Finite Group Databasebeta

← #25079424

Subgroups — #25079424

Order 11008.

696 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
1#19144985C211yesmaximal, characteristic, complemented
2#19144594C211yesmaximal, characteristic
3#476×D43C211yesmaximal, characteristic, complemented
4D4×#10621872C211yesmaximal, characteristic, complemented
5#19134173C211yesmaximal, characteristic, complemented
6#19134171C211yesmaximal, characteristic, complemented
7#19134127C211yesmaximal, characteristic, complemented
8#19134125C211yesmaximal, characteristic, complemented
9#19134048C211yesmaximal, characteristic, complemented
10#19134046C211yesmaximal, characteristic, complemented
11#19134002C211yesmaximal, characteristic, complemented
12#19133344C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133269C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C22×#10621872—21no—
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583257—21no—
21#14583257—21no—
22#14583251C2211yescharacteristic, complemented
23#14583250C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583211—21no—
26#14583190C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583188—21no—
29#14583187—21no—
30#14583186C2211yescharacteristic
31#14583180C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583091C2211yescharacteristic
34#14583031—21no—
35D8×Dic43—21no—
36#14582979—21no—
37#14582978C2211yescharacteristic
38#14582976C2211yescharacteristic
39#14582970—21no—
40#14582967—21no—
41D4×C43⋊C8C2211yescharacteristic
42#14582951C2211yescharacteristic
43#106×D43—21no—
44#14582921C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46#14582897—21no—
47#14582897—21no—
48#102×D43—21no—
49#14582861—21no—
50C4×#10621872C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582646C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71C2×#10621882—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—44no—
76C2×#10621872D411yescharacteristic
77C2×#10621872D411yescharacteristic
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063323—21no—
85#13063312—21no—
86#13063296—21no—
87#13063296—21no—
88C4×D172C2311yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43D411yescharacteristic
92#13063287D411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C22⋊C4×D43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063258—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110#13063250—21no—
111#13063250—21no—
112#13063248—21no—
113#13063248—21no—
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063235D411yescharacteristic
127#13063235D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
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—
156Q8×D43—82no—
157#10621900—42no—
158#10621900—42no—
159D4×D43—22no—
160D4×D43—41no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—41no—
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43#4111yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—41no—
174D8×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—42no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—21no—
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189#10621882—42no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621872—22no—
210#10621872—22no—
211#10621872—42no—
212#10621872—42no—
213#10621872—42no—
214C8×D43—42no—
215C23×C43—21no—
216C23×C43—41no—
217C22×D43—21no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—81no—
221C22×D43#12111yescharacteristic
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43#13712yes—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—42no—
238C22⋊D43—82no—
239C2×Dic43—21no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—82no—
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247D172—21no—
248D172—21no—
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—41no—
252C4×D43—42no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—42no—
256C4×D43—82no—
257C4×D43#13512yes—
258C4×D43AGL(1,ℤ/8)12yes—
259Dic86—41no—
260Dic86—41no—
261Dic86—82no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#19168—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×#12111yescharacteristic
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—84no—
287C2×D43#46312yes—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43C2×#13511yescharacteristic
292C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C43C2×#13711yescharacteristic
294C4×C43#57511yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300Dic43#46312yes—
301#3141—431no—
302#3100—431no—
303C2×#476—431no—
304D4×M16—431no—
305#1703—431no—
306#1703—431no—
307#1697—431no—
308#1697—431no—
309#1683—431no—
310#1683—431no—
311#1677—431no—
312#1677D4311yescharacteristic, complemented
313#1565—431no—
314#1548—431no—
315#1547—431no—
316C2×C43—42no—
317C2×C43—161no—
318C2×C43C2×#46311yescharacteristic
319C2×C43#305611yescharacteristic
320C2×C43#306811yescharacteristic
321D43—22no—
322D43—81no—
323C22×M16—861no—
324#532—431no—
325C2×C4⋊Q8—431no—
326C2×C4×D4—431no—
327#489—861no—
328#489—861no—
329#487—431no—
330#487—431no—
331#486—431no—
332#486C2×D4311yescharacteristic, complemented
333#480—861no—
334#476—431no—
335#476—431no—
336#476—431no—
337#476—861no—
338#476—861no—
339#476C2×D4311yescharacteristic
340#474—431no—
341#474—431no—
342#459—431no—
343#459C2×D4311yescharacteristic
344#447—861no—
345C4×D8—861no—
346C4×D8—861no—
347#436—431no—
348#436—431no—
349#435—861no—
350#435—861no—
351C8×D4—431no—
352C8×D4C2×D4311yescharacteristic
353#431—431no—
354C2×#106—861no—
355#423—431no—
356C2×C4⋊C8—431no—
357#417—861no—
358#417—861no—
359C2×#102—861no—
360#407—861no—
361C4×M16—431no—
362#335—431no—
363#335—431no—
364#334—431no—
365#334C2×D4311yescharacteristic, complemented
366#333—431no—
367#333—431no—
368#333—431no—
369#333C2×D4311yescharacteristic, complemented
370#332—431no—
371#332—431no—
372#331—431no—
373#331C2×D4311yescharacteristic, complemented
374C43#1916811yescharacteristic, complemented, Sylow
375C2×#41—861no—
376C22×Q8—861no—
377C22×D4—431no—
378C23×C4—861no—
379C2×D8—21no—
380C2×D8—861no—
381C2×M16—431no—
382C2×M16—431no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—1724no—
387C22×C8—21no—
388C22×C8—861no—
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392C4⋊Q8—861no—
393C4⋊Q8—861no—
394C4⋊Q8—861no—
395C4⋊Q8C22×D4311yescharacteristic
396#127C22×D4311yescharacteristic
397#124—861no—
398#121—861no—
399#121—861no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—431no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4C22×D4311yescharacteristic
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413#107—861no—
414#107—861no—
415#106—21no—
416#106—861no—
417#106—861no—
418#106—861no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8C22×D4311yescharacteristic
425C4⋊C8C22×D4311yescharacteristic
426C4⋊C8C22×D4311yescharacteristic
427#103—861no—
428#103—861no—
429#103—861no—
430#103—861no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443C22⋊C8—21no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448#97—431no—
449#97—431no—
450C4×C8—431no—
451C4×C8—861no—
452C4×C8C22×D4311yescharacteristic
453C24—861no—
454#41—1722no—
455#41—1722no—
456C2×Q8—21no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—3442no—
460C2×Q8—1721no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—431no—
465C2×D4—861no—
466C2×D4—862no—
467C2×D4—1721no—
468C2×D4—1721no—
469C2×D4D4×D4311yescharacteristic
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1721no—
481C22×C4—1721no—
482D8—42no—
483D8—1722no—
484M16—862no—
485M16—862no—
486M16—1722no—
487M16—1722no—
488M16—1722no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—42no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—1722no—
499C2×C8—1722no—
500C2×C8D4×D4311yescharacteristic
501C2×C8D4×D4311yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—431no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C4⋊C4D4×D4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—41no—
525C23—431no—
526C23—861no—
527C23—3441no—
528C23—1722no—
529C23—1722no—
530Q8—81no—
531Q8—3441no—
532Q8—3442no—
533Q8—1721no—
534Q8—1721no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—81no—
541D4—861no—
542D4—861no—
543D4—3442no—
544D4—1722no—
545D4#1306335412yes—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—431no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—3442no—
559C2×C4—3442no—
560C2×C4—1721no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—861no—
577C8—861no—
578C8—1721no—
579C8—1721no—
580C8—1721no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—432no—
588C22—861no—
589C22—861no—
590C22—3444no—
591C22—1721no—
592C22—1721no—
593C22—1721no—
594C22#121×D4311yescharacteristic
595C4—21no—
596C4—41no—
597C4—81no—
598C4—432no—
599C4—861no—
600C4—861no—
601C4—3441no—
602C4—3441no—
603C4—1721no—
604C4#135×D4311yescharacteristic
605C4AGL(1,ℤ/8)×D4311yescharacteristic
606C4C2×#1306335411yescharacteristic
607C4#1458369611yescharacteristic
608C2—42no—
609C2—161no—
610C2—862no—
611C2—3441no—
612C2#463×D4311yescharacteristic
613C2#1914421811yescharacteristic
614C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#19144594C2
hypercenter#1677D43
hypocenterC43#19168
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. #19144985C2semidirect
3. #476×D43C2semidirect
4. D4×#10621872C2semidirect
5. #19134173C2semidirect
6. #19134171C2semidirect
7. #19134127C2semidirect
8. #19134125C2semidirect
9. #19134048C2semidirect
10. #19134046C2semidirect
11. #19134002C2semidirect
12. #19133344C2semidirect
13. #19133274C2semidirect
14. #19133269C2semidirect
15. C43×#1677C2semidirect
22. #14583251C22semidirect
23. #14583250C22semidirect
24. #14583245C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582646C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#486C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#331C22semidirect
312. #1677D43semidirect
332. #486C2×D43semidirect
365. #334C2×D43semidirect
369. #333C2×D43semidirect
373. #331C2×D43semidirect
374. C43#19168semidirect

Maximal subgroups

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

subgroupindex
#191449852
#191445942
#476×D432
D4×#106218722
#191341732
#191341712
#191341272
#191341252
#191340482
#191340462
#191340022
#191333442
#191332742
#191332692
C43×#16772
#1916843