Finite Group Databasebeta

← #25082048

Subgroups — #25082048

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145547C211yesmaximal, characteristic, complemented
2#19144747C211yesmaximal, characteristic
3#19144660C211yesmaximal, characteristic, complemented
4#19143704C211yesmaximal, characteristic, complemented
5#19134042C211yesmaximal, characteristic, complemented
6#19134035C211yesmaximal, characteristic, complemented
7#19134028C211yesmaximal, characteristic, complemented
8#19134021C211yesmaximal, characteristic, complemented
9#19133964C211yesmaximal, characteristic, complemented
10#19133959C211yesmaximal, characteristic, complemented
11#19133946C211yesmaximal, characteristic, complemented
12#19133939C211yesmaximal, characteristic, complemented
13#19133376C211yesmaximal, characteristic, complemented
14#19133245C211yesmaximal, characteristic, complemented
15C43×#1552C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583278C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583237—21no—
23#14583224—21no—
24#14583185C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583180C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583121—21no—
29#14583121—21no—
30#14583106C2211yescharacteristic
31#14583101C2211yescharacteristic
32#14583100C2211yescharacteristic
33#14583095C2211yescharacteristic
34#14583059—21no—
35#14583059—21no—
36#14583059—21no—
37#14583046—21no—
38#14583023C2211yescharacteristic
39#14583023C2211yescharacteristic
40#14583012—21no—
41#14583001—21no—
42C4×#10621885—21no—
43C4×#10621884—21no—
44#14582964C2211yescharacteristic
45#14582964C2211yescharacteristic
46C8×C22⋊D43—21no—
47C8×C22⋊D43—21no—
48#14582952C2211yescharacteristic
49#14582952C2211yescharacteristic
50#14582951—21no—
51C4⋊C8×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621873—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×D344—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063313—21no—
82#13063299—21no—
83#13063299—21no—
84C4×Dic86D411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×D172—21no—
87C4×D172—21no—
88C4×D172D411yescharacteristic
89C4×D172C2311yescharacteristic
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92#13063284D411yescharacteristic
93#13063282—21no—
94C42×D43—21no—
95#13063259—21no—
96#13063258—21no—
97#13063257—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—21no—
111#13063247—21no—
112#13063247—21no—
113#13063247—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#125×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150C2×C22⋊D43—41no—
151#10621898—22no—
152#10621898—22no—
153#10621898—81no—
154#10621898—81no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43—41no—
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183#10621885—42no—
184#10621885—81no—
185#10621885—81no—
186#10621884—42no—
187#10621884—81no—
188#10621884—81no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C2×D411yescharacteristic
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208D344—42no—
209#10621873—42no—
210C8×D43—81no—
211C8×D43—81no—
212C23×C43#12111yescharacteristic
213C22×D43—21no—
214C22×D43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—24no—
233C22⋊D43—82no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238D172—21no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244D172#13512yes—
245C4×D43—24no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—81no—
249C4×D43—82no—
250Dic86—21no—
251Dic86—41no—
252Dic86—41no—
253Dic86#13512yes—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19413—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—22no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×#13511yescharacteristic
283C4×C43#57611yescharacteristic
284C4×C43#57711yescharacteristic
285Dic43—22no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289#3210—431no—
290#3115—431no—
291#3107—431no—
292#2988—431no—
293#1682—431no—
294#1681—431no—
295#1680—431no—
296#1679—431no—
297#1670—431no—
298#1669—431no—
299#1666—431no—
300#1665—431no—
301#1572—431no—
302#1552D4311yescharacteristic, complemented
303#1540—431no—
304C2×C43—41no—
305C2×C43#304511yescharacteristic
306C2×C43#305011yescharacteristic
307C2×C43#306911yescharacteristic
308D43—42no—
309D43—161no—
310#533C2×D4311yescharacteristic
311#532—431no—
312C4×#41—431no—
313#494—431no—
314#492—431no—
315#487—431no—
316#486—431no—
317#485—861no—
318#482—861no—
319#475—431no—
320#475—431no—
321#474—431no—
322#474—431no—
323#464—861no—
324#464—861no—
325#462—431no—
326#461—431no—
327#460—431no—
328#459—431no—
329#452—861no—
330#452—861no—
331#452—861no—
332#449—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335#442—861no—
336#440—861no—
337C4×Q16—861no—
338C4×SD16—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432C2×D4311yescharacteristic
344#431—431no—
345#431—431no—
346#431—861no—
347C2×C4⋊C8—861no—
348C2×C4⋊C8C2×D4311yescharacteristic
349#335—431no—
350#335—431no—
351#334—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332C2×D4311yescharacteristic
356#332C2×D4311yescharacteristic
357#332C2×D4311yescharacteristic
358#332C2×D4311yescharacteristic
359#331—431no—
360#331—431no—
361C43#1941311yescharacteristic, complemented, Sylow
362C2×#41—431no—
363C2×#41—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—21no—
373C22×C8—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8C22×D4311yescharacteristic
377C4⋊Q8C22×D4311yescharacteristic
378#127—431no—
379#125—21no—
380#124—861no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—861no—
384#121—861no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—431no—
388C4×Q8—431no—
389C4×D4—431no—
390C4×D4—431no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4—861no—
395#117—21no—
396#117—431no—
397#117—861no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—21no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8—861no—
439#41—862no—
440#41—862no—
441#41—3441no—
442#41—3441no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×D4—431no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—1721no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—1721no—
457C22×C4#1062189811yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460Q16—3441no—
461Q16—3441no—
462Q16—1722no—
463SD16—3441no—
464SD16—3441no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—81no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—3441no—
480C2×C8—3441no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—431no—
488C4⋊C4—431no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C22⋊C4—41no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—41no—
500C42—861no—
501C42—861no—
502C42—861no—
503C42#1062189811yescharacteristic
504C42D4×D4311yescharacteristic
505C42D4×D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—861no—
508C23—1721no—
509C23#1306329811yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—432no—
515Q8—861no—
516Q8—1721no—
517Q8—1721no—
518D4—432no—
519D4—864no—
520D4—861no—
521D4—3441no—
522D4—3442no—
523D4—1721no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—864no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3442no—
539C2×C4—3441no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329811yescharacteristic
544C2×C4#1306329811yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C2×#1062189811yescharacteristic
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—861no—
554C8—861no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—862no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—1721no—
567C22—1721no—
568C22C2×#1306329811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—81no—
575C4—862no—
576C4—3441no—
577C4—1721no—
578C4—1721no—
579C4#135×D4311yescharacteristic
580C4#135×D4311yescharacteristic
581C4#1458370311yescharacteristic
582C4#1458370811yescharacteristic
583C2—41no—
584C2—1722no—
585C2—6881no—
586C2#1914413311yescharacteristic
587C2#1914417511yescharacteristic
588C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1552C2
socleC22×C43C2×#121
prime radical#19144747C2
hypercenter#1552D43
hypocenterC43#19413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
1. #19145547C2semidirect
3. #19144660C2semidirect
4. #19143704C2semidirect
5. #19134042C2semidirect
6. #19134035C2semidirect
7. #19134028C2semidirect
8. #19134021C2semidirect
9. #19133964C2semidirect
10. #19133959C2semidirect
11. #19133946C2semidirect
12. #19133939C2semidirect
13. #19133376C2semidirect
14. #19133245C2semidirect
15. C43×#1552C2semidirect
302. #1552D43semidirect
361. C43#19413semidirect

Maximal subgroups

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

subgroupindex
#191455472
#191447472
#191446602
#191437042
#191340422
#191340352
#191340282
#191340212
#191339642
#191339592
#191339462
#191339392
#191333762
#191332452
C43×#15522
#1941343