Finite Group Databasebeta

← #25086096

Subgroups — #25086096

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147503C211yesmaximal, characteristic, complemented
2Q8×#10621873C211yesmaximal, characteristic, complemented
3#19146420C211yesmaximal, characteristic
4SD16×D172C211yesmaximal, characteristic
5#19134217C211yesmaximal, characteristic, complemented
6#19134068C211yesmaximal, characteristic, complemented
7#19134011C211yesmaximal, characteristic, complemented
8#19133995C211yesmaximal, characteristic, complemented
9#19133970C211yesmaximal, characteristic, complemented
10#19133804C211yesmaximal, characteristic, complemented
11#19133762C211yesmaximal, characteristic, complemented
12#19133713C211yesmaximal, characteristic
13#19133675C211yesmaximal, characteristic, complemented
14#19133433C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17Q8×Dic86C2211yescharacteristic, complemented
18#14583606C2211yescharacteristic
19Q8×D172C2211yescharacteristic
20D4×D172C2211yescharacteristic
21#14583306—21no—
22#14583304C2211yescharacteristic, complemented
23#14583297—21no—
24#14583297C2211yescharacteristic, complemented
25#14583272C2211yescharacteristic
26#14583272C2211yescharacteristic
27#14583250C2211yescharacteristic, complemented
28#14583246C2211yescharacteristic
29#14583218—21no—
30#14583208—21no—
31#14583194C2211yescharacteristic, complemented
32#14583190—21no—
33#14583190C2211yescharacteristic
34#14583190C2211yescharacteristic
35#14583189C2211yescharacteristic
36#14583185—21no—
37#14583185C2211yescharacteristic, complemented
38#14583177—21no—
39#14583129—21no—
40#14583128—21no—
41#14583104C2211yescharacteristic
42#14583100C2211yescharacteristic
43#14583099C2211yescharacteristic
44#14583052—21no—
45#14583051—21no—
46#14583039—21no—
47#14583029C2211yescharacteristic, complemented
48#14583000—21no—
49C4×#10621873—21no—
50C4×#10621873C2211yescharacteristic
51C8×D172C2211yescharacteristic
52C2×#13063247—21no—
53#14582650C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582642C2211yescharacteristic
58#14582631C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—41no—
74C2×#10621873D411yescharacteristic
75C2×#10621883—21no—
76C2×#10621884—21no—
77SD16×D43—44no—
78C2×C8×D43—21no—
79#13063325—21no—
80#13063325—21no—
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063324—21no—
85#13063324—41no—
86#13063322C2311yescharacteristic
87#13063316—21no—
88#13063305—21no—
89#13063305—41no—
90#13063304—21no—
91#13063302—41no—
92#13063300—21no—
93#13063299—21no—
94#13063295—41no—
95Q8×Dic43—21no—
96C4×Dic86—21no—
97C4×Dic86C2311yescharacteristic
98C4×D172—21no—
99C4×D172C2311yescharacteristic
100D4×Dic43—21no—
101C2×C4⋊Dic43—21no—
102#13063259—21no—
103#13063259—21no—
104#13063258—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257D411yescharacteristic
111#13063256—21no—
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063250—41no—
117#13063250D411yescharacteristic
118#13063249—21no—
119#13063248—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—21no—
124#13063247—21no—
125#13063247D411yescharacteristic
126#13063246—21no—
127#13063245—21no—
128(C2×D43)⋊C8—21no—
129#13063235—21no—
130C2×SD16×C43D411yescharacteristic
131C22×C8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43D411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43D411yescharacteristic
139#102×C43D411yescharacteristic
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—41no—
150C22×Dic43—41no—
151Q8×D43—42no—
152Q8×D43—81no—
153D4×D43—42no—
154D4×D43—81no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—41no—
159C2×D172—42no—
160C2×D172—81no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—41no—
168C2×Dic86—41no—
169C2×Dic86C2×D411yescharacteristic
170SD16×C43SD1614yescomplemented
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—81no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C42×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621884—42no—
187#10621883—42no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209#10621873—22no—
210#10621873—42no—
211#10621873—81no—
212#10621873—81no—
213#10621873—82no—
214C8×D43—42no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—41no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43—161no—
221Q8×C43—21no—
222Q8×C43C2×SD1612yes—
223D4×C43—21no—
224D4×C43C2×SD1612yes—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C22⋊D43—82no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—161no—
241D172—21no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—81no—
247D172—82no—
248D172#13712yes—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—82no—
252Dic86—21no—
253Dic86—21no—
254Dic86—41no—
255Dic86—41no—
256Dic86—82no—
257Dic86—81no—
258Dic86—81no—
259Dic86—161no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43C2×SD1612yes—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19765—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43D4211yescharacteristic
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—164no—
281C4×C43—22no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43C22×SD1611yescharacteristic
286C4×C43C2×#13711yescharacteristic
287C4×C43#57711yescharacteristic
288C4×C43#57711yescharacteristic
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#3385—431no—
296Q8×SD16—431no—
297#3295—431no—
298D4×SD16—431no—
299#1714—431no—
300#1686—431no—
301#1678—431no—
302#1675—431no—
303#1671—431no—
304#1643—431no—
305#1637—431no—
306#1629—431no—
307#1623—431no—
308#1582—431no—
309SD16⋊C8D4311yescharacteristic, complemented
310C2×C43—42no—
311C2×C43#326611yescharacteristic
312C2×C43D4×SD1611yescharacteristic
313C2×C43#328811yescharacteristic
314D43—42no—
315D43—161no—
316C22×SD16—861no—
317Q82—431no—
318#554—431no—
319D4×Q8—431no—
320D42—431no—
321#501—861no—
322#500—431no—
323#498—431no—
324#498—861no—
325#492—431no—
326#492—431no—
327#487—431no—
328#486—431no—
329#481—861no—
330#479—861no—
331#477—431no—
332#476—431no—
333#476—431no—
334#476—431no—
335#476—861no—
336#475—431no—
337#475—861no—
338#474—861no—
339#465—861no—
340#465—861no—
341#461—431no—
342#460—431no—
343#460—431no—
344#450—861no—
345#450—861no—
346#448—861no—
347#446—431no—
348C8×Q8C2×D4311yescharacteristic, complemented
349#440—861no—
350C4×SD16—431no—
351C4×SD16—861no—
352C4×SD16C2×D4311yescharacteristic
353C8×D4—431no—
354C8×D4C2×D4311yescharacteristic
355C2×#102—861no—
356#335C2×D4311yescharacteristic, complemented
357#334—431no—
358#333—431no—
359#333—431no—
360#332—431no—
361#331—431no—
362Q8⋊C8—431no—
363Q8⋊C8C2×D4311yescharacteristic, complemented
364D4⋊C8—431no—
365D4⋊C8C2×D4311yescharacteristic
366#322C2×D4311yescharacteristic, complemented
367C43#1976511yescharacteristic, complemented, Sylow
368C22×Q8—861no—
369C22×D4—861no—
370C22×D4—861no—
371C2×SD16—431no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×SD16—1721no—
378C2×SD16—1724no—
379C2×SD16D17211yescharacteristic
380C22×C8—21no—
381C22×C8—861no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—1721no—
389#127—431no—
390#125—861no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C22⋊Q8—1721no—
394C22⋊Q8—1721no—
395#121—861no—
396#121—861no—
397#120—1721no—
398C4×Q8—431no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8C22×D4311yescharacteristic
402C4×D4—431no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4C22×D4311yescharacteristic
406C2×C4⋊C4—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#106—431no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106D17211yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—861no—
422C4⋊C8C22×D4311yescharacteristic
423C4⋊C8C22×D4311yescharacteristic
424#103—431no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—1721no—
429#103D17211yescharacteristic
430#102—431no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102D17211yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—861no—
441#97—861no—
442C4×C8—21no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446C24—1721no—
447C2×Q8—431no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—3441no—
452C2×Q8—1721no—
453C2×Q8—1721no—
454C2×Q8—1722no—
455C2×Q8C2×D17211yescharacteristic
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1721no—
463C2×D4—1722no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4C2×D17211yescharacteristic
467C22×C4—21no—
468C22×C4—861no—
469C22×C4—1721no—
470C22×C4—1721no—
471SD16—862no—
472SD16—3441no—
473SD16—3442no—
474SD16—3441no—
475SD16—1722no—
476SD16—1722no—
477SD16—1722no—
478SD16#1062187314yescomplemented
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—81no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—1722no—
486C2×C8C2×D17211yescharacteristic
487C2×C8C2×D17211yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C2×C8D4×D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4C2×D17211yescharacteristic
506C4⋊C4C2×D17211yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—861no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C42—21no—
513C42—861no—
514C42—1721no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—861no—
518C23—3442no—
519C23—3442no—
520C23—1721no—
521C23—6881no—
522Q8—21no—
523Q8—861no—
524Q8—861no—
525Q8—3441no—
526Q8—3441no—
527Q8—3442no—
528Q8—1721no—
529Q8—1721no—
530Q8—6881no—
531Q8C2×#1062187312yes—
532D4—21no—
533D4—432no—
534D4—861no—
535D4—3441no—
536D4—3442no—
537D4—3442no—
538D4—1721no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4C2×#1062187312yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—3442no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—6881no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C22×D17211yescharacteristic
560C2×C4#1306337111yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—1721no—
568C8—1721no—
569C8C2×#1062187312yes—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—862no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—1721no—
578C22—1721no—
579C22—6884no—
580C22D4×D17211yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—3441no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4C22×#1062187311yescharacteristic
592C4#137×D4311yescharacteristic
593C4#1458370911yescharacteristic
594C4#1458371111yescharacteristic
595C2—42no—
596C2—1722no—
597C2—6881no—
598C2#1914610711yescharacteristic
599C2D4×#1062187311yescharacteristic
600C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×SD16⋊C8C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenterSD16⋊C8D43
hypocenterC43#19765
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
1. #19147503C2semidirect
2. Q8×#10621873C2semidirect
5. #19134217C2semidirect
6. #19134068C2semidirect
7. #19134011C2semidirect
8. #19133995C2semidirect
9. #19133970C2semidirect
10. #19133804C2semidirect
11. #19133762C2semidirect
13. #19133675C2semidirect
14. #19133433C2semidirect
15. C43×SD16⋊C8C2semidirect
17. Q8×Dic86C22semidirect
22. #14583304C22semidirect
24. #14583297C22semidirect
27. #14583250C22semidirect
31. #14583194C22semidirect
37. #14583185C22semidirect
47. #14583029C22semidirect
53. #14582650C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582644C22semidirect
58. #14582631C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#335C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
170. SD16×C43SD16semidirect
309. SD16⋊C8D43semidirect
348. C8×Q8C2×D43semidirect
356. #335C2×D43semidirect
363. Q8⋊C8C2×D43semidirect
366. #322C2×D43semidirect
367. C43#19765semidirect
478. SD16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191475032
Q8×#106218732
#191464202
SD16×D1722
#191342172
#191340682
#191340112
#191339952
#191339702
#191338042
#191337622
#191337132
#191336752
#191334332
C43×SD16⋊C82
#1976543