Finite Group Databasebeta

← D43×#1859 #25097447

Subgroups — D43×#1859 #25097447

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#520×D43C211yesmaximal, characteristic
2#428×D43C211yesmaximal, characteristic, complemented
3C2×#104×D43C211yesmaximal, characteristic
4#417×D43C211yesmaximal, characteristic
5#384×D43C211yesmaximal, characteristic, complemented
6#19134824C211yesmaximal, characteristic, complemented
7#19134823C211yesmaximal, characteristic, complemented
8#19134822C211yesmaximal, characteristic, complemented
9#19134821C211yesmaximal, characteristic, complemented
10#19134820C211yesmaximal, characteristic, complemented
11#19134819C211yesmaximal, characteristic, complemented
12#19134818C211yesmaximal, characteristic, complemented
13#343×D43C211yesmaximal, characteristic, complemented
14#339×D43C211yesmaximal, characteristic, complemented
15C43×#1859C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583381—21no—
21#14583380—21no—
22#14583380C2211yescharacteristic
23#14583379—21no—
24#14583379C2211yescharacteristic
25#14583378—21no—
26#14583378—22no—
27C4×Q8×D43—21no—
28C4×D4×D43—21no—
29C4×D4×D43—22no—
30#117×D43—21no—
31#117×D43C2211yescharacteristic
32C2×C4⋊C4×D43—21no—
33C2×C4⋊C4×D43—22no—
34C2×C4⋊C4×D43C2211yescharacteristic
35C2×C4⋊C4×D43C2211yescharacteristic
36C2×C42×D43C2211yescharacteristic
37#14582942C2211yescharacteristic, complemented
38#14582941C2211yescharacteristic, complemented
39#14582940—21no—
40#14582939C2211yescharacteristic, complemented
41#14582938—21no—
42#107×D43—21no—
43#106×D43—21no—
44C2×#13063253C2211yescharacteristic
45C2×#13063252C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47#104×D43C418yescomplemented
48#14582901C2211yescharacteristic
49#14582900C2211yescharacteristic
50#14582899—21no—
51#14582898C2211yescharacteristic
52#14582897—21no—
53#103×D43—21no—
54#102×D43—21no—
55#14582769C2211yescharacteristic, complemented
56#14582768—22no—
57#14582768C2211yescharacteristic, complemented
58#14582768C2211yescharacteristic, complemented
59#14582668C2211yescharacteristic, complemented
60#14582667C2211yescharacteristic, complemented
61#14582667C2211yescharacteristic, complemented
62#14582660C2211yescharacteristic, complemented
63#14582659C2211yescharacteristic, complemented
64#14582658C2211yescharacteristic, complemented
65C43×#520C2211yescharacteristic
66C43×#428C2211yescharacteristic, complemented
67C2×#104×C43C2211yescharacteristic
68C43×#417C2211yescharacteristic
69C43×#384C2211yescharacteristic, complemented
70C43×#343C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72C2×#10621902D411yescharacteristic
73C2×#10621898—21no—
74C2×#10621898C2311yescharacteristic
75C2×#10621900—21no—
76C2×#10621900D411yescharacteristic
77#41×D43—22no—
78#41×D43—22no—
79#41×D43C2×C414yes—
80#41×D43Q814yes—
81C2×Q8×D43D411yescharacteristic
82C2×D4×D43—21no—
83C2×D4×D43D411yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—22no—
87C22×C4×D43—21no—
88C22×C4×D43D412yes—
89C22×C4×D43C2311yescharacteristic
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2311yescharacteristic
92C2×#10621872—21no—
93C2×#10621872—21no—
94M16×D43—22no—
95M16×D43—22no—
96M16×D43—22no—
97M16×D43C2×C414yescomplemented
98C2×C8×D43—21no—
99C2×C8×D43—21no—
100Q8×Dic43—21no—
101C4×Dic86—22no—
102C4×Dic86—21no—
103#13063290—22no—
104#13063290—21no—
105C4×D172—22no—
106C4×D172—21no—
107D4×Dic43—21no—
108D4×Dic43—22no—
109#13063287—22no—
110#13063287—21no—
111C4×C22⋊D43—22no—
112C4×C22⋊D43—22no—
113C4×C22⋊D43—22no—
114(C22⋊D43)⋊C4—22no—
115(C22⋊D43)⋊C4—22no—
116(C22⋊D43)⋊C4—22no—
117#13063284—21no—
118#13063284C2311yescharacteristic
119#13063283—21no—
120#13063283—21no—
121#13063283D411yescharacteristic
122#13063283D411yescharacteristic
123#13063282—22no—
124#13063282—21no—
125#13063281—22no—
126#13063281—21no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—22no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—22no—
132C2×Dic43⋊C4—22no—
133C2×Dic43⋊C4—22no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D412yes—
136C4⋊C4×D43—22no—
137C4⋊C4×D43—22no—
138C4⋊C4×D43—21no—
139C4⋊C4×D43—21no—
140C4⋊C4×D43—21no—
141C4⋊C4×D43—21no—
142C4⋊C4×D43—21no—
143C4⋊C4×D43—21no—
144C4⋊C4×D43—21no—
145C4⋊C4×D43—21no—
146C4⋊C4×D43—21no—
147C4⋊C4×D43—21no—
148C4⋊C4×D43—48no—
149C4⋊C4×D43D411yescharacteristic
150C4⋊C4×D43D411yescharacteristic
151C22⋊C4×D43—22no—
152C22⋊C4×D43—21no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43C2311yescharacteristic
155C42×D43—22no—
156C42×D43—21no—
157C42×D43—22no—
158C42×D43C2×C414yescomplemented
159#13063259—21no—
160#13063258—21no—
161#13063258—21no—
162#13063257—21no—
163#13063256—21no—
164#13063256—21no—
165#13063253C2×C414yescomplemented
166#13063252C2×C414yescomplemented
167#13063251C2×C414yescomplemented
168#13063250—21no—
169#13063249—21no—
170#13063248—21no—
171#13063247—21no—
172#13063246—21no—
173#13063245—21no—
174C2×#41×C43C2311yescharacteristic
175C2×M16×C43C2311yescharacteristic
176C2×M16×C43C2311yescharacteristic
177C4×Q8×C43—21no—
178C4×D4×C43—21no—
179C4×D4×C43—22no—
180#117×C43—21no—
181#117×C43C2311yescharacteristic
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43—22no—
184C2×C4⋊C4×C43C2311yescharacteristic
185C2×C4⋊C4×C43C2311yescharacteristic
186C2×C42×C43C2311yescharacteristic
187#107×C43—21no—
188#106×C43—21no—
189#104×C43C2×C414yescomplemented
190#103×C43—21no—
191#102×C43—21no—
192C23×D43—21no—
193C23×D43C2×D411yescharacteristic
194#41×C43—21no—
195#41×C43—21no—
196#41×C43C22×C412yes—
197#41×C43C2×Q812yes—
198C2×Q8×C43C2×D411yescharacteristic
199C2×D4×C43—21no—
200C2×D4×C43C2×D411yescharacteristic
201C22×C4×C43—21no—
202C22×C4×C43—22no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—21no—
208C2×C22⋊D43—21no—
209C2×C22⋊D43—21no—
210C22×Dic43—21no—
211C22×Dic43—22no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43C2×D412yes—
215C22×Dic43C2×D411yescharacteristic
216#10621902—22no—
217#10621902C4⋊C414yescomplemented
218Q8×D43—22no—
219Q8×D43C4⋊C414yescomplemented
220#10621900—24no—
221#10621900—24no—
222#10621900—22no—
223#10621900C4⋊C414yescomplemented
224D4×D43—22no—
225D4×D43—24no—
226D4×D43—24no—
227D4×D43C4⋊C414yescomplemented
228#10621898—21no—
229#10621898—21no—
230#10621898—24no—
231#10621898—24no—
232#10621898C22×C412yes—
233#10621898C2×Q812yes—
234C2×D172—21no—
235C2×D172C2×D411yescharacteristic
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—24no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—22no—
248C2×C4×D43—21no—
249C2×C4×D43—22no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43—41no—
253C2×C4×D43—41no—
254C2×C4×D43—84no—
255C2×C4×D43C22×C412yes—
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×C4×D43C2×D411yescharacteristic
260C2×C4×D43C2×Q812yes—
261C2×C4×D43#4112yes—
262C2×C4×D43#4112yes—
263C2×Dic86—21no—
264C2×Dic86C2×D411yescharacteristic
265M16×C43—21no—
266M16×C43—21no—
267M16×C43—21no—
268M16×C43C22×C412yescomplemented
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C4⋊C4×C43—22no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—44no—
277C4⋊C4×C43C2×D411yescharacteristic
278C4⋊C4×C43C2×D411yescharacteristic
279C22⋊C4×C43—22no—
280C22⋊C4×C43—21no—
281C42×C43—22no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43C22×C412yescomplemented
285C22⋊Dic43—22no—
286C22⋊Dic43—21no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291C4⋊Dic43—22no—
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43—44no—
297C4⋊Dic43C2×D411yescharacteristic
298C4⋊Dic43C2×D411yescharacteristic
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301Dic43⋊C4—22no—
302Dic43⋊C4—21no—
303Dic43⋊C4—22no—
304Dic43⋊C4—21no—
305Dic43⋊C4—44no—
306Dic43⋊C4—44no—
307Dic43⋊C4—41no—
308Dic43⋊C4—41no—
309C4×Dic43—22no—
310C4×Dic43—22no—
311C4×Dic43—22no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—24no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43C22×C412yescomplemented
318#10621877—21no—
319#10621877—21no—
320#10621877—21no—
321#10621877C22×C412yescomplemented
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324#10621872—24no—
325#10621872—42no—
326C8×D43—24no—
327C8×D43—42no—
328C23×C43—21no—
329C23×C43C22×D411yescharacteristic
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—21no—
333C22×D43—24no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43C4×D412yes—
337C22×D43#12011yescharacteristic
338C22×D43#12011yescharacteristic
339C22×D43C22⋊Q812yes—
340Q8×C43—21no—
341Q8×C43C2×C4⋊C412yescomplemented
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—21no—
345D4×C43C2×C4⋊C412yescomplemented
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—21no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—21no—
353C2×C4×C43—22no—
354C2×C4×C43—21no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43—41no—
358C2×C4×C43—82no—
359C2×C4×C43C23×C411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×Q811yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C2×C4×C43C2×#4111yescharacteristic
365C22⋊D43—22no—
366C22⋊D43—22no—
367C22⋊D43—24no—
368C22⋊D43—24no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—21no—
373C2×Dic43—24no—
374C2×Dic43—21no—
375C2×Dic43—22no—
376C2×Dic43—21no—
377C2×Dic43—42no—
378C2×Dic43—42no—
379C2×Dic43—41no—
380C2×Dic43—82no—
381C2×Dic43C4×D412yes—
382C2×Dic43#12011yescharacteristic
383C2×Dic43#12011yescharacteristic
384C2×Dic43C22⋊Q812yes—
385D172—24no—
386D172—21no—
387D172C2×C4⋊C412yescomplemented
388C4×D43—216no—
389C4×D43—24no—
390C4×D43—22no—
391C4×D43—22no—
392C4×D43—24no—
393C4×D43—44no—
394C4×D43—42no—
395C4×D43—42no—
396C4×D43—82no—
397C4×D43—82no—
398C4×D43—82no—
399C4×D43—82no—
400C4×D43—82no—
401C4×D43C2×C4⋊C412yes—
402C4×D43C2×C4⋊C412yes—
403C4×D43C4×D412yes—
404C4×D43C4×D412yes—
405C4×D43C22⋊Q812yes—
406C4×D43C22⋊Q812yes—
407C4×D43#12312yes—
408C4×D43#12312yes—
409Dic86—21no—
410Dic86—24no—
411Dic86C2×C4⋊C412yescomplemented
412C8×C43—22no—
413C8×C43—41no—
414C43⋊C8—22no—
415C43⋊C8—41no—
416C2×#1859—431nomaximal, Sylow
417C22×C43—21no—
418C22×C43—21no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43C2×C4×D411yescharacteristic
423C22×C43C2×#12011yescharacteristic
424C22×C43C2×C22⋊Q811yescharacteristic
425C2×D43—21no—
426C2×D43—21no—
427C2×D43—24no—
428C2×D43—24no—
429C2×D43—22no—
430C2×D43—41no—
431C2×D43—41no—
432C2×D43—48no—
433C2×D43#38512yes—
434C2×D43#38512yes—
435C2×D43#45312yes—
436C2×D43#45612yes—
437C4×C43—24no—
438C4×C43—22no—
439C4×C43—42no—
440C4×C43—41no—
441C4×C43—41no—
442C4×C43—81no—
443C4×C43C22×C4⋊C411yescharacteristic
444C4×C43C2×C4×D411yescharacteristic
445C4×C43C2×C22⋊Q811yescharacteristic
446C4×C43C2×#12311yescharacteristic
447Dic43—24no—
448Dic43—22no—
449Dic43—42no—
450Dic43—41no—
451Dic43—41no—
452Dic43—81no—
453Dic43#38512yes—
454Dic43#38512yes—
455C2×#520—431no—
456C2×#428—431no—
457C22×#104—431no—
458C2×#417—431no—
459C2×#384—431no—
460#1859—431no—
461#1859—431no—
462#1859—431no—
463#1859—431no—
464#1859—431no—
465#1859—431no—
466#1859—431no—
467#1859D4311yescharacteristic, direct product factor
468C2×#343—431no—
469C2×#339—431no—
470C2×C43—21no—
471C2×C43—21no—
472C2×C43—42no—
473C2×C43C2×#38511yescharacteristic
474C2×C43C2×#45311yescharacteristic
475C2×C43C2×#45611yescharacteristic
476D43—22no—
477D43—42no—
478D43#185914yesdirect product factor
479C22×#41—431no—
480C22×M16—431no—
481C22×M16—431no—
482#520—431no—
483#520—431no—
484#520—431no—
485#520—861no—
486#520—862no—
487#520—861no—
488#520—861no—
489#520—861no—
490#520C2×D4311yescharacteristic
491C2×C4×Q8—861no—
492C2×C4×D4—862no—
493C2×C4×D4—861no—
494C2×#117—431no—
495C2×#117—861no—
496C22×C4⋊C4—431no—
497C22×C4⋊C4—431no—
498C22×C4⋊C4—861no—
499C22×C4⋊C4—862no—
500C22×C42—431no—
501#428—431no—
502#428—431no—
503#428—431no—
504#428—861no—
505#428—861no—
506#428C2×D4311yescharacteristic, complemented
507C2×#107—861no—
508C2×#106—861no—
509C2×#104—431no—
510C2×#104—431no—
511C2×#104—431no—
512C2×#104—438no—
513C2×#104C2×D4311yescharacteristic
514#417—431no—
515#417—431no—
516#417—431no—
517#417—861no—
518#417—861no—
519#417C2×D4311yescharacteristic
520C2×#103—861no—
521C2×#102—861no—
522#384—431no—
523#384—431no—
524#384—431no—
525#384—862no—
526#384C2×D4311yescharacteristic, complemented
527#343—431no—
528#343—431no—
529#343—431no—
530#343C2×D4311yescharacteristic, complemented
531#339—431no—
532#339—431no—
533#339—431no—
534#339C2×D4311yescharacteristic, complemented
535C43C2×#185911yescharacteristic, complemented, Sylow
536C2×#41—434no—
537C2×#41—434no—
538C2×#41—431no—
539C2×#41—431no—
540C2×#41—431no—
541C2×#41—861no—
542C2×#41—861no—
543C2×#41—862no—
544C2×#41—862no—
545C2×#41C22×D4311yescharacteristic
546C22×Q8—431no—
547C22×D4—431no—
548C22×D4—861no—
549C23×C4—431no—
550C23×C4—432no—
551C23×C4—861no—
552C23×C4—861no—
553C23×C4—862no—
554C23×C4—861no—
555C2×M16—431no—
556C2×M16—434no—
557C2×M16—431no—
558C2×M16—861no—
559C2×M16—861no—
560C2×M16—862no—
561C2×M16—862no—
562C2×M16—862no—
563C2×M16C22×D4311yescharacteristic
564C2×M16C22×D4311yescharacteristic
565C22×C8—861no—
566C22×C8—861no—
567C4×Q8—21no—
568C4×Q8—861no—
569C4×Q8—862no—
570C4×Q8—861no—
571C4×Q8—862no—
572C4×Q8—861no—
573C4×D4—21no—
574C4×D4—22no—
575C4×D4—861no—
576C4×D4—862no—
577C4×D4—862no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—861no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585C4×D4—861no—
586C4×D4—862no—
587#117—21no—
588#117—431no—
589#117—431no—
590#117—431no—
591#117—861no—
592#117—862no—
593#117—861no—
594#117—862no—
595#117—861no—
596#117—861no—
597#117—861no—
598#117C22×D4311yescharacteristic
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—432no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—862no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—862no—
619C2×C4⋊C4—861no—
620C2×C4⋊C4—861no—
621C2×C4⋊C4—862no—
622C2×C4⋊C4—862no—
623C2×C4⋊C4—862no—
624C2×C4⋊C4—1728no—
625C2×C4⋊C4C22×D4311yescharacteristic
626C2×C4⋊C4C22×D4311yescharacteristic
627C2×C22⋊C4—861no—
628C2×C22⋊C4—862no—
629C2×C42—431no—
630C2×C42—434no—
631C2×C42—861no—
632C2×C42—862no—
633C2×C42—862no—
634C2×C42—861no—
635C2×C42C22×D4311yescharacteristic
636#107—21no—
637#107—861no—
638#107—861no—
639#107—861no—
640#106—21no—
641#106—861no—
642#106—861no—
643#106—861no—
644#104—434no—
645#104—434no—
646#104—434no—
647#104C4×D4314yescomplemented
648#103—21no—
649#103—861no—
650#103—861no—
651#103—861no—
652#102—21no—
653#102—861no—
654#102—861no—
655#102—861no—
656C24—431no—
657C24—861no—
658#41—21no—
659#41—21no—
660#41—434no—
661#41—434no—
662#41—432no—
663#41—432no—
664#41—864no—
665#41—864no—
666#41—864no—
667#41—864no—
668#41—862no—
669#41—862no—
670#41—861no—
671#41—861no—
672#41C2×C4×D4312yes—
673#41Q8×D4312yes—
674C2×Q8—434no—
675C2×Q8—431no—
676C2×Q8—861no—
677C2×Q8—862no—
678C2×Q8D4×D4311yescharacteristic
679C2×D4—21no—
680C2×D4—434no—
681C2×D4—431no—
682C2×D4—861no—
683C2×D4—862no—
684C2×D4—861no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4D4×D4311yescharacteristic
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—431no—
695C22×C4—432no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—861no—
705C22×C4—864no—
706C22×C4—864no—
707C22×C4—864no—
708C22×C4—861no—
709C22×C4—864no—
710C22×C4—864no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—862no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—862no—
721C22×C4—861no—
722C22×C4—3444no—
723C22×C4—1721no—
724C22×C4—1721no—
725C22×C4—1724no—
726C22×C4—1724no—
727C22×C4D4×D4312yes—
728C22×C4C23×D4311yescharacteristic
729M16—21no—
730M16—21no—
731M16—21no—
732M16—432no—
733M16—864no—
734M16—861no—
735M16—861no—
736M16—861no—
737M16—1722no—
738M16C2×C4×D4312yescomplemented
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—864no—
742C2×C8—861no—
743C2×C8—861no—
744C2×C8—1722no—
745C4⋊C4—22no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—44no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—862no—
754C4⋊C4—861no—
755C4⋊C4—862no—
756C4⋊C4—861no—
757C4⋊C4—862no—
758C4⋊C4—862no—
759C4⋊C4—862no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—1724no—
765C4⋊C4—1721no—
766C4⋊C4—1721no—
767C4⋊C4—1724no—
768C4⋊C4—1724no—
769C4⋊C4D4×D4311yescharacteristic
770C4⋊C4D4×D4311yescharacteristic
771C22⋊C4—22no—
772C22⋊C4—21no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—862no—
776C22⋊C4—862no—
777C22⋊C4—862no—
778C22⋊C4—861no—
779C42—22no—
780C42—21no—
781C42—21no—
782C42—432no—
783C42—864no—
784C42—861no—
785C42—861no—
786C42—862no—
787C42—862no—
788C42—862no—
789C42—861no—
790C42—861no—
791C42C2×C4×D4312yescomplemented
792C23—21no—
793C23—431no—
794C23—432no—
795C23—431no—
796C23—432no—
797C23—862no—
798C23—862no—
799C23—864no—
800C23—861no—
801C23—1722no—
802C23—1722no—
803C23C2×D4×D4311yescharacteristic
804Q8—21no—
805Q8—432no—
806Q8—864no—
807Q8—861no—
808Q8C4⋊C4×D4312yescomplemented
809D4—22no—
810D4—22no—
811D4—21no—
812D4—432no—
813D4—864no—
814D4—864no—
815D4—864no—
816D4—862no—
817D4—862no—
818D4—861no—
819D4C4⋊C4×D4312yescomplemented
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—82no—
833C2×C4—432no—
834C2×C4—431no—
835C2×C4—431no—
836C2×C4—432no—
837C2×C4—432no—
838C2×C4—432no—
839C2×C4—432no—
840C2×C4—432no—
841C2×C4—432no—
842C2×C4—432no—
843C2×C4—432no—
844C2×C4—432no—
845C2×C4—864no—
846C2×C4—864no—
847C2×C4—8616no—
848C2×C4—864no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—861no—
853C2×C4—862no—
854C2×C4—862no—
855C2×C4—861no—
856C2×C4—861no—
857C2×C4—862no—
858C2×C4—3442no—
859C2×C4—3442no—
860C2×C4—3442no—
861C2×C4—3442no—
862C2×C4—3442no—
863C2×C4—3442no—
864C2×C4—1722no—
865C2×C4—1724no—
866C2×C4—1722no—
867C2×C4—1722no—
868C2×C4—1721no—
869C2×C4—1722no—
870C2×C4C22×C4×D4311yescharacteristic
871C2×C4C2×D4×D4311yescharacteristic
872C2×C4C2×D4×D4311yescharacteristic
873C2×C4C2×Q8×D4311yescharacteristic
874C2×C4#41×D4311yescharacteristic
875C2×C4#41×D4311yescharacteristic
876C8—22no—
877C8—41no—
878C8—862no—
879C8—1721no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—432no—
886C22—432no—
887C22—432no—
888C22—432no—
889C22—864no—
890C22—864no—
891C22—861no—
892C22—861no—
893C22—862no—
894C22—1728no—
895C22—1721no—
896C22—1721no—
897C22C4×D4×D4311yescharacteristic
898C22#120×D4311yescharacteristic
899C22C22⋊Q8×D4311yescharacteristic
900C4—24no—
901C4—22no—
902C4—42no—
903C4—41no—
904C4—41no—
905C4—81no—
906C4—432no—
907C4—432no—
908C4—864no—
909C4—862no—
910C4—3441no—
911C4—1721no—
912C4—1722no—
913C4—1721no—
914C4C2×C4⋊C4×D4311yescharacteristic
915C4C4×D4×D4311yescharacteristic
916C4C22⋊Q8×D4311yescharacteristic
917C4#123×D4311yescharacteristic
918C2—21no—
919C2—21no—
920C2—42no—
921C2—434no—
922C2—862no—
923C2—1722no—
924C2#385×D4311yescharacteristic
925C2#453×D4311yescharacteristic
926C2#456×D4311yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1859C2
socleC22×C43C2×#120
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1859D43
hypocenterC43C2×#1859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
2. #428×D43C2semidirect
5. #384×D43C2semidirect
6. #19134824C2semidirect
7. #19134823C2semidirect
8. #19134822C2semidirect
9. #19134821C2semidirect
10. #19134820C2semidirect
11. #19134819C2semidirect
12. #19134818C2semidirect
13. #343×D43C2semidirect
14. #339×D43C2semidirect
15. C43×#1859C2semidirect
37. #14582942C22semidirect
38. #14582941C22semidirect
40. #14582939C22semidirect
47. #104×D43C4semidirect
55. #14582769C22semidirect
57. #14582768C22semidirect
58. #14582768C22semidirect
59. #14582668C22semidirect
60. #14582667C22semidirect
61. #14582667C22semidirect
62. #14582660C22semidirect
63. #14582659C22semidirect
64. #14582658C22semidirect
66. C43×#428C22semidirect
69. C43×#384C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
97. M16×D43C2×C4semidirect
158. C42×D43C2×C4semidirect
165. #13063253C2×C4semidirect
166. #13063252C2×C4semidirect
167. #13063251C2×C4semidirect
189. #104×C43C2×C4semidirect
217. #10621902C4⋊C4semidirect
219. Q8×D43C4⋊C4semidirect
223. #10621900C4⋊C4semidirect
227. D4×D43C4⋊C4semidirect
268. M16×C43C22×C4semidirect
284. C42×C43C22×C4semidirect
317. C4×Dic43C22×C4semidirect
321. #10621877C22×C4semidirect
341. Q8×C43C2×C4⋊C4semidirect
345. D4×C43C2×C4⋊C4semidirect
387. D172C2×C4⋊C4semidirect
411. Dic86C2×C4⋊C4semidirect
467. #1859D43direct (N × H)
478. D43#1859direct (N × H)
506. #428C2×D43semidirect
526. #384C2×D43semidirect
530. #343C2×D43semidirect
534. #339C2×D43semidirect
535. C43C2×#1859semidirect
647. #104C4×D43semidirect
738. M16C2×C4×D43semidirect
791. C42C2×C4×D43semidirect
808. Q8C4⋊C4×D43semidirect
819. D4C4⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
#520×D432
#428×D432
C2×#104×D432
#417×D432
#384×D432
#191348242
#191348232
#191348222
#191348212
#191348202
#191348192
#191348182
#343×D432
#339×D432
C43×#18592
C2×#185943