Finite Group Databasebeta

← D43×#1805 #25096058

Subgroups — D43×#1805 #25096058

Order 11008.

1510 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic
2C2×C4⋊C8×D43C211yesmaximal, characteristic
3C2×#103×D43C212yesmaximal
4#382×D43C211yesmaximal, characteristic
5#19134611C211yesmaximal, characteristic, complemented
6#19134610C211yesmaximal, characteristic, complemented
7#19134609C212yesmaximal, complemented
8#19134608C212yesmaximal, complemented
9#19134607C211yesmaximal, characteristic, complemented
10#340×D43C212yesmaximal
11C43×#1805C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×C8×D43C2212yes—
14C2×Q8×Dic43C2211yescharacteristic
15C2×C4×Dic86—21no—
16C2×C4×Dic86C2211yescharacteristic
17C2×#13063290—21no—
18C2×#13063290C2211yescharacteristic
19C4×Q8×D43—24no—
20C4×Q8×D43C418yescomplemented
21C2×C4⋊C4×D43—21no—
22C2×C4⋊C4×D43C2212yes—
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C42×D43—21no—
25C2×C42×D43C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2212yes—
28C4⋊C8×D43—24no—
29C2×#13063250C2212yes—
30C2×#13063249C2212yes—
31C2×#13063248C2212yes—
32#103×D43—28no—
33#14582765C2211yescharacteristic
34#14582764C2212yes—
35#14582763—21no—
36#14582763—21no—
37#95×D43—21no—
38#95×D43—21no—
39#14582662C2212yes—
40#14582661C2212yes—
41#14582661C2212yes—
42C2×C4×Q8×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C43×#382C2211yescharacteristic
46C43×#340C2212yes—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C2×Q8×D43—22no—
50C2×Q8×D43—22no—
51C2×Q8×D43—22no—
52C2×Q8×D43C2×C414yes—
53C2×Q8×D43D414yes—
54C2×Q8×D43Q814yes—
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43—22no—
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8C2312yes—
62C2×C8×D43—24no—
63C2×C8×D43—24no—
64C2×C8×D43—24no—
65Q8×Dic43—22no—
66Q8×Dic43C2×C414yescomplemented
67C4×Dic86—22no—
68C4×Dic86—28no—
69C4×Dic86C2×C414yescomplemented
70#13063290—28no—
71#13063290—22no—
72#13063290C2×C414yescomplemented
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2312yes—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—22no—
80C4⋊C4×D43—28no—
81C4⋊C4×D43—22no—
82C4⋊C4×D43—24no—
83C4⋊C4×D43—24no—
84C4⋊C4×D43C2×C414yes—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C42×D43—28no—
92C42×D43C2×C414yes—
93C42×D43D414yes—
94C4⋊(C43⋊C8)—22no—
95Dic43⋊C8—24no—
96#13063250—24no—
97#13063249—24no—
98#13063248—24no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C22×Q8×C43C2311yescharacteristic
104C22×C8×C43C2312yes—
105C4×Q8×C43—22no—
106C4×Q8×C43C2×C414yescomplemented
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2312yes—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C4⋊C8×C43—22no—
113#103×C43—24no—
114#95×C43—21no—
115#95×C43—21no—
116C23×D43C2×D411yescharacteristic
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43—21no—
120C2×Q8×C43C22×C412yes—
121C2×Q8×C43C2×D412yes—
122C2×Q8×C43C2×Q812yes—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135Q8×D43—28no—
136Q8×D43—28no—
137Q8×D43—28no—
138Q8×D43C4⋊C4116yes—
139C2×C4×D43—24no—
140C2×C4×D43—24no—
141C2×C4×D43—24no—
142C2×C4×D43—24no—
143C2×C4×D43—24no—
144C2×C4×D43—24no—
145C2×C4×D43—44no—
146C2×C4×D43—44no—
147C2×C4×D43—44no—
148C2×C4×D43—44no—
149C2×C4×D43C22⋊C414yes—
150C2×C4×D43C22⋊C414yes—
151C2×C4×D43C22×C412yes—
152C2×C4×D43C2×D412yes—
153C2×C4×D43C2×D412yes—
154C2×C4×D43C2×Q812yes—
155C2×C4×D43#4112yes—
156C2×C4×D43#4112yes—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—24no—
161C2×Dic86—24no—
162C2×Dic86—24no—
163C2×Dic86C22×C412yes—
164C2×Dic86C2×D412yes—
165C2×Dic86C2×Q812yes—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C4⋊C4×C43—24no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43C22×C412yes—
174C42×C43—24no—
175C42×C43C22×C412yes—
176C42×C43C2×D412yes—
177C4⋊Dic43—21no—
178C4⋊Dic43—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—44no—
186C4×Dic43—24no—
187C4×Dic43—24no—
188C4×Dic43—24no—
189C4×Dic43C22⋊C414yes—
190C4×Dic43C22⋊C414yes—
191C4×Dic43C22×C412yes—
192C4×Dic43C2×D412yes—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C8×D43—48no—
197C23×C43C22×D411yescharacteristic
198C22×D43C2×C22⋊C412yes—
199C22×D43#12112yes—
200C22×D43C22⋊Q812yes—
201C22×D43#13514yes—
202C22×D43#13714yes—
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—22no—
206Q8×C43C2×C4⋊C414yes—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43C2×C22⋊C412yes—
218C2×C4×C43C2×C22⋊C412yes—
219C2×C4×C43C23×C411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×Q811yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43C2×C22⋊C412yes—
236C2×Dic43C2×C22⋊C412yes—
237C2×Dic43C2×C22⋊C412yes—
238C2×Dic43#12112yes—
239C2×Dic43C22⋊Q812yes—
240C4×D43—216no—
241C4×D43—28no—
242C4×D43—28no—
243C4×D43—48no—
244C4×D43—88no—
245C4×D43C2×C4⋊C414yes—
246C4×D43#11714yes—
247C4×D43#12114yes—
248C4×D43C22⋊Q814yes—
249Dic86—22no—
250Dic86—22no—
251Dic86—22no—
252Dic86—216no—
253Dic86C2×C4⋊C414yes—
254C8×C43—42no—
255C43⋊C8—42no—
256C2×#1805—431nomaximal, Sylow
257C22×C43C22×C22⋊C411yescharacteristic
258C22×C43C2×#12111yescharacteristic
259C22×C43C2×C22⋊Q811yescharacteristic
260C22×C43C2×#13512yes—
261C22×C43C2×#13712yes—
262C2×D43#38014yes—
263C2×D43#41614yes—
264C2×D43#41914yes—
265C2×D43#46418yes—
266C2×D43#47918yes—
267C4×C43—22no—
268C4×C43—22no—
269C4×C43—24no—
270C4×C43—42no—
271C4×C43—82no—
272C4×C43C22×C4⋊C411yescharacteristic
273C4×C43C2×#11711yescharacteristic
274C4×C43C2×#12111yescharacteristic
275C4×C43C2×C22⋊Q811yescharacteristic
276Dic43—22no—
277Dic43—22no—
278Dic43—24no—
279Dic43—42no—
280Dic43—82no—
281Dic43#38014yes—
282C22×C4×Q8—431no—
283C22×C4⋊C8—431no—
284C22×#103—432no—
285C2×#382—431no—
286#1805—431no—
287#1805—432no—
288#1805—431no—
289#1805—432no—
290#1805—431no—
291#1805D4311yescharacteristic, direct product factor
292C2×#340—432no—
293C2×C43C2×#38011yescharacteristic
294C2×C43C2×#41611yescharacteristic
295C2×C43C2×#41911yescharacteristic
296C2×C43C2×#46412yes—
297C2×C43C2×#47912yes—
298D43#180518yesdirect product factor
299C23×Q8—431no—
300C23×C8—432no—
301C2×C4×Q8—431no—
302C2×C4×Q8—438no—
303C2×C4×Q8—431no—
304C2×C4×Q8—431no—
305C2×C4×Q8—861no—
306C2×C4×Q8—861no—
307C2×C4×Q8—864no—
308C2×C4×Q8C2×D4311yescharacteristic
309C22×C4⋊C4—431no—
310C22×C4⋊C4—432no—
311C22×C4⋊C4—861no—
312C22×C42—431no—
313C22×C42—861no—
314C2×C4⋊C8—432no—
315C2×C4⋊C8—431no—
316C2×C4⋊C8—864no—
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×#103—432no—
319C2×#103—432no—
320C2×#103—432no—
321C2×#103—868no—
322C2×#103C2×D4312yes—
323#382—432no—
324#382—431no—
325#382—861no—
326#382—861no—
327#382C2×D4311yescharacteristic
328C2×#95—861no—
329C2×#95—861no—
330#340—432no—
331#340—432no—
332#340—432no—
333#340C2×D4312yes—
334C43C2×#180511yescharacteristic, complemented, Sylow
335C22×Q8—434no—
336C22×Q8—434no—
337C22×Q8—434no—
338C22×Q8—431no—
339C22×Q8—861no—
340C22×Q8—862no—
341C22×Q8—862no—
342C22×Q8—862no—
343C22×Q8C22×D4311yescharacteristic
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—861no—
348C23×C4—861no—
349C23×C4—862no—
350C22×C8—432no—
351C22×C8—864no—
352C22×C8—864no—
353C22×C8—864no—
354C22×C8C22×D4312yes—
355C4×Q8—22no—
356C4×Q8—434no—
357C4×Q8—434no—
358C4×Q8—434no—
359C4×Q8—868no—
360C4×Q8—868no—
361C4×Q8—862no—
362C4×Q8—862no—
363C4×Q8—862no—
364C4×Q8C4×D4314yescomplemented
365C2×C4⋊C4—21no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—434no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—868no—
371C2×C4⋊C4—864no—
372C2×C4⋊C4—864no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4C22×D4312yes—
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C42—21no—
381C2×C42—431no—
382C2×C42—431no—
383C2×C42—431no—
384C2×C42—434no—
385C2×C42—434no—
386C2×C42—868no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42C22×D4311yescharacteristic
391C4⋊C8—22no—
392C4⋊C8—864no—
393C4⋊C8—862no—
394#103—24no—
395#103—864no—
396#103—864no—
397#103—864no—
398#95—21no—
399#95—21no—
400#95—862no—
401#95—862no—
402#95—861no—
403#95—861no—
404C24—431no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—4316no—
409C2×Q8—432no—
410C2×Q8—432no—
411C2×Q8—432no—
412C2×Q8—864no—
413C2×Q8—864no—
414C2×Q8—864no—
415C2×Q8—868no—
416C2×Q8—868no—
417C2×Q8—868no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8C2×C4×D4312yes—
422C2×Q8D4×D4312yes—
423C2×Q8Q8×D4312yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—431no—
428C22×C4—432no—
429C22×C4—432no—
430C22×C4—432no—
431C22×C4—432no—
432C22×C4—432no—
433C22×C4—432no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—434no—
437C22×C4—434no—
438C22×C4—864no—
439C22×C4—864no—
440C22×C4—864no—
441C22×C4—864no—
442C22×C4—864no—
443C22×C4—864no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—862no—
447C22×C4—1724no—
448C22×C4—1724no—
449C22×C4—1724no—
450C22×C4—1724no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—862no—
458C2×C8—862no—
459C2×C8—862no—
460C2×C8—1728no—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—432no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—864no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—1724no—
474C4⋊C4C2×C4×D4312yes—
475C42—24no—
476C42—434no—
477C42—434no—
478C42—432no—
479C42—432no—
480C42—864no—
481C42—864no—
482C42—864no—
483C42C2×C4×D4312yes—
484C42D4×D4312yes—
485C23—432no—
486C23—432no—
487C23—432no—
488C23—434no—
489C23—434no—
490C23C2×D4×D4311yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—22no—
494Q8—434no—
495Q8—8616no—
496Q8—862no—
497Q8—862no—
498Q8—862no—
499Q8C4⋊C4×D4314yes—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—432no—
513C2×C4—434no—
514C2×C4—434no—
515C2×C4—434no—
516C2×C4—434no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—868no—
520C2×C4—868no—
521C2×C4—8616no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—3448no—
529C2×C4—1728no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4C22⋊C4×D4312yes—
535C2×C4C22⋊C4×D4312yes—
536C2×C4C22×C4×D4311yescharacteristic
537C2×C4C2×D4×D4311yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C2×Q8×D4311yescharacteristic
540C2×C4#41×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C8—42no—
543C8—1722no—
544C22—438no—
545C22—434no—
546C22—438no—
547C22—434no—
548C22—434no—
549C22C2×C22⋊C4×D4311yescharacteristic
550C22#121×D4311yescharacteristic
551C22C22⋊Q8×D4311yescharacteristic
552C22#135×D4312yes—
553C22#137×D4312yes—
554C4—22no—
555C4—22no—
556C4—24no—
557C4—42no—
558C4—82no—
559C4—434no—
560C4—862no—
561C4—862no—
562C4—864no—
563C4—3442no—
564C4—1722no—
565C4C2×C4⋊C4×D4311yescharacteristic
566C4#117×D4311yescharacteristic
567C4#121×D4311yescharacteristic
568C4C22⋊Q8×D4311yescharacteristic
569C2—438no—
570C2#380×D4311yescharacteristic
571C2#416×D4311yescharacteristic
572C2#419×D4311yescharacteristic
573C2#464×D4312yes—
574C2#479×D4312yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1805C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1805D43
hypocenterC43C2×#1805
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
5. #19134611C2semidirect
6. #19134610C2semidirect
7. #19134609C2semidirect
8. #19134608C2semidirect
9. #19134607C2semidirect
11. C43×#1805C2semidirect
20. C4×Q8×D43C4semidirect
66. Q8×Dic43C2×C4semidirect
69. C4×Dic86C2×C4semidirect
72. #13063290C2×C4semidirect
106. C4×Q8×C43C2×C4semidirect
291. #1805D43direct (N × H)
298. D43#1805direct (N × H)
334. C43C2×#1805semidirect
364. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×C4⋊C8×D432
C2×#103×D432
#382×D432
#191346112
#191346102
#191346092
#191346082
#191346072
#340×D432
C43×#18052
C2×#180543