Finite Group Databasebeta

← #25080411

Subgroups — #25080411

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145173C211yesmaximal, characteristic, complemented
2#19144688C211yesmaximal, characteristic, complemented
3#19144685C211yesmaximal, characteristic, complemented
4C8×D4×D43C211yesmaximal, characteristic, complemented
5#19134005C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133993C211yesmaximal, characteristic, complemented
9#19133992C211yesmaximal, characteristic, complemented
10#19133949C211yesmaximal, characteristic, complemented
11#19133948C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic, complemented
13#19133289C211yesmaximal, characteristic, complemented
14#19133287C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C22×C8×D43—21no—
17#14583450C2211yescharacteristic
18#14583447C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583302C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic, complemented
22#14583246C2211yescharacteristic, complemented
23#14583219—21no—
24#14583216—21no—
25#14583190C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583186C2211yescharacteristic
28#14583134—21no—
29#14583134—21no—
30#14583095C2211yescharacteristic
31#14583094C2211yescharacteristic
32#14583091C2211yescharacteristic
33#14583034—21no—
34#14583031—21no—
35#14583011—21no—
36#14583010—21no—
37#14583008—21no—
38#14583008—21no—
39#14582979—21no—
40#14582979—21no—
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582964C2211yescharacteristic
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582955C2211yescharacteristic
47#14582955C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582650C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621902—21no—
68C2×#10621900—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71C2×D344—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—44no—
81C2×C8×D43D411yescharacteristic
82C2×C8×D43D411yescharacteristic
83#13063325C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063314—21no—
86#13063312—21no—
87#13063300—21no—
88#13063300—21no—
89#13063296—21no—
90#13063296—21no—
91C4×D172C2311yescharacteristic
92D4×Dic43—21no—
93D4×Dic43—21no—
94D4×Dic43D411yescharacteristic
95#13063287—21no—
96#13063287—21no—
97#13063287D411yescharacteristic
98C4×C22⋊D43—21no—
99(C22⋊D43)⋊C4—21no—
100C4⋊C4×D43D411yescharacteristic
101C22⋊C4×D43—21no—
102C42×D43C2311yescharacteristic
103#13063258—21no—
104#13063258—21no—
105#13063257—21no—
106#13063256—21no—
107#13063256—21no—
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112#13063247—21no—
113#13063247—21no—
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063245—21no—
119#13063245—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156#10621902—82no—
157#10621900—82no—
158D4×D43—22no—
159D4×D43—22no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—41no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—41no—
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43#4111yescharacteristic
174C2×Dic86—21no—
175D8×C43—42no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—42no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—21no—
188C22⋊Dic43—41no—
189C22⋊Dic43—41no—
190#10621882—42no—
191#10621882—42no—
192#10621882—42no—
193#10621882—42no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—21no—
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43#4111yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—42no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211D344—42no—
212C8×D43—22no—
213C8×D43—41no—
214C8×D43—42no—
215C8×D43—42no—
216C8×D43—42no—
217C23×C43—21no—
218C23×C43—41no—
219C22×D43—24no—
220C22×D43—21no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—41no—
224C22×D43#12111yescharacteristic
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—81no—
232D4×C43#13512yes—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—24no—
241C22⋊D43—82no—
242C2×Dic43—21no—
243C2×Dic43—42no—
244C2×Dic43—41no—
245C2×Dic43—82no—
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248C2×Dic43#12111yescharacteristic
249D172—21no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—81no—
255D172—82no—
256D172#13512yes—
257C4×D43—22no—
258C4×D43—21no—
259C4×D43—21no—
260C4×D43—21no—
261C4×D43—21no—
262C4×D43—42no—
263C4×D43—42no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—82no—
267Dic86—81no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—21no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8AGL(1,ℤ/8)12yes—
278#19258—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43C2×#12111yescharacteristic
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—22no—
289C2×D43—48no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43#47212yes—
296C4×C43—21no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43C2×#13511yescharacteristic
300C4×C43C2×#13511yescharacteristic
301C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C43#57511yescharacteristic
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—41no—
307Dic43—81no—
308#3169—431no—
309#3109—431no—
310#3109—431no—
311C2×C8×D4—431no—
312#1677—431no—
313#1677—431no—
314#1677—431no—
315#1677D4311yescharacteristic, complemented
316#1675—431no—
317#1675—431no—
318#1667—431no—
319#1667—431no—
320#1568—431no—
321#1551—431no—
322#1551—431no—
323C2×C43—42no—
324C2×C43—161no—
325C2×C43#303611yescharacteristic
326C2×C43#305011yescharacteristic
327C2×C43C2×#47211yescharacteristic
328D43—22no—
329D43—42no—
330D43—161no—
331C23×C8—861no—
332#532—431no—
333#532—431no—
334C2×C4×D4—431no—
335#500—431no—
336#493—431no—
337#486—431no—
338#486C2×D4311yescharacteristic, complemented
339#481—861no—
340#481—861no—
341#476—431no—
342#476—431no—
343#476—431no—
344#476C2×D4311yescharacteristic
345#466—861no—
346#466—861no—
347#459—431no—
348#459—431no—
349#459—431no—
350#459C2×D4311yescharacteristic
351#447—861no—
352#447—861no—
353#442—861no—
354#442—861no—
355#442—861no—
356#442—861no—
357C4×D8—861no—
358C4×D8—861no—
359C8×D4—431no—
360C8×D4—431no—
361C8×D4—431no—
362C8×D4—861no—
363C8×D4—861no—
364C8×D4C2×D4311yescharacteristic
365#432—431no—
366#432—431no—
367C2×C4⋊C8—431no—
368C2×C22⋊C8—861no—
369C2×C4×C8—431no—
370#335—431no—
371#335—431no—
372#334—431no—
373#334C2×D4311yescharacteristic, complemented
374#333—431no—
375#333—431no—
376#333—431no—
377#333C2×D4311yescharacteristic, complemented
378#331—431no—
379#331—431no—
380#331—431no—
381#331C2×D4311yescharacteristic, complemented
382C43#1925811yescharacteristic, complemented, Sylow
383C2×#41—861no—
384C2×#41—861no—
385C22×D4—431no—
386C23×C4—861no—
387C2×D8—21no—
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×D8—861no—
392C2×D8—861no—
393C22×C8—21no—
394C22×C8—431no—
395C22×C8—431no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8—861no—
399C22×C8—861no—
400C22×C8—1724no—
401C4⋊Q8—431no—
402C4⋊Q8C22×D4311yescharacteristic
403#127—431no—
404#127C22×D4311yescharacteristic
405#124—861no—
406#124—861no—
407#121—861no—
408#121—861no—
409#121—861no—
410#121—861no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4—861no—
420C4×D4C22×D4311yescharacteristic
421C2×C4⋊C4—431no—
422C2×C22⋊C4—861no—
423C2×C42—431no—
424#107—861no—
425#107—861no—
426#106—21no—
427#106—861no—
428#106—861no—
429#106—861no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—861no—
434C4⋊C8C22×D4311yescharacteristic
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449C22⋊C8—21no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455#97—861no—
456#97—861no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8C22×D4311yescharacteristic
461C24—861no—
462#41—3442no—
463#41—3442no—
464C2×Q8—21no—
465C2×Q8—861no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—431no—
470C2×D4—861no—
471C2×D4—862no—
472C2×D4—862no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4—1721no—
478C2×D4D4×D4311yescharacteristic
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—1721no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4—1721no—
491D8—42no—
492D8—1722no—
493D8—1722no—
494D8—1722no—
495D8—1722no—
496D8—1722no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—42no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—862no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—1721no—
508C2×C8—1722no—
509C2×C8—1722no—
510C2×C8—1722no—
511C2×C8—1722no—
512C2×C8D4×D4311yescharacteristic
513C2×C8D4×D4311yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—431no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4D4×D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C22⋊C4—1721no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42C23×D4311yescharacteristic
533C23—21no—
534C23—41no—
535C23—431no—
536C23—864no—
537C23—861no—
538C23—1722no—
539C23—1722no—
540C23—1721no—
541Q8—81no—
542Q8—3441no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—432no—
550D4—864no—
551D4—861no—
552D4—3441no—
553D4—3442no—
554D4—3442no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4#1306334612yes—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3442no—
574C2×C4—3442no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—432no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—432no—
601C22—861no—
602C22—861no—
603C22—862no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—1728no—
608C22—1721no—
609C22—1721no—
610C22#121×D4311yescharacteristic
611C4—21no—
612C4—41no—
613C4—81no—
614C4—861no—
615C4—861no—
616C4—861no—
617C4—3441no—
618C4—1721no—
619C4#135×D4311yescharacteristic
620C4C2×#1306334611yescharacteristic
621C4AGL(1,ℤ/8)×D4311yescharacteristic
622C4#1458369611yescharacteristic
623C2—42no—
624C2—161no—
625C2—862no—
626C2—1722no—
627C2—6881no—
628C2#1914405711yescharacteristic
629C2#1914417111yescharacteristic
630C2#472×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
hypercenter#1677D43
hypocenterC43#19258
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #19145173C2semidirect
2. #19144688C2semidirect
3. #19144685C2semidirect
4. C8×D4×D43C2semidirect
5. #19134005C2semidirect
6. #19134004C2semidirect
7. #19134001C2semidirect
8. #19133993C2semidirect
9. #19133992C2semidirect
10. #19133949C2semidirect
11. #19133948C2semidirect
12. #19133355C2semidirect
13. #19133289C2semidirect
14. #19133287C2semidirect
15. C43×#1677C2semidirect
20. #14583302C22semidirect
21. #14583275C22semidirect
22. #14583246C22semidirect
51. #14582651C22semidirect
52. #14582651C22semidirect
53. #14582650C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#486C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#331C22semidirect
315. #1677D43semidirect
338. #486C2×D43semidirect
373. #334C2×D43semidirect
377. #333C2×D43semidirect
381. #331C2×D43semidirect
382. C43#19258semidirect

Maximal subgroups

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

subgroupindex
#191451732
#191446882
#191446852
C8×D4×D432
#191340052
#191340042
#191340012
#191339932
#191339922
#191339492
#191339482
#191333552
#191332892
#191332872
C43×#16772
#1925843