Finite Group Databasebeta

← #25087943

Subgroups — #25087943

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147492C211yesmaximal, characteristic, complemented
2#19146953C211yesmaximal, characteristic, complemented
3D4×#10621873C211yesmaximal, characteristic, complemented
4#19146196C211yesmaximal, characteristic
5#19134182C211yesmaximal, characteristic, complemented
6#19134095C211yesmaximal, characteristic, complemented
7#19134068C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133936C211yesmaximal, characteristic, complemented
10#19133882C211yesmaximal, characteristic, complemented
11#19133860C211yesmaximal, characteristic, complemented
12#19133713C211yesmaximal, characteristic, complemented
13#19133669C211yesmaximal, characteristic, complemented
14#19133487C211yesmaximal, characteristic, complemented
15C8×D8×C43C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C22×#10621873—21no—
18#14583606C2211yescharacteristic, complemented
19D4×Dic86C2211yescharacteristic
20#14583553C2211yescharacteristic
21D4×D172C2211yescharacteristic
22#14583307—21no—
23#14583297C2211yescharacteristic, complemented
24#14583297C2211yescharacteristic, complemented
25#14583297C2211yescharacteristic, complemented
26#14583272C2211yescharacteristic
27#14583272C2211yescharacteristic
28#14583272C2211yescharacteristic
29#14583230—21no—
30#14583218—21no—
31#14583201—21no—
32#14583190C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583187—21no—
35#14583185C2211yescharacteristic, complemented
36#14583179C2211yescharacteristic, complemented
37#14583146—21no—
38#14583128—21no—
39#14583128—21no—
40#14583105C2211yescharacteristic
41#14583104C2211yescharacteristic
42#14583100C2211yescharacteristic
43#14583094C2211yescharacteristic
44#14583052—21no—
45#14583051—21no—
46#14583045—21no—
47#14583040—21no—
48#14583029C2211yescharacteristic, complemented
49#14583011—21no—
50C4×#10621873C2211yescharacteristic
51#14582978C2211yescharacteristic
52C2×#13063257—21no—
53#14582650C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582642C2211yescharacteristic
58#14582631C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic, complemented
63C43×#335C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C82×C43C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C22×Dic86—21no—
69C22×D172—21no—
70C2×D4×D43—21no—
71#13063349—44no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621873—21no—
76C2×#10621873—21no—
77C2×#10621873—21no—
78C2×#10621873—44no—
79C2×#10621873—41no—
80C2×#10621873D411yescharacteristic
81C2×#10621883—21no—
82C2×#10621882—21no—
83C2×#10621872—21no—
84#13063325C2311yescharacteristic
85#13063325C2311yescharacteristic
86#13063325C2311yescharacteristic
87#13063324—21no—
88#13063322C2311yescharacteristic
89#13063316—21no—
90#13063309—41no—
91#13063305—21no—
92#13063304—21no—
93#13063304—21no—
94#13063302—41no—
95#13063302—41no—
96#13063300—21no—
97#13063299—21no—
98#13063299—21no—
99#13063295—41no—
100C4×Dic86C2311yescharacteristic
101C4×D172C2311yescharacteristic
102D4×Dic43—21no—
103D4×Dic43—21no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—21no—
106#13063258—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257—21no—
113#13063257—41no—
114#13063257D411yescharacteristic
115#13063256—21no—
116C4⋊(C43⋊C8)C2311yescharacteristic
117C4⋊(C43⋊C8)C2311yescharacteristic
118Dic43⋊C8—21no—
119#13063250—21no—
120#13063250—21no—
121#13063250D411yescharacteristic
122#13063248—21no—
123#13063247—21no—
124#13063247—21no—
125#13063247D411yescharacteristic
126#13063246—21no—
127#13063246—21no—
128#13063245—21no—
129(C2×D43)⋊C8—21no—
130#13063235—21no—
131C2×D8×C43D411yescharacteristic
132C22×C8×C43—21no—
133C22×C8×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43D411yescharacteristic
140#102×C43D411yescharacteristic
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×D4×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156#10621900—42no—
157#10621900—81no—
158D4×D43—42no—
159D4×D43—81no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—41no—
164C2×D172—42no—
165C2×D172—81no—
166C2×D172C2×D411yescharacteristic
167C2×C4×D43—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—42no—
172C2×Dic86—41no—
173C2×Dic86—81no—
174C2×Dic86C2×D411yescharacteristic
175D8×C43SD1614yescomplemented
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—42no—
180C2×C8×C43—42no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191C22⋊Dic43—41no—
192#10621883—42no—
193#10621882—42no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—41no—
204C4⋊Dic43—41no—
205C4⋊Dic43C2×D411yescharacteristic
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210C4×Dic43—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213#10621873—22no—
214#10621873—42no—
215#10621873—42no—
216#10621873—42no—
217#10621873—42no—
218#10621873—81no—
219#10621873—81no—
220#10621873—82no—
221#10621872—42no—
222C23×C43—21no—
223C23×C43—21no—
224C22×D43—21no—
225C22×D43—41no—
226C22×D43—82no—
227C22×D43—82no—
228C22×D43—161no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43C2×SD1612yes—
232D4×C43C2×SD1612yescomplemented
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C22⋊D43—82no—
243C22⋊D43—82no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—82no—
251C2×Dic43—82no—
252C2×Dic43—161no—
253D172—21no—
254D172—21no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—81no—
260D172—82no—
261C4×D43—41no—
262C4×D43—41no—
263Dic86—21no—
264Dic86—21no—
265Dic86—41no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269Dic86—82no—
270Dic86—81no—
271C8×C43—22no—
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43C2×SD1612yescomplemented
277C8×C43AGL(1,ℤ/8)12yescomplemented
278C43⋊C8—41no—
279C43⋊C8—41no—
280#19890—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43D4211yescharacteristic
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—164no—
295C4×C43—21no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43C22×SD1611yescharacteristic
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57711yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308#3384—431no—
309#3335—431no—
310D4×SD16—431no—
311#3272—431no—
312#1705—431no—
313#1691—431no—
314#1686—431no—
315#1671—431no—
316#1665—431no—
317#1654—431no—
318#1651—431no—
319#1629—431no—
320#1622—431no—
321#1590—431no—
322C8×D8D4311yescharacteristic, complemented
323C2×C43—42no—
324C2×C43—42no—
325C2×C43#327211yescharacteristic
326C2×C43D4×SD1611yescharacteristic
327C2×C43#329111yescharacteristic
328D43—81no—
329D43—161no—
330C2×AGL(1,ℤ/8)—861no—
331C22×SD16—861no—
332#554—431no—
333D4×Q8—431no—
334#547—431no—
335D42—431no—
336#501—861no—
337#498—431no—
338#498—431no—
339#498—431no—
340#492—431no—
341#492—431no—
342#492—431no—
343#483—861no—
344#481—861no—
345#478—861no—
346#476—431no—
347#476—431no—
348#476—861no—
349#475—431no—
350#474—431no—
351#468—861no—
352#465—861no—
353#465—861no—
354#461—431no—
355#461—431no—
356#460—431no—
357#459—431no—
358#450—861no—
359#450—861no—
360#449—861no—
361#448—861no—
362#446—431no—
363#442—861no—
364C4×SD16—431no—
365C4×D8C2×D4311yescharacteristic
366#436—431no—
367C8×D4C2×D4311yescharacteristic
368C8×D4C2×D4311yescharacteristic, complemented
369C2×#106—861no—
370#335C2×D4311yescharacteristic, complemented
371#334—431no—
372#333—431no—
373#332—431no—
374#332—431no—
375#331—431no—
376Q8⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8C2×D4311yescharacteristic
379D4⋊C8C2×D4311yescharacteristic, complemented
380C82C2×D4311yescharacteristic, complemented
381C43#1989011yescharacteristic, complemented, Sylow
382C2×#41—861no—
383C22×Q8—861no—
384C22×D4—861no—
385C22×D4—861no—
386AGL(1,ℤ/8)—1724no—
387C2×SD16—431no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—1721no—
396C2×SD16—1724no—
397C2×D8—861no—
398C2×D8D17211yescharacteristic
399C2×M16—861no—
400C22×C8—21no—
401C22×C8—21no—
402C4⋊Q8—431no—
403C4⋊Q8—431no—
404C4⋊Q8—431no—
405C4⋊Q8—861no—
406#127—431no—
407#125—861no—
408#123—1721no—
409C22⋊Q8—861no—
410C22⋊Q8—861no—
411C22⋊Q8—861no—
412C22⋊Q8—1721no—
413C22⋊Q8—1721no—
414#121—861no—
415#121—861no—
416#121—861no—
417#120—1721no—
418C4×Q8—431no—
419C4×D4—431no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4C22×D4311yescharacteristic
423C4×D4C22×D4311yescharacteristic
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426#107—861no—
427#107D17211yescharacteristic
428#106—431no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—1721no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—861no—
440C4⋊C8C22×D4311yescharacteristic
441C4⋊C8C22×D4311yescharacteristic
442#103—431no—
443#103—861no—
444#103—861no—
445#103—861no—
446#102—431no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102D17211yescharacteristic
453#102D17211yescharacteristic
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—861no—
457#97—861no—
458C4×C8C22×D4311yescharacteristic
459C4×C8C22×D4311yescharacteristic
460C4×C8C22×D4311yescharacteristic
461C24—1721no—
462#41—3441no—
463#41—1722no—
464C2×Q8—431no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—3441no—
469C2×Q8—1721no—
470C2×Q8—1722no—
471C2×D4—431no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—3441no—
476C2×D4—3441no—
477C2×D4—1721no—
478C2×D4—1722no—
479C2×D4—1721no—
480C2×D4—1721no—
481C2×D4—1722no—
482C2×D4C2×D17211yescharacteristic
483C2×D4C2×D17211yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—861no—
487C22×C4—1721no—
488C22×C4—1721no—
489C22×C4—1721no—
490SD16—862no—
491SD16—3442no—
492SD16—3441no—
493SD16—3441no—
494SD16—1722no—
495SD16—1722no—
496SD16—1722no—
497SD16—1722no—
498SD16—1722no—
499D8—1722no—
500D8#1062187314yescomplemented
501M16—1722no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8C2×D17211yescharacteristic
510C2×C8C2×D17211yescharacteristic
511C2×C8D4×D4311yescharacteristic
512C2×C8D4×D4311yescharacteristic
513C4⋊C4—431no—
514C4⋊C4—431no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4C2×D17211yescharacteristic
527C4⋊C4C2×D17211yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—861no—
531C22⋊C4—1721no—
532C22⋊C4—1721no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C42—861no—
536C42C23×D4311yescharacteristic
537C23—21no—
538C23—21no—
539C23—861no—
540C23—3442no—
541C23—3442no—
542C23—1721no—
543C23—6881no—
544Q8—861no—
545Q8—861no—
546Q8—3441no—
547Q8—3442no—
548Q8—1721no—
549Q8—1721no—
550Q8—1721no—
551Q8—1721no—
552D4—21no—
553D4—21no—
554D4—861no—
555D4—861no—
556D4—3441no—
557D4—3442no—
558D4—3442no—
559D4—3442no—
560D4—1721no—
561D4—1721no—
562D4—1721no—
563D4—1721no—
564D4C2×#1062187312yes—
565D4C2×#1062187312yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—6881no—
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4C22×D17211yescharacteristic
585C2×C4#1306337111yescharacteristic
586C8—22no—
587C8—21no—
588C8—21no—
589C8—41no—
590C8—41no—
591C8—1721no—
592C8—1721no—
593C8C2×#1062187312yescomplemented
594C8#1306334912yescomplemented
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—1721no—
605C22—1721no—
606C22—1721no—
607C22—6884no—
608C22D4×D17211yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—3441no—
613C4—3441no—
614C4—3441no—
615C4—1721no—
616C4—1721no—
617C4—1721no—
618C4C22×#1062187311yescharacteristic
619C4C2×#1306334911yescharacteristic
620C4#1458370611yescharacteristic
621C4#1458371111yescharacteristic
622C2—42no—
623C2—42no—
624C2—3441no—
625C2—6881no—
626C2#1914619611yescharacteristic
627C2D4×#1062187311yescharacteristic
628C2#1914638911yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC8×D8×C43C2
socleC22×C43D42
prime radical#19146196C2
hypercenterC8×D8D43
hypocenterC43#19890
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
1. #19147492C2semidirect
2. #19146953C2semidirect
3. D4×#10621873C2semidirect
5. #19134182C2semidirect
6. #19134095C2semidirect
7. #19134068C2semidirect
8. #19133970C2semidirect
9. #19133936C2semidirect
10. #19133882C2semidirect
11. #19133860C2semidirect
12. #19133713C2semidirect
13. #19133669C2semidirect
14. #19133487C2semidirect
15. C8×D8×C43C2semidirect
18. #14583606C22semidirect
23. #14583297C22semidirect
24. #14583297C22semidirect
25. #14583297C22semidirect
35. #14583185C22semidirect
36. #14583179C22semidirect
48. #14583029C22semidirect
53. #14582650C22semidirect
54. #14582647C22semidirect
55. #14582646C22semidirect
56. #14582644C22semidirect
58. #14582631C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#335C22semidirect
65. C43×D4⋊C8C22semidirect
66. C82×C43C22semidirect
175. D8×C43SD16semidirect
232. D4×C43C2×SD16semidirect
276. C8×C43C2×SD16semidirect
277. C8×C43AGL(1,ℤ/8)semidirect
322. C8×D8D43semidirect
368. C8×D4C2×D43semidirect
370. #335C2×D43semidirect
379. D4⋊C8C2×D43semidirect
380. C82C2×D43semidirect
381. C43#19890semidirect
500. D8#10621873semidirect
565. D4C2×#10621873semidirect
593. C8C2×#10621873semidirect
594. C8#13063349semidirect

Maximal subgroups

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

subgroupindex
#191474922
#191469532
D4×#106218732
#191461962
#191341822
#191340952
#191340682
#191339702
#191339362
#191338822
#191338602
#191337132
#191336692
#191334872
C8×D8×C432
#1989043