Finite Group Databasebeta

← #25064769

Subgroups — #25064769

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148551C211yesmaximal, characteristic
2#19143612C211yesmaximal, characteristic, complemented
3#19143244C211yesmaximal, characteristic, complemented
4#19133223C212yesmaximal, complemented
5#19133217C212yesmaximal, complemented
6#19133203C211yesmaximal, characteristic, complemented
7#19133199C212yesmaximal, complemented
8#19133191C212yesmaximal, complemented
9#19133187C211yesmaximal, characteristic, complemented
10#19133181C211yesmaximal, characteristic, complemented
11C43×#1530C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic
13#14583623C411yescharacteristic
14#14583613—21no—
15#14583578—22no—
16#14583564C411yescharacteristic
17#14583556C412yes—
18#14583546—21no—
19#14583537C412yes—
20#14583534C411yescharacteristic
21#14583514—21no—
22#14583481—22no—
23#14583433C2211yescharacteristic
24#14583428C2212yes—
25#124×D43C2212yes—
26#14583371—21no—
27C4×#10621898C2211yescharacteristic
28#14583023—21no—
29#14582976—21no—
30#14582974—22no—
31#14582961—22no—
32#14582954C2212yescomplemented
33#14582954C2212yescomplemented
34#14582954C2212yescomplemented
35#14582925—21no—
36#14582865—21no—
37C4×#10621877C2211yescharacteristic, complemented
38C4×#10621877C2211yescharacteristic, complemented
39#14582851C2212yescomplemented
40#14582640C2211yescharacteristic, complemented
41#14582640C2212yescomplemented
42#14582640C2211yescharacteristic, complemented
43#14582639C2212yescomplemented
44#14582639C2212yescomplemented
45#14582638C2211yescharacteristic
46#14582638C2212yes—
47#14582638C2211yescharacteristic
48C43×#532C2211yescharacteristic
49C43×#432C2211yescharacteristic, complemented
50C2×#97×C43C2211yescharacteristic, complemented
51C43×#329C2212yescomplemented
52C43×#329C2212yescomplemented
53C2×#10621898D411yescharacteristic
54C2×Q8×D43C2×C412yes—
55C2×D4×D43—21no—
56C2×D4×D43C2×C412yes—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621872—22no—
60#13063324—21no—
61#13063320—22no—
62#13063319—21no—
63#13063318—22no—
64#13063317C2311yescharacteristic
65#13063314C2×C412yes—
66#13063313C2311yescharacteristic
67#13063312—21no—
68#13063312—22no—
69#13063312C2×C412yes—
70#13063311—22no—
71#13063311—22no—
72#13063308—21no—
73#13063308—22no—
74#13063307—22no—
75#13063306—22no—
76#13063305—21no—
77#13063304—22no—
78#13063304C2×C411yescharacteristic
79#13063303—22no—
80#13063301C2×C412yes—
81#13063299C2×C411yescharacteristic
82#13063297—22no—
83#13063296—22no—
84#13063296—21no—
85#13063296C2×C412yes—
86#13063293—22no—
87#13063293—22no—
88Q8×Dic43C2×C412yes—
89C4×Dic86C2×C411yescharacteristic
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86D411yescharacteristic
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C411yescharacteristic
94C4×D172D411yescharacteristic
95D4×Dic43—21no—
96D4×Dic43C2×C412yes—
97#13063287—21no—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—22no—
100C4×C22⋊D43C2×C412yes—
101C4×C22⋊D43D412yes—
102(C22⋊D43)⋊C4—22no—
103#13063284D411yescharacteristic
104#13063283—21no—
105#13063282—21no—
106#13063282D412yes—
107#13063281—22no—
108C2×(C2×D43)⋊C4—22no—
109C22⋊C4×D43—22no—
110C22⋊C4×D43—22no—
111C42×D43C2312yes—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063236C2311yescharacteristic
119#13063236C2312yes—
120#13063236C2311yescharacteristic
121C4×C43⋊C8—21no—
122C4×C43⋊C8—21no—
123C8×Dic43—22no—
124C2×#41×C43C2×C412yes—
125C22×C8×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127#127×C43C2×C411yescharacteristic
128#124×C43C2312yes—
129#121×C43—21no—
130#121×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136#97×C43—21no—
137#97×C43C2312yes—
138#97×C43C2311yescharacteristic
139#97×C43C2311yescharacteristic
140C23×D43—22no—
141#41×C43—82no—
142C2×Q8×C43C22×C412yes—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43C22×C412yes—
147C22×C4×C43—22no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43C22⋊C412yes—
155C22×Dic43—22no—
156Q8×D43—82no—
157D4×D43—44no—
158D4×D43—82no—
159#10621898—42no—
160C2×D172C22⋊C411yescharacteristic
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—22no—
164C2×C4×D43C22×C412yes—
165C2×C4×D43C2×D412yes—
166C2×C4×D43C2×D412yes—
167C2×Dic86—22no—
168C2×Dic86C22⋊C411yescharacteristic
169C2×Dic86C22×C411yescharacteristic
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—22no—
173C2×C8×C43—42no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—21no—
187C22⋊Dic43C22⋊C412yes—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4C22⋊C412yes—
196(C2×D43)⋊C4C22⋊C412yes—
197C4⋊Dic43—22no—
198C4⋊Dic43C22⋊C411yescharacteristic
199C4⋊Dic43C22⋊C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—22no—
207Dic43⋊C4C22⋊C412yes—
208Dic43⋊C4C22⋊C412yes—
209C4×Dic43—21no—
210C4×Dic43—22no—
211C4×Dic43C22×C412yes—
212C4×Dic43C2×D412yes—
213C4×Dic43C2×D412yes—
214#10621877—42no—
215#10621877—42no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—21no—
219#10621872—44no—
220C23×C43—22no—
221C23×C43C2×C22⋊C411yescharacteristic
222C22×D43—21no—
223C22×D43—44no—
224C22×D43—82no—
225C22×D43—82no—
226C22×D43C2×C22⋊C412yes—
227Q8×C43—42no—
228D4×C43—42no—
229D4×C43—42no—
230D4×C43—81no—
231D4×C43—82no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C22⋊D43—42no—
244C22⋊D43—44no—
245C22⋊D43—82no—
246C22⋊D43—81no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—82no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254D172—22no—
255D172—41no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—82no—
261Dic86—22no—
262Dic86—41no—
263Dic86—82no—
264C8×C43—42no—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—22no—
268C43⋊C8—42no—
269C43⋊C8—41no—
270#17681—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43C22×C22⋊C411yescharacteristic
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—164no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—42no—
291C4×C43#42112yes—
292Dic43—22no—
293Dic43—22no—
294Dic43—22no—
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298#3514—431no—
299#2971—431no—
300#2923—431no—
301#1535—432no—
302#1533—432no—
303#1530D4311yescharacteristic, complemented
304#1529—431no—
305#1529—432no—
306#1527—432no—
307#1525—431no—
308#1524—431no—
309C2×C43—41no—
310C2×C43—82no—
311C2×C43#288811yescharacteristic
312C2×C43C2×#42111yescharacteristic
313C2×C43#290111yescharacteristic
314D43—42no—
315D43—81no—
316#559—431no—
317#556—431no—
318#555—861no—
319#551—862no—
320D4×Q8—431no—
321#548—432no—
322#546—432no—
323#546—861no—
324D42—431no—
325#542—861no—
326#538—862no—
327#532C2×D4311yescharacteristic
328#529—432no—
329#529—431no—
330C2×#124—432no—
331#518—861no—
332C4×#41—431no—
333C8×Q8—861no—
334#436—862no—
335#436—861no—
336#433—862no—
337#432—432no—
338#432—432no—
339#432—432no—
340#432C2×D4311yescharacteristic, complemented
341#424—861no—
342#408—861no—
343C4×M16—431no—
344C4×M16—431no—
345C4×M16—432no—
346C2×#97C2×D4311yescharacteristic, complemented
347#330—431no—
348#330—431no—
349#330—432no—
350#329—432no—
351#329—432no—
352#329—431no—
353#329—431no—
354#329—432no—
355#329C2×D4312yescomplemented
356#329C2×D4312yescomplemented
357C43#1768111yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C2×#41C4×D4312yes—
360C22×Q8—432no—
361C22×D4—432no—
362C22×D4—861no—
363C2×M16—862no—
364C2×M16—861no—
365C2×M16—861no—
366C22×C8—21no—
367C4⋊Q8—861no—
368C4⋊Q8C4×D4311yescharacteristic
369#127C4×D4311yescharacteristic
370#126—862no—
371#126—862no—
372#126—861no—
373#125—431no—
374#124—432no—
375#124—432no—
376#124—431no—
377#124—862no—
378#124—862no—
379#124—862no—
380#124—861no—
381#124C22×D4312yes—
382#123—862no—
383#123—862no—
384#123—862no—
385#123—861no—
386C22⋊Q8—432no—
387C22⋊Q8—431no—
388C22⋊Q8—862no—
389C22⋊Q8—861no—
390C22⋊Q8—862no—
391#121—21no—
392#121—21no—
393#121—432no—
394#121—431no—
395#121—862no—
396#121—861no—
397#121—862no—
398#120—862no—
399#120—862no—
400C4×Q8—431no—
401C4×Q8—431no—
402C4×Q8—432no—
403C4×Q8—431no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—432no—
407C4×D4—432no—
408C4×D4—432no—
409C4×D4—431no—
410C4×D4—431no—
411C4×D4—431no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417#117—431no—
418#117—432no—
419#117—862no—
420#117—861no—
421#117—861no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—862no—
424C2×C22⋊C4—862no—
425C2×C42—432no—
426C2×C42C22×D4311yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—862no—
429C4⋊C8—862no—
430C4⋊C8—862no—
431C22⋊C8—21no—
432C22⋊C8—862no—
433C22⋊C8—862no—
434C22⋊C8—862no—
435#97—21no—
436#97—431no—
437#97—432no—
438#97—431no—
439#97C22×D4311yescharacteristic
440#97C22×D4311yescharacteristic
441#97C22×D4312yes—
442C4×C8—862no—
443C4×C8—861no—
444C4×C8—861no—
445C24—862no—
446#41—82no—
447#41—1722no—
448C2×Q8—431no—
449C2×Q8—431no—
450C2×Q8—862no—
451C2×Q8—3442no—
452C2×Q8C2×C4×D4312yes—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—432no—
457C2×D4—431no—
458C2×D4—431no—
459C2×D4—862no—
460C2×D4—861no—
461C2×D4—862no—
462C2×D4—3442no—
463C2×D4—1724no—
464C2×D4C2×C4×D4312yes—
465C22×C4—22no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—861no—
472C22×C4C2×C4×D4311yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475M16—1724no—
476M16—1722no—
477M16—1722no—
478C2×C8—22no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—861no—
483C2×C8—862no—
484C2×C8—861no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—431no—
488C4⋊C4—431no—
489C4⋊C4—432no—
490C4⋊C4—432no—
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—432no—
502C22⋊C4—432no—
503C22⋊C4—432no—
504C22⋊C4—862no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—432no—
517C42—432no—
518C42—432no—
519C42—862no—
520C42—861no—
521C42C2×C4×D4311yescharacteristic
522C42D4×D4311yescharacteristic
523C42D4×D4311yescharacteristic
524C42C23×D4311yescharacteristic
525C23—22no—
526C23—432no—
527C23—861no—
528C23—3442no—
529C23—3442no—
530C23—1724no—
531C23C22⋊C4×D4311yescharacteristic
532Q8—42no—
533Q8—862no—
534Q8—3442no—
535Q8—1721no—
536D4—42no—
537D4—42no—
538D4—81no—
539D4—82no—
540D4—862no—
541D4—3442no—
542D4—3441no—
543D4—1721no—
544D4—1722no—
545D4—1724no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—3442no—
558C2×C4—3442no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4C22⋊C4×D4311yescharacteristic
564C2×C4C22⋊C4×D4311yescharacteristic
565C2×C4C22⋊C4×D4311yescharacteristic
566C2×C4C22×C4×D4311yescharacteristic
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C8—41no—
570C8—41no—
571C8—42no—
572C8—862no—
573C8—1722no—
574C8—1721no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—862no—
582C22—862no—
583C22—862no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—6884no—
588C22C2×C22⋊C4×D4311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—862no—
596C4—862no—
597C4—862no—
598C4—1721no—
599C4—1721no—
600C4—1721no—
601C4#1458291412yes—
602C2—41no—
603C2—82no—
604C2—3441no—
605C2—1722no—
606C2#1914307111yescharacteristic
607C2C2×#1458291411yescharacteristic
608C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1530C2
socleC22×C43C22×C22⋊C4
prime radical#19148551C2
cosocleC42×C43C24
hypercenter#1530D43
hypocenterC43#17681
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1530

Complements

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

NH ≅ G/Ntype
2. #19143612C2semidirect
3. #19143244C2semidirect
4. #19133223C2semidirect
5. #19133217C2semidirect
6. #19133203C2semidirect
7. #19133199C2semidirect
8. #19133191C2semidirect
9. #19133187C2semidirect
10. #19133181C2semidirect
11. C43×#1530C2semidirect
32. #14582954C22semidirect
33. #14582954C22semidirect
34. #14582954C22semidirect
37. C4×#10621877C22semidirect
38. C4×#10621877C22semidirect
39. #14582851C22semidirect
40. #14582640C22semidirect
41. #14582640C22semidirect
42. #14582640C22semidirect
43. #14582639C22semidirect
44. #14582639C22semidirect
49. C43×#432C22semidirect
50. C2×#97×C43C22semidirect
51. C43×#329C22semidirect
52. C43×#329C22semidirect
303. #1530D43semidirect
340. #432C2×D43semidirect
346. C2×#97C2×D43semidirect
355. #329C2×D43semidirect
356. #329C2×D43semidirect
357. C43#17681semidirect

Maximal subgroups

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

subgroupindex
#191485512
#191436122
#191432442
#191332232
#191332172
#191332032
#191331992
#191331912
#191331872
#191331812
C43×#15302
#1768143