Finite Group Databasebeta

← #25079793

Subgroups — #25079793

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145738C211yesmaximal, characteristic, complemented
2#19145535C211yesmaximal, characteristic
3#492×D43C211yesmaximal, characteristic
4#19143526C211yesmaximal, characteristic, complemented
5#19134068C211yesmaximal, characteristic, complemented
6#19134067C211yesmaximal, characteristic, complemented
7#19134064C211yesmaximal, characteristic, complemented
8#19133946C211yesmaximal, characteristic, complemented
9#19133945C211yesmaximal, characteristic, complemented
10#19133942C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133342C211yesmaximal, characteristic, complemented
13#19133265C211yesmaximal, characteristic, complemented
14#19133261C211yesmaximal, characteristic
15C43×#1686C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C2×SD16×D43—21no—
18#14583453C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21#14583296—21no—
22#14583273C2211yescharacteristic
23#14583272C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583270—21no—
26#14583270—21no—
27#14583270—21no—
28#14583248—21no—
29#14583244—21no—
30#14583231—21no—
31#14583228—21no—
32#14583185C2211yescharacteristic, complemented
33#14583184C2211yescharacteristic, complemented
34#14583181C2211yescharacteristic, complemented
35#14583100C2211yescharacteristic
36#14583099C2211yescharacteristic
37#14583096C2211yescharacteristic
38#14583051—21no—
39#14583048—21no—
40#14583029C2211yescharacteristic, complemented
41#14583027—21no—
42Q8×C43⋊C8C2211yescharacteristic, complemented
43#14583023—21no—
44#14583023C2211yescharacteristic, complemented
45#14582951C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582924—21no—
48#14582921C2211yescharacteristic
49#14582856—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#475C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C43×#446C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621883—21no—
77C2×#10621884—21no—
78C2×#10621884—21no—
79C2×#10621884—21no—
80SD16×D43—44no—
81SD16×D43—44no—
82C2×#10621872—21no—
83C2×C8×D43D411yescharacteristic
84C2×C8×D43D411yescharacteristic
85#13063325C2311yescharacteristic
86#13063324—21no—
87#13063324—21no—
88#13063324D411yescharacteristic
89#13063323—21no—
90#13063323D411yescharacteristic
91#13063322C2311yescharacteristic
92#13063321—21no—
93#13063321—21no—
94#13063321—21no—
95#13063315—21no—
96#13063305D411yescharacteristic
97#13063303—21no—
98#13063301D411yescharacteristic
99C4×Dic86—21no—
100C4×Dic86C2311yescharacteristic
101#13063282—21no—
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C42×D43C2311yescharacteristic
105#13063257—21no—
106#13063256—21no—
107#13063256—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063249—21no—
117#13063248—21no—
118#13063247—21no—
119#13063246—21no—
120#13063245—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123#13063235—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C2×SD16×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×Q8×C43C2311yescharacteristic
137#106×C43—21no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#103×C43—21no—
143#102×C43—21no—
144#97×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155Q8×D43—42no—
156Q8×D43—42no—
157D4×D43—42no—
158D4×D43—42no—
159D4×D43—81no—
160D4×D43—81no—
161D4×D43—82no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×C4×D43—41no—
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86C2×D411yescharacteristic
173SD16×C43—42no—
174SD16×C43—42no—
175SD16×C43—81no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D411yescharacteristic
185C42×C43—21no—
186C42×C43C2411yescharacteristic
187#10621884—42no—
188#10621884—42no—
189#10621884—81no—
190#10621883—42no—
191#10621883—42no—
192#10621883—81no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43C2×D411yescharacteristic
209C4×Dic43#4111yescharacteristic
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215#10621873—42no—
216#10621873—42no—
217#10621873—81no—
218#10621872—42no—
219C8×D43—22no—
220C8×D43SD1614yescomplemented
221C23×C43—41no—
222C22×D43—41no—
223C22×D43—82no—
224C22×D43—82no—
225C22×D43—82no—
226C22×D43#12111yescharacteristic
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—41no—
230Q8×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—81no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—82no—
243C22⋊D43—82no—
244C22⋊D43—82no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43#12111yescharacteristic
249C2×Dic43#12111yescharacteristic
250C2×Dic43#12111yescharacteristic
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—81no—
256C4×D43—21no—
257C4×D43—21no—
258C4×D43—22no—
259C4×D43—82no—
260C4×D43C2×SD1612yes—
261C4×D43AGL(1,ℤ/8)12yes—
262Dic86—21no—
263Dic86—21no—
264Dic86—42no—
265Dic86—41no—
266Dic86—41no—
267Dic86—82no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43C2×SD1612yes—
273C43⋊C8—21no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8C2×SD1612yes—
278#19202—431nomaximal, Sylow
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43C2×#12111yescharacteristic
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—164no—
289C2×D43#46012yes—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43C22×SD1611yescharacteristic
295C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C43#57711yescharacteristic
297C4×C43#57711yescharacteristic
298Dic43—21no—
299Dic43—41no—
300Dic43—41no—
301Dic43—81no—
302Dic43#46012yes—
303Dic43#47112yes—
304#3229—431no—
305#3208—431no—
306C2×#492—431no—
307#2960—431no—
308#1686—431no—
309#1686—431no—
310#1686—431no—
311#1686D4311yescharacteristic, complemented
312#1666—431no—
313#1666—431no—
314#1666—431no—
315#1666—431no—
316#1564—431no—
317#1546—431no—
318#1545—431no—
319C2×C43—161no—
320C2×C43C2×#46011yescharacteristic
321C2×C43#305711yescharacteristic
322C2×C43C2×#47111yescharacteristic
323D43—22no—
324D43—161no—
325C22×SD16—861no—
326C22×SD16—861no—
327#533—431no—
328C2×C4⋊Q8—431no—
329C2×#127—431no—
330#498—861no—
331#492—431no—
332#492—431no—
333#492—431no—
334#492—861no—
335#492—861no—
336#492—861no—
337#492C2×D4311yescharacteristic
338#487—861no—
339#486—861no—
340#483—861no—
341#483—861no—
342#475—431no—
343#475—431no—
344#475—431no—
345#475C2×D4311yescharacteristic, complemented
346#460—431no—
347#460—431no—
348#460—431no—
349#460C2×D4311yescharacteristic
350#450—861no—
351#450—861no—
352#446—431no—
353#446—861no—
354#446C2×D4311yescharacteristic, complemented
355C8×Q8—431no—
356C8×Q8—431no—
357C8×Q8—861no—
358#431—431no—
359#431—431no—
360#424—861no—
361#423—431no—
362#405—861no—
363C2×C4×C8—431no—
364#335—431no—
365#335C2×D4311yescharacteristic, complemented
366#334—431no—
367#334—431no—
368#332—431no—
369#332—431no—
370#332—431no—
371#332C2×D4311yescharacteristic, complemented
372#331—431no—
373#331—431no—
374#331—431no—
375#331C2×D4311yescharacteristic
376C43#1920211yescharacteristic, complemented, Sylow
377C22×Q8—861no—
378C22×D4—861no—
379C22×D4—861no—
380C22×D4—861no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×SD16—1724no—
394C2×SD16—1724no—
395C2×M16—861no—
396C22×C8—431no—
397C22×C8—431no—
398C4⋊Q8—431no—
399C4⋊Q8—431no—
400C4⋊Q8—431no—
401C4⋊Q8—861no—
402C4⋊Q8—861no—
403C4⋊Q8—861no—
404C4⋊Q8C22×D4311yescharacteristic
405#127—431no—
406#127—861no—
407#127—861no—
408#127—861no—
409#127C22×D4311yescharacteristic
410#125—861no—
411C22⋊Q8—431no—
412C22⋊Q8—431no—
413C22⋊Q8—861no—
414C4×Q8—431no—
415C4×Q8—861no—
416C4×Q8C22×D4311yescharacteristic
417#117—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C42—431no—
421#106—21no—
422#106—861no—
423#106—861no—
424#106—861no—
425C4⋊C8—21no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8C22×D4311yescharacteristic
434C4⋊C8C22×D4311yescharacteristic
435C4⋊C8C22×D4311yescharacteristic
436#103—21no—
437#103—861no—
438#103—861no—
439#103—861no—
440#102—21no—
441#102—861no—
442#102—861no—
443#102—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446#97—21no—
447#97—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8—861no—
452C4×C8—861no—
453C4×C8—861no—
454C4×C8—861no—
455C4×C8C22×D4311yescharacteristic
456C24—1721no—
457C2×Q8—21no—
458C2×Q8—431no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—1721no—
462C2×Q8—1722no—
463C2×Q8—1722no—
464C2×Q8D4×D4311yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—3441no—
472C2×D4—3441no—
473C2×D4—3442no—
474C2×D4—1722no—
475C2×D4—1722no—
476C2×D4—1721no—
477C2×D4—1721no—
478C2×D4—1721no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—1721no—
483SD16—42no—
484SD16—42no—
485SD16—81no—
486SD16—3441no—
487SD16—3441no—
488SD16—3441no—
489SD16—1722no—
490SD16—1722no—
491SD16—1722no—
492SD16—1722no—
493SD16—1722no—
494SD16—1722no—
495M16—1722no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—431no—
500C2×C8—434no—
501C2×C8—431no—
502C2×C8—862no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8D4×D4311yescharacteristic
507C2×C8D4×D4311yescharacteristic
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—431no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4D4×D4311yescharacteristic
523C22⋊C4—861no—
524C22⋊C4—861no—
525C42—21no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—861no—
530C42C23×D4311yescharacteristic
531C23—41no—
532C23—431no—
533C23—3442no—
534C23—3442no—
535C23—3442no—
536C23—1721no—
537Q8—21no—
538Q8—21no—
539Q8—41no—
540Q8—41no—
541Q8—861no—
542Q8—861no—
543Q8—3442no—
544Q8—1722no—
545Q8—1721no—
546Q8—1721no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—81no—
552D4—3441no—
553D4—3442no—
554D4—3442no—
555D4—3442no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—432no—
566C2×C4—432no—
567C2×C4—431no—
568C2×C4—862no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3442no—
574C2×C4—1721no—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—432no—
583C8—861no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C8SD16×D4312yes—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—432no—
592C22—861no—
593C22—861no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22—6884no—
598C22#121×D4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—432no—
604C4—432no—
605C4—861no—
606C4—3441no—
607C4—1721no—
608C4—1721no—
609C4C2×SD16×D4311yescharacteristic
610C4AGL(1,ℤ/8)×D4311yescharacteristic
611C4#1458370811yescharacteristic
612C4#1458370911yescharacteristic
613C2—161no—
614C2—862no—
615C2—6881no—
616C2#460×D4311yescharacteristic
617C2#1914423211yescharacteristic
618C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1686C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1686D43
hypocenterC43#19202
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1686

Complements

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

NH ≅ G/Ntype
1. #19145738C2semidirect
4. #19143526C2semidirect
5. #19134068C2semidirect
6. #19134067C2semidirect
7. #19134064C2semidirect
8. #19133946C2semidirect
9. #19133945C2semidirect
10. #19133942C2semidirect
11. #19133941C2semidirect
12. #19133342C2semidirect
13. #19133265C2semidirect
15. C43×#1686C2semidirect
32. #14583185C22semidirect
33. #14583184C22semidirect
34. #14583181C22semidirect
40. #14583029C22semidirect
42. Q8×C43⋊C8C22semidirect
44. #14583023C22semidirect
51. #14582652C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#475C22semidirect
63. C43×#446C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
220. C8×D43SD16semidirect
311. #1686D43semidirect
345. #475C2×D43semidirect
354. #446C2×D43semidirect
365. #335C2×D43semidirect
371. #332C2×D43semidirect
376. C43#19202semidirect

Maximal subgroups

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

subgroupindex
#191457382
#191455352
#492×D432
#191435262
#191340682
#191340672
#191340642
#191339462
#191339452
#191339422
#191339412
#191333422
#191332652
#191332612
C43×#16862
#1920243