Finite Group Databasebeta

← #25079013

Subgroups — #25079013

Order 11008.

672 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#19144377C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic
3C8×#10621898C211yesmaximal, characteristic, complemented
4#19134022C211yesmaximal, characteristic, complemented
5#19134015C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133974C211yesmaximal, characteristic, complemented
9#19133967C211yesmaximal, characteristic, complemented
10#19133940C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12C2×#14582650C211yesmaximal, characteristic, complemented
13#19133252C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3167C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17C4×#10621898C2211yescharacteristic
18#14583203—21no—
19#14583196—21no—
20#14583191C2211yescharacteristic
21#14583186C2211yescharacteristic
22#14583181C2211yescharacteristic
23#14583176C2211yescharacteristic
24#14583118—21no—
25#14583111—21no—
26#14583106C2211yescharacteristic
27#14583101C2211yescharacteristic
28#14583096C2211yescharacteristic
29#14583091C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C8×Dic86C2211yescharacteristic
32C8×D172C2211yescharacteristic
33C8×D172C2211yescharacteristic
34C8×C22⋊D43—21no—
35C8×C22⋊D43—21no—
36#14582952C2211yescharacteristic
37#14582950—21no—
38#14582935—21no—
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41#14582895—21no—
42#14582893—21no—
43C4×C8×D43—21no—
44#14582650C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#465—21no—
63C43×#465—21no—
64C4×SD16×C43—21no—
65C4×SD16×C43—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C4×Dic86D411yescharacteristic
78C4×Dic86C2311yescharacteristic
79C4×D172D411yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83#13063284D411yescharacteristic
84#13063282—21no—
85C42×D43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063256—21no—
89#13063256—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100#13063249—21no—
101#13063249—21no—
102#13063248—21no—
103#13063248—21no—
104#13063246—21no—
105#13063246—21no—
106#13063245—21no—
107#13063245—21no—
108C22⋊(C43⋊C8)—21no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C8×Dic43—21no—
114C2×#41×C43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C22×C8×C43D411yescharacteristic
118C22×C8×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#106×C43—21no—
136#106×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141C4×C8×C43D411yescharacteristic
142C4×C8×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#10621898SD1614yescomplemented
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×Dic86C2×D411yescharacteristic
166SD16×C43—42no—
167SD16×C43—42no—
168C2×C8×C43—22no—
169C2×C8×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#10621884—42no—
193#10621883—42no—
194#10621882—42no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43C2×D411yescharacteristic
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8—42no—
212C8×D43—42no—
213C8×D43—42no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216C22×D43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—81no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—81no—
227D4×C43—82no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43C2×SD1612yes—
239C2×C4×C43#13512yes—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—24no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247D172—21no—
248D172C2×SD1612yes—
249C4×D43—24no—
250C4×D43—42no—
251C4×D43—41no—
252C4×D43—41no—
253Dic86—21no—
254Dic86C2×SD1612yes—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43#13512yescomplemented
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19124—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43#46512yes—
272C22×C43C2×#12111yescharacteristic
273C2×D43—22no—
274C2×D43—41no—
275C2×D43—41no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#46512yes—
283C4×C43C22×SD1611yescharacteristic
284C4×C43C2×#13511yescharacteristic
285C4×C43C2×#13511yescharacteristic
286C4×C43#57511yescharacteristic
287Dic43—22no—
288Dic43—41no—
289Dic43—41no—
290#3167D4311yescharacteristic, complemented
291#3076—431no—
292#3035—431no—
293C8×#41—431no—
294#1680—431no—
295#1679—431no—
296#1678—431no—
297#1677—431no—
298#1672—431no—
299#1671—431no—
300#1666—431no—
301#1665—431no—
302C2×#334—431no—
303#1542—431no—
304#1540—431no—
305C2×C43—22no—
306C2×C43—161no—
307C2×C43#303511yescharacteristic
308C2×C43C2×#46511yescharacteristic
309C2×C43#306711yescharacteristic
310D43—42no—
311C2×#135—861no—
312#533C2×D4311yescharacteristic
313#532C2×D4311yescharacteristic
314C4×#41—431no—
315#498C2×D4311yescharacteristic
316#492C2×D4311yescharacteristic
317#487C2×D4311yescharacteristic
318#486C2×D4311yescharacteristic
319#479—861no—
320#478—861no—
321#477—431no—
322#476—431no—
323#475—431no—
324#474—431no—
325#465—21no—
326#465—21no—
327#464—861no—
328#463—861no—
329#462—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333C8×Q8—431no—
334C8×Q8—431no—
335C4×SD16—21no—
336C4×SD16—21no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—861no—
340C8×D4—861no—
341#431—431no—
342#431—861no—
343#427—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8—431no—
346#416—861no—
347#416—861no—
348C2×C4×C8—861no—
349C2×C4×C8C2×D4311yescharacteristic
350#334—431no—
351#334—431no—
352#334—431no—
353#334—431no—
354#333—431no—
355#333—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#332—431no—
360#331—431no—
361#331—431no—
362C43#1912411yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C2×#41—431no—
365#135—1724no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—861no—
373C22×C8—861no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8C22⋊D4311yescharacteristic
377C22×C8C22⋊D4311yescharacteristic
378C4⋊Q8C22×D4311yescharacteristic
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#127C22×D4311yescharacteristic
382#125—21no—
383#124—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—21no—
387#121—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—431no—
391C4×Q8—431no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—431no—
395C4×D4—431no—
396C4×D4—861no—
397C4×D4—861no—
398#117—21no—
399#117—431no—
400#117—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—861no—
404#107—861no—
405#106—21no—
406#106—21no—
407#106—861no—
408#106—861no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
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#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22⋊D4311yescharacteristic
438C4×C8C22⋊D4311yescharacteristic
439C4×C8C22×D4311yescharacteristic
440C4×C8C22×D4311yescharacteristic
441#41—42no—
442#41—42no—
443#41—434no—
444#41—862no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—431no—
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×C4D4×D4311yescharacteristic
460C22×C4#1062190011yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462Q16—1722no—
463SD16—42no—
464SD16—42no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—22no—
469C2×C8—41no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—1722no—
477C2×C8—1722no—
478C2×C8—1722no—
479C2×C8—1722no—
480C2×C8C2×C22⋊D4311yescharacteristic
481C2×C8C2×C22⋊D4311yescharacteristic
482C2×C8C2×C22⋊D4311yescharacteristic
483C2×C8C2×C22⋊D4311yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C42—41no—
503C42—861no—
504C42—861no—
505C42—861no—
506C42D4×D4311yescharacteristic
507C42#1062190011yescharacteristic
508C42C2×C22⋊D4311yescharacteristic
509C42C23×D4311yescharacteristic
510C23—41no—
511C23—861no—
512C23#1306329611yescharacteristic
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—432no—
519Q8—861no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—432no—
527D4—864no—
528D4—861no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—861no—
537C2×C4—864no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—1722no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329611yescharacteristic
544C2×C4#1306329611yescharacteristic
545C2×C4#1306329611yescharacteristic
546C2×C4SD16×D4312yes—
547C2×C4#1306334612yes—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C22×C22⋊D4311yescharacteristic
550C2×C4C2×#1062190011yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C8#1306334512yescomplemented
561C22—21no—
562C22—21no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—862no—
567C22—1721no—
568C22—1721no—
569C22#1458312512yes—
570C22C2×#1306329611yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—862no—
578C4—1721no—
579C4—1721no—
580C4#1458312512yes—
581C4C2×SD16×D4311yescharacteristic
582C4C2×#1306334511yescharacteristic
583C4C2×#1306334611yescharacteristic
584C4#1458369711yescharacteristic
585C2—22no—
586C2—161no—
587C2—1722no—
588C2#1914404411yescharacteristic
589C2C2×#1458312511yescharacteristic
590C2#1914431111yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3167C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#3167D43
hypocenterC43#19124
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19144377C2semidirect
3. C8×#10621898C2semidirect
4. #19134022C2semidirect
5. #19134015C2semidirect
6. #19134008C2semidirect
7. #19134001C2semidirect
8. #19133974C2semidirect
9. #19133967C2semidirect
10. #19133940C2semidirect
11. #19133933C2semidirect
12. C2×#14582650C2semidirect
13. #19133252C2semidirect
14. #19133244C2semidirect
15. C43×#3167C2semidirect
160. #10621898SD16semidirect
258. C8×C43#135semidirect
290. #3167D43semidirect
362. C43#19124semidirect
560. C8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191440442
C8×#106218982
#191340222
#191340152
#191340082
#191340012
#191339742
#191339672
#191339402
#191339332
C2×#145826502
#191332522
#191332442
C43×#31672
#1912443