Finite Group Databasebeta

← #25084194

Subgroups — #25084194

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145921C211yesmaximal, characteristic
2#19145725C211yesmaximal, characteristic, complemented
3#19145619C211yesmaximal, characteristic, complemented
4#19134163C211yesmaximal, characteristic, complemented
5#19134156C211yesmaximal, characteristic, complemented
6#19134101C211yesmaximal, characteristic, complemented
7#19134094C211yesmaximal, characteristic, complemented
8#19134039C211yesmaximal, characteristic, complemented
9#19134032C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133970C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133288C211yesmaximal, characteristic, complemented
14C2×#14582644C211yesmaximal, characteristic, complemented
15C43×#2994C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583294—21no—
21#14583269—21no—
22#14583246C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583218—21no—
25#14583218—21no—
26#14583196—21no—
27#14583194C2211yescharacteristic
28#14583190—21no—
29#14583190—21no—
30#14583189C2211yescharacteristic
31#14583133—21no—
32#14583130—21no—
33#14583111—21no—
34#14583109C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583104C2211yescharacteristic
38#14583099C2211yescharacteristic
39#14583094C2211yescharacteristic
40#14583054—21no—
41#14583037—21no—
42#14582956C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#424—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C22×C43⋊C8—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063313—21no—
84#13063299—21no—
85#13063299—21no—
86C4×D172—21no—
87C4×D172—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063257—21no—
94#13063257—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063247—21no—
107#13063247—21no—
108#13063247—21no—
109#13063247—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114#13063236—21no—
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118#126×C43—21no—
119#125×C43D411yescharacteristic
120#124×C43D411yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153#10621898—82no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—81no—
163C2×Dic86—81no—
164M16×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43—81no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C42×C43—21no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189#10621885—81no—
190#10621885—81no—
191#10621884—81no—
192#10621883—81no—
193#10621883—81no—
194#10621882—81no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—41no—
204C4⋊Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C23×C43—21no—
211C23×C43#12111yescharacteristic
212C22×D43—41no—
213Q8×C43—21no—
214Q8×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—42no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—82no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—82no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244C4×D43—82no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—82no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43#47112yes—
268C22×C43C2×#12111yescharacteristic
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43#57611yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57811yescharacteristic
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286#3247—431no—
287#3227—431no—
288#3218—431no—
289#2994D4311yescharacteristic, complemented
290#1702—431no—
291#1701—431no—
292#1692—431no—
293#1691—431no—
294#1682—431no—
295#1681—431no—
296#1672—431no—
297#1671—431no—
298#1573—431no—
299#1551—431no—
300C2×#332—431no—
301C2×C43—22no—
302C2×C43—81no—
303C2×C43#304611yescharacteristic
304C2×C43#306211yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—161no—
307#532—431no—
308C2×C4⋊Q8—431no—
309#529C2×D4311yescharacteristic
310#498—431no—
311#498—431no—
312#497—861no—
313#491—861no—
314#486—431no—
315#486—431no—
316#481—861no—
317#481—861no—
318#478—861no—
319#477—431no—
320#476—431no—
321#476—861no—
322#476—861no—
323#466—861no—
324#465—861no—
325#463—861no—
326#462—431no—
327#462—431no—
328#461—431no—
329#461—431no—
330#460—431no—
331#459—431no—
332#451—861no—
333#448—861no—
334#446C2×D4311yescharacteristic
335C8×Q8C2×D4311yescharacteristic
336#436C2×D4311yescharacteristic
337#435—21no—
338C8×D4—21no—
339C8×D4C2×D4311yescharacteristic
340#433—21no—
341#432—431no—
342#431C2×D4311yescharacteristic
343#424—21no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8C2×D4311yescharacteristic
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C22×Q8—861no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377#127—431no—
378#126—21no—
379#125D17211yescharacteristic
380#124—861no—
381#124D17211yescharacteristic
382#123—21no—
383C22⋊Q8D17211yescharacteristic
384#121—861no—
385#121—861no—
386#121D17211yescharacteristic
387C4×Q8C22×D4311yescharacteristic
388C4×D4—21no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4C22×D4311yescharacteristic
392#117—21no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8C22⋊D4311yescharacteristic
411C4⋊C8C22⋊D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—861no—
429C22⋊C8C22⋊D4311yescharacteristic
430C22⋊C8C22⋊D4311yescharacteristic
431#97—21no—
432#97—861no—
433C4×C8—21no—
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—3442no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—3441no—
441C2×Q8—3441no—
442C2×Q8—1721no—
443C2×Q8C2×D17211yescharacteristic
444C2×D4—21no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C2×D4C2×D17211yescharacteristic
450C22×C4—21no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4C2×D17211yescharacteristic
454C22×C4#1062189811yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—3441no—
457Q16—3441no—
458SD16—3441no—
459SD16—3441no—
460SD16—3441no—
461D8—3441no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—81no—
466C2×C8—81no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—3441no—
472C2×C8C2×C22⋊D4311yescharacteristic
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4C2×D17211yescharacteristic
489C4⋊C4C2×D17211yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—21no—
498C42C2×D17211yescharacteristic
499C42#1062189811yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—1721no—
504C23#1306329911yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—3441no—
508Q8—3442no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—3441no—
517D4—3442no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521D4—1721no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—3442no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306329911yescharacteristic
538C2×C4#1306329911yescharacteristic
539C2×C4#1306329911yescharacteristic
540C2×C4C22×C22⋊D4311yescharacteristic
541C2×C4C22×D17211yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—3441no—
559C22—3441no—
560C22—3441no—
561C22#1458316212yes—
562C22C2×#1306329911yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—3441no—
571C4—3441no—
572C4—3441no—
573C4#1458370411yescharacteristic
574C4#1458371011yescharacteristic
575C4#1458371111yescharacteristic
576C4#1458371411yescharacteristic
577C2—22no—
578C2—81no—
579C2—6881no—
580C2#1914414511yescharacteristic
581C2#1914427511yescharacteristic
582C2C2×#1458316211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2994C2
socleC22×C43C2×#121
prime radical#19145921C2
hypercenter#2994D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #19145725C2semidirect
3. #19145619C2semidirect
4. #19134163C2semidirect
5. #19134156C2semidirect
6. #19134101C2semidirect
7. #19134094C2semidirect
8. #19134039C2semidirect
9. #19134032C2semidirect
10. #19133977C2semidirect
11. #19133970C2semidirect
12. #19133380C2semidirect
13. #19133288C2semidirect
14. C2×#14582644C2semidirect
15. C43×#2994C2semidirect
289. #2994D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191457252
#191456192
#191341632
#191341562
#191341012
#191340942
#191340392
#191340322
#191339772
#191339702
#191333802
#191332882
C2×#145826442
C43×#29942
#1958943