Finite Group Databasebeta

← #25086073

Subgroups — #25086073

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147233C211yesmaximal, characteristic, complemented
2SD16×D172C211yesmaximal, characteristic
3D4×#10621884C211yesmaximal, characteristic
4#19134218C211yesmaximal, characteristic, complemented
5#19134067C211yesmaximal, characteristic, complemented
6#19134016C211yesmaximal, characteristic, complemented
7#19133981C211yesmaximal, characteristic, complemented
8#19133945C211yesmaximal, characteristic, complemented
9#19133858C211yesmaximal, characteristic, complemented
10#19133857C211yesmaximal, characteristic, complemented
11#19133773C211yesmaximal, characteristic
12#19133691C211yesmaximal, characteristic, complemented
13#19133429C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3386C211yesmaximal, characteristic, complemented
16C22×#10621884—21no—
17C2×SD16×D43—21no—
18Q8×D172C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583295C2211yescharacteristic, complemented
21#14583273C2211yescharacteristic
22#14583272C2211yescharacteristic
23#14583249—21no—
24#14583249C2211yescharacteristic, complemented
25#14583247C2211yescharacteristic
26#14583184—21no—
27#14583184C2211yescharacteristic, complemented
28#14583130—21no—
29#14583129—21no—
30#14583104C2211yescharacteristic
31#14583101—21no—
32#14583101C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583051—21no—
37#14583049—21no—
38#14583039—21no—
39#14583038—21no—
40Q8×C43⋊C8C2211yescharacteristic, complemented
41C4×#10621884—21no—
42C4×#10621884C2211yescharacteristic
43C8×D172C2211yescharacteristic
44D4×C43⋊C8C2211yescharacteristic
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C43×#557C2211yescharacteristic, complemented
57D4×Q8×C43C2211yescharacteristic
58C43×#501—21no—
59C43×#500C2211yescharacteristic, complemented
60C43×#478—21no—
61C43×#477—21no—
62C43×#475C2211yescharacteristic, complemented
63C43×#474C2211yescharacteristic
64C43×#446C2211yescharacteristic, complemented
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×Q8×D43—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77C2×#10621884—21no—
78C2×#10621884—21no—
79C2×#10621884—44no—
80C2×#10621884D411yescharacteristic
81SD16×D43—44no—
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84#13063325—21no—
85#13063325C2311yescharacteristic
86#13063322C2311yescharacteristic
87#13063305—21no—
88#13063305—41no—
89#13063300—21no—
90#13063299—21no—
91#13063295—41no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94#13063256—21no—
95#13063256—41no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249D411yescharacteristic
107#13063248—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C22×Q8×C43—21no—
118C2×SD16×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—21no—
124#125×C43—41no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#106×C43—21no—
137#106×C43D411yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43—21no—
143#102×C43D411yescharacteristic
144#97×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C2×C22⋊D43—41no—
158Q8×D43—42no—
159Q8×D43—81no—
160D4×D43—42no—
161D4×D43—81no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—41no—
166C2×D172—42no—
167C2×D172—81no—
168C2×D172C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—41no—
171C2×Dic86—21no—
172C2×Dic86—41no—
173SD16×C43SD1614yescomplemented
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196#10621884—22no—
197#10621884—42no—
198#10621884—42no—
199#10621884—42no—
200#10621884—42no—
201#10621884—42no—
202#10621884—81no—
203#10621883—42no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—41no—
210C4⋊Dic43C2×D411yescharacteristic
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—42no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218#10621873—42no—
219#10621873—81no—
220C8×D43—42no—
221C23×C43—21no—
222C22×D43—21no—
223C22×D43—41no—
224C22×D43—82no—
225C22×D43—82no—
226C22×D43—161no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—21no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234Q8×C43—82no—
235Q8×C43C2×SD1612yescomplemented
236D4×C43—21no—
237D4×C43C2×SD1612yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—82no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254D172—21no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—81no—
260D172—82no—
261D172AGL(1,ℤ/8)12yes—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—82no—
265Dic86—41no—
266Dic86—41no—
267Dic86—82no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43C2×SD1612yescomplemented
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#19764—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43D4211yescharacteristic
282C2×D43—22no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—164no—
289C4×C43—22no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43C22×SD1611yescharacteristic
298C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C43#57711yescharacteristic
300C4×C43#57711yescharacteristic
301Dic43—41no—
302Dic43—81no—
303#3386D4311yescharacteristic, complemented
304#3359—431no—
305D4×SD16—431no—
306D4×SD16—431no—
307#1714—431no—
308#1686—431no—
309#1679—431no—
310#1673—431no—
311#1666—431no—
312#1651—431no—
313#1651—431no—
314#1639—431no—
315#1626—431no—
316#1582—431no—
317SD16⋊C8—431no—
318C2×C43—42no—
319C2×C43#326511yescharacteristic
320C2×C43D4×SD1611yescharacteristic
321C2×C43#328911yescharacteristic
322D43—42no—
323D43—161no—
324C22×SD16—861no—
325C22×SD16—861no—
326#557C2×D4311yescharacteristic, complemented
327D4×Q8—431no—
328D4×Q8C2×D4311yescharacteristic
329D42—431no—
330#501—21no—
331#500C2×D4311yescharacteristic, complemented
332#498—431no—
333#492—431no—
334#492—431no—
335#487—431no—
336#487—861no—
337#486—431no—
338#478—21no—
339#477—21no—
340#475—431no—
341#475—861no—
342#475C2×D4311yescharacteristic, complemented
343#474C2×D4311yescharacteristic
344#465—861no—
345#465—861no—
346#461—431no—
347#461—431no—
348#461—431no—
349#461—861no—
350#460—431no—
351#460—431no—
352#450—861no—
353#450—861no—
354#448—861no—
355#448—861no—
356#446C2×D4311yescharacteristic, complemented
357C8×Q8—431no—
358#440—21no—
359C4×SD16—431no—
360C4×SD16—861no—
361C4×SD16C2×D4311yescharacteristic
362C8×D4—431no—
363C8×D4—431no—
364#335—431no—
365#334—431no—
366#332—431no—
367#332—431no—
368#332—431no—
369#331—431no—
370Q8⋊C8—431no—
371Q8⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8—431no—
374#322—431no—
375C43#1976411yescharacteristic, complemented, Sylow
376C22×Q8—21no—
377C22×Q8—861no—
378C22×D4—861no—
379C22×D4—861no—
380C2×SD16—431no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—1724no—
391C2×SD16—1724no—
392C2×SD16C22⋊D4311yescharacteristic
393C22×C8—861no—
394C22×C8—861no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8—431no—
398C4⋊Q8—861no—
399C4⋊Q8C22×D4311yescharacteristic
400C4⋊Q8C22×D4311yescharacteristic
401#127—431no—
402#125—21no—
403#125—41no—
404C22⋊Q8—21no—
405C22⋊Q8—41no—
406C22⋊Q8—861no—
407C22⋊Q8—1721no—
408#121—861no—
409#121—861no—
410#120—1721no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C22×D4311yescharacteristic
414C4×Q8C22×D4311yescharacteristic
415C4×D4—21no—
416C4×D4—431no—
417C4×D4—861no—
418C4×D4C22×D4311yescharacteristic
419#107—21no—
420#107—21no—
421#107—21no—
422#106—21no—
423#106—431no—
424#106—861no—
425#106—1721no—
426#106C22⋊D4311yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—861no—
432C4⋊C8C22×D4311yescharacteristic
433#103—21no—
434#103—431no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103C22⋊D4311yescharacteristic
442#102—21no—
443#102—431no—
444#102—861no—
445#102—861no—
446#102—1721no—
447#102C22⋊D4311yescharacteristic
448C22⋊C8—861no—
449C22⋊C8—861no—
450#97—21no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C24—1721no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—41no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×Q8—861no—
462C2×Q8—3441no—
463C2×Q8—1721no—
464C2×Q8—1722no—
465C2×Q8D4×D4311yescharacteristic
466C2×Q8C2×C22⋊D4311yescharacteristic
467C2×D4—431no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—3441no—
472C2×D4—3441no—
473C2×D4—1721no—
474C2×D4—1722no—
475C2×D4—1721no—
476C2×D4—1722no—
477C2×D4C2×C22⋊D4311yescharacteristic
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—861no—
481C22×C4—1721no—
482SD16—862no—
483SD16—3441no—
484SD16—3441no—
485SD16—1722no—
486SD16—1722no—
487SD16—1722no—
488SD16—1722no—
489SD16—1722no—
490SD16—1722no—
491SD16—1722no—
492SD16#1062188414yescomplemented
493C2×C8—21no—
494C2×C8—431no—
495C2×C8—431no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—1722no—
501C2×C8—1722no—
502C2×C8C2×C22⋊D4311yescharacteristic
503C2×C8C2×C22⋊D4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—431no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1721no—
518C4⋊C4D4×D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C4⋊C4C2×C22⋊D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—861no—
524C22⋊C4—1721no—
525C22⋊C4—1721no—
526C42—21no—
527C42—21no—
528C42—41no—
529C42C23×D4311yescharacteristic
530C23—21no—
531C23—861no—
532C23—3442no—
533C23—3442no—
534C23—1721no—
535C23—6881no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—82no—
544Q8—3442no—
545Q8—1721no—
546Q8—1721no—
547Q8C2×#1062188412yescomplemented
548D4—21no—
549D4—432no—
550D4—861no—
551D4—3441no—
552D4—3442no—
553D4—3442no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4C2×#1062188412yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—861no—
570C2×C4—3442no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C22×C22⋊D4311yescharacteristic
576C2×C4#1306337011yescharacteristic
577C8—21no—
578C8—41no—
579C8—861no—
580C8—861no—
581C8—1721no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C8C2×#1062188412yescomplemented
586C22—22no—
587C22—41no—
588C22—41no—
589C22—862no—
590C22—3441no—
591C22—3441no—
592C22—3441no—
593C22—1721no—
594C22—1721no—
595C22—6884no—
596C22D4×C22⋊D4311yescharacteristic
597C4—22no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—3441no—
606C4—1721no—
607C4C22×#1062188411yescharacteristic
608C4AGL(1,ℤ/8)×D4311yescharacteristic
609C4#1458370711yescharacteristic
610C4#1458370911yescharacteristic
611C2—42no—
612C2—1722no—
613C2—6881no—
614C2#1914608411yescharacteristic
615C2D4×#1062188411yescharacteristic
616C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3386C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenter#3386D43
hypocenterC43#19764
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3386

Complements

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

NH ≅ G/Ntype
1. #19147233C2semidirect
4. #19134218C2semidirect
5. #19134067C2semidirect
6. #19134016C2semidirect
7. #19133981C2semidirect
8. #19133945C2semidirect
9. #19133858C2semidirect
10. #19133857C2semidirect
12. #19133691C2semidirect
13. #19133429C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3386C2semidirect
20. #14583295C22semidirect
24. #14583249C22semidirect
27. #14583184C22semidirect
40. Q8×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
56. C43×#557C22semidirect
59. C43×#500C22semidirect
62. C43×#475C22semidirect
64. C43×#446C22semidirect
173. SD16×C43SD16semidirect
235. Q8×C43C2×SD16semidirect
270. C8×C43C2×SD16semidirect
303. #3386D43semidirect
326. #557C2×D43semidirect
331. #500C2×D43semidirect
342. #475C2×D43semidirect
356. #446C2×D43semidirect
375. C43#19764semidirect
492. SD16#10621884semidirect
547. Q8C2×#10621884semidirect
585. C8C2×#10621884semidirect

Maximal subgroups

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

subgroupindex
#191472332
SD16×D1722
D4×#106218842
#191342182
#191340672
#191340162
#191339812
#191339452
#191338582
#191338572
#191337732
#191336912
#191334292
SD16⋊(C43⋊C8)2
C43×#33862
#1976443