Finite Group Databasebeta

← #25080585

Subgroups — #25080585

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144917C211yesmaximal, characteristic, complemented
2#19144757C211yesmaximal, characteristic, complemented
3#41×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134051C211yesmaximal, characteristic, complemented
5#19134044C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19134030C211yesmaximal, characteristic, complemented
8#19134023C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19134009C211yesmaximal, characteristic, complemented
11#19134002C211yesmaximal, characteristic, complemented
12#19133356C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133300C211yesmaximal, characteristic, complemented
15C43×#3115C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583253—21no—
18#14583253—21no—
19#14583249C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583240—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583109C2211yescharacteristic
27#14583104C2211yescharacteristic
28#14583061—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14583004—21no—
32#14582999—21no—
33D4×C43⋊C8—21no—
34D4×C43⋊C8—21no—
35D4×C43⋊C8C2211yescharacteristic
36D4×C43⋊C8C2211yescharacteristic
37#14582956C2211yescharacteristic
38#14582952—21no—
39#14582952C2211yescharacteristic
40#14582895—21no—
41#14582895—21no—
42C2×C4×C43⋊C8—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#442—21no—
65C43×#440—21no—
66C43×#432C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8D411yescharacteristic
72C22×C43⋊C8D411yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063317—21no—
76#13063304—21no—
77#13063304—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80#13063284—21no—
81#13063258—21no—
82#13063256—21no—
83C4⋊(C43⋊C8)—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)C2311yescharacteristic
86C4⋊(C43⋊C8)C2311yescharacteristic
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89#13063249—21no—
90#13063249—21no—
91#13063249—21no—
92#13063249—21no—
93#13063249—21no—
94#13063248—21no—
95#13063248—21no—
96#13063246—21no—
97#13063246—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106C4×C43⋊C8—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—42no—
147#41×C43—42no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165SD16×C43—42no—
166D8×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—42no—
189#10621883—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43#13512yes—
216D4×C43—24no—
217D4×C43—21no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—81no—
223D4×C43—82no—
224D4×C43#13512yes—
225C2×C4×C43—24no—
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—42no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×Dic43—41no—
246C2×Dic43—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—81no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19278—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—22no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43C2×#12111yescharacteristic
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—22no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43C2×#13511yescharacteristic
280C4×C43C2×#13511yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57511yescharacteristic
283Dic43—81no—
284Dic43—81no—
285#3131—431no—
286#3116—431no—
287#3115D4311yescharacteristic
288C8×#41—431no—
289#1684—431no—
290#1683—431no—
291#1682—431no—
292#1681—431no—
293#1680—431no—
294#1679—431no—
295#1678—431no—
296#1677—431no—
297#1568—431no—
298#1554—431no—
299#1553—431no—
300C2×C43—41no—
301C2×C43—42no—
302C2×C43—161no—
303C2×C43#304011yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43#306711yescharacteristic
306#533—431no—
307#532C2×D4311yescharacteristic
308C4×#41C2×D4311yescharacteristic
309#488—861no—
310#488—861no—
311#487—431no—
312#487—431no—
313#486—431no—
314#486—431no—
315#485—861no—
316#482—21no—
317#477—431no—
318#476—431no—
319#475C2×D4311yescharacteristic
320#474C2×D4311yescharacteristic
321#462—431no—
322#461—431no—
323#460C2×D4311yescharacteristic
324#459C2×D4311yescharacteristic
325#452—861no—
326#449—21no—
327C8×Q8—431no—
328C8×Q8—431no—
329#442—21no—
330#441—861no—
331#440—21no—
332#440—861no—
333C8×D4—431no—
334C8×D4—431no—
335C8×D4—861no—
336C8×D4—861no—
337#432—431no—
338#432C2×D4311yescharacteristic
339#431—431no—
340#431—861no—
341#416—861no—
342#416—861no—
343C2×C4×C8—431no—
344C2×C4×C8—861no—
345#335—431no—
346#335—431no—
347#334—431no—
348#334—431no—
349#333—431no—
350#333—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#331—431no—
356#331—431no—
357C43#1927811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41C22⋊D4311yescharacteristic
360C2×Q16—861no—
361C2×SD16—21no—
362C2×SD16—861no—
363C2×D8—21no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—861no—
373#124—21no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—21no—
377#121—21no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8C22⋊D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C22⋊D4311yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—861no—
390#117C22⋊D4311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D4311yescharacteristic
393#107—21no—
394#107—861no—
395#106—21no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421C22⋊C8—21no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435#41—22no—
436#41—22no—
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×C22⋊D4311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—1722no—
457SD16—42no—
458SD16—1722no—
459D8—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—1721no—
471C2×C8—1721no—
472C2×C8—1722no—
473C2×C8—1722no—
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—41no—
490C22⋊C4—41no—
491C22⋊C4—1721no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—1721no—
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—41no—
502C23#1306329711yescharacteristic
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—3441no—
507Q8—1721no—
508Q8—1721no—
509Q8#1306334512yes—
510D4—24no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4#1306334512yes—
519C2×C4—24no—
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—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4#1306329711yescharacteristic
536C2×C4#1306329711yescharacteristic
537C2×C4#1306329711yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C22×C22⋊D4311yescharacteristic
540C2×C4C2×#1062190011yescharacteristic
541C8—41no—
542C8—41no—
543C8—861no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C2×#1306329711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—3441no—
570C4—3441no—
571C4C2×#1306334511yescharacteristic
572C4C2×#1306334511yescharacteristic
573C4#1458369511yescharacteristic
574C4#1458369511yescharacteristic
575C2—41no—
576C2—42no—
577C2—161no—
578C2#1914408711yescharacteristic
579C2#1914417311yescharacteristic
580C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3115C2
socleC22×C43C2×#121
hypercenter#3115D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #19144917C2semidirect
2. #19144757C2semidirect
3. #41×C43⋊C8C2semidirect
4. #19134051C2semidirect
5. #19134044C2semidirect
6. #19134037C2semidirect
7. #19134030C2semidirect
8. #19134023C2semidirect
9. #19134016C2semidirect
10. #19134009C2semidirect
11. #19134002C2semidirect
12. #19133356C2semidirect
13. #19133306C2semidirect
14. #19133300C2semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191449172
#191447572
#41×C43⋊C82
#191340512
#191340442
#191340372
#191340302
#191340232
#191340162
#191340092
#191340022
#191333562
#191333062
#191333002
C43×#31152
#1927843