Finite Group Databasebeta

← #25084190

Subgroups — #25084190

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145720C211yesmaximal, characteristic, complemented
2#19145619C211yesmaximal, characteristic, complemented
3#19143755C211yesmaximal, characteristic, complemented
4#19134161C211yesmaximal, characteristic, complemented
5#19134154C211yesmaximal, characteristic, complemented
6#19134103C211yesmaximal, characteristic, complemented
7#19134096C211yesmaximal, characteristic, complemented
8#19134037C211yesmaximal, characteristic, complemented
9#19134030C211yesmaximal, characteristic, complemented
10#19133979C211yesmaximal, characteristic, complemented
11#19133972C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14C2×#14582646C211yesmaximal, characteristic, complemented
15C43×#3247C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583294—21no—
20#14583269—21no—
21#14583245C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583215—21no—
24#14583215—21no—
25#14583189—21no—
26#14583189—21no—
27#14583109C2211yescharacteristic
28#14583109C2211yescharacteristic
29#14583104C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583054—21no—
32#14583037—21no—
33#14583030C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582926—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#478—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#466—21no—
62C43×#465—21no—
63C43×#463—21no—
64C43×#460C2211yescharacteristic
65C43×#459C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75#13063325—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82#13063256—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108#13063236—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×D8×C43—21no—
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43—21no—
122#124×C43D411yescharacteristic
123#123×C43—21no—
124C22⋊Q8×C43D411yescharacteristic
125#121×C43—21no—
126#121×C43—21no—
127#121×C43D411yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×Dic43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—81no—
163C2×Dic86—81no—
164SD16×C43—81no—
165D8×C43—81no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189#10621885—81no—
190#10621885—81no—
191#10621883—81no—
192#10621883—81no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199#10621877—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43—41no—
212C23×C43#12111yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—81no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—42no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—81no—
224D4×C43—82no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—82no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43#47112yes—
271C22×C43C2×#12111yescharacteristic
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43#57611yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57811yescharacteristic
284Dic43—81no—
285Dic43—81no—
286#3247D4311yescharacteristic
287#3227—431no—
288#3218—431no—
289#2994—431no—
290#1702—431no—
291#1701—431no—
292#1692—431no—
293#1691—431no—
294#1682—431no—
295#1681—431no—
296#1672—431no—
297#1671—431no—
298#1573—431no—
299#1551—431no—
300C2×#332—431no—
301C2×C43—22no—
302C2×C43—81no—
303C2×C43—161no—
304C2×C43#304611yescharacteristic
305C2×C43#306211yescharacteristic
306C2×C43C2×#47111yescharacteristic
307#532C2×D4311yescharacteristic
308C2×C4⋊Q8—431no—
309#529C2×D4311yescharacteristic
310#498—431no—
311#498—431no—
312#497—861no—
313#491—861no—
314#486—431no—
315#486—431no—
316#481—861no—
317#481—861no—
318#478—21no—
319#477C2×D4311yescharacteristic
320#476—861no—
321#476—861no—
322#476C2×D4311yescharacteristic
323#466—21no—
324#465—21no—
325#463—21no—
326#462—431no—
327#462—431no—
328#461—431no—
329#461—431no—
330#460C2×D4311yescharacteristic
331#459C2×D4311yescharacteristic
332#451—861no—
333#448—861no—
334#446—431no—
335C8×Q8—431no—
336#436—431no—
337#435—861no—
338C8×D4—431no—
339C8×D4—861no—
340#433—861no—
341#432—431no—
342#431—431no—
343#424—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8C2×D4311yescharacteristic
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—861no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—21no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—21no—
367C2×M16—861no—
368C22×C8—21no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8C22×D4311yescharacteristic
377#127C22×D4311yescharacteristic
378#126—21no—
379#125C22⋊D4311yescharacteristic
380#124—21no—
381#124C22⋊D4311yescharacteristic
382#123—21no—
383C22⋊Q8C22⋊D4311yescharacteristic
384#121—21no—
385#121—21no—
386#121C22⋊D4311yescharacteristic
387C4×Q8C22×D4311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C22×D4311yescharacteristic
392#117—21no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C42C22×D4311yescharacteristic
396#107—21no—
397#106—21no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—431no—
427C22⋊C8—431no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—861no—
432#97—861no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—3441no—
441C2×Q8—3441no—
442C2×Q8—1721no—
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C2×C22⋊D4311yescharacteristic
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—1721no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—3441no—
457Q16—3441no—
458SD16—81no—
459SD16—3441no—
460SD16—3441no—
461D8—81no—
462M16—3441no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—81no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8—3441no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4C2×C22⋊D4311yescharacteristic
489C4⋊C4C2×C22⋊D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42D4×D4311yescharacteristic
499C42#1062190011yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—41no—
504C23#1306329711yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—81no—
508Q8—3442no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—3442no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306329711yescharacteristic
538C2×C4#1306329711yescharacteristic
539C2×C4#1306329711yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C8—41no—
544C8—41no—
545C8—861no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22#1458316012yes—
562C22C2×#1306329711yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—3441no—
572C4—3441no—
573C4#1458370211yescharacteristic
574C4#1458370611yescharacteristic
575C4#1458370711yescharacteristic
576C4#1458371311yescharacteristic
577C2—22no—
578C2—81no—
579C2—161no—
580C2#1914414311yescharacteristic
581C2#1914427711yescharacteristic
582C2C2×#1458316011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3247C2
socleC22×C43C2×#121
hypercenter#3247D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3247

Complements

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

NH ≅ G/Ntype
1. #19145720C2semidirect
2. #19145619C2semidirect
3. #19143755C2semidirect
4. #19134161C2semidirect
5. #19134154C2semidirect
6. #19134103C2semidirect
7. #19134096C2semidirect
8. #19134037C2semidirect
9. #19134030C2semidirect
10. #19133979C2semidirect
11. #19133972C2semidirect
12. #19133378C2semidirect
13. #19133290C2semidirect
14. C2×#14582646C2semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191457202
#191456192
#191437552
#191341612
#191341542
#191341032
#191340962
#191340372
#191340302
#191339792
#191339722
#191333782
#191332902
C2×#145826462
C43×#32472
#1958943