Finite Group Databasebeta

← #25086455

Subgroups — #25086455

Order 11008.

680 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#19147383C211yesmaximal, characteristic, complemented
2#19146413C211yesmaximal, characteristic, complemented
3SD16×D172C211yesmaximal, characteristic, complemented
4#19134236C211yesmaximal, characteristic, complemented
5#19134137C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133943C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133758C211yesmaximal, characteristic, complemented
11#19133654C211yesmaximal, characteristic, complemented
12#19133648C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3361C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17Q8×D172C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583275C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583258—21no—
22#14583249C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic
24#14583245C2211yescharacteristic, complemented
25#14583217—21no—
26#14583189—21no—
27#14583186C2211yescharacteristic
28#14583184C2211yescharacteristic, complemented
29#14583130—21no—
30#14583129—21no—
31#14583111—21no—
32#14583104C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583051—21no—
37#14583049—21no—
38#14583039—21no—
39#14583030C2211yescharacteristic, complemented
40#14583009—21no—
41C4×#10621884C2211yescharacteristic
42C8×D172C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063245—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C43×#559C2211yescharacteristic, complemented
57C43×#554C2211yescharacteristic
58C43×#488—21no—
59C43×#486C2211yescharacteristic, complemented
60C43×#478—21no—
61C43×#477C2211yescharacteristic, complemented
62C43×#463—21no—
63C43×#459C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×SD16×C43C2211yescharacteristic
66C4×D8×C43—21no—
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×#10621884D411yescharacteristic
76SD16×D43—44no—
77C2×#10621882—21no—
78C2×#10621882—41no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81#13063325—21no—
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063305—21no—
85#13063305—41no—
86#13063300—21no—
87#13063299—21no—
88#13063295—41no—
89C4×D172—21no—
90C4×D172C2311yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98#13063249—21no—
99#13063249—41no—
100#13063249D411yescharacteristic
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×SD16×C43D411yescharacteristic
117C2×D8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119#127×C43C2311yescharacteristic
120#125×C43—21no—
121#124×C43—21no—
122#124×C43—21no—
123#123×C43—41no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43C2311yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137#103×C43—21no—
138#103×C43D411yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C2×C22⋊D43—41no—
157Q8×D43—42no—
158Q8×D43—81no—
159D4×D43—42no—
160D4×D43—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—41no—
165C2×D172—42no—
166C2×D172—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172SD16×C43—22no—
173D8×C43—42no—
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—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43C2411yescharacteristic
194#10621884—22no—
195#10621884—42no—
196#10621884—81no—
197#10621883—42no—
198#10621882—42no—
199#10621882—82no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43C2×D411yescharacteristic
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214#10621873—42no—
215#10621873—81no—
216C8×D43—42no—
217C23×C43—21no—
218C23×C43—41no—
219C22×D43—21no—
220C22×D43—41no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—161no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—81no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43AGL(1,ℤ/8)12yes—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—161no—
245C2×C4×C43—161no—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C22⋊D43—82no—
250C2×Dic43—21no—
251C2×Dic43—41no—
252D172—21no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—41no—
257D172—81no—
258D172—82no—
259D172#13512yes—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—82no—
263Dic86—41no—
264Dic86—41no—
265Dic86—82no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C43⋊C8—21no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#19789—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43D4211yescharacteristic
283C2×D43—22no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—164no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43C2×#13511yescharacteristic
298C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C43#57711yescharacteristic
300C4×C43#57711yescharacteristic
301Dic43—41no—
302Dic43—81no—
303#3373—431no—
304#3361D4311yescharacteristic, complemented
305#3295—431no—
306D4×SD16—431no—
307#1717—431no—
308#1698—431no—
309#1681—431no—
310#1677—431no—
311#1666—431no—
312#1643—431no—
313#1637—431no—
314#1620—431no—
315#1619—431no—
316#1582—431no—
317SD16⋊C8—431no—
318C2×C43—42no—
319C2×C43—161no—
320C2×C43#326511yescharacteristic
321C2×C43#328211yescharacteristic
322C2×C43#328811yescharacteristic
323D43—42no—
324D43—161no—
325C22×SD16—861no—
326#559C2×D4311yescharacteristic, complemented
327#554C2×D4311yescharacteristic
328D4×Q8—431no—
329D42—431no—
330#493—431no—
331#492—431no—
332#489—861no—
333#488—21no—
334#487—431no—
335#486—431no—
336#486—431no—
337#486C2×D4311yescharacteristic, complemented
338#481—861no—
339#478—21no—
340#477C2×D4311yescharacteristic, complemented
341#476—431no—
342#476—861no—
343#475—431no—
344#465—861no—
345#465—861no—
346#463—21no—
347#463—861no—
348#461—431no—
349#460—431no—
350#460—431no—
351#459—431no—
352#459C2×D4311yescharacteristic
353#450—861no—
354#450—861no—
355#448—861no—
356#446—431no—
357C8×Q8C2×D4311yescharacteristic, complemented
358#442—861no—
359C4×SD16—431no—
360C4×SD16C2×D4311yescharacteristic
361C4×D8—21no—
362C8×D4—431no—
363C8×D4—431no—
364C2×#102—861no—
365#335—431no—
366#334—431no—
367#333—431no—
368#332—431no—
369#331—431no—
370#331—431no—
371Q8⋊C8—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375#322—431no—
376C43#1978911yescharacteristic, complemented, Sylow
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—1724no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—21no—
389C2×D8—861no—
390C2×D8—1721no—
391C22×C8—861no—
392C22×C8—861no—
393C4⋊Q8—431no—
394C4⋊Q8—861no—
395C4⋊Q8C22×D4311yescharacteristic
396#127—431no—
397#127C22×D4311yescharacteristic
398#125—21no—
399#124—21no—
400#124—21no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—861no—
405C22⋊Q8—1721no—
406#121—861no—
407#121—861no—
408#120—1721no—
409C4×Q8C22×D4311yescharacteristic
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4C22×D4311yescharacteristic
417C2×C4⋊C4—21no—
418#107—21no—
419#106—431no—
420#106—861no—
421#106—861no—
422#106C22⋊D4311yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429#103—21no—
430#103—431no—
431#103—861no—
432#103—861no—
433#103—1721no—
434#103C22⋊D4311yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—431no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102C22⋊D4311yescharacteristic
448C22⋊C8—861no—
449C22⋊C8—861no—
450#97—861no—
451C4×C8—21no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8C22×D4311yescharacteristic
455C24—1721no—
456C2×Q8—21no—
457C2×Q8—861no—
458C2×Q8—3441no—
459C2×Q8—1721no—
460C2×Q8—1722no—
461C2×Q8D4×D4311yescharacteristic
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—431no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—3441no—
471C2×D4—3441no—
472C2×D4—1721no—
473C2×D4—1722no—
474C2×D4—1721no—
475C2×D4—1722no—
476C2×D4C2×C22⋊D4311yescharacteristic
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—861no—
481C22×C4—1721no—
482SD16—22no—
483SD16—862no—
484SD16—3441no—
485SD16—3441no—
486SD16—1722no—
487SD16—1722no—
488SD16—1722no—
489D8—42no—
490D8—3442no—
491D8—1722no—
492C2×C8—21no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—3441no—
500C2×C8—1722no—
501C2×C8C2×C22⋊D4311yescharacteristic
502C2×C8C2×C22⋊D4311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—431no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1721no—
513C4⋊C4D4×D4311yescharacteristic
514C4⋊C4C2×C22⋊D4311yescharacteristic
515C4⋊C4C2×C22⋊D4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—861no—
522C22⋊C4—1721no—
523C22⋊C4—1721no—
524C42—21no—
525C42—21no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—41no—
529C23—861no—
530C23—3442no—
531C23—3442no—
532C23—1721no—
533C23—6881no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—3442no—
540Q8—1721no—
541Q8—1721no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—432no—
549D4—861no—
550D4—3441no—
551D4—3442no—
552D4—3442no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4#1306335012yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4—861no—
569C2×C4—3442no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—861no—
580C8—861no—
581C8—1721no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—862no—
592C22—3441no—
593C22—3441no—
594C22—3441no—
595C22—1721no—
596C22—1721no—
597C22—6884no—
598C22D4×C22⋊D4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—3441no—
607C4—1721no—
608C4#135×D4311yescharacteristic
609C4C2×#1306335011yescharacteristic
610C4#1458370611yescharacteristic
611C4#1458370711yescharacteristic
612C2—42no—
613C2—161no—
614C2—1722no—
615C2—6881no—
616C2#1914609111yescharacteristic
617C2#1914629611yescharacteristic
618C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3361C2
socleC22×C43D42
prime radical#19133648C2
hypercenter#3361D43
hypocenterC43#19789
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3361

Complements

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

NH ≅ G/Ntype
1. #19147383C2semidirect
2. #19146413C2semidirect
3. SD16×D172C2semidirect
4. #19134236C2semidirect
5. #19134137C2semidirect
6. #19134030C2semidirect
7. #19134001C2semidirect
8. #19133943C2semidirect
9. #19133802C2semidirect
10. #19133758C2semidirect
11. #19133654C2semidirect
13. #19133432C2semidirect
14. #19133405C2semidirect
15. C43×#3361C2semidirect
22. #14583249C22semidirect
24. #14583245C22semidirect
28. #14583184C22semidirect
39. #14583030C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
56. C43×#559C22semidirect
59. C43×#486C22semidirect
61. C43×#477C22semidirect
64. C8×Q8×C43C22semidirect
304. #3361D43semidirect
326. #559C2×D43semidirect
337. #486C2×D43semidirect
340. #477C2×D43semidirect
357. C8×Q8C2×D43semidirect
376. C43#19789semidirect

Maximal subgroups

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

subgroupindex
#191473832
#191464132
SD16×D1722
#191342362
#191341372
#191340302
#191340012
#191339432
#191338022
#191337582
#191336542
#191336482
#191334322
#191334052
C43×#33612
#1978943