Finite Group Databasebeta

← D43×#1860 #25097455

Subgroups — D43×#1860 #25097455

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 918 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#382×D43C211yesmaximal, characteristic, complemented
6#19134831C211yesmaximal, characteristic, complemented
7#19134830C211yesmaximal, characteristic, complemented
8#19134829C211yesmaximal, characteristic, complemented
9#19134828C211yesmaximal, characteristic, complemented
10#19134827C211yesmaximal, characteristic, complemented
11#19134826C211yesmaximal, characteristic, complemented
12#19134825C211yesmaximal, characteristic, complemented
13#343×D43C211yesmaximal, characteristic, complemented
14#339×D43C211yesmaximal, characteristic, complemented
15C43×#1860C211yesmaximal, 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×D43C2211yescharacteristic
34C2×C4⋊C4×D43C2211yescharacteristic
35C2×C42×D43C2211yescharacteristic
36#14582942C2211yescharacteristic, complemented
37#14582941C2211yescharacteristic, complemented
38#14582940—21no—
39#14582939C2211yescharacteristic, complemented
40#14582938—21no—
41#107×D43—21no—
42#106×D43—21no—
43C2×#13063253C2211yescharacteristic
44C2×#13063252C2211yescharacteristic
45C2×#13063251C2211yescharacteristic
46#104×D43C418yescomplemented
47#14582901C2211yescharacteristic
48#14582900C2211yescharacteristic
49#14582899—21no—
50#14582898C2211yescharacteristic
51#14582897—21no—
52#103×D43—21no—
53#102×D43—21no—
54#14582765C2211yescharacteristic, complemented
55#14582764C2211yescharacteristic, complemented
56#14582764C2211yescharacteristic, complemented
57#14582763—22no—
58#95×D43—22no—
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×#382C2211yescharacteristic, 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⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—22no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4D412yes—
133C4⋊C4×D43—22no—
134C4⋊C4×D43—22no—
135C4⋊C4×D43—21no—
136C4⋊C4×D43—21no—
137C4⋊C4×D43—21no—
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×D43D411yescharacteristic
146C4⋊C4×D43D411yescharacteristic
147C22⋊C4×D43—22no—
148C22⋊C4×D43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43C2311yescharacteristic
151C42×D43—22no—
152C42×D43—21no—
153C42×D43—22no—
154C42×D43C2×C414yescomplemented
155#13063259—21no—
156#13063258—21no—
157#13063258—21no—
158#13063257—21no—
159#13063256—21no—
160#13063256—21no—
161#13063253C2×C414yescomplemented
162#13063252C2×C414yescomplemented
163#13063251C2×C414yescomplemented
164#13063250—21no—
165#13063249—21no—
166#13063248—21no—
167#13063247—21no—
168#13063246—21no—
169#13063245—21no—
170C43⋊#95—22no—
171C43⋊#95—22no—
172C43⋊#95—22no—
173C2×#41×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C2×M16×C43C2311yescharacteristic
176C4×Q8×C43—21no—
177C4×D4×C43—21no—
178C4×D4×C43—22no—
179#117×C43—21no—
180#117×C43C2311yescharacteristic
181C2×C4⋊C4×C43—21no—
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C42×C43C2311yescharacteristic
185#107×C43—21no—
186#106×C43—21no—
187#104×C43C2×C414yescomplemented
188#103×C43—21no—
189#102×C43—21no—
190#95×C43—22no—
191C23×D43—21no—
192C23×D43C2×D411yescharacteristic
193#41×C43—21no—
194#41×C43—21no—
195#41×C43C22×C412yes—
196#41×C43C2×Q812yes—
197C2×Q8×C43C2×D411yescharacteristic
198C2×D4×C43—21no—
199C2×D4×C43C2×D411yescharacteristic
200C22×C4×C43—21no—
201C22×C4×C43—22no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—21no—
207C2×C22⋊D43—21no—
208C2×C22⋊D43—21no—
209C22×Dic43—21no—
210C22×Dic43—22no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43C2×D412yes—
214C22×Dic43C2×D411yescharacteristic
215#10621902—22no—
216#10621902C4⋊C414yes—
217Q8×D43—22no—
218Q8×D43C4⋊C414yes—
219#10621900—24no—
220#10621900—24no—
221#10621900—22no—
222#10621900C4⋊C414yes—
223D4×D43—22no—
224D4×D43—24no—
225D4×D43—24no—
226D4×D43C4⋊C414yes—
227#10621898—21no—
228#10621898—21no—
229#10621898—24no—
230#10621898—24no—
231#10621898C22×C412yes—
232#10621898C2×Q812yes—
233C2×D172—21no—
234C2×D172C2×D411yescharacteristic
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—24no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—22no—
245C2×C4×D43—21no—
246C2×C4×D43—22no—
247C2×C4×D43—42no—
248C2×C4×D43—42no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—41no—
252C2×C4×D43—41no—
253C2×C4×D43—84no—
254C2×C4×D43C22×C412yes—
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×C4×D43C2×Q812yes—
260C2×C4×D43#4112yes—
261C2×C4×D43#4112yes—
262C2×Dic86—21no—
263C2×Dic86C2×D411yescharacteristic
264M16×C43—21no—
265M16×C43—21no—
266M16×C43—21no—
267M16×C43C22×C412yescomplemented
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C4⋊C4×C43—22no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43C2×D411yescharacteristic
276C4⋊C4×C43C2×D411yescharacteristic
277C22⋊C4×C43—22no—
278C22⋊C4×C43—21no—
279C42×C43—22no—
280C42×C43—21no—
281C42×C43—21no—
282C42×C43C22×C412yescomplemented
283C22⋊Dic43—22no—
284C22⋊Dic43—21no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289C4⋊Dic43—22no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43C2×D411yescharacteristic
295C4⋊Dic43C2×D411yescharacteristic
296Dic43⋊C4—22no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—21no—
300Dic43⋊C4—22no—
301Dic43⋊C4—21no—
302Dic43⋊C4—41no—
303Dic43⋊C4—41no—
304C4×Dic43—22no—
305C4×Dic43—22no—
306C4×Dic43—22no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—24no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43C22×C412yescomplemented
313#10621877—21no—
314#10621877—21no—
315#10621877—21no—
316#10621877C22×C412yescomplemented
317C2×C43⋊C8—21no—
318C2×C43⋊C8—21no—
319#10621872—24no—
320#10621872—42no—
321C8×D43—24no—
322C8×D43—42no—
323C23×C43—21no—
324C23×C43C22×D411yescharacteristic
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—21no—
328C22×D43—24no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43C4×D412yes—
332C22×D43#12011yescharacteristic
333C22×D43#12011yescharacteristic
334C22×D43C22⋊Q812yes—
335Q8×C43—21no—
336Q8×C43C2×C4⋊C412yes—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—21no—
340D4×C43C2×C4⋊C412yes—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—21no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43—41no—
353C2×C4×C43—82no—
354C2×C4×C43C23×C411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×Q811yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C22⋊D43—22no—
361C22⋊D43—22no—
362C22⋊D43—24no—
363C22⋊D43—24no—
364C2×Dic43—21no—
365C2×Dic43—24no—
366C2×Dic43—22no—
367C2×Dic43—21no—
368C2×Dic43—22no—
369C2×Dic43—21no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—41no—
375C2×Dic43—82no—
376C2×Dic43C4×D412yes—
377C2×Dic43#12011yescharacteristic
378C2×Dic43#12011yescharacteristic
379C2×Dic43C22⋊Q812yes—
380D172—24no—
381D172—21no—
382D172C2×C4⋊C412yes—
383C4×D43—24no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—24no—
387C4×D43—48no—
388C4×D43—42no—
389C4×D43—44no—
390C4×D43—42no—
391C4×D43—82no—
392C4×D43—82no—
393C4×D43—82no—
394C4×D43—82no—
395C4×D43—82no—
396C4×D43C2×C4⋊C412yes—
397C4×D43C2×C4⋊C412yes—
398C4×D43C4×D412yes—
399C4×D43C4×D412yes—
400C4×D43C22⋊Q812yes—
401C4×D43C22⋊Q812yes—
402C4×D43#12312yes—
403C4×D43#12312yes—
404Dic86—21no—
405Dic86—24no—
406Dic86C2×C4⋊C412yes—
407C8×C43—22no—
408C8×C43—41no—
409C43⋊C8—22no—
410C43⋊C8—41no—
411C2×#1860—431nomaximal, Sylow
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—22no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43C2×C4×D411yescharacteristic
418C22×C43C2×#12011yescharacteristic
419C22×C43C2×C22⋊Q811yescharacteristic
420C2×D43—21no—
421C2×D43—21no—
422C2×D43—24no—
423C2×D43—24no—
424C2×D43—22no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43—48no—
428C2×D43#38512yes—
429C2×D43#38512yes—
430C2×D43#45412yes—
431C2×D43#45512yes—
432C4×C43—22no—
433C4×C43—42no—
434C4×C43—42no—
435C4×C43—41no—
436C4×C43—41no—
437C4×C43—81no—
438C4×C43C22×C4⋊C411yescharacteristic
439C4×C43C2×C4×D411yescharacteristic
440C4×C43C2×C22⋊Q811yescharacteristic
441C4×C43C2×#12311yescharacteristic
442Dic43—22no—
443Dic43—42no—
444Dic43—42no—
445Dic43—41no—
446Dic43—41no—
447Dic43—81no—
448Dic43#38512yes—
449Dic43#38512yes—
450C2×#520—431no—
451C2×#428—431no—
452C22×#104—431no—
453C2×#417—431no—
454C2×#382—431no—
455#1860—431no—
456#1860—431no—
457#1860—431no—
458#1860—431no—
459#1860—431no—
460#1860—431no—
461#1860—431no—
462#1860D4311yescharacteristic, direct product factor
463C2×#343—431no—
464C2×#339—431no—
465C2×C43—21no—
466C2×C43—21no—
467C2×C43—42no—
468C2×C43C2×#38511yescharacteristic
469C2×C43C2×#45511yescharacteristic
470C2×C43C2×#45411yescharacteristic
471D43—22no—
472D43—42no—
473D43#186014yesdirect product factor
474C22×#41—431no—
475C22×M16—431no—
476C22×M16—431no—
477#520—431no—
478#520—431no—
479#520—431no—
480#520—861no—
481#520—862no—
482#520—861no—
483#520—861no—
484#520—861no—
485#520C2×D4311yescharacteristic
486C2×C4×Q8—861no—
487C2×C4×D4—862no—
488C2×C4×D4—861no—
489C2×#117—431no—
490C2×#117—861no—
491C22×C4⋊C4—431no—
492C22×C4⋊C4—431no—
493C22×C4⋊C4—861no—
494C22×C42—431no—
495#428—431no—
496#428—431no—
497#428—431no—
498#428—861no—
499#428—861no—
500#428C2×D4311yescharacteristic, complemented
501C2×#107—861no—
502C2×#106—861no—
503C2×#104—431no—
504C2×#104—431no—
505C2×#104—431no—
506C2×#104—438no—
507C2×#104C2×D4311yescharacteristic
508#417—431no—
509#417—431no—
510#417—431no—
511#417—861no—
512#417—861no—
513#417C2×D4311yescharacteristic
514C2×#103—861no—
515C2×#102—861no—
516#382—431no—
517#382—431no—
518#382—431no—
519#382—862no—
520#382C2×D4311yescharacteristic, complemented
521C2×#95—862no—
522#343—431no—
523#343—431no—
524#343—431no—
525#343C2×D4311yescharacteristic, complemented
526#339—431no—
527#339—431no—
528#339—431no—
529#339C2×D4311yescharacteristic, complemented
530C43C2×#186011yescharacteristic, complemented, Sylow
531C2×#41—434no—
532C2×#41—434no—
533C2×#41—431no—
534C2×#41—431no—
535C2×#41—431no—
536C2×#41—861no—
537C2×#41—861no—
538C2×#41—862no—
539C2×#41—862no—
540C2×#41C22×D4311yescharacteristic
541C22×Q8—431no—
542C22×D4—431no—
543C22×D4—861no—
544C23×C4—431no—
545C23×C4—432no—
546C23×C4—861no—
547C23×C4—862no—
548C23×C4—861no—
549C23×C4—861no—
550C2×M16—431no—
551C2×M16—434no—
552C2×M16—431no—
553C2×M16—861no—
554C2×M16—861no—
555C2×M16—862no—
556C2×M16—862no—
557C2×M16—862no—
558C2×M16C22×D4311yescharacteristic
559C2×M16C22×D4311yescharacteristic
560C22×C8—861no—
561C22×C8—861no—
562C4×Q8—21no—
563C4×Q8—861no—
564C4×Q8—862no—
565C4×Q8—861no—
566C4×Q8—862no—
567C4×Q8—861no—
568C4×D4—21no—
569C4×D4—22no—
570C4×D4—861no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574C4×D4—862no—
575C4×D4—861no—
576C4×D4—862no—
577C4×D4—862no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—861no—
581C4×D4—862no—
582#117—21no—
583#117—431no—
584#117—431no—
585#117—431no—
586#117—861no—
587#117—862no—
588#117—861no—
589#117—862no—
590#117—861no—
591#117—861no—
592#117—861no—
593#117C22×D4311yescharacteristic
594C2×C4⋊C4—21no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—432no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4C22×D4311yescharacteristic
616C2×C4⋊C4C22×D4311yescharacteristic
617C2×C22⋊C4—861no—
618C2×C22⋊C4—862no—
619C2×C42—431no—
620C2×C42—434no—
621C2×C42—861no—
622C2×C42—862no—
623C2×C42—862no—
624C2×C42—861no—
625C2×C42C22×D4311yescharacteristic
626#107—21no—
627#107—861no—
628#107—861no—
629#107—861no—
630#106—21no—
631#106—861no—
632#106—861no—
633#106—861no—
634#104—434no—
635#104—434no—
636#104—434no—
637#104C4×D4314yescomplemented
638#103—21no—
639#103—861no—
640#103—861no—
641#103—861no—
642#102—21no—
643#102—861no—
644#102—861no—
645#102—861no—
646#95—22no—
647#95—862no—
648#95—862no—
649#95—862no—
650C24—431no—
651C24—861no—
652#41—21no—
653#41—21no—
654#41—434no—
655#41—434no—
656#41—432no—
657#41—432no—
658#41—864no—
659#41—864no—
660#41—864no—
661#41—864no—
662#41—862no—
663#41—862no—
664#41—861no—
665#41—861no—
666#41C2×C4×D4312yes—
667#41Q8×D4312yes—
668C2×Q8—434no—
669C2×Q8—431no—
670C2×Q8—861no—
671C2×Q8—862no—
672C2×Q8D4×D4311yescharacteristic
673C2×D4—21no—
674C2×D4—434no—
675C2×D4—431no—
676C2×D4—861no—
677C2×D4—862no—
678C2×D4—861no—
679C2×D4—864no—
680C2×D4—864no—
681C2×D4—861no—
682C2×D4—861no—
683C2×D4D4×D4311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—431no—
689C22×C4—432no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—432no—
698C22×C4—861no—
699C22×C4—864no—
700C22×C4—864no—
701C22×C4—861no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—862no—
705C22×C4—864no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—862no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—862no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—3444no—
715C22×C4—1721no—
716C22×C4—1721no—
717C22×C4—1724no—
718C22×C4—1724no—
719C22×C4—1722no—
720C22×C4—1722no—
721C22×C4D4×D4312yes—
722C22×C4C23×D4311yescharacteristic
723M16—21no—
724M16—21no—
725M16—21no—
726M16—432no—
727M16—864no—
728M16—861no—
729M16—861no—
730M16—861no—
731M16—1722no—
732M16C2×C4×D4312yescomplemented
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—864no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—1722no—
739C4⋊C4—22no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—862no—
747C4⋊C4—861no—
748C4⋊C4—862no—
749C4⋊C4—861no—
750C4⋊C4—862no—
751C4⋊C4—862no—
752C4⋊C4—862no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—1721no—
758C4⋊C4—1721no—
759C4⋊C4D4×D4311yescharacteristic
760C4⋊C4D4×D4311yescharacteristic
761C22⋊C4—22no—
762C22⋊C4—21no—
763C22⋊C4—861no—
764C22⋊C4—861no—
765C22⋊C4—862no—
766C22⋊C4—862no—
767C22⋊C4—862no—
768C22⋊C4—861no—
769C42—22no—
770C42—21no—
771C42—21no—
772C42—432no—
773C42—864no—
774C42—861no—
775C42—861no—
776C42—862no—
777C42—862no—
778C42—862no—
779C42—861no—
780C42—861no—
781C42C2×C4×D4312yescomplemented
782C23—21no—
783C23—431no—
784C23—432no—
785C23—431no—
786C23—432no—
787C23—862no—
788C23—862no—
789C23—864no—
790C23—861no—
791C23—1722no—
792C23—1722no—
793C23C2×D4×D4311yescharacteristic
794Q8—21no—
795Q8—432no—
796Q8—864no—
797Q8—861no—
798Q8C4⋊C4×D4312yes—
799D4—22no—
800D4—22no—
801D4—21no—
802D4—432no—
803D4—864no—
804D4—864no—
805D4—864no—
806D4—862no—
807D4—862no—
808D4—861no—
809D4C4⋊C4×D4312yes—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—82no—
823C2×C4—432no—
824C2×C4—431no—
825C2×C4—431no—
826C2×C4—432no—
827C2×C4—432no—
828C2×C4—432no—
829C2×C4—432no—
830C2×C4—432no—
831C2×C4—432no—
832C2×C4—432no—
833C2×C4—432no—
834C2×C4—432no—
835C2×C4—864no—
836C2×C4—864no—
837C2×C4—864no—
838C2×C4—861no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—861no—
843C2×C4—861no—
844C2×C4—862no—
845C2×C4—3442no—
846C2×C4—3442no—
847C2×C4—3442no—
848C2×C4—3442no—
849C2×C4—3442no—
850C2×C4—3442no—
851C2×C4—1722no—
852C2×C4—1724no—
853C2×C4—1722no—
854C2×C4—1728no—
855C2×C4—1722no—
856C2×C4—1721no—
857C2×C4—1721no—
858C2×C4—1721no—
859C2×C4—1722no—
860C2×C4C22×C4×D4311yescharacteristic
861C2×C4C2×D4×D4311yescharacteristic
862C2×C4C2×D4×D4311yescharacteristic
863C2×C4C2×Q8×D4311yescharacteristic
864C2×C4#41×D4311yescharacteristic
865C2×C4#41×D4311yescharacteristic
866C8—22no—
867C8—41no—
868C8—862no—
869C8—1721no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—41no—
874C22—41no—
875C22—432no—
876C22—432no—
877C22—432no—
878C22—432no—
879C22—864no—
880C22—864no—
881C22—861no—
882C22—861no—
883C22—862no—
884C22—1728no—
885C22—1721no—
886C22—1721no—
887C22C4×D4×D4311yescharacteristic
888C22#120×D4311yescharacteristic
889C22C22⋊Q8×D4311yescharacteristic
890C4—22no—
891C4—42no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—432no—
897C4—432no—
898C4—862no—
899C4—3441no—
900C4—1722no—
901C4—1721no—
902C4—1722no—
903C4—1721no—
904C4C2×C4⋊C4×D4311yescharacteristic
905C4C4×D4×D4311yescharacteristic
906C4C22⋊Q8×D4311yescharacteristic
907C4#123×D4311yescharacteristic
908C2—21no—
909C2—21no—
910C2—42no—
911C2—434no—
912C2—862no—
913C2—1722no—
914C2#385×D4311yescharacteristic
915C2#455×D4311yescharacteristic
916C2#454×D4311yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1860C2
socleC22×C43C2×#120
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1860D43
hypocenterC43C2×#1860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1860

Complements

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

NH ≅ G/Ntype
2. #428×D43C2semidirect
5. #382×D43C2semidirect
6. #19134831C2semidirect
7. #19134830C2semidirect
8. #19134829C2semidirect
9. #19134828C2semidirect
10. #19134827C2semidirect
11. #19134826C2semidirect
12. #19134825C2semidirect
13. #343×D43C2semidirect
14. #339×D43C2semidirect
15. C43×#1860C2semidirect
36. #14582942C22semidirect
37. #14582941C22semidirect
39. #14582939C22semidirect
46. #104×D43C4semidirect
54. #14582765C22semidirect
55. #14582764C22semidirect
56. #14582764C22semidirect
59. #14582668C22semidirect
60. #14582667C22semidirect
61. #14582667C22semidirect
62. #14582660C22semidirect
63. #14582659C22semidirect
64. #14582658C22semidirect
66. C43×#428C22semidirect
69. C43×#382C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
97. M16×D43C2×C4semidirect
154. C42×D43C2×C4semidirect
161. #13063253C2×C4semidirect
162. #13063252C2×C4semidirect
163. #13063251C2×C4semidirect
187. #104×C43C2×C4semidirect
267. M16×C43C22×C4semidirect
282. C42×C43C22×C4semidirect
312. C4×Dic43C22×C4semidirect
316. #10621877C22×C4semidirect
462. #1860D43direct (N × H)
473. D43#1860direct (N × H)
500. #428C2×D43semidirect
520. #382C2×D43semidirect
525. #343C2×D43semidirect
529. #339C2×D43semidirect
530. C43C2×#1860semidirect
637. #104C4×D43semidirect
732. M16C2×C4×D43semidirect
781. C42C2×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
#382×D432
#191348312
#191348302
#191348292
#191348282
#191348272
#191348262
#191348252
#343×D432
#339×D432
C43×#18602
C2×#186043