Finite Group Databasebeta

← #25084192

Subgroups — #25084192

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#19145915C211yesmaximal, characteristic
2#19145720C211yesmaximal, characteristic, complemented
3#19145624C211yesmaximal, characteristic, complemented
4#19143751C211yesmaximal, characteristic, complemented
5#19134162C211yesmaximal, characteristic, complemented
6#19134155C211yesmaximal, characteristic, complemented
7#19134104C211yesmaximal, characteristic, complemented
8#19134097C211yesmaximal, characteristic, complemented
9#19134038C211yesmaximal, characteristic, complemented
10#19134031C211yesmaximal, characteristic, complemented
11#19133980C211yesmaximal, characteristic, complemented
12#19133973C211yesmaximal, characteristic, complemented
13#19133381C211yesmaximal, characteristic, complemented
14C2×#14582644C211yesmaximal, characteristic, complemented
15C43×#1551C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583293—21no—
21#14583268—21no—
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583215—21no—
25#14583215—21no—
26#14583199—21no—
27#14583191C2211yescharacteristic
28#14583189—21no—
29#14583189—21no—
30#14583186C2211yescharacteristic
31#14583133—21no—
32#14583126—21no—
33#14583114—21no—
34#14583110C2211yescharacteristic
35#14583110C2211yescharacteristic
36#14583105C2211yescharacteristic
37#14583105C2211yescharacteristic
38#14583096C2211yescharacteristic
39#14583091C2211yescharacteristic
40#14583057—21no—
41#14583040—21no—
42#14583026C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14582976C2211yescharacteristic
45#14582970—21no—
46#14582964C2211yescharacteristic
47C8×C22⋊D43—21no—
48#14582959—21no—
49#14582952C2211yescharacteristic
50#14582924—21no—
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C22×Dic86—21no—
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621882—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063325—21no—
78#13063325—21no—
79#13063325—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063319—21no—
83#13063317D411yescharacteristic
84#13063313D411yescharacteristic
85#13063308—21no—
86#13063304D411yescharacteristic
87#13063299D411yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×D172C2311yescharacteristic
90C4×C22⋊D43—21no—
91#13063282—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94#13063258—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)D411yescharacteristic
102C4⋊(C43⋊C8)D411yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063248—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063245—21no—
119C22⋊(C43⋊C8)D411yescharacteristic
120C22⋊(C43⋊C8)D411yescharacteristic
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130#127×C43C2311yescharacteristic
131#124×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155C22×Dic43—41no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—41no—
161C2×Dic86—81no—
162C2×Dic86—81no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178#10621883—81no—
179#10621882—81no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—81no—
205Dic172—81no—
206#10621873—81no—
207#10621873—81no—
208#10621872—81no—
209C8×D43—81no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212C22×D43—21no—
213Q8×C43—81no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219D4×C43—82no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—82no—
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—42no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—82no—
240D172—21no—
241D172—21no—
242C4×D43—41no—
243C4×D43—41no—
244Dic86—21no—
245Dic86—21no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
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—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43#47112yes—
268C22×C43C2×#12111yescharacteristic
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—81no—
277C4×C43#57611yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43—81no—
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#1551D4311yescharacteristic, complemented
300C2×#332—431no—
301C2×C43—22no—
302C2×C43—161no—
303C2×C43#304611yescharacteristic
304C2×C43#306211yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—81no—
307#532C2×D4311yescharacteristic
308C2×C4⋊Q8—431no—
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#432C2×D4311yescharacteristic
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#333C2×D4311yescharacteristic
351#333C2×D4311yescharacteristic
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331C2×D4311yescharacteristic
357#331C2×D4311yescharacteristic
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—861no—
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—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—861no—
379#125—431no—
380#124—21no—
381#124—431no—
382#123—861no—
383C22⋊Q8—431no—
384#121—21no—
385#121—21no—
386#121—431no—
387C4×Q8—431no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—431no—
391C4×D4—861no—
392#117—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
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—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
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—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—21no—
432#97—861no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—431no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3441no—
442C2×Q8—3441no—
443C2×Q8—1721no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—431no—
449C2×D4—861no—
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—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8—3441no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—431no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C42—861no—
498C42#1062189811yescharacteristic
499C42D4×D4311yescharacteristic
500C42D4×D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—41no—
503C23—861no—
504C23#1306329811yescharacteristic
505Q8—81no—
506Q8—861no—
507Q8—861no—
508Q8—3442no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519D4—861no—
520D4—861no—
521D4—1722no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—3442no—
533C2×C4—1721no—
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—81no—
556C22—81no—
557C22—81no—
558C22—1721no—
559C22—1721no—
560C22—1721no—
561C22#1458316112yes—
562C22C2×#1306329811yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—81no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4—1721no—
572C4—1721no—
573C4#1458370111yescharacteristic
574C4#1458370611yescharacteristic
575C4#1458370911yescharacteristic
576C4#1458371511yescharacteristic
577C2—22no—
578C2—161no—
579C2—3441no—
580C2#1914414411yescharacteristic
581C2#1914427811yescharacteristic
582C2C2×#1458316111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#1551D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
2. #19145720C2semidirect
3. #19145624C2semidirect
4. #19143751C2semidirect
5. #19134162C2semidirect
6. #19134155C2semidirect
7. #19134104C2semidirect
8. #19134097C2semidirect
9. #19134038C2semidirect
10. #19134031C2semidirect
11. #19133980C2semidirect
12. #19133973C2semidirect
13. #19133381C2semidirect
14. C2×#14582644C2semidirect
15. C43×#1551C2semidirect
299. #1551D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191457202
#191456242
#191437512
#191341622
#191341552
#191341042
#191340972
#191340382
#191340312
#191339802
#191339732
#191333812
C2×#145826442
C43×#15512
#1958943