Finite Group Databasebeta

← #25081947

Subgroups — #25081947

Order 11008.

676 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145712C211yesmaximal, characteristic
2#19144062C211yesmaximal, characteristic
3#462×D43C211yesmaximal, characteristic, complemented
4#19143674C211yesmaximal, characteristic, complemented
5#19134038C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19134036C211yesmaximal, characteristic, complemented
8#19133990C211yesmaximal, characteristic, complemented
9#19133989C211yesmaximal, characteristic, complemented
10#19133988C211yesmaximal, characteristic, complemented
11#19133987C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133265C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic
15C43×#1682C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17C2×Q16×D43—21no—
18#14583447C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20C4×Q8×D43C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583211—21no—
25#14583211—21no—
26#14583177—21no—
27#14583177—21no—
28#14583120—21no—
29#14583119—21no—
30#14583110C2211yescharacteristic
31#14583110C2211yescharacteristic
32#14583109C2211yescharacteristic
33#14583109C2211yescharacteristic
34#14583108—21no—
35#14583107—21no—
36#14583106C2211yescharacteristic
37#14583096C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86—21no—
40C8×Dic86C2211yescharacteristic
41#14583023—21no—
42#14583023C2211yescharacteristic
43#14582951—21no—
44#14582951C2211yescharacteristic
45#14582950—21no—
46#14582950C2211yescharacteristic
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582897—21no—
50#103×D43—21no—
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43D411yescharacteristic
70#13063354—44no—
71C2×Dic172—21no—
72C2×Dic172—21no—
73C2×#10621885—21no—
74C2×#10621885—21no—
75C2×#10621885—21no—
76Q16×D43—44no—
77C2×#10621883—21no—
78C2×#10621872—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063323—21no—
85#13063312—21no—
86#13063296—21no—
87#13063296—21no—
88Q8×Dic43D411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91#13063290—21no—
92#13063290D411yescharacteristic
93D4×Dic43—21no—
94D4×Dic43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43D411yescharacteristic
99C42×D43—21no—
100C42×D43C2311yescharacteristic
101#13063259—21no—
102#13063259—21no—
103#13063258—21no—
104#13063258—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115#13063250—21no—
116#13063250—21no—
117#13063249—21no—
118#13063248—21no—
119#13063248—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8D411yescharacteristic
125(C2×D43)⋊C8D411yescharacteristic
126C4×C43⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C2×Q16×C43—21no—
132C2×SD16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×Q8×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144C4×C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153Q8×D43—22no—
154Q8×D43—42no—
155Q8×D43—42no—
156Q8×D43D814yes—
157#10621900—42no—
158#10621900—42no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169C2×Dic86C2×D411yescharacteristic
170Q16×C43—42no—
171SD16×C43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C42×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185#10621885—42no—
186#10621885—42no—
187#10621885—42no—
188#10621883—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43#4111yescharacteristic
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211Dic172—42no—
212Dic172—42no—
213#10621872—42no—
214C8×D43—42no—
215C23×C43—41no—
216C22×D43#12111yescharacteristic
217Q8×C43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43C2×D812yes—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—82no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—82no—
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C2×Dic43#12111yescharacteristic
241C4×D43—24no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—41no—
245C4×D43—81no—
246C4×D43—82no—
247C4×D43C2×D812yes—
248C4×D43#13512yes—
249Dic86—21no—
250Dic86—24no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—82no—
256Dic86C2×D812yes—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19404—431nomaximal, Sylow
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43#46612yes—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43C22×D811yescharacteristic
280C4×C43C2×#13511yescharacteristic
281C4×C43#57811yescharacteristic
282C4×C43#57811yescharacteristic
283Dic43—21no—
284Dic43—22no—
285Dic43—21no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Dic43#46612yes—
290#3226—431no—
291#3037—431no—
292C2×#462—431no—
293#2982—431no—
294#1682—431no—
295#1682—431no—
296#1682—431no—
297#1682D4311yescharacteristic, complemented
298#1674—431no—
299#1674—431no—
300#1674—431no—
301#1674—431no—
302#1571—431no—
303#1546—431no—
304#1540—431no—
305C2×C43—161no—
306C2×C43#304411yescharacteristic
307C2×C43C2×#46611yescharacteristic
308C2×C43#306911yescharacteristic
309D43—22no—
310C2×#137—861no—
311C22×Q16—861no—
312#532—431no—
313C2×C4⋊Q8—431no—
314C2×C4×Q8—431no—
315#500—431no—
316#500—431no—
317#486—431no—
318#486C2×D4311yescharacteristic
319#480—861no—
320#480—861no—
321#474—861no—
322#474—861no—
323#464—861no—
324#464—861no—
325#462—431no—
326#462—431no—
327#462—431no—
328#462—431no—
329#462—431no—
330#462—861no—
331#462—861no—
332#462C2×D4311yescharacteristic
333#460—431no—
334#460C2×D4311yescharacteristic
335C8×Q8—431no—
336C8×Q8—431no—
337C8×Q8—431no—
338C8×Q8—861no—
339C8×Q8—861no—
340C8×Q8C2×D4311yescharacteristic
341#431—431no—
342#431—431no—
343#431—861no—
344#431—861no—
345#423—431no—
346C2×C4⋊C8—431no—
347#417—861no—
348C2×#103—861no—
349#335—431no—
350#335—431no—
351#335—431no—
352#335C2×D4311yescharacteristic
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332C2×D4311yescharacteristic
359#331—431no—
360#331C2×D4311yescharacteristic
361C43#1940411yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C22×Q8—431no—
364C22×Q8—861no—
365#137—1724no—
366C2×Q16—21no—
367C2×Q16—861no—
368C2×Q16—861no—
369C2×Q16—861no—
370C2×Q16—861no—
371C2×Q16—861no—
372C2×Q16—1724no—
373C2×SD16—21no—
374C2×SD16—861no—
375C2×M16—861no—
376C22×C8—861no—
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8C22×D4311yescharacteristic
383#127C22×D4311yescharacteristic
384#124—861no—
385#121—861no—
386#121—861no—
387C4×Q8—431no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×Q8—861no—
391C4×Q8—861no—
392C4×Q8C22×D4311yescharacteristic
393C4×D4—861no—
394C4×D4—861no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C42—431no—
400C2×C42—861no—
401#107—861no—
402#107—861no—
403#107—861no—
404#107—861no—
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—21no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—431no—
432C22⋊C8—431no—
433C22⋊C8—861no—
434C4×C8—21no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8—861no—
439C4×C8—861no—
440C4×C8C22×D4311yescharacteristic
441#41—1722no—
442#41—1722no—
443C2×Q8—21no—
444C2×Q8—434no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×Q8—862no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—1721no—
451C2×Q8—1722no—
452C2×Q8—1722no—
453C2×Q8D4×D4311yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—1721no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1721no—
464C22×C4—1721no—
465Q16—42no—
466Q16—1722no—
467Q16—1722no—
468Q16—1722no—
469Q16—1722no—
470Q16—1722no—
471SD16—42no—
472SD16—1722no—
473M16—1722no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1722no—
483C2×C8D4×D4311yescharacteristic
484C2×C8D4×D4311yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—431no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C4⋊C4D4×D4311yescharacteristic
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—21no—
503C42—431no—
504C42—431no—
505C42—431no—
506C42—861no—
507C42—861no—
508C42—861no—
509C42C23×D4311yescharacteristic
510C23—41no—
511C23—431no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—432no—
516Q8—864no—
517Q8—861no—
518Q8—3442no—
519Q8—1721no—
520Q8—1721no—
521Q8—1721no—
522Q8—1721no—
523Q8D8×D4312yes—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—3442no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—431no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—431no—
537C2×C4—431no—
538C2×C4—864no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—3441no—
544C2×C4—3442no—
545C2×C4—3442no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×D4×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—861no—
558C8—861no—
559C8—1721no—
560C8—1721no—
561C8—1721no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—432no—
566C22—861no—
567C22—861no—
568C22#121×D4311yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—81no—
573C4—432no—
574C4—861no—
575C4—861no—
576C4—862no—
577C4—3441no—
578C4—3441no—
579C4—1721no—
580C4C2×D8×D4311yescharacteristic
581C4#135×D4311yescharacteristic
582C4#1458371311yescharacteristic
583C4#1458371511yescharacteristic
584C2—161no—
585C2—862no—
586C2#1914412311yescharacteristic
587C2#466×D4311yescharacteristic
588C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1682C2
socleC22×C43C2×#121
prime radical#14583447C22
hypercenter#1682D43
hypocenterC43#19404
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

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

NH ≅ G/Ntype
3. #462×D43C2semidirect
4. #19143674C2semidirect
5. #19134038C2semidirect
6. #19134037C2semidirect
7. #19134036C2semidirect
8. #19133990C2semidirect
9. #19133989C2semidirect
10. #19133988C2semidirect
11. #19133987C2semidirect
12. #19133368C2semidirect
13. #19133265C2semidirect
15. C43×#1682C2semidirect
297. #1682D43semidirect
361. C43#19404semidirect

Maximal subgroups

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

subgroupindex
#191457122
#191440622
#462×D432
#191436742
#191340382
#191340372
#191340362
#191339902
#191339892
#191339882
#191339872
#191333682
#191332652
#191332412
C43×#16822
#1940443