Finite Group Databasebeta

← #25079025

Subgroups — #25079025

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#19145155C211yesmaximal, characteristic, complemented
2#19144377C211yesmaximal, characteristic, complemented
3#19144052C211yesmaximal, characteristic
4#19143551C211yesmaximal, characteristic, complemented
5#19134024C211yesmaximal, characteristic, complemented
6#19134017C211yesmaximal, characteristic, complemented
7#19134014C211yesmaximal, characteristic, complemented
8#19134007C211yesmaximal, characteristic, complemented
9#19133980C211yesmaximal, characteristic, complemented
10#19133973C211yesmaximal, characteristic, complemented
11#19133946C211yesmaximal, characteristic, complemented
12#19133939C211yesmaximal, characteristic, complemented
13C2×#14582649C211yesmaximal, characteristic, complemented
14#19133242C211yesmaximal, characteristic, complemented
15C43×#1542C211yesmaximal, characteristic, complemented
16C2×#13063347—21no—
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583273C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583203—21no—
24#14583196—21no—
25#14583191C2211yescharacteristic
26#14583186C2211yescharacteristic
27#14583181C2211yescharacteristic
28#14583176C2211yescharacteristic
29#14583130—21no—
30#14583130—21no—
31#14583122—21no—
32#14583115—21no—
33#14583110C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583100C2211yescharacteristic
36#14583095C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583023C2211yescharacteristic
39C4×#10621884—21no—
40C4×#10621884—21no—
41#14582964C2211yescharacteristic
42#14582964C2211yescharacteristic
43(C22⋊D43)⋊C8—21no—
44(C22⋊D43)⋊C8—21no—
45#14582950—21no—
46#14582935—21no—
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582896—21no—
49#14582893—21no—
50C2×C4×C43⋊C8C2211yescharacteristic
51C4×C8×D43—21no—
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69#13063347—44no—
70C2×Dic172—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×D344—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8D411yescharacteristic
78C22×C43⋊C8D411yescharacteristic
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063313—21no—
84#13063299—21no—
85#13063299—21no—
86C4×Dic86D411yescharacteristic
87C4×Dic86C2311yescharacteristic
88C4×D172—21no—
89C4×D172—21no—
90C4×D172D411yescharacteristic
91C4×D172C2311yescharacteristic
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94#13063284D411yescharacteristic
95#13063282—21no—
96C42×D43—21no—
97#13063258—21no—
98#13063258—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108#13063250—21no—
109#13063250—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063247—21no—
115#13063247—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119#13063245—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122C4×C43⋊C8D411yescharacteristic
123C4×C43⋊C8D411yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131#125×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43—21no—
136#117×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4111yescharacteristic
150C2×C22⋊D43—21no—
151C2×C22⋊D43—41no—
152#10621898—22no—
153#10621898—42no—
154#10621898—42no—
155#10621898SD1614yescomplemented
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165C2×Dic86C2×D411yescharacteristic
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—42no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C42×C43—41no—
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621884—42no—
185#10621884—42no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208Dic172—42no—
209D344—42no—
210#10621873—42no—
211#10621873—42no—
212C8×D43—42no—
213C8×D43—42no—
214C23×C43#12111yescharacteristic
215C22×D43—21no—
216C22×D43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43C2×SD1612yes—
229C2×C4×C43#13512yes—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—24no—
234C22⋊D43—82no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239D172—21no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245D172C2×SD1612yes—
246C4×D43—24no—
247C4×D43—42no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—82no—
251Dic86—21no—
252Dic86—41no—
253Dic86—41no—
254Dic86C2×SD1612yes—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8#13512yescomplemented
265#19124—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43#46512yes—
269C22×C43C2×#12111yescharacteristic
270C2×D43—22no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#46512yes—
282C4×C43C22×SD1611yescharacteristic
283C4×C43C2×#13511yescharacteristic
284C4×C43C2×#13511yescharacteristic
285C4×C43#57511yescharacteristic
286Dic43—22no—
287Dic43—41no—
288Dic43—41no—
289Dic43—81no—
290#3167—431no—
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#1542D4311yescharacteristic, complemented
304#1540—431no—
305C2×C43—22no—
306C2×C43#303511yescharacteristic
307C2×C43C2×#46511yescharacteristic
308C2×C43#306711yescharacteristic
309D43—42no—
310D43—161no—
311C2×#135—861no—
312#533C2×D4311yescharacteristic
313#532—431no—
314C4×#41—431no—
315#498—431no—
316#492—431no—
317#487—431no—
318#486—431no—
319#479—861no—
320#478—861no—
321#477—431no—
322#476—431no—
323#475—431no—
324#474—431no—
325#465—861no—
326#465—861no—
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—861no—
336C4×SD16—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—861no—
340C8×D4—861no—
341#431—861no—
342#431C2×D4311yescharacteristic
343#427—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8C2×D4311yescharacteristic
346#416—861no—
347#416—861no—
348C2×C4×C8—431no—
349C2×C4×C8—861no—
350#334—431no—
351#334—431no—
352#334—431no—
353#334—431no—
354#333C2×D4311yescharacteristic
355#333C2×D4311yescharacteristic
356#332—431no—
357#332—431no—
358#332C2×D4311yescharacteristic
359#332C2×D4311yescharacteristic
360#331—431no—
361#331—431no—
362C43#1912411yescharacteristic, complemented, Sylow
363C2×#41—431no—
364C2×#41—861no—
365#135—1724no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—21no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C4⋊Q8—431no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#127—431no—
382#125—21no—
383#124—861no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—861no—
387#121—861no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—431no—
391C4×Q8—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
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—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—21no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
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#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C4×C8—21no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—861no—
440C4×C8—861no—
441#41—434no—
442#41—862no—
443#41—1722no—
444#41—1722no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—431no—
448C2×Q8—861no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—1721no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4#1062189811yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462Q16—1722no—
463SD16—1722no—
464SD16—1722no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—862no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1722no—
481C2×C8—1722no—
482C2×C8—1721no—
483C2×C8—1722no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—431no—
491C4⋊C4—431no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C22⋊C4—41no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—41no—
503C42—861no—
504C42—861no—
505C42—861no—
506C42#1062189811yescharacteristic
507C42D4×D4311yescharacteristic
508C42D4×D4311yescharacteristic
509C42C23×D4311yescharacteristic
510C23—861no—
511C23—1721no—
512C23#1306329811yescharacteristic
513Q8—41no—
514Q8—41no—
515Q8—81no—
516Q8—432no—
517Q8—861no—
518Q8—1721no—
519Q8—1721no—
520D4—432no—
521D4—864no—
522D4—861no—
523D4—3441no—
524D4—3442no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4—1721no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—861no—
535C2×C4—864no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3442no—
539C2×C4—1722no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329811yescharacteristic
544C2×C4#1306329811yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4SD16×D4312yes—
547C2×C4#1306334812yes—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×#1062189811yescharacteristic
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—432no—
556C8—861no—
557C8—861no—
558C8—861no—
559C8—1721no—
560C8—1721no—
561C22—21no—
562C22—21no—
563C22—862no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22—1721no—
568C22—1721no—
569C22#1458313112yes—
570C22C2×#1306329811yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—81no—
576C4—862no—
577C4—3441no—
578C4—1721no—
579C4—1721no—
580C4#1458313112yes—
581C4C2×SD16×D4311yescharacteristic
582C4#135×D4311yescharacteristic
583C4C2×#1306334811yescharacteristic
584C4#1458369611yescharacteristic
585C2—22no—
586C2—1722no—
587C2—6881no—
588C2#1914404811yescharacteristic
589C2C2×#1458313111yescharacteristic
590C2#1914431411yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1542C2
socleC22×C43C2×#121
prime radical#19144052C2
hypercenter#1542D43
hypocenterC43#19124
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #19145155C2semidirect
2. #19144377C2semidirect
4. #19143551C2semidirect
5. #19134024C2semidirect
6. #19134017C2semidirect
7. #19134014C2semidirect
8. #19134007C2semidirect
9. #19133980C2semidirect
10. #19133973C2semidirect
11. #19133946C2semidirect
12. #19133939C2semidirect
13. C2×#14582649C2semidirect
14. #19133242C2semidirect
15. C43×#1542C2semidirect
155. #10621898SD16semidirect
264. C43⋊C8#135semidirect
303. #1542D43semidirect
362. C43#19124semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191443772
#191440522
#191435512
#191340242
#191340172
#191340142
#191340072
#191339802
#191339732
#191339462
#191339392
C2×#145826492
#191332422
C43×#15422
#1912443