Finite Group Databasebeta

← #25079595

Subgroups — #25079595

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144660C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic
3#19143613C211yesmaximal, characteristic, complemented
4#19134153C211yesmaximal, characteristic, complemented
5#19134139C211yesmaximal, characteristic, complemented
6#19134105C211yesmaximal, characteristic, complemented
7#19134057C211yesmaximal, characteristic, complemented
8#19134036C211yesmaximal, characteristic, complemented
9#19134022C211yesmaximal, characteristic, complemented
10#19133986C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133300C211yesmaximal, characteristic, complemented
14#19133295C211yesmaximal, characteristic, complemented
15C43×#3182C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17C4×#10621898C2211yescharacteristic
18#14583237—21no—
19#14583181C2211yescharacteristic
20#14583176C2211yescharacteristic
21#14583118—21no—
22#14583111—21no—
23#14583106C2211yescharacteristic
24#14583106C2211yescharacteristic
25#14583101C2211yescharacteristic
26#14583101C2211yescharacteristic
27#14583096C2211yescharacteristic
28#14583091C2211yescharacteristic
29#14583059—21no—
30C8×Dic86C2211yescharacteristic
31C8×Dic86C2211yescharacteristic
32C4×#10621885—21no—
33C4×#10621884—21no—
34#14582978C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582975—21no—
37#14582975—21no—
38#14582956C2211yescharacteristic
39#14582954—21no—
40#14582952C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582895—21no—
43#14582851—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#468—21no—
63C43×#468—21no—
64C43×#440—21no—
65C43×#440—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78C4×Dic86D411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172D411yescharacteristic
81C4×D172C2311yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284D411yescharacteristic
85#13063282—21no—
86C42×D43—21no—
87#13063258—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97Dic43⋊C8—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063248—21no—
103#13063246—21no—
104#13063246—21no—
105#13063245—21no—
106C22⋊(C43⋊C8)—21no—
107C22⋊(C43⋊C8)—21no—
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110#13063236—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C8×Dic43—21no—
114C2×#41×C43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×M16×C43D411yescharacteristic
118C2×M16×C43D411yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#125×C43—21no—
124#124×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#107×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#97×C43D411yescharacteristic
142#97×C43D411yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C22×C4×C43—41no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×C22⋊D43—21no—
159#10621898—22no—
160#10621898—41no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×Dic86C2×D411yescharacteristic
166SD16×C43—42no—
167SD16×C43—42no—
168M16×C43—22no—
169M16×C43—41no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43—41no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—21no—
191#10621885—42no—
192#10621885—42no—
193#10621884—42no—
194#10621884—42no—
195#10621883—42no—
196#10621882—42no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—42no—
213#10621872—42no—
214#10621872—42no—
215C23×C43—41no—
216C23×C43#12111yescharacteristic
217C22×D43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—82no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C22⋊D43—42no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249D172—21no—
250D172—21no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—81no—
255Dic86—21no—
256Dic86AGL(1,ℤ/8)12yes—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43#13512yescomplemented
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19182—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43C2×#12111yescharacteristic
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×#13511yescharacteristic
286C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C43#57511yescharacteristic
288C4×C43#57511yescharacteristic
289Dic43—22no—
290Dic43—41no—
291Dic43—41no—
292#3182D4311yescharacteristic, complemented
293#3107—431no—
294#3035—431no—
295#2971—431no—
296#1701—431no—
297#1699—431no—
298#1693—431no—
299#1685—431no—
300#1682—431no—
301#1680—431no—
302#1674—431no—
303#1666—431no—
304#1565—431no—
305#1553—431no—
306#1552—431no—
307C2×C43—41no—
308C2×C43—161no—
309C2×C43#303511yescharacteristic
310C2×C43#305511yescharacteristic
311C2×C43#306911yescharacteristic
312D43—81no—
313C2×#135—861no—
314#533C2×D4311yescharacteristic
315#532C2×D4311yescharacteristic
316C4×#41—431no—
317#500C2×D4311yescharacteristic
318#492C2×D4311yescharacteristic
319#487C2×D4311yescharacteristic
320#486C2×D4311yescharacteristic
321#485—861no—
322#475—431no—
323#474—431no—
324#468—21no—
325#468—21no—
326#464—861no—
327#463—861no—
328#462—431no—
329#462—431no—
330#461—431no—
331#461—431no—
332#460—431no—
333#459—431no—
334#452—861no—
335C8×Q8—431no—
336C8×Q8—431no—
337#440—21no—
338#440—21no—
339C4×Q16—861no—
340C4×SD16—861no—
341#436—431no—
342#436—431no—
343#436—861no—
344#436—861no—
345#432—431no—
346#432—861no—
347#431—431no—
348C2×C4⋊C8—431no—
349#416—861no—
350C4×M16—861no—
351C4×M16C2×D4311yescharacteristic
352#335—431no—
353#335—431no—
354#334—431no—
355#334—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#332—431no—
360#332—431no—
361#332—431no—
362#331—431no—
363#331—431no—
364C43#1918211yescharacteristic, complemented, Sylow
365C2×#41—21no—
366C2×#41—431no—
367#135—1724no—
368C2×Q16—861no—
369C2×Q16—861no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×D8—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16C22⋊D4311yescharacteristic
379C2×M16C22⋊D4311yescharacteristic
380C22×C8—861no—
381C4⋊Q8C22×D4311yescharacteristic
382C4⋊Q8C22×D4311yescharacteristic
383C4⋊Q8C22×D4311yescharacteristic
384#127C22×D4311yescharacteristic
385#125—21no—
386#124—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—21no—
390#121—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—431no—
394C4×Q8—431no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401#117—21no—
402#117—431no—
403#117—861no—
404C2×C42—861no—
405C2×C42C22×D4311yescharacteristic
406#107—21no—
407#107—21no—
408#107—861no—
409#106—861no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419#103—21no—
420#103—21no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#102—21no—
427#102—21no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435#97—861no—
436#97C22⋊D4311yescharacteristic
437#97C22⋊D4311yescharacteristic
438C4×C8—861no—
439C4×C8—861no—
440C4×C8—861no—
441C4×C8C22×D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443#41—42no—
444#41—42no—
445#41—862no—
446#41—1721no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—431no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—431no—
456C2×D4—861no—
457C22×C4—41no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4D4×D4311yescharacteristic
462C22×C4#1062190011yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464Q16—1722no—
465Q16—1722no—
466SD16—42no—
467SD16—42no—
468SD16—1722no—
469SD16—1722no—
470SD16—1722no—
471D8—1722no—
472M16—22no—
473M16—41no—
474M16—1722no—
475M16—1722no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1722no—
483C2×C8C2×C22⋊D4311yescharacteristic
484C2×C8C2×C22⋊D4311yescharacteristic
485C2×C8C2×C22⋊D4311yescharacteristic
486C2×C8C2×C22⋊D4311yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C42—41no—
506C42—861no—
507C42—861no—
508C42—861no—
509C42D4×D4311yescharacteristic
510C42#1062190011yescharacteristic
511C42C2×C22⋊D4311yescharacteristic
512C42C23×D4311yescharacteristic
513C23—41no—
514C23—861no—
515C23#1306329611yescharacteristic
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—432no—
523Q8—861no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—861no—
531D4—861no—
532D4—1722no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—3441no—
546C2×C4—1722no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4#1306329611yescharacteristic
550C2×C4#1306329611yescharacteristic
551C2×C4#1306329611yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C22×C22⋊D4311yescharacteristic
554C2×C4C2×#1062190011yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—1721no—
559C8—1721no—
560C8—1721no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8#1306334512yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22C2×#1306329611yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—862no—
583C4—1721no—
584C4—1721no—
585C4C2×#1306334511yescharacteristic
586C4AGL(1,ℤ/8)×D4311yescharacteristic
587C4#1458369511yescharacteristic
588C4#1458369711yescharacteristic
589C2—41no—
590C2—161no—
591C2—3441no—
592C2#1914404411yescharacteristic
593C2#1914420811yescharacteristic
594C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3182C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#3182D43
hypocenterC43#19182
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #19144660C2semidirect
3. #19143613C2semidirect
4. #19134153C2semidirect
5. #19134139C2semidirect
6. #19134105C2semidirect
7. #19134057C2semidirect
8. #19134036C2semidirect
9. #19134022C2semidirect
10. #19133986C2semidirect
11. #19133940C2semidirect
12. #19133347C2semidirect
13. #19133300C2semidirect
14. #19133295C2semidirect
15. C43×#3182C2semidirect
260. C8×C43#135semidirect
292. #3182D43semidirect
364. C43#19182semidirect
564. C8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191446602
#191440442
#191436132
#191341532
#191341392
#191341052
#191340572
#191340362
#191340222
#191339862
#191339402
#191333472
#191333002
#191332952
C43×#31822
#1918243