Finite Group Databasebeta

← D43×#1592 #25066349

Subgroups — D43×#1592 #25066349

Order 11008.

730 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#446×D43C211yesmaximal, characteristic, complemented
2C4×SD16×D43C211yesmaximal, characteristic
3#436×D43C211yesmaximal, characteristic
4#19133500C211yesmaximal, characteristic, complemented
5#19133499C211yesmaximal, characteristic, complemented
6#19133498C211yesmaximal, characteristic, complemented
7#19133497C211yesmaximal, characteristic, complemented
8#19133496C211yesmaximal, characteristic, complemented
9#19133495C211yesmaximal, characteristic, complemented
10#19133494C211yesmaximal, characteristic, complemented
11#335×D43C211yesmaximal, characteristic, complemented
12Q8⋊C8×D43C211yesmaximal, characteristic, complemented
13D4⋊C8×D43C211yesmaximal, characteristic
14#322×D43C211yesmaximal, characteristic, complemented
15C43×#1592C211yesmaximal, characteristic, complemented
16C2×SD16×D43C411yescharacteristic
17C2×M16×D43—21no—
18C4×Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583030C2211yescharacteristic, complemented
21#14583029C2211yescharacteristic, complemented
22#14583028—21no—
23#14583027—21no—
24#14583026C2211yescharacteristic, complemented
25#14582990C411yescharacteristic
26C4×#10621873C2211yescharacteristic
27SD16×Dic43C411yescharacteristic
28C4×#10621884C2211yescharacteristic
29#14582986C411yescharacteristic
30C4×#10621883C2211yescharacteristic
31#14582984C411yescharacteristic
32#14582978C2211yescharacteristic
33#14582977C2211yescharacteristic
34#14582976C2211yescharacteristic
35#14582975—21no—
36#14582974—21no—
37#106×D43C411yescharacteristic
38C4⋊C8×D43—21no—
39C4⋊C8×D43C2211yescharacteristic
40C4⋊C8×D43C2211yescharacteristic
41#103×D43C411yescharacteristic
42#102×D43C411yescharacteristic
43C22⋊C8×D43—21no—
44#97×D43—21no—
45C4×C8×D43C2211yescharacteristic
46C4×C8×D43C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582651C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53#14582629C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59#14582620C2211yescharacteristic, complemented
60C43×#446C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×Q8×D43C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73SD16×D43—24no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77M16×D43—44no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43C2×C411yescharacteristic
82C2×C8×D43C2×C411yescharacteristic
83C2×C8×D43D411yescharacteristic
84C2×C8×D43D411yescharacteristic
85Q8×Dic43C2×C411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89#13063290C2×C411yescharacteristic
90C4×D172C2311yescharacteristic
91D4×Dic43C2×C411yescharacteristic
92#13063287C2×C411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43C2×C411yescharacteristic
97C4⋊C4×D43C2×C411yescharacteristic
98C22⋊C4×D43—21no—
99C42×D43—21no—
100C42×D43C2311yescharacteristic
101#13063257C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103#13063256C2×C411yescharacteristic
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250C2×C411yescharacteristic
112#13063249C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115#13063246C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063236—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×SD16×C43C2×C411yescharacteristic
132C2×M16×C43—21no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43C2×C411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43—21no—
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152Q8×D43—22no—
153Q8×D43—22no—
154D4×D43—22no—
155D4×D43—22no—
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43C22×C411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86C22×C411yescharacteristic
169SD16×C43—22no—
170M16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C22×C411yescharacteristic
175C2×C8×C43C22×C411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C42×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621884—22no—
186#10621883—22no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43C22×C411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210#10621873—22no—
211#10621872—42no—
212#10621872—42no—
213C8×D43—22no—
214C8×D43—22no—
215C8×D43—22no—
216C8×D43—42no—
217C8×D43—42no—
218C8×D43—42no—
219C8×D43M1614yescomplemented
220C23×C43—21no—
221C22×D43—21no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43C4×D411yescharacteristic
226Q8×C43—21no—
227Q8×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—42no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—42no—
243C2×Dic43C4×D411yescharacteristic
244C2×Dic43C4×D411yescharacteristic
245C2×Dic43C4×D411yescharacteristic
246D172—21no—
247D172—21no—
248C4×D43—22no—
249C4×D43—42no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—42no—
255C4×D43C2×M1612yes—
256C4×D43#13112yes—
257C4×D43AGL(1,ℤ/8)12yes—
258C4×D43#13712yes—
259Dic86—21no—
260Dic86—21no—
261Dic86—42no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43C2×M1612yescomplemented
269C43⋊C8—21no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8C2×M1612yescomplemented
276C2×#1592—431nomaximal, Sylow
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43C2×C4×D411yescharacteristic
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—84no—
285C2×D43#43612yes—
286C2×D43#44012yes—
287C2×D43#44412yes—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43C22×M1611yescharacteristic
293C4×C43C2×#13111yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43C2×#13711yescharacteristic
296Dic43—21no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43#43612yes—
301Dic43#44012yes—
302C2×#446—431no—
303C2×C4×SD16—431no—
304C2×#436—431no—
305#1592—431no—
306#1592—431no—
307#1592—431no—
308#1592—431no—
309#1592—431no—
310#1592—431no—
311#1592—431no—
312#1592D4311yescharacteristic, direct product factor
313C2×#335—431no—
314C2×Q8⋊C8—431no—
315C2×D4⋊C8—431no—
316C2×#322—431no—
317C2×C43—81no—
318C2×C43C2×#43611yescharacteristic
319C2×C43C2×#44011yescharacteristic
320C2×C43C2×#44411yescharacteristic
321D43—81no—
322D43#159214yesdirect product factor
323C22×SD16—431no—
324C22×M16—861no—
325C2×C4×Q8—431no—
326C2×C4×D4—431no—
327#446—431no—
328#446—431no—
329#446—431no—
330#446—861no—
331#446—861no—
332#446C2×D4311yescharacteristic, complemented
333C4×SD16—431no—
334C4×SD16—431no—
335C4×SD16—431no—
336C4×SD16—431no—
337C4×SD16—431no—
338C4×SD16—431no—
339C4×SD16—431no—
340C4×SD16C2×D4311yescharacteristic
341#436—431no—
342#436—431no—
343#436—431no—
344#436—861no—
345#436—861no—
346#436C2×D4311yescharacteristic
347C2×#106—431no—
348C2×C4⋊C8—431no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—861no—
351C2×#103—431no—
352C2×#102—431no—
353C2×C22⋊C8—861no—
354C2×#97—861no—
355C2×C4×C8—431no—
356C2×C4×C8—431no—
357C2×C4×C8—431no—
358#335—431no—
359#335—431no—
360#335—431no—
361#335C2×D4311yescharacteristic, complemented
362Q8⋊C8—431no—
363Q8⋊C8—431no—
364Q8⋊C8—431no—
365Q8⋊C8C2×D4311yescharacteristic, complemented
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8C2×D4311yescharacteristic
370#322—431no—
371#322—431no—
372#322—431no—
373#322C2×D4311yescharacteristic, complemented
374C43C2×#159211yescharacteristic, complemented, Sylow
375C22×Q8—431no—
376C22×D4—431no—
377C23×C4—861no—
378C2×SD16—431no—
379C2×SD16—431no—
380C2×SD16—431no—
381C2×SD16—864no—
382C2×SD16C4×D4311yescharacteristic
383C2×M16—21no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—1724no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—861no—
393C22×C8—861no—
394C22×C8—861no—
395C4×Q8—431no—
396C4×Q8—431no—
397C4×Q8—431no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×Q8C22×D4311yescharacteristic
401C4×D4—431no—
402C4×D4—431no—
403C4×D4—431no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4C22×D4311yescharacteristic
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—431no—
412C2×C42—861no—
413#106—431no—
414#106—431no—
415#106—431no—
416#106C4×D4311yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425C4⋊C8C22×D4311yescharacteristic
426C4⋊C8C22×D4311yescharacteristic
427#103—431no—
428#103—431no—
429#103—431no—
430#103C4×D4311yescharacteristic
431#102—431no—
432#102—431no—
433#102—431no—
434#102C4×D4311yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—21no—
440#97—861no—
441#97—861no—
442#97—861no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452C4×C8C22×D4311yescharacteristic
453C4×C8C22×D4311yescharacteristic
454C24—861no—
455C2×Q8—431no—
456C2×Q8—861no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8C2×C4×D4311yescharacteristic
460C2×D4—431no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4—861no—
464C2×D4C2×C4×D4311yescharacteristic
465C22×C4—21no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—1722no—
476C22×C4—1722no—
477SD16—22no—
478SD16—862no—
479SD16—862no—
480SD16—862no—
481M16—42no—
482M16—1722no—
483M16—1722no—
484M16—1722no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—431no—
489C2×C8—434no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—862no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—1722no—
500C2×C8—1722no—
501C2×C8—1722no—
502C2×C8C2×C4×D4311yescharacteristic
503C2×C8C2×C4×D4311yescharacteristic
504C2×C8D4×D4311yescharacteristic
505C2×C8D4×D4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—431no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4C2×C4×D4311yescharacteristic
515C4⋊C4C2×C4×D4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C42—21no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—861no—
525C42—861no—
526C42—861no—
527C42C23×D4311yescharacteristic
528C23—21no—
529C23—431no—
530C23—861no—
531C23—1722no—
532C23—1722no—
533C23—1722no—
534Q8—21no—
535Q8—21no—
536Q8—861no—
537Q8—861no—
538Q8—1722no—
539D4—21no—
540D4—21no—
541D4—861no—
542D4—861no—
543D4—1722no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—431no—
550C2×C4—431no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—431no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C22×C4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—432no—
577C8—861no—
578C8—861no—
579C8—861no—
580C8—1721no—
581C8—1721no—
582C8—1721no—
583C8M16×D4312yescomplemented
584C22—41no—
585C22—41no—
586C22—41no—
587C22—432no—
588C22—432no—
589C22—432no—
590C22—3444no—
591C22—1721no—
592C22—1721no—
593C22—1721no—
594C22C4×D4×D4311yescharacteristic
595C4—21no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—432no—
600C4—432no—
601C4—861no—
602C4—1721no—
603C4—1721no—
604C4—1721no—
605C4C2×M16×D4311yescharacteristic
606C4#131×D4311yescharacteristic
607C4AGL(1,ℤ/8)×D4311yescharacteristic
608C4#137×D4311yescharacteristic
609C2—81no—
610C2—434no—
611C2—3441no—
612C2#436×D4311yescharacteristic
613C2#440×D4311yescharacteristic
614C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1592C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenter#1592D43
hypocenterC43C2×#1592
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
1. #446×D43C2semidirect
4. #19133500C2semidirect
5. #19133499C2semidirect
6. #19133498C2semidirect
7. #19133497C2semidirect
8. #19133496C2semidirect
9. #19133495C2semidirect
10. #19133494C2semidirect
11. #335×D43C2semidirect
12. Q8⋊C8×D43C2semidirect
14. #322×D43C2semidirect
15. C43×#1592C2semidirect
20. #14583030C22semidirect
21. #14583029C22semidirect
24. #14583026C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582651C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582620C22semidirect
60. C43×#446C22semidirect
63. C43×#335C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
219. C8×D43M16semidirect
268. C8×C43C2×M16semidirect
275. C43⋊C8C2×M16semidirect
312. #1592D43direct (N × H)
322. D43#1592direct (N × H)
332. #446C2×D43semidirect
361. #335C2×D43semidirect
365. Q8⋊C8C2×D43semidirect
373. #322C2×D43semidirect
374. C43C2×#1592semidirect
583. C8M16×D43semidirect

Maximal subgroups

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

subgroupindex
#446×D432
C4×SD16×D432
#436×D432
#191335002
#191334992
#191334982
#191334972
#191334962
#191334952
#191334942
#335×D432
Q8⋊C8×D432
D4⋊C8×D432
#322×D432
C43×#15922
C2×#159243