Finite Group Databasebeta

← D43×#1885 #25098145

Subgroups — D43×#1885 #25098145

Order 11008.

1966 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
1C2×#124×D43C211yesmaximal, characteristic
2#518×D43C211yesmaximal, characteristic
3#419×D43C212yesmaximal, complemented
4C2×#100×D43C211yesmaximal, characteristic
5#19134984C211yesmaximal, characteristic, complemented
6#19134983C211yesmaximal, characteristic, complemented
7#19134982C212yesmaximal, complemented
8#19134981C211yesmaximal, characteristic, complemented
9#19134980C212yesmaximal, complemented
10#339×D43C212yesmaximal, complemented
11C43×#1885C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×D4×D43C2211yescharacteristic
14C2×M16×D43C2212yes—
15C2×#13063314C2211yescharacteristic
16C2×#13063313C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×#13063311—22no—
19#124×D43—24no—
20#124×D43C418yescomplemented
21#14583374C2211yescharacteristic
22#14583373C2212yes—
23#14583372—22no—
24#14583371—24no—
25C4×D4×D43—24no—
26#117×D43C2212yes—
27C2×C22⋊C4×D43—22no—
28C2×C22⋊C4×D43—22no—
29C2×C42×D43C2211yescharacteristic
30#14582909C2212yescomplemented
31#14582908C2212yescomplemented
32#14582907C2212yescomplemented
33#14582906—24no—
34#103×D43—24no—
35C2×#13063242C2211yescharacteristic
36C2×#13063241C2212yes—
37#100×D43—24no—
38#14582660C2212yescomplemented
39#14582659C2212yescomplemented
40#14582658C2212yescomplemented
41C2×#124×C43C2211yescharacteristic
42C43×#518C2211yescharacteristic
43C43×#419C2212yescomplemented
44C2×#100×C43C2211yescharacteristic
45C43×#339C2212yescomplemented
46C24×D43D412yes—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C2×Q8×D43—22no—
50C2×Q8×D43—22no—
51C2×Q8×D43—22no—
52C2×Q8×D43—24no—
53C2×Q8×D43C2×C414yescomplemented
54C22×D172C2311yescharacteristic
55C22×C22⋊D43D412yes—
56C2×D4×D43—22no—
57C2×D4×D43—22no—
58C2×D4×D43—24no—
59C2×D4×D43C2×C414yes—
60C2×D4×D43D414yes—
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—24no—
64C22×C4×D43C2311yescharacteristic
65C2×#10621877C2312yes—
66C2×#10621872—22no—
67M16×D43—24no—
68M16×D43—24no—
69C2×C8×D43—22no—
70#13063314—22no—
71#13063314C2×C414yescomplemented
72#13063313—22no—
73#13063313C2×C414yescomplemented
74#13063312—22no—
75#13063312C2×C414yescomplemented
76#13063311—216no—
77C4×D172—24no—
78D4×Dic43—24no—
79#13063287—24no—
80C4×C22⋊D43—28no—
81(C22⋊D43)⋊C4—28no—
82#13063284C2312yes—
83#13063283D414yes—
84#13063282—22no—
85#13063281—22no—
86C4⋊C4×D43D414yes—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×(C2×D43)⋊C4—24no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C22⋊C4×D43—24no—
93C22⋊C4×D43—24no—
94C22⋊C4×D43—216no—
95C22⋊C4×D43—22no—
96C22⋊C4×D43—24no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C42×D43—22no—
100C42×D43—22no—
101C42×D43C2×C414yescomplemented
102#13063250—24no—
103#13063249—24no—
104#13063248—24no—
105#13063242—22no—
106#13063241—24no—
107C22×Q8×C43C2311yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C2×M16×C43C2312yes—
110#124×C43—22no—
111#124×C43C2×C414yescomplemented
112C4×D4×C43—24no—
113#117×C43C2312yes—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C42×C43C2311yescharacteristic
117#103×C43—24no—
118#100×C43—22no—
119C24×C43C2×D412yes—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—24no—
123C23×D43—48no—
124C23×D43C22⋊C418yes—
125C23×D43C2×D411yescharacteristic
126C23×D43C2×D412yes—
127C2×Q8×C43—21no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×Q8×C43C22×C412yescomplemented
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43C22×C412yes—
134C2×D4×C43C2×D412yes—
135C22×C4×C43—24no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C2×C22⋊D43C22⋊C418yes—
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146Q8×D43—28no—
147Q8×D43—28no—
148Q8×D43—44no—
149Q8×D43—44no—
150D4×D43—28no—
151D4×D43—28no—
152D4×D43—28no—
153D4×D43—28no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172C22×C412yes—
157C2×D172C2×D412yes—
158C2×C4×D43—28no—
159C2×C4×D43—24no—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—44no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×C4×D43—42no—
166C2×C4×D43—88no—
167C2×C4×D43C22×C412yes—
168C2×C4×D43C2×D412yes—
169C2×C4×D43C2×D412yes—
170C2×C4×D43C2×D412yes—
171C2×C4×D43#4114yes—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—21no—
175C2×Dic86—24no—
176C2×Dic86—42no—
177C2×Dic86—42no—
178C2×Dic86C22×C412yescomplemented
179M16×C43—22no—
180M16×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43C2×D414yes—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—28no—
185C22⋊C4×C43—22no—
186C42×C43—21no—
187C42×C43—22no—
188C42×C43C22×C412yescomplemented
189C22⋊Dic43—24no—
190C22⋊Dic43—28no—
191C22⋊Dic43—22no—
192(C2×D43)⋊C4—28no—
193(C2×D43)⋊C4—28no—
194(C2×D43)⋊C4—28no—
195(C2×D43)⋊C4—24no—
196C4⋊Dic43C2×D414yes—
197Dic43⋊C4—24no—
198C4×Dic43—21no—
199C4×Dic43—22no—
200C4×Dic43—24no—
201C4×Dic43—24no—
202C4×Dic43C22×C412yescomplemented
203#10621877—22no—
204#10621877—22no—
205C2×C43⋊C8—22no—
206#10621872—44no—
207C8×D43—44no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—44no—
211C23×C43C2×C22⋊C414yes—
212C23×C43C22×D411yescharacteristic
213C22×D43—24no—
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—28no—
217C22×D43—28no—
218C22×D43—416no—
219C22×D43—48no—
220C22×D43—44no—
221C22×D43—88no—
222C22×D43—84no—
223C22×D43C2×C22⋊C412yes—
224C22×D43C2×C22⋊C414yes—
225C22×D43#12011yescharacteristic
226C22×D43#12011yescharacteristic
227C22×D43#12312yes—
228Q8×C43—24no—
229Q8×C43—42no—
230D4×C43—24no—
231D4×C43—24no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—84no—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D412yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4112yes—
243C22⋊D43—216no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—84no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43#12012yes—
253C2×Dic43#12312yes—
254D172—24no—
255D172—24no—
256C4×D43—48no—
257C4×D43—44no—
258C4×D43—44no—
259C4×D43—48no—
260C4×D43—88no—
261C4×D43C4×D414yes—
262C4×D43C4×D414yes—
263C4×D43#12114yes—
264C4×D43#12114yes—
265Dic86—24no—
266Dic86—42no—
267Dic86—48no—
268C8×C43—42no—
269C43⋊C8—42no—
270C2×#1885—431nomaximal, Sylow
271C22×C43—22no—
272C22×C43—24no—
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—82no—
276C22×C43C22×C22⋊C411yescharacteristic
277C22×C43C2×#12011yescharacteristic
278C22×C43C2×#12311yescharacteristic
279C2×D43—22no—
280C2×D43—24no—
281C2×D43—24no—
282C2×D43—24no—
283C2×D43—44no—
284C2×D43—416no—
285C2×D43—44no—
286C2×D43—88no—
287C2×D43—82no—
288C2×D43#38612yes—
289C2×D43#38612yes—
290C2×D43#45514yes—
291C4×C43—42no—
292C4×C43—44no—
293C4×C43—42no—
294C4×C43C2×C4×D412yes—
295C4×C43C2×#12112yes—
296Dic43—42no—
297Dic43—44no—
298Dic43—42no—
299Dic43#38614yes—
300C22×#124—431no—
301C2×#518—431no—
302C2×#419—432no—
303C22×#100—431no—
304#1885—432no—
305#1885—431no—
306#1885—432no—
307#1885—431no—
308#1885—431no—
309#1885D4311yescharacteristic, direct product factor
310C2×#339—432no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43—44no—
314C2×C43C2×#38611yescharacteristic
315C2×C43C2×#45512yes—
316D43—22no—
317D43—44no—
318D43#188514yesdirect product factor
319C23×Q8—431no—
320C23×D4—431no—
321C22×M16—432no—
322C2×#124—431no—
323C2×#124—431no—
324C2×#124—438no—
325C2×#124—431no—
326C2×#124—862no—
327C2×#124—864no—
328C2×#124C2×D4311yescharacteristic
329#518—431no—
330#518—432no—
331#518—862no—
332#518—864no—
333#518C2×D4311yescharacteristic
334C2×C4×D4—864no—
335C2×#117—432no—
336C22×C22⋊C4—862no—
337C22×C22⋊C4—862no—
338C22×C42—431no—
339#419—432no—
340#419—432no—
341#419—432no—
342#419—864no—
343#419C2×D4312yescomplemented
344C2×#103—864no—
345C2×#100—431no—
346C2×#100—432no—
347C2×#100—864no—
348C2×#100C2×D4311yescharacteristic
349#339—432no—
350#339—432no—
351#339—432no—
352#339C2×D4312yescomplemented
353C43C2×#188511yescharacteristic, complemented, Sylow
354C25—432no—
355C22×Q8—434no—
356C22×Q8—431no—
357C22×Q8—861no—
358C22×Q8—862no—
359C22×Q8—862no—
360C22×Q8—862no—
361C22×Q8—864no—
362C22×Q8C22×D4311yescharacteristic
363C22×D4—432no—
364C22×D4—434no—
365C22×D4—434no—
366C22×D4—431no—
367C22×D4—862no—
368C22×D4—862no—
369C22×D4—864no—
370C22×D4C22×D4311yescharacteristic
371C23×C4—431no—
372C23×C4—864no—
373C23×C4—861no—
374C23×C4—861no—
375C2×M16—432no—
376C2×M16—862no—
377C2×M16—864no—
378C2×M16—864no—
379C2×M16C22×D4312yes—
380C22×C8—862no—
381#124—22no—
382#124—434no—
383#124—434no—
384#124—434no—
385#124—862no—
386#124—8616no—
387#124—862no—
388#124—862no—
389#124C4×D4314yescomplemented
390C4×D4—24no—
391C4×D4—864no—
392C4×D4—868no—
393C4×D4—864no—
394C4×D4—868no—
395C4×D4—864no—
396#117—432no—
397#117—434no—
398#117—862no—
399#117—862no—
400#117C22×D4312yes—
401C2×C4⋊C4—434no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4—8616no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—864no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C42—431no—
415C2×C42—434no—
416C2×C42—862no—
417C2×C42—862no—
418C2×C42—861no—
419C2×C42C22×D4311yescharacteristic
420#103—24no—
421#103—864no—
422#103—864no—
423#103—864no—
424#100—22no—
425#100—864no—
426#100—862no—
427C24—431no—
428C24—438no—
429C24—432no—
430C24—862no—
431C24—864no—
432C24—862no—
433C24—1728no—
434C24D4×D4312yes—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—432no—
439C2×Q8—864no—
440C2×Q8—868no—
441C2×Q8—868no—
442C2×Q8—861no—
443C2×Q8—862no—
444C2×Q8—862no—
445C2×Q8—1722no—
446C2×Q8—1722no—
447C2×Q8—1724no—
448C2×Q8—1724no—
449C2×Q8C2×C4×D4312yescomplemented
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—438no—
453C2×D4—432no—
454C2×D4—432no—
455C2×D4—868no—
456C2×D4—868no—
457C2×D4—868no—
458C2×D4—868no—
459C2×D4—864no—
460C2×D4—864no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4C2×C4×D4312yes—
464C2×D4D4×D4312yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—431no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—434no—
474C22×C4—868no—
475C22×C4—864no—
476C22×C4—864no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—3448no—
482C22×C4—1721no—
483C22×C4—1721no—
484C22×C4—1722no—
485C22×C4—1724no—
486C22×C4C23×D4311yescharacteristic
487M16—22no—
488M16—22no—
489M16—862no—
490M16—862no—
491M16—1724no—
492C2×C8—22no—
493C2×C8—862no—
494C2×C8—1724no—
495C4⋊C4—434no—
496C4⋊C4—864no—
497C4⋊C4D4×D4314yes—
498C22⋊C4—24no—
499C22⋊C4—28no—
500C22⋊C4—22no—
501C22⋊C4—864no—
502C22⋊C4—868no—
503C22⋊C4—868no—
504C22⋊C4—868no—
505C22⋊C4—864no—
506C22⋊C4—868no—
507C22⋊C4—862no—
508C42—21no—
509C42—22no—
510C42—432no—
511C42—864no—
512C42—864no—
513C42—861no—
514C42—862no—
515C42C2×C4×D4312yescomplemented
516C23—22no—
517C23—22no—
518C23—44no—
519C23—431no—
520C23—432no—
521C23—431no—
522C23—432no—
523C23—434no—
524C23—864no—
525C23—868no—
526C23—868no—
527C23—862no—
528C23—862no—
529C23—3444no—
530C23—3448no—
531C23—1724no—
532C23—1728no—
533C23—17216no—
534C23C22⋊C4×D4314yes—
535C23C2×D4×D4311yescharacteristic
536Q8—24no—
537Q8—42no—
538Q8—864no—
539Q8—1728no—
540Q8—1722no—
541D4—24no—
542D4—24no—
543D4—8616no—
544D4—864no—
545D4—864no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—84no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—434no—
557C2×C4—434no—
558C2×C4—434no—
559C2×C4—434no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—864no—
563C2×C4—3448no—
564C2×C4—3444no—
565C2×C4—1728no—
566C2×C4—1724no—
567C2×C4—1724no—
568C2×C4—1728no—
569C2×C4—1722no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×D4×D4312yes—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4#41×D4312yes—
576C8—42no—
577C8—1722no—
578C22—22no—
579C22—24no—
580C22—44no—
581C22—44no—
582C22—82no—
583C22—432no—
584C22—434no—
585C22—432no—
586C22—864no—
587C22—864no—
588C22—862no—
589C22—864no—
590C22—3442no—
591C22—3448no—
592C22—1724no—
593C22—17216no—
594C22—1724no—
595C22C2×C22⋊C4×D4311yescharacteristic
596C22#120×D4311yescharacteristic
597C22#123×D4311yescharacteristic
598C4—42no—
599C4—42no—
600C4—44no—
601C4—434no—
602C4—1722no—
603C4—1722no—
604C4—1724no—
605C4C4×D4×D4312yes—
606C4#121×D4312yes—
607C2—21no—
608C2—21no—
609C2—44no—
610C2—434no—
611C2—862no—
612C2—1724no—
613C2#386×D4311yescharacteristic
614C2#455×D4312yes—
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1885C2
socleC22×C43C2×#120
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1885D43
hypocenterC43C2×#1885
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1885

Complements

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

NH ≅ G/Ntype
3. #419×D43C2semidirect
5. #19134984C2semidirect
6. #19134983C2semidirect
7. #19134982C2semidirect
8. #19134981C2semidirect
9. #19134980C2semidirect
10. #339×D43C2semidirect
11. C43×#1885C2semidirect
20. #124×D43C4semidirect
30. #14582909C22semidirect
31. #14582908C22semidirect
32. #14582907C22semidirect
38. #14582660C22semidirect
39. #14582659C22semidirect
40. #14582658C22semidirect
43. C43×#419C22semidirect
45. C43×#339C22semidirect
53. C2×Q8×D43C2×C4semidirect
71. #13063314C2×C4semidirect
73. #13063313C2×C4semidirect
75. #13063312C2×C4semidirect
101. C42×D43C2×C4semidirect
111. #124×C43C2×C4semidirect
130. C2×Q8×C43C22×C4semidirect
178. C2×Dic86C22×C4semidirect
188. C42×C43C22×C4semidirect
202. C4×Dic43C22×C4semidirect
309. #1885D43direct (N × H)
318. D43#1885direct (N × H)
343. #419C2×D43semidirect
352. #339C2×D43semidirect
353. C43C2×#1885semidirect
389. #124C4×D43semidirect
449. C2×Q8C2×C4×D43semidirect
515. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D432
#518×D432
#419×D432
C2×#100×D432
#191349842
#191349832
#191349822
#191349812
#191349802
#339×D432
C43×#18852
C2×#188543