Finite Group Databasebeta

← #25079635

Subgroups — #25079635

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145329C211yesmaximal, characteristic, complemented
2#19144050C211yesmaximal, characteristic, complemented
3#19143615C211yesmaximal, characteristic, complemented
4#19134154C211yesmaximal, characteristic, complemented
5#19134130C211yesmaximal, characteristic, complemented
6#19134096C211yesmaximal, characteristic, complemented
7#19134072C211yesmaximal, characteristic, complemented
8#19134037C211yesmaximal, characteristic, complemented
9#19134013C211yesmaximal, characteristic, complemented
10#19133979C211yesmaximal, characteristic, complemented
11#19133953C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133298C211yesmaximal, characteristic, complemented
14#19133290C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583449C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583275C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583150—21no—
23#14583150—21no—
24#14583121—21no—
25#14583114—21no—
26#14583109C2211yescharacteristic
27#14583104C2211yescharacteristic
28#14583099C2211yescharacteristic
29#14583094C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32#14583009—21no—
33#14583009—21no—
34#14582977—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582977C2211yescharacteristic
38#14582956—21no—
39#14582956C2211yescharacteristic
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41#14582893—21no—
42C4×#10621877—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C4×SD16×C43—21no—
65C4×D8×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877D411yescharacteristic
78C2×#10621877D411yescharacteristic
79C22×C43⋊C8—21no—
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063313—21no—
83#13063299—21no—
84#13063299—21no—
85C4×D172—21no—
86C4×D172—21no—
87#13063256—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—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
96#13063248—21no—
97#13063248—21no—
98#13063246—21no—
99#13063246—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103#13063245—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107#13063236—21no—
108#13063236D411yescharacteristic
109#13063236D411yescharacteristic
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C2×#41×C43—21no—
115C2×#41×C43D411yescharacteristic
116C2×SD16×C43—21no—
117C2×D8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119#127×C43C2311yescharacteristic
120#124×C43—21no—
121#121×C43—21no—
122#121×C43—21no—
123C4×Q8×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43D411yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43D411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43—21no—
145#41×C43—22no—
146#41×C43—41no—
147#41×C43—82no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C2×C22⋊D43—41no—
164#10621898—42no—
165#10621898—42no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171SD16×C43—42no—
172D8×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43#4111yescharacteristic
192C42×C43C2411yescharacteristic
193#10621885—42no—
194#10621884—42no—
195#10621883—42no—
196#10621882—42no—
197#10621882—42no—
198#10621882—42no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203#10621877—22no—
204#10621877—41no—
205#10621877—42no—
206#10621877—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C2×C43⋊C8C2×D411yescharacteristic
216C23×C43—21no—
217C23×C43—41no—
218C23×C43#12111yescharacteristic
219C22×D43—41no—
220Q8×C43—21no—
221Q8×C43—81no—
222Q8×C43AGL(1,ℤ/8)12yes—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—42no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—81no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—81no—
245C2×C4×C43—82no—
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C22⋊D43—82no—
253C2×Dic43—41no—
254D172—41no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—81no—
259C4×D43—82no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8#13512yescomplemented
272#19184—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43C2×#12111yescharacteristic
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—22no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43C2×#13511yescharacteristic
295C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C43#57511yescharacteristic
297C4×C43#57511yescharacteristic
298Dic43—81no—
299#3184—431no—
300#3106D4311yescharacteristic, complemented
301#3035—431no—
302#2971—431no—
303#1701—431no—
304#1697—431no—
305#1691—431no—
306#1687—431no—
307#1682—431no—
308#1678—431no—
309#1672—431no—
310#1668—431no—
311#1565—431no—
312#1553—431no—
313#1551—431no—
314C2×C43—41no—
315C2×C43—81no—
316C2×C43—161no—
317C2×C43#303511yescharacteristic
318C2×C43#305511yescharacteristic
319C2×C43#306811yescharacteristic
320D43—161no—
321C2×#135—861no—
322#532—431no—
323#532C2×D4311yescharacteristic
324C4×#41C2×D4311yescharacteristic
325#498—431no—
326#493—431no—
327#486—431no—
328#486—431no—
329#482—21no—
330#477C2×D4311yescharacteristic
331#476C2×D4311yescharacteristic
332#469—861no—
333#469—861no—
334#464—861no—
335#463—861no—
336#462—431no—
337#461—431no—
338#460—431no—
339#460C2×D4311yescharacteristic
340#459—431no—
341#459C2×D4311yescharacteristic
342#449—21no—
343C8×Q8—431no—
344C8×Q8—431no—
345#442—861no—
346#442—861no—
347C4×SD16—21no—
348C4×D8—21no—
349#436—431no—
350#436—431no—
351#436—861no—
352#436—861no—
353#432—431no—
354#432—861no—
355#431C2×D4311yescharacteristic
356C2×C4⋊C8—431no—
357#416—861no—
358C4×M16—431no—
359C4×M16—861no—
360#335—431no—
361#335—431no—
362#334—431no—
363#334—431no—
364#333—431no—
365#333—431no—
366#332—431no—
367#332—431no—
368#331—431no—
369#331—431no—
370#331—431no—
371#331—431no—
372C43#1918411yescharacteristic, complemented, Sylow
373C2×#41—21no—
374C2×#41—861no—
375C2×#41C22⋊D4311yescharacteristic
376#135—1724no—
377C2×Q16—861no—
378C2×SD16—21no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×D8—21no—
382C2×D8—861no—
383C2×D8—861no—
384C2×D8—861no—
385C2×M16—431no—
386C2×M16—431no—
387C2×M16—861no—
388C2×M16—861no—
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392#127—431no—
393#127C22×D4311yescharacteristic
394#124—21no—
395#124—861no—
396#121—21no—
397#121—21no—
398#121—861no—
399#121—861no—
400C4×Q8C22⋊D4311yescharacteristic
401C4×Q8C22×D4311yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4C22⋊D4311yescharacteristic
409C4×D4C22×D4311yescharacteristic
410#117—21no—
411#117C22⋊D4311yescharacteristic
412C2×C42—21no—
413C2×C42C22×D4311yescharacteristic
414#107—21no—
415#106—21no—
416#106—861no—
417#106—861no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425C4⋊C8C22×D4311yescharacteristic
426C4⋊C8C22×D4311yescharacteristic
427#103—21no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439C22⋊C8—21no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443#97—431no—
444#97—431no—
445#97—861no—
446C4×C8—21no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8—861no—
451#41—22no—
452#41—41no—
453#41—82no—
454#41—1722no—
455#41—1722no—
456C2×Q8—21no—
457C2×Q8—861no—
458C2×Q8C2×C22⋊D4311yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—1721no—
468C2×D4C2×C22⋊D4311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—1721no—
474C22×C4D4×D4311yescharacteristic
475C22×C4#1062190011yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477Q16—1722no—
478SD16—42no—
479SD16—1722no—
480SD16—1722no—
481D8—42no—
482D8—1722no—
483D8—1722no—
484D8—1722no—
485M16—862no—
486M16—1722no—
487M16—1721no—
488M16—1722no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—1722no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4C2×C22⋊D4311yescharacteristic
507C4⋊C4C2×C22⋊D4311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42D4×D4311yescharacteristic
519C42#1062190011yescharacteristic
520C42C2×C22⋊D4311yescharacteristic
521C42C23×D4311yescharacteristic
522C23—21no—
523C23—41no—
524C23—1721no—
525C23#1306329711yescharacteristic
526Q8—21no—
527Q8—81no—
528Q8—1721no—
529Q8—1721no—
530Q8#1306335012yes—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—3441no—
541D4—3442no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—3442no—
561C2×C4—1721no—
562C2×C4#1306329711yescharacteristic
563C2×C4#1306329711yescharacteristic
564C2×C4#1306329711yescharacteristic
565C2×C4C2×D4×D4311yescharacteristic
566C2×C4C22×C22⋊D4311yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C8—41no—
569C8—41no—
570C8—432no—
571C8—861no—
572C8—861no—
573C8—861no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—3441no—
588C22—3441no—
589C22—3441no—
590C22C2×#1306329711yescharacteristic
591C4—21no—
592C4—22no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—3441no—
600C4#135×D4311yescharacteristic
601C4C2×#1306335011yescharacteristic
602C4#1458369611yescharacteristic
603C4#1458369711yescharacteristic
604C2—41no—
605C2—81no—
606C2—161no—
607C2—6881no—
608C2#1914404611yescharacteristic
609C2#1914421611yescharacteristic
610C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3106C2
socleC22×C43C2×#121
hypercenter#3106D43
hypocenterC43#19184
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19145329C2semidirect
2. #19144050C2semidirect
3. #19143615C2semidirect
4. #19134154C2semidirect
5. #19134130C2semidirect
6. #19134096C2semidirect
7. #19134072C2semidirect
8. #19134037C2semidirect
9. #19134013C2semidirect
10. #19133979C2semidirect
11. #19133953C2semidirect
12. #19133348C2semidirect
13. #19133298C2semidirect
14. #19133290C2semidirect
15. C43×#3106C2semidirect
271. C43⋊C8#135semidirect
300. #3106D43semidirect
372. C43#19184semidirect

Maximal subgroups

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

subgroupindex
#191453292
#191440502
#191436152
#191341542
#191341302
#191340962
#191340722
#191340372
#191340132
#191339792
#191339532
#191333482
#191332982
#191332902
C43×#31062
#1918443