19147013C211yesmaximal, characteristic
3#19146891C211yesmaximal, characteristic, complemented
4#19134203C211yesmaximal, characteristic, complemented
5#19134170C211yesmaximal, characteristic, complemented
6#19134167C211yesmaximal, characteristic, complemented
7#19133997C211yesmaximal, characteristic, complemented
8#19133982C211yesmaximal, characteristic, complemented
9#19133823C211yesmaximal, characteristic, complemented
10#19133821C211yesmaximal, characteristic, complemented
11#19133760C211yesmaximal, characteristic, complemented
12#19133758C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3329C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583302—21no—
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583243—21no—
25#14583223—21no—
26#14583220—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583179—21no—
31#14583179C2211yescharacteristic
32#14583176—21no—
33#14583176C2211yescharacteristic
34#14583144—21no—
35#14583133—21no—
36#14583104C2211yescharacteristic
37#14583036—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C4×#10621882—21no—
40C4×#10621882C2211yescharacteristic
41#14582978C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582935—21no—
44#14582906—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
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×Q8×D43—21no—
68C2×#10621883—21no—
69C2×#10621882D411yescharacteristic
70C2×#10621872—21no—
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063311—41no—
76#13063305—21no—
77#13063305—41no—
78#13063299—21no—
79#13063296—21no—
80C4×D172—21no—
81C4×D172C2311yescharacteristic
82#13063284—21no—
83#13063283—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98#13063250—21no—
99#13063250—21no—
100#13063249—21no—
101#13063249—41no—
102#13063248—21no—
103#13063248—41no—
104#13063246—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—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—41no—
165SD16×C43—22no—
166SD16×C43—81no—
167M16×C43—81no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43—41no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—41no—
189#10621883—81no—
190#10621882—22no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621872—81no—
209C23×C43—21no—
210C23×C43—21no—
211C22×D43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—82no—
216Q8×C43—81no—
217Q8×C43#13512yes—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—161no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—82no—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C22⋊D43—161no—
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241D172—21no—
242D172—21no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—82no—
246Dic86—41no—
247Dic86—41no—
248Dic86—82no—
249Dic86—81no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13712yes—
259#19905—431nomaximal, Sylow
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43D4211yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—22no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13711yescharacteristic
279C4×C43#57611yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—41no—
282Dic43—81no—
283Dic43—81no—
284Q8×D8—431no—
285#3341—431no—
286#3329—431no—
287#3329D4311yescharacteristic, complemented
288#1710—431no—
289#1703—431no—
290#1703—431no—
291#1676—431no—
292#1673—431no—
293#1646—431no—
294#1646—431no—
295#1637—431no—
296#1637—431no—
297#1589—431no—
298C8×SD16—431no—
299C2×C43—81no—
300C2×C43—81no—
301C2×C43#327611yescharacteristic
302C2×C43#328011yescharacteristic
303C2×C43#329011yescharacteristic
304D43—81no—
305#555—431no—
306#555C2×D4311yescharacteristic
307D4×Q8—431no—
308D4×Q8C2×D4311yescharacteristic
309#500—431no—
310#500—431no—
311#500—861no—
312#487—431no—
313#487—431no—
314#487—431no—
315#487C2×D4311yescharacteristic
316#485—21no—
317#485—861no—
318#482—861no—
319#482—861no—
320#477—431no—
321#477C2×D4311yescharacteristic
322#476—431no—
323#476—431no—
324#474—431no—
325#474—431no—
326#474—861no—
327#474—861no—
328#468—21no—
329#468—861no—
330#466—861no—
331#461—431no—
332#461C2×D4311yescharacteristic
333#448—21no—
334#448—861no—
335C8×Q8—431no—
336C4×SD16C2×D4311yescharacteristic
337C4×D8—431no—
338C4×D8—861no—
339#436—431no—
340#436C2×D4311yescharacteristic
341C8×D4—431no—
342#427—861no—
343#419—21no—
344#419—861no—
345#335—431no—
346#334—431no—
347#333—431no—
348#333—431no—
349#332—431no—
350#332—431no—
351Q8⋊C8—431no—
352D4⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355C82—431no—
356C43#1990511yescharacteristic, complemented, Sylow
357C22×Q8—21no—
358C22×Q8—861no—
359C2×SD16—21no—
360C2×SD16—861no—
361C2×SD16C22⋊D4311yescharacteristic
362C2×D8—431no—
363C2×M16—21no—
364C2×M16—861no—
365C22×C8—861no—
366C4⋊Q8—21no—
367C4⋊Q8—431no—
368C4⋊Q8—431no—
369C4⋊Q8—861no—
370C4⋊Q8C22×D4311yescharacteristic
371C4⋊Q8C22×D4311yescharacteristic
372#124—41no—
373#124—1721no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376C22⋊Q8—861no—
377C22⋊Q8—1721no—
378#121—21no—
379#121—21no—
380#121—861no—
381#121—861no—
382C4×Q8C22×D4311yescharacteristic
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—861no—
386C4×D4C22×D4311yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—21no—
390#117—861no—
391#117—861no—
392#107—21no—
393#107—431no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#107—861no—
399#107—861no—
400#107—861no—
401#106—861no—
402#106—861no—
403#106C22⋊D4311yescharacteristic
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—1721no—
418#103—1721no—
419#103C22⋊D4311yescharacteristic
420#102—431no—
421#102—431no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102C22⋊D4311yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8C22×D4311yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—42no—
438C2×Q8—81no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3441no—
442C2×Q8—1721no—
443C2×Q8—1722no—
444C2×Q8C2×C22⋊D4311yescharacteristic
445C2×D4—41no—
446C2×D4—431no—
447C2×D4—1721no—
448C2×D4D4×D4311yescharacteristic
449C2×D4C2×C22⋊D4311yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—861no—
454C22×C4—1721no—
455SD16—22no—
456SD16—81no—
457SD16—3441no—
458D8—862no—
459M16—81no—
460M16—3441no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8C2×C22⋊D4311yescharacteristic
470C2×C8C2×C22⋊D4311yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1721no—
483C4⋊C4D4×D4311yescharacteristic
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C4⋊C4C2×C22⋊D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—861no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C42—21no—
496C42—41no—
497C42—1721no—
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—21no—
501C23—861no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—81no—
507Q8—3441no—
508Q8—3442no—
509Q8—1721no—
510Q8—1721no—
511Q8#1306334512yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—161no—
517D4—861no—
518D4—861no—
519D4—6881no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—861no—
532C2×C4—3442no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4C2×D4×D4311yescharacteristic
538C2×C4C22×C22⋊D4311yescharacteristic
539C2×C4#1306337011yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—432no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22D4×C22⋊D4311yescharacteristic
559C4—22no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—3441no—
567C4—3441no—
568C4—1721no—
569C4C2×#1306334511yescharacteristic
570C4#137×D4311yescharacteristic
571C4#1458370211yescharacteristic
572C4#1458371511yescharacteristic
573C2—81no—
574C2—81no—
575C2—3441no—
576C2#1914623511yescharacteristic
577C2#1914627611yescharacteristic
578C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3329C2
socleC22×C43D42
prime radical#19147013C2
hypercenter#3329D43
hypocenterC43#19905
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. #19146891C2semidirect
4. #19134203C2semidirect
5. #19134170C2semidirect
6. #19134167C2semidirect
7. #19133997C2semidirect
8. #19133982C2semidirect
9. #19133823C2semidirect
10. #19133821C2semidirect
11. #19133760C2semidirect
12. #19133758C2semidirect
13. #19133478C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3329C2semidirect
287. #3329D43semidirect
356. C43#19905semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191470132
#191468912
#191342032
#191341702
#191341672
#191339972
#191339822
#191338232
#191338212
#191337602
#191337582
#191334782
SD16×C43⋊C82
C43×#33292
#1990543