Finite Group Databasebeta

← #25084200

Subgroups — #25084200

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#19145922C211yesmaximal, characteristic
2#19145723C211yesmaximal, characteristic, complemented
3#19145622C211yesmaximal, characteristic, complemented
4#19143751C211yesmaximal, characteristic, complemented
5#19134166C211yesmaximal, characteristic, complemented
6#19134159C211yesmaximal, characteristic, complemented
7#19134100C211yesmaximal, characteristic, complemented
8#19134093C211yesmaximal, characteristic, complemented
9#19134042C211yesmaximal, characteristic, complemented
10#19134035C211yesmaximal, characteristic, complemented
11#19133976C211yesmaximal, characteristic, complemented
12#19133969C211yesmaximal, characteristic, complemented
13#19133378C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C2×C43×#332C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583291—21no—
21#14583267—21no—
22#14583247C2211yescharacteristic
23#14583247C2211yescharacteristic
24#14583217—21no—
25#14583217—21no—
26#14583200—21no—
27#14583195C2211yescharacteristic
28#14583190C2211yescharacteristic
29#14583186—21no—
30#14583186—21no—
31#14583135—21no—
32#14583128—21no—
33#14583115—21no—
34#14583106C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583101C2211yescharacteristic
38#14583100C2211yescharacteristic
39#14583095C2211yescharacteristic
40#14583055—21no—
41#14583038—21no—
42#14583026C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14582976C2211yescharacteristic
45#14582970—21no—
46#14582964C2211yescharacteristic
47C8×C22⋊D43—21no—
48#14582959—21no—
49#14582956C2211yescharacteristic
50#14582952C2211yescharacteristic
51#14582924—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C2×C4⋊Q8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×D344—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063319—21no—
79#13063317D411yescharacteristic
80#13063313—21no—
81#13063313D411yescharacteristic
82#13063308—21no—
83#13063304D411yescharacteristic
84#13063299—21no—
85#13063299—21no—
86#13063299D411yescharacteristic
87C4×Dic86C2311yescharacteristic
88C4×D172—21no—
89C4×D172—21no—
90C4×D172C2311yescharacteristic
91C4×C22⋊D43—21no—
92#13063282—21no—
93#13063259—21no—
94#13063257—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063249—21no—
107#13063249—21no—
108#13063249—21no—
109#13063249—21no—
110#13063247—21no—
111#13063247—21no—
112#13063247—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063236—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×Q8×C43—21no—
128C22×C8×C43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43—21no—
131C4⋊Q8×C43—21no—
132C4⋊Q8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C4⋊C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—81no—
148C2×Q8×C43—81no—
149C22×C4×C43—41no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×C22⋊D43—21no—
154C2×C22⋊D43—41no—
155#10621898—82no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43—81no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43#4111yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621885—81no—
182#10621885—81no—
183#10621884—81no—
184#10621884—81no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199C4×Dic43—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206D344—81no—
207#10621873—81no—
208#10621872—81no—
209C8×D43—81no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212C22×D43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—82no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—82no—
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—42no—
233C22⋊D43—82no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238D172—21no—
239D172—21no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—82no—
248Dic86—21no—
249Dic86—21no—
250Dic86—81no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43#47112yes—
265C22×C43C2×#12111yescharacteristic
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#57611yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57811yescharacteristic
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285Dic43—81no—
286#3247—431no—
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×#332D4311yescharacteristic, complemented
301C2×C43—22no—
302C2×C43#304611yescharacteristic
303C2×C43#306211yescharacteristic
304C2×C43C2×#47111yescharacteristic
305D43—81no—
306D43—161no—
307#532—431no—
308C2×C4⋊Q8C2×D4311yescharacteristic
309#529—431no—
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—861no—
319#477—431no—
320#476—431no—
321#476—861no—
322#476—861no—
323#466—861no—
324#465—861no—
325#463—861no—
326#462—431no—
327#462—431no—
328#461—431no—
329#461—431no—
330#460—431no—
331#459—431no—
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⋊C8C2×D4311yescharacteristic
345C2×C4⋊C8C2×D4311yescharacteristic
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332C2×D4311yescharacteristic
353#332C2×D4311yescharacteristic
354#332C2×D4311yescharacteristic
355#332C2×D4311yescharacteristic
356#331—431no—
357#331—431no—
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C22×Q8—21no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C2×M16—861no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—861no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—431no—
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377#127—431no—
378#126—861no—
379#125—431no—
380#124—431no—
381#124—861no—
382#123—861no—
383C22⋊Q8—431no—
384#121—431no—
385#121—861no—
386#121—861no—
387C4×Q8—431no—
388C4×D4—431no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392#117—861no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—861no—
420#102—861no—
421#102—861no—
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—3442no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×Q8—431no—
443C2×Q8—861no—
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—1721no—
450C22×C4—41no—
451C22×C4—861no—
452C22×C4—1721no—
453C22×C4#1062189811yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456Q16—3441no—
457Q16—3441no—
458SD16—3441no—
459SD16—3441no—
460SD16—3441no—
461D8—3441no—
462M16—3441no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—81no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—431no—
483C4⋊C4—431no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—861no—
498C42#1062189811yescharacteristic
499C42D4×D4311yescharacteristic
500C42D4×D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—861no—
503C23—1721no—
504C23#1306329811yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8—861no—
511Q8—861no—
512Q8—3441no—
513D4—861no—
514D4—861no—
515D4—3441no—
516D4—3442no—
517D4—1722no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521D4—1721no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306329811yescharacteristic
538C2×C4#1306329811yescharacteristic
539C2×C4#1306329811yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—861no—
548C8—861no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22—1721no—
559C22—1721no—
560C22—1721no—
561C22#1458316512yes—
562C22C2×#1306329811yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—81no—
568C4—81no—
569C4—3441no—
570C4—1721no—
571C4—1721no—
572C4—1721no—
573C4#1458370011yescharacteristic
574C4#1458370511yescharacteristic
575C4#1458370511yescharacteristic
576C4#1458371211yescharacteristic
577C2—22no—
578C2—3441no—
579C2—6881no—
580C2#1914415011yescharacteristic
581C2#1914427311yescharacteristic
582C2C2×#1458316511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#332C2
socleC22×C43C2×#121
prime radical#19145922C2
hypercenterC2×#332D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #19145723C2semidirect
3. #19145622C2semidirect
4. #19143751C2semidirect
5. #19134166C2semidirect
6. #19134159C2semidirect
7. #19134100C2semidirect
8. #19134093C2semidirect
9. #19134042C2semidirect
10. #19134035C2semidirect
11. #19133976C2semidirect
12. #19133969C2semidirect
13. #19133378C2semidirect
14. #19133288C2semidirect
15. C2×C43×#332C2semidirect
300. C2×#332D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459222
#191457232
#191456222
#191437512
#191341662
#191341592
#191341002
#191340932
#191340422
#191340352
#191339762
#191339692
#191333782
#191332882
C2×C43×#3322
#1958943