Finite Group Databasebeta

← #25086028

Subgroups — #25086028

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621882C211yesmaximal, characteristic, complemented
2#19147226C211yesmaximal, characteristic
3Q16×D172C211yesmaximal, characteristic, complemented
4#19134264C211yesmaximal, characteristic, complemented
5#19134084C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19133987C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133842C211yesmaximal, characteristic, complemented
11#19133788C211yesmaximal, characteristic, complemented
12#19133696C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3278C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17Q8×D172C2211yescharacteristic
18Q8×D172C2211yescharacteristic
19#14583302—21no—
20#14583302C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583279C2211yescharacteristic
23#14583245—21no—
24#14583245C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583179—21no—
27#14583179—21no—
28#14583179C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583176—21no—
31#14583176C2211yescharacteristic
32#14583141—21no—
33#14583109C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583091—21no—
36#14583091C2211yescharacteristic
37#14583056—21no—
38#14583056—21no—
39Q8×C43⋊C8C2211yescharacteristic
40Q8×C43⋊C8C2211yescharacteristic
41C4×#10621882—21no—
42C4×#10621882—21no—
43C4×#10621882C2211yescharacteristic
44C8×D172C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C2×#137×C43—21no—
57C43×#550C2211yescharacteristic
58D4×Q8×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#452—21no—
64C43×#448—21no—
65C4×Q16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73Q16×D43—44no—
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×C8×D43—21no—
77#13063325—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063305—21no—
82#13063305—21no—
83#13063305—41no—
84#13063305—41no—
85C4×D172—21no—
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—41no—
94#13063258D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111(C2×D43)⋊C8—21no—
112C4×C43⋊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×C43D411yescharacteristic
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—21no—
124C2×M16×C43—21no—
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43—21no—
128#127×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132#121×C43—41no—
133C4×Q8×C43C2311yescharacteristic
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C4×D4×C43C2311yescharacteristic
138#107×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#103×C43D411yescharacteristic
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43C2×D411yescharacteristic
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163Q8×D43—42no—
164Q8×D43—42no—
165Q8×D43—81no—
166Q8×D43—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—41no—
174C2×Dic86—41no—
175Q16×C43—42no—
176Q16×C43D814yescomplemented
177SD16×C43—42no—
178SD16×C43—42no—
179SD16×C43—81no—
180M16×C43—42no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43C2411yescharacteristic
198#10621885—42no—
199#10621885—42no—
200#10621882—22no—
201#10621882—42no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—41no—
204(C2×D43)⋊C4—41no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—41no—
210C4⋊Dic43—41no—
211C4⋊Dic43C2×D411yescharacteristic
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218Dic172—42no—
219Dic172—81no—
220C8×D43—42no—
221C23×C43—21no—
222C23×C43—41no—
223C22×D43—21no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—82no—
229Q8×C43C2×D812yes—
230Q8×C43C2×D812yes—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—82no—
238D4×C43—81no—
239D4×C43—161no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—82no—
249C2×C4×C43—82no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256D172—21no—
257D172#13712yescomplemented
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—82no—
261C4×D43—82no—
262Dic86—41no—
263Dic86—41no—
264Dic86—41no—
265Dic86—41no—
266Dic86—82no—
267Dic86—82no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43C2×D812yes—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#19761—431nomaximal, Sylow
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43D4211yescharacteristic
285C2×D43—22no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43C22×D811yescharacteristic
296C4×C43C2×#13711yescharacteristic
297C4×C43#57611yescharacteristic
298C4×C43#57811yescharacteristic
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302Q8×D8—431no—
303#3358—431no—
304D4×Q16—431no—
305#3278D4311yescharacteristic, complemented
306#1722—431no—
307#1689—431no—
308#1682—431no—
309#1674—431no—
310#1665—431no—
311#1649—431no—
312#1649—431no—
313#1641—431no—
314#1627—431no—
315#1581—431no—
316#1579—431no—
317C2×C43—81no—
318C2×C43—161no—
319C2×C43#327011yescharacteristic
320C2×C43D4×D811yescharacteristic
321C2×C43#328911yescharacteristic
322D43—42no—
323C2×#137—21no—
324C22×Q16—861no—
325#550C2×D4311yescharacteristic
326D4×Q8—431no—
327D4×Q8—431no—
328D4×Q8C2×D4311yescharacteristic
329#500—431no—
330#500—431no—
331#500—861no—
332#494—431no—
333#492C2×D4311yescharacteristic
334#486—431no—
335#486—431no—
336#486—861no—
337#474—431no—
338#474—431no—
339#474—431no—
340#474—861no—
341#474—861no—
342#474—861no—
343#468—21no—
344#467—861no—
345#462—431no—
346#462—431no—
347#462C2×D4311yescharacteristic
348#460C2×D4311yescharacteristic
349#459—431no—
350#459—861no—
351#452—21no—
352#451—861no—
353#451—861no—
354#448—21no—
355C8×Q8—431no—
356C8×Q8—431no—
357C4×Q16C2×D4311yescharacteristic
358C4×D8—431no—
359C4×D8—861no—
360C4×D8—861no—
361#436C2×D4311yescharacteristic
362C8×D4—431no—
363#335—431no—
364#334—431no—
365#332—431no—
366#332—431no—
367#332—431no—
368#331—431no—
369Q8⋊C8—431no—
370Q8⋊C8—431no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373#322—431no—
374C43#1976111yescharacteristic, complemented, Sylow
375C2×#41—21no—
376C22×Q8—21no—
377C22×Q8—861no—
378C22×Q8—861no—
379#137—44no—
380C2×Q16—21no—
381C2×Q16—861no—
382C2×Q16—861no—
383C2×Q16—861no—
384C2×Q16—861no—
385C2×Q16—1724no—
386C2×Q16C22⋊D4311yescharacteristic
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×D8—431no—
391C2×D8—861no—
392C2×M16—21no—
393C22×C8—861no—
394C4⋊Q8—21no—
395C4⋊Q8—431no—
396C4⋊Q8—431no—
397C4⋊Q8—861no—
398C4⋊Q8—861no—
399C4⋊Q8C22×D4311yescharacteristic
400#127—21no—
401#127C22×D4311yescharacteristic
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406C22⋊Q8—1721no—
407C22⋊Q8—1721no—
408#121—21no—
409#121—41no—
410C4×Q8C22×D4311yescharacteristic
411C4×Q8C22×D4311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4C22×D4311yescharacteristic
418#107—431no—
419#107—861no—
420#107—861no—
421#107—861no—
422#107—861no—
423#107—861no—
424#107—1721no—
425#107C22⋊D4311yescharacteristic
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8C22×D4311yescharacteristic
432#103—21no—
433#103—861no—
434#103—861no—
435#103C22⋊D4311yescharacteristic
436#103C22⋊D4311yescharacteristic
437#102—21no—
438#102—431no—
439#102—431no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—1721no—
447C22⋊C8—21no—
448C22⋊C8—861no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8—861no—
452C4×C8—861no—
453C4×C8C22×D4311yescharacteristic
454#41—42no—
455#41—81no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—3441no—
463C2×Q8—3441no—
464C2×Q8—1721no—
465C2×Q8—1721no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×Q8C2×C22⋊D4311yescharacteristic
469C2×Q8C2×C22⋊D4311yescharacteristic
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—431no—
476C2×D4D4×D4311yescharacteristic
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—861no—
481C22×C4—1721no—
482C22×C4—1721no—
483Q16—42no—
484Q16—3441no—
485Q16—1722no—
486Q16—1722no—
487Q16—1722no—
488Q16#1062188214yescomplemented
489SD16—42no—
490SD16—42no—
491SD16—81no—
492D8—862no—
493D8—1722no—
494M16—42no—
495C2×C8—21no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—1722no—
503C2×C8C2×C22⋊D4311yescharacteristic
504C2×C8C2×C22⋊D4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4D4×D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—861no—
524C22⋊C4—1721no—
525C22⋊C4—1721no—
526C42—21no—
527C42—21no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—41no—
531C23—861no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536Q8—82no—
537Q8—3442no—
538Q8—3442no—
539Q8—1721no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543Q8C2×#1062188212yes—
544Q8C2×#1062188212yes—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—82no—
552D4—81no—
553D4—161no—
554D4—432no—
555D4—861no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—861no—
567C2×C4—3442no—
568C2×C4—3442no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—21no—
577C8—41no—
578C8—861no—
579C8—861no—
580C8—1721no—
581C8—1721no—
582C8—1721no—
583C8—1721no—
584C8C2×#1062188212yes—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—862no—
592C22—1721no—
593C22—1721no—
594C22D4×C22⋊D4311yescharacteristic
595C4—22no—
596C4—22no—
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—3441no—
603C4—3441no—
604C4—1721no—
605C4C22×#1062188211yescharacteristic
606C4#137×D4311yescharacteristic
607C4#1458370211yescharacteristic
608C4#1458371511yescharacteristic
609C2—81no—
610C2—161no—
611C2—1722no—
612C2#1914615911yescharacteristic
613C2D4×#1062188211yescharacteristic
614C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3278C2
socleC22×C43D42
prime radical#19147226C2
hypercenter#3278D43
hypocenterC43#19761
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3278

Complements

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

NH ≅ G/Ntype
1. Q8×#10621882C2semidirect
3. Q16×D172C2semidirect
4. #19134264C2semidirect
5. #19134084C2semidirect
6. #19134037C2semidirect
7. #19133987C2semidirect
8. #19133933C2semidirect
9. #19133844C2semidirect
10. #19133842C2semidirect
11. #19133788C2semidirect
12. #19133696C2semidirect
13. #19133422C2semidirect
14. #19133414C2semidirect
15. C43×#3278C2semidirect
176. Q16×C43D8semidirect
257. D172#137semidirect
305. #3278D43semidirect
374. C43#19761semidirect
488. Q16#10621882semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191472262
Q16×D1722
#191342642
#191340842
#191340372
#191339872
#191339332
#191338442
#191338422
#191337882
#191336962
#191334222
#191334142
C43×#32782
#1976143