Finite Group Databasebeta

← #25079601

Subgroups — #25079601

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#19145313C211yesmaximal, characteristic, complemented
2#19144666C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic
4#19134156C211yesmaximal, characteristic, complemented
5#19134142C211yesmaximal, characteristic, complemented
6#19134108C211yesmaximal, characteristic, complemented
7#19134060C211yesmaximal, characteristic, complemented
8#19134039C211yesmaximal, characteristic, complemented
9#19134025C211yesmaximal, characteristic, complemented
10#19133989C211yesmaximal, characteristic, complemented
11#19133943C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133296C211yesmaximal, characteristic, complemented
15C43×#2971C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583240—21no—
24#14583184C2211yescharacteristic
25#14583179C2211yescharacteristic
26#14583145—21no—
27#14583145—21no—
28#14583121—21no—
29#14583114—21no—
30#14583109C2211yescharacteristic
31#14583109C2211yescharacteristic
32#14583104C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583061—21no—
37#14583001—21no—
38#14583001—21no—
39C4×#10621885—21no—
40C4×#10621883—21no—
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582893—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436—21no—
61C43×#436C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C4×M16×C43—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621884—21no—
76C2×#10621882—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063317—21no—
83#13063313—21no—
84#13063304—21no—
85#13063304—21no—
86#13063299—21no—
87#13063299—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×D172—21no—
91C4×D172—21no—
92#13063284—21no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102#13063250—21no—
103#13063250—21no—
104#13063249—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063247—21no—
110#13063247—21no—
111#13063246—21no—
112#13063245—21no—
113#13063245—21no—
114C22⋊(C43⋊C8)—21no—
115C4×C43⋊C8—21no—
116C2×#41×C43D411yescharacteristic
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43D411yescharacteristic
120C2×M16×C43D411yescharacteristic
121C4×Q8×C43D411yescharacteristic
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128#117×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—41no—
157#10621898—42no—
158#10621898—42no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166M16×C43—22no—
167M16×C43—41no—
168M16×C43—42no—
169M16×C43—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191#10621885—42no—
192#10621885—42no—
193#10621884—42no—
194#10621883—42no—
195#10621883—42no—
196#10621882—42no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—41no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—42no—
213#10621873—42no—
214#10621873—42no—
215C23×C43—21no—
216C23×C43#12111yescharacteristic
217C22×D43—41no—
218Q8×C43—21no—
219Q8×C43AGL(1,ℤ/8)12yes—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—42no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—81no—
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C22⋊D43—82no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—81no—
250C4×D43—82no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—41no—
256Dic86—41no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43#13512yescomplemented
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—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C2×#12111yescharacteristic
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—22no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43C2×#13511yescharacteristic
286C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C43#57511yescharacteristic
288C4×C43#57511yescharacteristic
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292#3182—431no—
293#3107—431no—
294#3035—431no—
295#2971D4311yescharacteristic, complemented
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—81no—
309C2×C43#303511yescharacteristic
310C2×C43#305511yescharacteristic
311C2×C43#306911yescharacteristic
312D43—161no—
313C2×#135—861no—
314#533—431no—
315#532—431no—
316C4×#41C2×D4311yescharacteristic
317#500—431no—
318#492—431no—
319#487—431no—
320#486—431no—
321#485—861no—
322#475—431no—
323#474—431no—
324#468—861no—
325#468—861no—
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×Q8C2×D4311yescharacteristic
336C8×Q8C2×D4311yescharacteristic
337#440—861no—
338#440—861no—
339C4×Q16—861no—
340C4×SD16—861no—
341#436—21no—
342#436—21no—
343#436C2×D4311yescharacteristic
344#436C2×D4311yescharacteristic
345#432—21no—
346#432C2×D4311yescharacteristic
347#431—431no—
348C2×C4⋊C8—431no—
349#416—861no—
350C4×M16—21no—
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—861no—
366C2×#41D17211yescharacteristic
367#135—1724no—
368C2×Q16—861no—
369C2×Q16—861no—
370C2×SD16—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×D8—861no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16C22⋊D4311yescharacteristic
379C2×M16C22⋊D4311yescharacteristic
380C22×C8—861no—
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384#127—431no—
385#125—861no—
386#124—861no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389#121—861no—
390#121—861no—
391C4×Q8—861no—
392C4×Q8—861no—
393C4×Q8D17211yescharacteristic
394C4×Q8C22×D4311yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4D17211yescharacteristic
400C4×D4C22×D4311yescharacteristic
401#117—21no—
402#117—861no—
403#117D17211yescharacteristic
404C2×C42—21no—
405C2×C42C22×D4311yescharacteristic
406#107—861no—
407#107—861no—
408#107—861no—
409#106—861no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
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#103—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—861no—
435#97—21no—
436#97C22⋊D4311yescharacteristic
437#97C22⋊D4311yescharacteristic
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—861no—
441C4×C8C22×D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443#41—22no—
444#41—41no—
445#41—1722no—
446#41—1722no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8C2×D17211yescharacteristic
451C2×D4—21no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—1721no—
456C2×D4C2×D17211yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—1721no—
461C22×C4C2×D17211yescharacteristic
462C22×C4#1062189811yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464Q16—1722no—
465Q16—1722no—
466SD16—1722no—
467SD16—1722no—
468SD16—1722no—
469SD16—1722no—
470SD16—1722no—
471D8—1722no—
472M16—22no—
473M16—41no—
474M16—42no—
475M16—42no—
476C2×C8—21no—
477C2×C8—21no—
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—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C4⋊C4C2×D17211yescharacteristic
498C4⋊C4C2×D17211yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—1721no—
509C42C2×D17211yescharacteristic
510C42#1062189811yescharacteristic
511C42C2×C22⋊D4311yescharacteristic
512C42C23×D4311yescharacteristic
513C23—21no—
514C23—1721no—
515C23#1306329911yescharacteristic
516Q8—21no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8—1721no—
522Q8—1721no—
523Q8#1306335312yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—3441no—
528D4—3442no—
529D4—1721no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—3442no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4#1306329911yescharacteristic
550C2×C4#1306329911yescharacteristic
551C2×C4#1306329911yescharacteristic
552C2×C4C22×C22⋊D4311yescharacteristic
553C2×C4C22×D17211yescharacteristic
554C2×C4C2×#1062189811yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—1721no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8#1306334512yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—3441no—
572C22—3441no—
573C22—3441no—
574C22C2×#1306329911yescharacteristic
575C4—21no—
576C4—22no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—41no—
581C4—41no—
582C4—3441no—
583C4—3441no—
584C4—3441no—
585C4C2×#1306334511yescharacteristic
586C4C2×#1306335311yescharacteristic
587C4#1458369711yescharacteristic
588C4#1458369911yescharacteristic
589C2—41no—
590C2—81no—
591C2—6881no—
592C2#1914405011yescharacteristic
593C2#1914421411yescharacteristic
594C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2971C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#2971D43
hypocenterC43#19182
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #19145313C2semidirect
2. #19144666C2semidirect
4. #19134156C2semidirect
5. #19134142C2semidirect
6. #19134108C2semidirect
7. #19134060C2semidirect
8. #19134039C2semidirect
9. #19134025C2semidirect
10. #19133989C2semidirect
11. #19133943C2semidirect
12. #19133347C2semidirect
13. #19133301C2semidirect
14. #19133296C2semidirect
15. C43×#2971C2semidirect
262. C8×C43#135semidirect
295. #2971D43semidirect
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
#191453132
#191446662
#191440502
#191341562
#191341422
#191341082
#191340602
#191340392
#191340252
#191339892
#191339432
#191333472
#191333012
#191332962
C43×#29712
#1918243