Finite Group Databasebeta

← #25079289

Subgroups — #25079289

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145150C211yesmaximal, characteristic, complemented
2#19144385C211yesmaximal, characteristic, complemented
3#19144044C211yesmaximal, characteristic
4#19143556C211yesmaximal, characteristic, complemented
5#19134152C211yesmaximal, characteristic, complemented
6#19134145C211yesmaximal, characteristic, complemented
7#19134134C211yesmaximal, characteristic, complemented
8#19134127C211yesmaximal, characteristic, complemented
9#19134100C211yesmaximal, characteristic, complemented
10#19134093C211yesmaximal, characteristic, complemented
11#19134066C211yesmaximal, characteristic, complemented
12#19134059C211yesmaximal, characteristic, complemented
13C2×#14582651C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583456C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583271C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583207—21no—
24#14583200—21no—
25#14583195C2211yescharacteristic
26#14583190C2211yescharacteristic
27#14583185C2211yescharacteristic
28#14583180C2211yescharacteristic
29#14583126—21no—
30#14583126—21no—
31#14583118—21no—
32#14583111—21no—
33#14583106C2211yescharacteristic
34#14583101C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583091C2211yescharacteristic
37#14583026C2211yescharacteristic
38#14583026C2211yescharacteristic
39C4×#10621883—21no—
40C4×#10621883—21no—
41#14582976C2211yescharacteristic
42#14582976C2211yescharacteristic
43#14582967—21no—
44#14582967—21no—
45#14582950—21no—
46#14582937—21no—
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582896—21no—
49#14582895—21no—
50C4×#10621872—21no—
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582651C2211yescharacteristic
55#14582651C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582646C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78C22×C43⋊C8D411yescharacteristic
79C22×C43⋊C8D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063317—21no—
83#13063304—21no—
84#13063304—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86D411yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×D172D411yescharacteristic
90C4×D172C2311yescharacteristic
91C4×C22⋊D43—21no—
92C4×C22⋊D43—21no—
93#13063284—21no—
94#13063284D411yescharacteristic
95#13063282—21no—
96C42×D43—21no—
97#13063259—21no—
98#13063259—21no—
99#13063257—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108#13063250—21no—
109#13063250—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8D411yescharacteristic
125C4×C43⋊C8D411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C2×#41×C43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131#127×C43C2311yescharacteristic
132#124×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43—21no—
145#41×C43—42no—
146#41×C43—42no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C22×C4×C43—41no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—21no—
157#10621898—22no—
158#10621898—22no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×D411yescharacteristic
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—42no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43—41no—
181#10621885—42no—
182#10621884—42no—
183#10621883—42no—
184#10621883—42no—
185#10621883—42no—
186#10621882—42no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—41no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—41no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621872—42no—
213#10621872—42no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216C22×D43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—81no—
224D4×C43—82no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—82no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43AGL(1,ℤ/8)12yes—
234C2×C4×C43#13712yes—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—42no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—21no—
245D172—21no—
246C4×D43—42no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—42no—
250Dic86—21no—
251Dic86—21no—
252Dic86—41no—
253Dic86—41no—
254Dic86—81no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8#13512yescomplemented
265#19156—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43#46812yes—
272C22×C43C2×#12111yescharacteristic
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—41no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—81no—
280C4×C43#46812yes—
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C43C2×#13711yescharacteristic
284C4×C43#57511yescharacteristic
285Dic43—41no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#3167—431no—
291#3076—431no—
292#3035—431no—
293#2965—431no—
294#1700—431no—
295#1699—431no—
296#1698—431no—
297#1697—431no—
298#1692—431no—
299#1691—431no—
300#1686—431no—
301#1685—431no—
302C2×#335—431no—
303#1542—431no—
304#1540D4311yescharacteristic, complemented
305C2×C43—22no—
306C2×C43—161no—
307C2×C43#303511yescharacteristic
308C2×C43C2×#46811yescharacteristic
309C2×C43#306711yescharacteristic
310D43—81no—
311C2×#135—861no—
312#533—431no—
313#532C2×D4311yescharacteristic
314C4×#41—431no—
315#498—431no—
316#492—431no—
317#487—431no—
318#486—431no—
319#479—861no—
320#478—861no—
321#477—431no—
322#476—431no—
323#475—431no—
324#474—431no—
325#465—861no—
326#465—861no—
327#464—861no—
328#463—861no—
329#462—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333#446—431no—
334#446—431no—
335C4×SD16—861no—
336C4×SD16—861no—
337#436—431no—
338#436—431no—
339#435—861no—
340#435—861no—
341#431—861no—
342#431C2×D4311yescharacteristic
343#427—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8C2×D4311yescharacteristic
346#416—861no—
347#416—861no—
348C4×M16—861no—
349C2×C4×C8—431no—
350#335—431no—
351#335—431no—
352#335—431no—
353#335—431no—
354#333—431no—
355#333—431no—
356#332—431no—
357#332—431no—
358#332C2×D4311yescharacteristic
359#332C2×D4311yescharacteristic
360#331C2×D4311yescharacteristic
361#331C2×D4311yescharacteristic
362C43#1915611yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C2×#41—431no—
365#135—1724no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C2×M16—861no—
373C2×M16—861no—
374C22×C8—21no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—861no—
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8C22×D4311yescharacteristic
381#127C22×D4311yescharacteristic
382#125—861no—
383#124—21no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386#121—21no—
387#121—21no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×Q8—861no—
391C4×Q8—861no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—431no—
395C4×D4—431no—
396C4×D4—861no—
397C4×D4—861no—
398#117—431no—
399#117—861no—
400#117—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—861no—
404#107—861no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—21no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434#97—861no—
435#97—861no—
436C4×C8—21no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441#41—42no—
442#41—42no—
443#41—862no—
444#41—862no—
445C2×Q8—21no—
446C2×Q8—431no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—431no—
454C2×D4—861no—
455C22×C4—41no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4#1062189811yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462Q16—1722no—
463SD16—1722no—
464SD16—1722no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468M16—1722no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—862no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1721no—
483C2×C8—1722no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—431no—
487C4⋊C4—431no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—1721no—
502C42—861no—
503C42—861no—
504C42—861no—
505C42—1721no—
506C42#1062189811yescharacteristic
507C42D4×D4311yescharacteristic
508C42D4×D4311yescharacteristic
509C42C23×D4311yescharacteristic
510C23—41no—
511C23—861no—
512C23#1306329811yescharacteristic
513Q8—41no—
514Q8—41no—
515Q8—861no—
516Q8—861no—
517Q8—3441no—
518Q8—1721no—
519Q8—1721no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—861no—
527D4—861no—
528D4—1722no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1722no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329811yescharacteristic
544C2×C4#1306329811yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4#1306334912yes—
547C2×C4#1306335412yes—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×#1062189811yescharacteristic
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—432no—
556C8—861no—
557C8—861no—
558C8—861no—
559C8—1721no—
560C8—1721no—
561C22—21no—
562C22—21no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—1721no—
567C22—1721no—
568C22—1721no—
569C22#1458314412yes—
570C22C2×#1306329811yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—3441no—
576C4—3441no—
577C4—1721no—
578C4—1721no—
579C4—1721no—
580C4#1458314412yes—
581C4#135×D4311yescharacteristic
582C4C2×#1306334911yescharacteristic
583C4C2×#1306335411yescharacteristic
584C4#1458369611yescharacteristic
585C2—22no—
586C2—161no—
587C2—3441no—
588C2#1914404811yescharacteristic
589C2C2×#1458314411yescharacteristic
590C2#1914431411yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1540C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#1540D43
hypocenterC43#19156
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #19145150C2semidirect
2. #19144385C2semidirect
4. #19143556C2semidirect
5. #19134152C2semidirect
6. #19134145C2semidirect
7. #19134134C2semidirect
8. #19134127C2semidirect
9. #19134100C2semidirect
10. #19134093C2semidirect
11. #19134066C2semidirect
12. #19134059C2semidirect
13. C2×#14582651C2semidirect
14. #19133250C2semidirect
15. C43×#1540C2semidirect
264. C43⋊C8#135semidirect
304. #1540D43semidirect
362. C43#19156semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191443852
#191440442
#191435562
#191341522
#191341452
#191341342
#191341272
#191341002
#191340932
#191340662
#191340592
C2×#145826512
#191332502
C43×#15402
#1915643