Finite Group Databasebeta

← #25081877

Subgroups — #25081877

Order 11008.

656 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145516C211yesmaximal, characteristic
2#475×D43C211yesmaximal, characteristic, complemented
3#19144062C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic, complemented
5#19134026C211yesmaximal, characteristic, complemented
6#19134025C211yesmaximal, characteristic, complemented
7#19134024C211yesmaximal, characteristic, complemented
8#19134023C211yesmaximal, characteristic, complemented
9#19133942C211yesmaximal, characteristic, complemented
10#19133941C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic
15C43×#1666C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583271C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583185C2211yescharacteristic
24#14583184C2211yescharacteristic
25#14583183—21no—
26#14583182—21no—
27#14583181C2211yescharacteristic
28#14583120—21no—
29#14583119—21no—
30#14583110C2211yescharacteristic
31#14583109C2211yescharacteristic
32#14583102—21no—
33#14583102—21no—
34#14583096C2211yescharacteristic
35#14583036—21no—
36#14583036—21no—
37Q8×C43⋊C8C2211yescharacteristic
38C8×Dic86—21no—
39C8×Dic86C2211yescharacteristic
40#14583023—21no—
41#14583023C2211yescharacteristic
42#14582951—21no—
43#14582951C2211yescharacteristic
44#14582950—21no—
45#14582950C2211yescharacteristic
46#106×D43—21no—
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582897—21no—
50#103×D43—21no—
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43D411yescharacteristic
70#13063354—44no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621872—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063323—21no—
83#13063312—21no—
84#13063296—21no—
85#13063296—21no—
86Q8×Dic43D411yescharacteristic
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90#13063290D411yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43D411yescharacteristic
97C42×D43—21no—
98C42×D43C2311yescharacteristic
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063249—21no—
117#13063249—21no—
118#13063249—21no—
119#13063248—21no—
120#13063248—21no—
121#13063246—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×Q8×C43C2311yescharacteristic
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#102×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×C22⋊D43—41no—
151C22×Dic43—41no—
152Q8×D43—22no—
153Q8×D43—81no—
154Q8×D43—81no—
155Q8×D43SD1614yescomplemented
156#10621900—42no—
157#10621900—42no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43#4111yescharacteristic
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—41no—
168C2×Dic86C2×D411yescharacteristic
169SD16×C43—42no—
170SD16×C43—81no—
171SD16×C43—81no—
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#10621883—42no—
187#10621883—81no—
188#10621883—81no—
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—
212#10621872—42no—
213C8×D43—42no—
214C23×C43—41no—
215C22×D43#12111yescharacteristic
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43C2×SD1612yes—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—81no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C22⋊D43—82no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—82no—
237C2×Dic43#12111yescharacteristic
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C4×D43—24no—
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—41no—
244C4×D43—81no—
245C4×D43—82no—
246C4×D43C2×SD1612yes—
247C4×D43#13512yes—
248Dic86—21no—
249Dic86—24no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—82no—
255Dic86C2×SD1612yes—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#19397—431nomaximal, Sylow
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43C2×#12111yescharacteristic
271C2×D43—21no—
272C2×D43—21no—
273C2×D43#46512yes—
274C4×C43—22no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43C22×SD1611yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—21no—
283Dic43—22no—
284Dic43—21no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288Dic43#46512yes—
289#3206—431no—
290C2×#475—431no—
291#3037—431no—
292#2982—431no—
293#1680—431no—
294#1680—431no—
295#1680—431no—
296#1680—431no—
297#1666—431no—
298#1666—431no—
299#1666—431no—
300#1666D4311yescharacteristic, complemented
301#1570—431no—
302#1549—431no—
303#1540—431no—
304C2×C43—161no—
305C2×C43#304311yescharacteristic
306C2×C43C2×#46511yescharacteristic
307C2×C43#306911yescharacteristic
308D43—22no—
309C2×#137—861no—
310#532—431no—
311C2×C4⋊Q8—431no—
312C2×C4×Q8—431no—
313#492—431no—
314#492C2×D4311yescharacteristic
315#487—431no—
316#487—431no—
317#475—431no—
318#475—431no—
319#475—431no—
320#475—861no—
321#475—861no—
322#475C2×D4311yescharacteristic
323#464—861no—
324#464—861no—
325#462—431no—
326#462—431no—
327#461—861no—
328#461—861no—
329#460—431no—
330#460C2×D4311yescharacteristic
331#448—861no—
332#448—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335C8×Q8—431no—
336C8×Q8—861no—
337C8×Q8—861no—
338C8×Q8C2×D4311yescharacteristic
339#431—431no—
340#431—431no—
341#431—861no—
342#431—861no—
343C2×#106—861no—
344#423—431no—
345C2×C4⋊C8—431no—
346#417—861no—
347C2×#103—861no—
348#334—431no—
349#334—431no—
350#334—431no—
351#334C2×D4311yescharacteristic
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332C2×D4311yescharacteristic
358#331—431no—
359#331C2×D4311yescharacteristic
360C43#1939711yescharacteristic, complemented, Sylow
361C2×#41—861no—
362C22×Q8—431no—
363C22×Q8—861no—
364#137—1724no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×M16—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8C22×D4311yescharacteristic
381#127C22×D4311yescharacteristic
382#124—861no—
383#121—861no—
384#121—861no—
385C4×Q8—431no—
386C4×Q8—431no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×D4—861no—
392C4×D4—861no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C42—431no—
398C2×C42—861no—
399#106—21no—
400#106—861no—
401#106—861no—
402#106—861no—
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—21no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#103—861no—
427#102—21no—
428#102—861no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C22⋊C8—861no—
432C4×C8—21no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8C22×D4311yescharacteristic
439#41—1722no—
440#41—1722no—
441C2×Q8—21no—
442C2×Q8—434no—
443C2×Q8—431no—
444C2×Q8—861no—
445C2×Q8—862no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—3441no—
449C2×Q8—3441no—
450C2×Q8—1721no—
451C2×Q8D4×D4311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—1721no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—1721no—
462C22×C4—1721no—
463Q16—1722no—
464Q16—1722no—
465SD16—42no—
466SD16—81no—
467SD16—81no—
468SD16—3441no—
469SD16—3441no—
470SD16—1722no—
471M16—1722no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1722no—
481C2×C8D4×D4311yescharacteristic
482C2×C8D4×D4311yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C4⋊C4D4×D4311yescharacteristic
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—21no—
501C42—431no—
502C42—431no—
503C42—431no—
504C42—861no—
505C42—861no—
506C42—861no—
507C42C23×D4311yescharacteristic
508C23—41no—
509C23—431no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—432no—
514Q8—864no—
515Q8—861no—
516Q8—3442no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8SD16×D4312yes—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—3442no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—431no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—431no—
535C2×C4—431no—
536C2×C4—864no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3441no—
542C2×C4—3442no—
543C2×C4—3442no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4#41×D4311yescharacteristic
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—432no—
564C22—861no—
565C22—861no—
566C22#121×D4311yescharacteristic
567C4—21no—
568C4—22no—
569C4—41no—
570C4—81no—
571C4—432no—
572C4—861no—
573C4—861no—
574C4—862no—
575C4—3441no—
576C4—3441no—
577C4—1721no—
578C4C2×SD16×D4311yescharacteristic
579C4#135×D4311yescharacteristic
580C4#1458370511yescharacteristic
581C4#1458370911yescharacteristic
582C2—161no—
583C2—862no—
584C2#1914411111yescharacteristic
585C2#465×D4311yescharacteristic
586C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1666C2
socleC22×C43C2×#121
prime radical#14583447C22
hypercenter#1666D43
hypocenterC43#19397
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1666

Complements

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

NH ≅ G/Ntype
2. #475×D43C2semidirect
4. #19143674C2semidirect
5. #19134026C2semidirect
6. #19134025C2semidirect
7. #19134024C2semidirect
8. #19134023C2semidirect
9. #19133942C2semidirect
10. #19133941C2semidirect
11. #19133940C2semidirect
12. #19133364C2semidirect
13. #19133278C2semidirect
15. C43×#1666C2semidirect
155. Q8×D43SD16semidirect
300. #1666D43semidirect
360. C43#19397semidirect

Maximal subgroups

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

subgroupindex
#191455162
#475×D432
#191440622
#191436742
#191340262
#191340252
#191340242
#191340232
#191339422
#191339412
#191339402
#191333642
#191332782
#191332412
C43×#16662
#1939743