Finite Group Databasebeta

← #25087904

Subgroups — #25087904

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621882C211yesmaximal, characteristic, complemented
2#19146938C211yesmaximal, characteristic
3#19146242C211yesmaximal, characteristic, complemented
4#19134211C211yesmaximal, characteristic, complemented
5#19134084C211yesmaximal, characteristic, complemented
6#19134081C211yesmaximal, characteristic, complemented
7#19133987C211yesmaximal, characteristic, complemented
8#19133982C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133842C211yesmaximal, characteristic, complemented
11#19133830C211yesmaximal, characteristic, complemented
12#19133828C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3276C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17Q8×D172C2211yescharacteristic
18#14583553C2211yescharacteristic
19#14583302—21no—
20#14583302C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583302C2211yescharacteristic
24#14583279C2211yescharacteristic
25#14583212—21no—
26#14583210—21no—
27#14583179—21no—
28#14583179C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583176—21no—
31#14583176C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583158—21no—
34#14583133—21no—
35#14583109C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583062—21no—
38#14583056—21no—
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621882—21no—
41C4×#10621882C2211yescharacteristic
42#14582978C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063258—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C2×#137×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58C43×#547C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#470—21no—
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C43×#451—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69#13063354—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621882D411yescharacteristic
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063309—41no—
81#13063305—21no—
82#13063305—21no—
83#13063305—41no—
84#13063299—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C2×C4⋊Dic43—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—41no—
97#13063258—41no—
98#13063258D411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×Q8×C43—21no—
118#137×C43—44no—
119C2×Q16×C43—21no—
120C2×Q16×C43—21no—
121C2×Q16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43D411yescharacteristic
124C2×M16×C43—21no—
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127C4⋊Q8×C43C2311yescharacteristic
128#123×C43—41no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—41no—
132#121×C43—21no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—21no—
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#103×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C2×C22⋊D43—41no—
162C22×Dic43—41no—
163Q8×D43—42no—
164Q8×D43—81no—
165#10621900—42no—
166#10621900—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—41no—
173Q16×C43—42no—
174Q16×C43—42no—
175Q16×C43—81no—
176SD16×C43—42no—
177SD16×C43D814yescomplemented
178M16×C43—42no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—41no—
195C22⋊C4×C43—41no—
196C42×C43—21no—
197C42×C43C2411yescharacteristic
198#10621885—42no—
199#10621883—42no—
200#10621882—22no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—41no—
203(C2×D43)⋊C4—41no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—41no—
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
218Dic172—42no—
219Dic172—81no—
220#10621872—42no—
221C23×C43—21no—
222C23×C43—21no—
223C22×D43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—82no—
230Q8×C43C2×D812yes—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—82no—
235D4×C43C2×D812yes—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—82no—
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—
254C2×Dic43—41no—
255C2×Dic43—82no—
256D172—21no—
257D172—21no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—82no—
261Dic86—41no—
262Dic86—41no—
263Dic86—41no—
264Dic86—41no—
265Dic86—82no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43C2×D812yes—
269C43⋊C8—22no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8#13712yescomplemented
275#19887—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43D4211yescharacteristic
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C4×C43—22no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43C22×D811yescharacteristic
294C4×C43C2×#13711yescharacteristic
295C4×C43#57611yescharacteristic
296C4×C43#57811yescharacteristic
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300Q8×D8—431no—
301#3334—431no—
302#3276—431no—
303#3276D4311yescharacteristic, complemented
304#1713—431no—
305#1689—431no—
306#1689—431no—
307#1674—431no—
308#1673—431no—
309#1649—431no—
310#1649—431no—
311#1647—431no—
312#1647—431no—
313#1589—431no—
314C8×SD16—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43#327611yescharacteristic
318C2×C43D4×D811yescharacteristic
319C2×C43#329311yescharacteristic
320D43—81no—
321C2×#137—21no—
322C2×#137—861no—
323D4×Q8—431no—
324D4×Q8C2×D4311yescharacteristic
325#547—431no—
326#547C2×D4311yescharacteristic
327#500—431no—
328#500—431no—
329#500—431no—
330#500—431no—
331#500—861no—
332#494—431no—
333#494C2×D4311yescharacteristic
334#480—861no—
335#480—861no—
336#474—431no—
337#474—431no—
338#474—431no—
339#474—431no—
340#474—861no—
341#474—861no—
342#470—21no—
343#470—861no—
344#466—861no—
345#462—431no—
346#462C2×D4311yescharacteristic
347#461—431no—
348#461C2×D4311yescharacteristic
349#452—21no—
350#452—861no—
351#451—21no—
352#451—861no—
353C8×Q8—431no—
354C4×SD16C2×D4311yescharacteristic
355C4×D8—431no—
356C4×D8—861no—
357#436—431no—
358#436C2×D4311yescharacteristic
359C8×D4—431no—
360C2×#107—861no—
361#335—431no—
362#334—431no—
363#332—431no—
364#332—431no—
365#332—431no—
366#332—431no—
367Q8⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371C82—431no—
372C43#1988711yescharacteristic, complemented, Sylow
373C2×#41—21no—
374C2×#41—861no—
375C22×Q8—21no—
376C22×Q8—861no—
377#137—44no—
378#137—1724no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×Q16—21no—
382C2×Q16—861no—
383C2×Q16—861no—
384C2×Q16—861no—
385C2×SD16—21no—
386C2×SD16—861no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—431no—
389C2×M16—21no—
390C2×M16—861no—
391C22×C8—861no—
392C4⋊Q8—21no—
393C4⋊Q8—431no—
394C4⋊Q8—431no—
395C4⋊Q8—861no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#123—41no—
399#123—1721no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C22⋊Q8—1721no—
406#121—21no—
407#121—861no—
408C4×Q8C22×D4311yescharacteristic
409C4×D4—21no—
410C4×D4—431no—
411C4×D4—861no—
412C4×D4C22×D4311yescharacteristic
413C4×D4C22×D4311yescharacteristic
414C2×C4⋊C4—21no—
415C2×C4⋊C4—861no—
416#107—431no—
417#107—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#107—861no—
422#107—861no—
423#107—861no—
424#107—861no—
425#107—1721no—
426#107—1721no—
427#106C22⋊D4311yescharacteristic
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—861no—
432C4⋊C8C22×D4311yescharacteristic
433#103—21no—
434#103—21no—
435#103—861no—
436#103—861no—
437#103C22⋊D4311yescharacteristic
438#102—431no—
439#102—431no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102C22⋊D4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452#41—42no—
453#41—81no—
454#41—3441no—
455#41—1722no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—41no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—3441no—
464C2×Q8—1721no—
465C2×Q8—1722no—
466C2×Q8C2×C22⋊D4311yescharacteristic
467C2×D4—41no—
468C2×D4—431no—
469C2×D4—1721no—
470C2×D4D4×D4311yescharacteristic
471C2×D4C2×C22⋊D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—861no—
477C22×C4—1721no—
478C22×C4—1721no—
479Q16—42no—
480Q16—42no—
481Q16—81no—
482Q16—3441no—
483Q16—1722no—
484Q16—1722no—
485SD16—42no—
486SD16—1722no—
487SD16#1062188214yescomplemented
488D8—862no—
489M16—42no—
490M16—1722no—
491C2×C8—21no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—1722no—
499C2×C8C2×C22⋊D4311yescharacteristic
500C2×C8C2×C22⋊D4311yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
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—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—861no—
523C22⋊C4—1721no—
524C22⋊C4—1721no—
525C42—21no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—861no—
530Q8—21no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—82no—
536Q8—3442no—
537Q8—1721no—
538Q8—1721no—
539Q8—1721no—
540Q8—1721no—
541Q8C2×#1062188212yes—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—82no—
546D4—861no—
547D4—861no—
548D4—3442no—
549D4C2×#1062188212yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—861no—
563C2×C4—3442no—
564C2×C4—3442no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4C22×C22⋊D4311yescharacteristic
571C2×C4#1306337011yescharacteristic
572C8—21no—
573C8—41no—
574C8—432no—
575C8—862no—
576C8—861no—
577C8—1721no—
578C8—1721no—
579C8—1721no—
580C8C2×#1062188212yes—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22D4×C22⋊D4311yescharacteristic
591C4—22no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4C22×#1062188211yescharacteristic
602C4#137×D4311yescharacteristic
603C4#1458370211yescharacteristic
604C4#1458371511yescharacteristic
605C2—42no—
606C2—81no—
607C2—3441no—
608C2#1914623511yescharacteristic
609C2D4×#1062188211yescharacteristic
610C2#1914639711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3276C2
socleC22×C43D42
prime radical#19146938C2
hypercenter#3276D43
hypocenterC43#19887
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3276

Complements

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

NH ≅ G/Ntype
1. Q8×#10621882C2semidirect
3. #19146242C2semidirect
4. #19134211C2semidirect
5. #19134084C2semidirect
6. #19134081C2semidirect
7. #19133987C2semidirect
8. #19133982C2semidirect
9. #19133844C2semidirect
10. #19133842C2semidirect
11. #19133830C2semidirect
12. #19133828C2semidirect
13. #19133478C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3276C2semidirect
177. SD16×C43D8semidirect
274. C43⋊C8#137semidirect
303. #3276D43semidirect
372. C43#19887semidirect
487. SD16#10621882semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191469382
#191462422
#191342112
#191340842
#191340812
#191339872
#191339822
#191338442
#191338422
#191338302
#191338282
#191334782
SD16×C43⋊C82
C43×#32762
#1988743