Finite Group Databasebeta

← #25080062

Subgroups — #25080062

Order 11008.

606 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
1#19145932C211yesmaximal, characteristic, complemented
2#19145150C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic, complemented
4#19134103C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134065C211yesmaximal, characteristic, complemented
7#19134058C211yesmaximal, characteristic, complemented
8#19134055C211yesmaximal, characteristic, complemented
9#19134048C211yesmaximal, characteristic, complemented
10#19134037C211yesmaximal, characteristic, complemented
11#19134030C211yesmaximal, characteristic, complemented
12C2×#14582651C211yesmaximal, characteristic, complemented
13#19133293C211yesmaximal, characteristic, complemented
14#19133290C211yesmaximal, characteristic, complemented
15C43×#3247C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583271C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583203—21no—
22#14583184C2211yescharacteristic
23#14583179C2211yescharacteristic
24#14583138—21no—
25#14583126—21no—
26#14583126—21no—
27#14583126—21no—
28#14583118—21no—
29#14583109C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621883—21no—
34C4×#10621883—21no—
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582651C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
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
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8D411yescharacteristic
75C22×C43⋊C8D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284—21no—
84#13063258—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
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
158C2×Dic86—21no—
159C2×Dic86—21no—
160SD16×C43—81no—
161D8×C43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—81no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621885—81no—
187#10621883—42no—
188#10621883—42no—
189#10621883—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—41no—
197#10621877—42no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—42no—
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—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13512yes—
259#19229—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43#47112yes—
269C22×C43C2×#12111yescharacteristic
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57611yescharacteristic
281C4×C43#57811yescharacteristic
282Dic43—81no—
283Dic43—81no—
284#3248—431no—
285#3247D4311yescharacteristic
286#3167—431no—
287#2966—431no—
288#1692—431no—
289#1691—431no—
290#1686—431no—
291#1685—431no—
292#1684—431no—
293#1683—431no—
294#1682—431no—
295#1681—431no—
296C2×#335—431no—
297#1552—431no—
298#1551—431no—
299C2×C43—22no—
300C2×C43—81no—
301C2×C43—161no—
302C2×C43#303511yescharacteristic
303C2×C43#306111yescharacteristic
304C2×C43C2×#47111yescharacteristic
305#533—431no—
306#532C2×D4311yescharacteristic
307#529C2×D4311yescharacteristic
308#498—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#479—861no—
313#478—21no—
314#477C2×D4311yescharacteristic
315#476C2×D4311yescharacteristic
316#475—431no—
317#474—431no—
318#467—861no—
319#466—21no—
320#465—21no—
321#465—861no—
322#465—861no—
323#465—861no—
324#464—861no—
325#463—21no—
326#462—431no—
327#461—431no—
328#460C2×D4311yescharacteristic
329#459C2×D4311yescharacteristic
330#446—431no—
331C8×Q8—431no—
332C4×SD16—861no—
333C4×SD16—861no—
334#436—431no—
335#435—861no—
336C8×D4—431no—
337C8×D4—861no—
338#433—861no—
339#432—431no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8C2×D4311yescharacteristic
342#405—861no—
343C2×C4×C8—431no—
344#335—431no—
345#335—431no—
346#335—431no—
347#335—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1922911yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C2×Q16—861no—
359C2×SD16—21no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—21no—
364C2×M16—861no—
365C22×C8—21no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8—861no—
369C22×C8—861no—
370C4⋊Q8—431no—
371C4⋊Q8—431no—
372C4⋊Q8C22×D4311yescharacteristic
373#127C22×D4311yescharacteristic
374#126—21no—
375#125—861no—
376#125C22⋊D4311yescharacteristic
377#124—21no—
378#124C22⋊D4311yescharacteristic
379#123—21no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8C22⋊D4311yescharacteristic
383#121—21no—
384#121—21no—
385#121C22⋊D4311yescharacteristic
386C4×Q8—861no—
387C4×Q8—861no—
388C4×Q8C22×D4311yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C22×D4311yescharacteristic
393#117—21no—
394#117—861no—
395C2×C42C22×D4311yescharacteristic
396#107—21no—
397#107—861no—
398#106—21no—
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—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—21no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—861no—
422#102—861no—
423#102—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—861no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434#41—82no—
435C2×Q8—21no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8C2×C22⋊D4311yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×C22⋊D4311yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4D4×D4311yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450Q16—3441no—
451SD16—81no—
452SD16—3441no—
453SD16—1722no—
454SD16—1722no—
455D8—81no—
456M16—1722no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—862no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—1721no—
471C2×C8—1722no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C4⋊C4C2×C22⋊D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—1721no—
494C42—21no—
495C42—1721no—
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—41no—
502C23#1306329711yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—81no—
506Q8—1721no—
507Q8—1721no—
508Q8—1721no—
509Q8—1721no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329711yescharacteristic
534C2×C4#1306329711yescharacteristic
535C2×C4#1306329711yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C8—41no—
540C8—41no—
541C8—432no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#1458316012yes—
558C22C2×#1306329711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—3441no—
568C4—3441no—
569C4#135×D4311yescharacteristic
570C4#1458369611yescharacteristic
571C4#1458370211yescharacteristic
572C4#1458371411yescharacteristic
573C2—22no—
574C2—81no—
575C2—161no—
576C2#1914404611yescharacteristic
577C2#1914426211yescharacteristic
578C2C2×#1458316011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3247C2
socleC22×C43C2×#121
hypercenter#3247D43
hypocenterC43#19229
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. #19145932C2semidirect
2. #19145150C2semidirect
3. #19143571C2semidirect
4. #19134103C2semidirect
5. #19134096C2semidirect
6. #19134065C2semidirect
7. #19134058C2semidirect
8. #19134055C2semidirect
9. #19134048C2semidirect
10. #19134037C2semidirect
11. #19134030C2semidirect
12. C2×#14582651C2semidirect
13. #19133293C2semidirect
14. #19133290C2semidirect
356. C43#19229semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191451502
#191435712
#191341032
#191340962
#191340652
#191340582
#191340552
#191340482
#191340372
#191340302
C2×#145826512
#191332932
#191332902
C43×#32472
#1922943