Finite Group Databasebeta

← #25079625

Subgroups — #25079625

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#19144649C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic, complemented
3#19143613C211yesmaximal, characteristic, complemented
4#19134153C211yesmaximal, characteristic, complemented
5#19134125C211yesmaximal, characteristic, complemented
6#19134091C211yesmaximal, characteristic, complemented
7#19134071C211yesmaximal, characteristic, complemented
8#19134036C211yesmaximal, characteristic, complemented
9#19134008C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133952C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133300C211yesmaximal, characteristic, complemented
14#19133290C211yesmaximal, characteristic, complemented
15C43×#3184C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17C4×#10621898C2211yescharacteristic
18#14583220—21no—
19#14583191C2211yescharacteristic
20#14583186C2211yescharacteristic
21#14583118—21no—
22#14583111—21no—
23#14583106C2211yescharacteristic
24#14583101C2211yescharacteristic
25#14583096C2211yescharacteristic
26#14583096C2211yescharacteristic
27#14583091C2211yescharacteristic
28#14583091C2211yescharacteristic
29#14583042—21no—
30C8×Dic86C2211yescharacteristic
31C8×Dic86C2211yescharacteristic
32C4×#10621883—21no—
33C4×#10621882—21no—
34#14582978C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582975—21no—
37#14582975—21no—
38#14582956C2211yescharacteristic
39#14582954—21no—
40#14582952C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582895—21no—
43#14582851—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#469—21no—
63C43×#469—21no—
64C43×#442—21no—
65C43×#442—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78C4×Dic86D411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172D411yescharacteristic
81C4×D172C2311yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284D411yescharacteristic
85#13063282—21no—
86C42×D43—21no—
87#13063258—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97Dic43⋊C8—21no—
98#13063249—21no—
99#13063249—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063245—21no—
106C22⋊(C43⋊C8)—21no—
107C22⋊(C43⋊C8)—21no—
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110#13063236—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C8×Dic43—21no—
114C2×#41×C43—21no—
115C2×#41×C43—21no—
116C2×D8×C43—21no—
117C2×D8×C43—21no—
118C2×M16×C43D411yescharacteristic
119C2×M16×C43D411yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#127×C43C2311yescharacteristic
124#124×C43—21no—
125#124×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#97×C43D411yescharacteristic
142#97×C43D411yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—82no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C2×C22⋊D43—21no—
164#10621898—22no—
165#10621898—41no—
166C2×D172C2×D411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×Dic86C2×D411yescharacteristic
171D8×C43—42no—
172D8×C43—42no—
173M16×C43—22no—
174M16×C43—41no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191C22⋊Dic43—21no—
192#10621885—42no—
193#10621884—42no—
194#10621883—42no—
195#10621883—42no—
196#10621882—42no—
197#10621882—42no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—42no—
214#10621872—42no—
215#10621872—42no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43#12111yescharacteristic
219C22×D43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—81no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—82no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—82no—
243C2×C4×C43—82no—
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C22⋊D43—42no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254D172—21no—
255D172—21no—
256C4×D43—42no—
257C4×D43—41no—
258C4×D43—41no—
259C4×D43—81no—
260Dic86—21no—
261Dic86AGL(1,ℤ/8)12yes—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43#13512yescomplemented
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19184—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43C2×#12111yescharacteristic
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C2×#13511yescharacteristic
293C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C43#57511yescharacteristic
295C4×C43#57511yescharacteristic
296Dic43—22no—
297Dic43—41no—
298Dic43—41no—
299#3184D4311yescharacteristic, complemented
300#3106—431no—
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—161no—
316C2×C43—161no—
317C2×C43#303511yescharacteristic
318C2×C43#305511yescharacteristic
319C2×C43#306811yescharacteristic
320D43—81no—
321C2×#135—861no—
322#532C2×D4311yescharacteristic
323#532C2×D4311yescharacteristic
324C4×#41—431no—
325#498C2×D4311yescharacteristic
326#493C2×D4311yescharacteristic
327#486C2×D4311yescharacteristic
328#486C2×D4311yescharacteristic
329#482—861no—
330#477—431no—
331#476—431no—
332#469—21no—
333#469—21no—
334#464—861no—
335#463—861no—
336#462—431no—
337#461—431no—
338#460—431no—
339#460—431no—
340#459—431no—
341#459—431no—
342#449—861no—
343C8×Q8—431no—
344C8×Q8—431no—
345#442—21no—
346#442—21no—
347C4×SD16—861no—
348C4×D8—861no—
349#436—431no—
350#436—431no—
351#436—861no—
352#436—861no—
353#432—431no—
354#432—861no—
355#431—431no—
356C2×C4⋊C8—431no—
357#416—861no—
358C4×M16—861no—
359C4×M16C2×D4311yescharacteristic
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—21no—
375C2×#41—431no—
376#135—1724no—
377C2×Q16—861no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—861no—
384C2×D8—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16C22⋊D4311yescharacteristic
388C2×M16C22⋊D4311yescharacteristic
389C22×C8—861no—
390C4⋊Q8C22×D4311yescharacteristic
391C4⋊Q8C22×D4311yescharacteristic
392#127C22×D4311yescharacteristic
393#127C22×D4311yescharacteristic
394#124—21no—
395#124—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400C4×Q8—431no—
401C4×Q8—431no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—431no—
407C4×D4—431no—
408C4×D4—861no—
409C4×D4—861no—
410#117—431no—
411#117—861no—
412C2×C42—861no—
413C2×C42C22×D4311yescharacteristic
414#107—861no—
415#106—21no—
416#106—21no—
417#106—861no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443#97—861no—
444#97C22⋊D4311yescharacteristic
445#97C22⋊D4311yescharacteristic
446C4×C8—861no—
447C4×C8—861no—
448C4×C8—861no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451#41—42no—
452#41—42no—
453#41—82no—
454#41—862no—
455#41—1721no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—431no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—431no—
468C2×D4—861no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4D4×D4311yescharacteristic
475C22×C4#1062190011yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477Q16—1722no—
478SD16—1722no—
479SD16—1722no—
480SD16—1722no—
481D8—42no—
482D8—42no—
483D8—1722no—
484D8—1722no—
485M16—22no—
486M16—41no—
487M16—1722no—
488M16—1722no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—1722no—
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊D4311yescharacteristic
498C2×C8C2×C22⋊D4311yescharacteristic
499C2×C8C2×C22⋊D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—431no—
505C4⋊C4—431no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42D4×D4311yescharacteristic
519C42#1062190011yescharacteristic
520C42C2×C22⋊D4311yescharacteristic
521C42C23×D4311yescharacteristic
522C23—41no—
523C23—41no—
524C23—861no—
525C23#1306329611yescharacteristic
526Q8—41no—
527Q8—41no—
528Q8—81no—
529Q8—432no—
530Q8—861no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—861no—
544D4—861no—
545D4—1722no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—3441no—
559C2×C4—1722no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4#1306329611yescharacteristic
563C2×C4#1306329611yescharacteristic
564C2×C4#1306329611yescharacteristic
565C2×C4C2×D4×D4311yescharacteristic
566C2×C4C22×C22⋊D4311yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C8#1306334512yescomplemented
578C22—21no—
579C22—21no—
580C22—21no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22C2×#1306329611yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—81no—
596C4—81no—
597C4—862no—
598C4—1721no—
599C4—1721no—
600C4C2×#1306334511yescharacteristic
601C4AGL(1,ℤ/8)×D4311yescharacteristic
602C4#1458369511yescharacteristic
603C4#1458369711yescharacteristic
604C2—41no—
605C2—161no—
606C2—161no—
607C2—3441no—
608C2#1914404411yescharacteristic
609C2#1914420811yescharacteristic
610C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3184C2
socleC22×C43C2×#121
hypercenter#3184D43
hypocenterC43#19184
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3184

Complements

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

NH ≅ G/Ntype
1. #19144649C2semidirect
2. #19144044C2semidirect
3. #19143613C2semidirect
4. #19134153C2semidirect
5. #19134125C2semidirect
6. #19134091C2semidirect
7. #19134071C2semidirect
8. #19134036C2semidirect
9. #19134008C2semidirect
10. #19133974C2semidirect
11. #19133952C2semidirect
12. #19133347C2semidirect
13. #19133300C2semidirect
14. #19133290C2semidirect
15. C43×#3184C2semidirect
265. C8×C43#135semidirect
299. #3184D43semidirect
372. C43#19184semidirect
577. C8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191446492
#191440442
#191436132
#191341532
#191341252
#191340912
#191340712
#191340362
#191340082
#191339742
#191339522
#191333472
#191333002
#191332902
C43×#31842
#1918443