Finite Group Databasebeta

← D43×#1518 #25063938

Subgroups — D43×#1518 #25063938

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic
3#382×D43C211yesmaximal, characteristic
4#19133160C211yesmaximal, characteristic, complemented
5#19133159C211yesmaximal, characteristic, complemented
6#19133158C211yesmaximal, characteristic, complemented
7#19133157C214yesmaximal, complemented
8#328×D43C214yesmaximal
9C43×#1518C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455—21no—
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583453—21no—
15#14583453C412yescomplemented
16#14583452—21no—
17#14583451—21no—
18#14583451C2212yes—
19C4⋊Q8×D43C411yescharacteristic, complemented
20C4⋊Q8×D43C411yescharacteristic, complemented
21#125×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43C2212yes—
24C4×Q8×D43—21no—
25C4×Q8×D43C412yescomplemented
26#117×D43—21no—
27C2×C4⋊C4×D43—21no—
28C2×C42×D43C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582951—21no—
31#14582950—21no—
32#14582949C2212yes—
33C4⋊C8×D43—21no—
34C22⋊C8×D43C2212yes—
35C4×C8×D43—21no—
36#14582765C2211yescharacteristic
37#14582764—21no—
38#14582763—21no—
39#14582763C2212yes—
40#95×D43—21no—
41#95×D43C2212yes—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#382C2211yescharacteristic
48C43×#328C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43—22no—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×C8×D43—22no—
56#13063325C2×C411yescharacteristic, complemented
57#13063325C2×C411yescharacteristic, complemented
58#13063324—21no—
59#13063324—21no—
60#13063324—21no—
61#13063324C2×C412yescomplemented
62#13063323—21no—
63#13063323C2×C412yescomplemented
64#13063317—21no—
65#13063316—21no—
66#13063316—21no—
67#13063315—22no—
68#13063315—22no—
69#13063305—21no—
70#13063305C2×C412yes—
71#13063304—21no—
72#13063304C2312yes—
73#13063303—22no—
74#13063303—22no—
75#13063302—22no—
76#13063302—22no—
77#13063301—21no—
78#13063301C2×C412yes—
79Q8×Dic43—21no—
80Q8×Dic43C2×C412yescomplemented
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86C2×C412yescomplemented
85#13063290—21no—
86#13063290—22no—
87#13063290—22no—
88#13063290C2×C412yescomplemented
89#13063284—21no—
90#13063283—21no—
91#13063283—21no—
92#13063282—22no—
93#13063281—22no—
94C2×C4⋊Dic43—21no—
95C2×Dic43⋊C4—22no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—44no—
102C4⋊C4×D43C2×C412yes—
103C22⋊C4×D43—22no—
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C42×D43—22no—
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C4⋊(C43⋊C8)—21no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120C4×C43⋊C8—21no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95C2312yes—
126C4⋊Q8×C43C2×C411yescharacteristic, complemented
127C4⋊Q8×C43C2×C411yescharacteristic, complemented
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2312yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2×C412yescomplemented
133#117×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138C4×C8×C43—21no—
139#95×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152Q8×D43—44no—
153Q8×D43—44no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—44no—
159C2×C4×D43—44no—
160C2×C4×D43—44no—
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43SD1614yes—
170C2×C4×D43Q1614yes—
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C22×C411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×Dic86—21no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86C22×C412yes—
179C2×C8×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C42×C43—22no—
189C42×C43C22×C411yescharacteristic
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C22⋊Dic43—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—42no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—44no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C2×C43⋊C8—22no—
228C8×D43—44no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234C22×D43C2×SD1612yes—
235C22×D43C2×Q1612yes—
236Q8×C43—42no—
237Q8×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×SD1612yes—
250C2×C4×C43C2×Q1612yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×SD1612yes—
267C2×Dic43C2×Q1612yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—44no—
277C4×D43—44no—
278C4×D43—88no—
279C4×D43#10314yes—
280C4×D43#10314yes—
281C4×D43#10314yes—
282C4×D43#10314yes—
283Dic86—44no—
284Dic86—44no—
285Dic86—42no—
286Dic86—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289C2×#1518—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43C22×SD1611yescharacteristic
294C22×C43C22×Q1611yescharacteristic
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—24no—
298C2×D43—24no—
299C2×D43#41012yes—
300C2×D43C2×#10312yes—
301C2×D43C2×#10312yes—
302C2×D43#42112yes—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—82no—
310C4×C43C2×#10312yes—
311C4×C43C2×#10312yes—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—42no—
317Dic43—42no—
318Dic43—82no—
319Dic43C2×#10312yes—
320Dic43C2×#10312yes—
321C2×#533—431no—
322C2×#431—431no—
323C2×#382—431no—
324#1518—431no—
325#1518—431no—
326#1518—434no—
327#1518—431no—
328#1518D4311yescharacteristic, direct product factor
329C2×#328—434no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43C2×#41011yescharacteristic
333C2×C43C22×#10311yescharacteristic
334C2×C43C2×#42111yescharacteristic
335D43—22no—
336D43#151814yesdirect product factor
337#533—431no—
338#533—431no—
339#533—432no—
340#533—432no—
341#533—431no—
342#533—861no—
343#533—861no—
344#533—861no—
345#533—861no—
346#533C2×D4311yescharacteristic
347C2×C4⋊Q8—431no—
348C2×C4⋊Q8—431no—
349C2×#125—861no—
350C2×C22⋊Q8—432no—
351C2×C22⋊Q8—861no—
352C2×C4×Q8—432no—
353C2×C4×Q8—861no—
354C2×#117—861no—
355C22×C4⋊C4—861no—
356C22×C42—431no—
357#431—431no—
358#431—432no—
359#431—861no—
360#431—861no—
361#431C2×D4311yescharacteristic
362C2×C4⋊C8—861no—
363C2×C22⋊C8—432no—
364C2×C4×C8—861no—
365#382—431no—
366#382—432no—
367#382—861no—
368#382—861no—
369#382C2×D4311yescharacteristic
370C2×#95—432no—
371C2×#95—861no—
372#328—434no—
373#328—434no—
374#328—434no—
375#328C2×D4314yes—
376C43C2×#151811yescharacteristic, complemented, Sylow
377C22×Q8—432no—
378C22×Q8—861no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—862no—
383C22×C8—862no—
384C4⋊Q8—432no—
385C4⋊Q8—432no—
386C4⋊Q8—431no—
387C4⋊Q8—431no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8—861no—
392C4⋊Q8C4×D4311yescharacteristic, complemented
393C4⋊Q8C4×D4311yescharacteristic, complemented
394#125—21no—
395#125—862no—
396#125—862no—
397#125—861no—
398#125—861no—
399#125—861no—
400C22⋊Q8—21no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—432no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8—861no—
411C22⋊Q8C22×D4312yes—
412C4×Q8—21no—
413C4×Q8—432no—
414C4×Q8—432no—
415C4×Q8—432no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×Q8—861no—
420C4×Q8—862no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×Q8C4×D4312yescomplemented
424#117—21no—
425#117—862no—
426#117—862no—
427#117—861no—
428#117—861no—
429#117—861no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—862no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—1724no—
440C2×C22⋊C4—862no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—862no—
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—862no—
456C4⋊C8—861no—
457C22⋊C8—432no—
458C22⋊C8—862no—
459C22⋊C8C22×D4312yes—
460C4×C8—21no—
461C4×C8—862no—
462C4×C8—861no—
463#95—21no—
464#95—432no—
465#95—862no—
466#95—862no—
467#95—861no—
468#95C22×D4312yes—
469C24—431no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×Q8—861no—
475C2×Q8—1724no—
476C2×Q8—1724no—
477C2×Q8C2×C4×D4312yes—
478C22×C4—22no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—434no—
485C22×C4—434no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1724no—
502C22×C4—1724no—
503C22×C4—1724no—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507C2×C8—22no—
508C2×C8—862no—
509C2×C8—1724no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—42no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—862no—
528C4⋊C4—861no—
529C4⋊C4—862no—
530C4⋊C4—1724no—
531C4⋊C4—1722no—
532C4⋊C4C2×C4×D4312yes—
533C22⋊C4—22no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C42—22no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—862no—
551C42—862no—
552C42—862no—
553C42C2×C4×D4311yescharacteristic
554C42C2×C4×D4311yescharacteristic
555C42D4×D4311yescharacteristic
556C42D4×D4311yescharacteristic
557C23—431no—
558C23—431no—
559C23—432no—
560C23—432no—
561C23—862no—
562C23—862no—
563C23C2×D4×D4311yescharacteristic
564Q8—42no—
565Q8—42no—
566Q8—1722no—
567Q8—1722no—
568Q8—1724no—
569Q8—1724no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—434no—
582C2×C4—434no—
583C2×C4—434no—
584C2×C4—434no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—3448no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1724no—
601C2×C4—1724no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4SD16×D4312yes—
612C2×C4Q16×D4312yes—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C8—42no—
616C8—1722no—
617C22—21no—
618C22—21no—
619C22—432no—
620C22—432no—
621C22—432no—
622C22—432no—
623C22—864no—
624C22—864no—
625C22—861no—
626C22—861no—
627C22C2×C22⋊C4×D4311yescharacteristic
628C22C2×SD16×D4311yescharacteristic
629C22C2×Q16×D4311yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—82no—
637C4—432no—
638C4—432no—
639C4—861no—
640C4—861no—
641C4—861no—
642C4—861no—
643C4—3442no—
644C4—1722no—
645C4—1722no—
646C4#103×D4312yes—
647C4#103×D4312yes—
648C2—21no—
649C2—21no—
650C2—434no—
651C2—862no—
652C2#410×D4311yescharacteristic
653C2C2×#103×D4311yescharacteristic
654C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1518C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1518D43
hypocenterC43C2×#1518
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
4. #19133160C2semidirect
5. #19133159C2semidirect
6. #19133158C2semidirect
7. #19133157C2semidirect
9. C43×#1518C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
15. #14583453C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
25. C4×Q8×D43C4semidirect
56. #13063325C2×C4semidirect
57. #13063325C2×C4semidirect
61. #13063324C2×C4semidirect
63. #13063323C2×C4semidirect
80. Q8×Dic43C2×C4semidirect
84. C4×Dic86C2×C4semidirect
88. #13063290C2×C4semidirect
126. C4⋊Q8×C43C2×C4semidirect
127. C4⋊Q8×C43C2×C4semidirect
132. C4×Q8×C43C2×C4semidirect
328. #1518D43direct (N × H)
336. D43#1518direct (N × H)
376. C43C2×#1518semidirect
392. C4⋊Q8C4×D43semidirect
393. C4⋊Q8C4×D43semidirect
423. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#431×D432
#382×D432
#191331602
#191331592
#191331582
#191331572
#328×D432
C43×#15182
C2×#151843