Finite Group Databasebeta

← #25087987

Subgroups — #25087987

Order 11008.

684 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#19147501C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3#19146215C211yesmaximal, characteristic
4#19134186C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134077C211yesmaximal, characteristic, complemented
7#19134011C211yesmaximal, characteristic, complemented
8#19134001C211yesmaximal, characteristic, complemented
9#19133722C211yesmaximal, characteristic, complemented
10#19133710C211yesmaximal, characteristic, complemented
11#19133673C211yesmaximal, characteristic, complemented
12#19133666C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621884C211yesmaximal, characteristic, complemented
15C43×#3362C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17#14583609C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583305—21no—
20#14583302C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583273C2211yescharacteristic
23#14583271C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic
25#14583219—21no—
26#14583206—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583176—21no—
31#14583150—21no—
32#14583131—21no—
33#14583099C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583044—21no—
38#14583032—21no—
39#14583030C2211yescharacteristic, complemented
40#14582997—21no—
41C4×#10621884C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#102×D43—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56Q82×C43C2211yescharacteristic, complemented
57C43×#550C2211yescharacteristic
58C43×#486—21no—
59C43×#486C2211yescharacteristic, complemented
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#460—21no—
63C43×#460C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69#13063350—44no—
70C2×#10621883—41no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—41no—
74C2×#10621884D411yescharacteristic
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C2×#10621877—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063317—21no—
83#13063303—41no—
84#13063301—21no—
85#13063300—21no—
86#13063299—21no—
87#13063295—41no—
88C4×D172—21no—
89C4×D172C2311yescharacteristic
90C4⋊C4×D43—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063247—21no—
104#13063247—21no—
105#13063246—21no—
106#13063246—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×#41×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—41no—
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43—21no—
124#127×C43C2311yescharacteristic
125#121×C43—21no—
126#121×C43—41no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#106×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
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—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161D4×D43—42no—
162D4×D43—81no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—41no—
167C2×D172—42no—
168C2×D172—81no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—41no—
172C2×Dic86—21no—
173SD16×C43—41no—
174SD16×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—41no—
192C42×C43C2411yescharacteristic
193#10621884—42no—
194#10621884—82no—
195#10621884—81no—
196#10621884SD1614yescomplemented
197#10621883—82no—
198#10621882—42no—
199#10621882—42no—
200#10621882—81no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—41no—
203(C2×D43)⋊C4—41no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209#10621877—42no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8C2×D411yescharacteristic
215C2×C43⋊C8C2×D411yescharacteristic
216C8×D43—81no—
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—81no—
228Q8×C43—161no—
229Q8×C43C2×SD1612yes—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—82no—
237D4×C43—81no—
238D4×C43—161no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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—
261D172C2×SD1612yes—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—161no—
265Dic86—81no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8C2×SD1612yes—
275#19893—431nomaximal, Sylow
276C22×C43—41no—
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—22no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43C22×SD1611yescharacteristic
298C4×C43#57511yescharacteristic
299C4×C43#57711yescharacteristic
300C4×C43#57711yescharacteristic
301Dic43—41no—
302Dic43—81no—
303#3385—431no—
304#3362D4311yescharacteristic, complemented
305#3295—431no—
306#3274—431no—
307#1706—431no—
308#1695—431no—
309#1688—431no—
310#1678—431no—
311#1677—431no—
312#1631—431no—
313#1629—431no—
314#1623—431no—
315#1622—431no—
316#1590—431no—
317C8×SD16—431no—
318C2×C43—81no—
319C2×C43—161no—
320C2×C43#327511yescharacteristic
321C2×C43D4×SD1611yescharacteristic
322C2×C43#329211yescharacteristic
323D43—42no—
324D43—161no—
325C2×AGL(1,ℤ/8)—861no—
326Q82C2×D4311yescharacteristic, complemented
327#554—431no—
328#550C2×D4311yescharacteristic
329D42—431no—
330#501—861no—
331#500—431no—
332#493—431no—
333#492—431no—
334#492—431no—
335#486—21no—
336#486—431no—
337#486C2×D4311yescharacteristic, complemented
338#481—861no—
339#479—861no—
340#477—431no—
341#476—21no—
342#476—431no—
343#476—431no—
344#476C2×D4311yescharacteristic
345#474—861no—
346#469—861no—
347#465—861no—
348#460—21no—
349#460—431no—
350#460—431no—
351#460C2×D4311yescharacteristic, complemented
352#459—431no—
353#450—861no—
354#449—861no—
355#447—861no—
356#446—431no—
357C8×Q8C2×D4311yescharacteristic, complemented
358#440—861no—
359C4×SD16—21no—
360C4×SD16—431no—
361C4×SD16C2×D4311yescharacteristic
362#436—431no—
363C8×D4—431no—
364C2×#102—861no—
365#334—431no—
366#334—431no—
367#333—431no—
368#333—431no—
369#331—431no—
370#331—431no—
371Q8⋊C8—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375C82—431no—
376C43#1989311yescharacteristic, complemented, Sylow
377C2×#41—21no—
378C22×D4—861no—
379C22×D4—861no—
380AGL(1,ℤ/8)—1724no—
381C2×SD16—21no—
382C2×SD16—431no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×SD16—1721no—
386C2×SD16—1721no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—861no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—41no—
396C4⋊Q8—431no—
397C4⋊Q8C22×D4311yescharacteristic
398#127—21no—
399#127—431no—
400#127C22×D4311yescharacteristic
401#125—861no—
402C22⋊Q8—861no—
403C22⋊Q8—1721no—
404#121—21no—
405#121—41no—
406#121—861no—
407#121—861no—
408#120—1721no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C22×D4311yescharacteristic
412C4×Q8C22×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4C22×D4311yescharacteristic
417C2×C4⋊C4—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#106—21no—
422#106—431no—
423#106—861no—
424#106—861no—
425#106C22⋊D4311yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—861no—
431C4⋊C8C22×D4311yescharacteristic
432#103—431no—
433#103—861no—
434#103C22⋊D4311yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—431no—
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—
456#41—42no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—41no—
460C2×Q8—861no—
461C2×Q8D4×D4311yescharacteristic
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—431no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4—1721no—
475C2×D4—1722no—
476C2×D4—1721no—
477C2×D4—1722no—
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—861no—
482C22×C4—1721no—
483SD16—41no—
484SD16—42no—
485SD16—434no—
486SD16—3442no—
487SD16—3442no—
488SD16—3441no—
489SD16—1722no—
490D8—3441no—
491D8—1722no—
492D8—1722no—
493M16—1722no—
494C2×C8—21no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—3441no—
502C2×C8C2×C22⋊D4311yescharacteristic
503C2×C8C2×C22⋊D4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4D4×D4311yescharacteristic
516C4⋊C4C2×C22⋊D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—861no—
521C22⋊C4—1721no—
522C22⋊C4—1721no—
523C42—21no—
524C42—21no—
525C42—41no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—41no—
529C23—861no—
530C23—3442no—
531C23—3442no—
532C23—1721no—
533C23—6881no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—81no—
538Q8—161no—
539Q8—3441no—
540Q8SD16×D4312yes—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—82no—
548D4—81no—
549D4—161no—
550D4—432no—
551D4—861no—
552D4—3441no—
553D4—3442no—
554D4—3442no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
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—82no—
568C2×C4—861no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—6881no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—432no—
580C8—862no—
581C8—861no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C22—41no—
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—22no—
600C4—21no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—3441no—
607C4—1721no—
608C4C2×SD16×D4311yescharacteristic
609C4#1458369711yescharacteristic
610C4#1458370511yescharacteristic
611C4#1458370711yescharacteristic
612C2—81no—
613C2—161no—
614C2—1722no—
615C2—6881no—
616C2#1914622711yescharacteristic
617C2SD16×C22⋊D4311yescharacteristic
618C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3362C2
socleC22×C43D42
prime radical#19146215C2
hypercenter#3362D43
hypocenterC43#19893
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3362

Complements

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

NH ≅ G/Ntype
1. #19147501C2semidirect
2. #19146421C2semidirect
4. #19134186C2semidirect
5. #19134116C2semidirect
6. #19134077C2semidirect
7. #19134011C2semidirect
8. #19134001C2semidirect
9. #19133722C2semidirect
10. #19133710C2semidirect
11. #19133673C2semidirect
12. #19133666C2semidirect
13. #19133486C2semidirect
14. C8×#10621884C2semidirect
15. C43×#3362C2semidirect
20. #14583302C22semidirect
23. #14583271C22semidirect
27. #14583194C22semidirect
39. #14583030C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. Q82×C43C22semidirect
59. C43×#486C22semidirect
63. C43×#460C22semidirect
64. C8×Q8×C43C22semidirect
196. #10621884SD16semidirect
304. #3362D43semidirect
326. Q82C2×D43semidirect
337. #486C2×D43semidirect
351. #460C2×D43semidirect
357. C8×Q8C2×D43semidirect
376. C43#19893semidirect

Maximal subgroups

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

subgroupindex
#191475012
#191464212
#191462152
#191341862
#191341162
#191340772
#191340112
#191340012
#191337222
#191337102
#191336732
#191336662
#191334862
C8×#106218842
C43×#33622
#1989343