Finite Group Databasebeta

← #25097477

Subgroups — #25097477

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#520×D43C211yesmaximal, characteristic
2#19143182C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic
4#19143111C211yesmaximal, characteristic
5#19137220C211yesmaximal, characteristic, complemented
6#19134827C211yesmaximal, characteristic, complemented
7#19134826C211yesmaximal, characteristic, complemented
8#19134825C211yesmaximal, characteristic, complemented
9#19134824C211yesmaximal, characteristic, complemented
10#19134823C211yesmaximal, characteristic, complemented
11#19134822C211yesmaximal, characteristic, complemented
12#19134821C211yesmaximal, characteristic, complemented
13#343×D43C211yesmaximal, characteristic, complemented
14#19134303C211yesmaximal, 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—
30C2×#13063283C2211yescharacteristic
31C2×#13063282C2211yescharacteristic
32#117×D43—21no—
33#117×D43C2211yescharacteristic
34C2×C4⋊C4×D43—21no—
35C2×C4⋊C4×D43C2211yescharacteristic
36#14582942C2211yescharacteristic, complemented
37#14582941C2211yescharacteristic, complemented
38#14582940—21no—
39#14582939C2211yescharacteristic, complemented
40#14582938—21no—
41#14582936—21no—
42#14582934—21no—
43#14582914C418yescomplemented
44C2×#13063253C2211yescharacteristic
45C2×#13063252C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47#14582906—21no—
48#14582902—21no—
49#14582901C2211yescharacteristic
50#14582900C2211yescharacteristic
51#14582898C2211yescharacteristic
52#14582894—21no—
53#14582892—21no—
54#14582796—22no—
55#14582773—22no—
56#14582769C2211yescharacteristic, complemented
57#14582768C2211yescharacteristic, complemented
58#14582764C2211yescharacteristic, 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×#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—22no—
86C22×C4×D43D412yes—
87C22×C4×D43C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621877C2311yescharacteristic
90C2×#10621872—21no—
91C2×#10621872—21no—
92M16×D43—22no—
93M16×D43—22no—
94M16×D43—22no—
95M16×D43C2×C414yescomplemented
96C2×C8×D43—21no—
97C2×C8×D43—21no—
98Q8×Dic43—21no—
99C4×Dic86—22no—
100C4×Dic86—21no—
101#13063290—22no—
102#13063290—21no—
103C4×D172—22no—
104C4×D172—21no—
105D4×Dic43—21no—
106D4×Dic43—22no—
107#13063287—22no—
108#13063287—21no—
109C4×C22⋊D43—22no—
110C4×C22⋊D43—22no—
111C4×C22⋊D43—22no—
112(C22⋊D43)⋊C4—22no—
113(C22⋊D43)⋊C4—22no—
114(C22⋊D43)⋊C4—22no—
115#13063284—21no—
116#13063284C2311yescharacteristic
117#13063283—21no—
118#13063283—21no—
119#13063283—21no—
120#13063283—21no—
121#13063283—21no—
122#13063283—21no—
123#13063283D411yescharacteristic
124#13063283D411yescharacteristic
125#13063282—22no—
126#13063282—21no—
127#13063282—22no—
128#13063282C2×C414yescomplemented
129#13063281—22no—
130#13063281—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—22no—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—22no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—22no—
138C2×Dic43⋊C4D412yes—
139C4⋊C4×D43—22no—
140C4⋊C4×D43—22no—
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×D43D411yescharacteristic
148C4⋊C4×D43D411yescharacteristic
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C22⋊C4×D43—22no—
152C22⋊C4×D43—21no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43C2311yescharacteristic
155C42×D43—22no—
156C42×D43—21no—
157#13063259—21no—
158#13063258—21no—
159#13063258—21no—
160#13063257—21no—
161#13063256—21no—
162#13063256—21no—
163#13063253C2×C414yescomplemented
164#13063252C2×C414yescomplemented
165#13063251C2×C414yescomplemented
166#13063250—21no—
167#13063249—21no—
168#13063248—21no—
169#13063247—21no—
170#13063246—21no—
171#13063245—21no—
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⋊C414yescomplemented
217Q8×D43—22no—
218Q8×D43C4⋊C414yescomplemented
219#10621900—24no—
220#10621900—24no—
221#10621900—22no—
222#10621900C4⋊C414yescomplemented
223D4×D43—22no—
224D4×D43—24no—
225D4×D43—24no—
226D4×D43C4⋊C414yescomplemented
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—21no—
242C2×C4×D43—21no—
243C2×C4×D43—22no—
244C2×C4×D43—21no—
245C2×C4×D43—22no—
246C2×C4×D43—84no—
247C2×C4×D43—82no—
248C2×C4×D43C22×C412yes—
249C2×C4×D43C2×D411yescharacteristic
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×C4×D43C2×Q812yes—
254C2×C4×D43#4112yes—
255C2×C4×D43#4112yes—
256C2×Dic86—21no—
257C2×Dic86C2×D411yescharacteristic
258M16×C43—21no—
259M16×C43—21no—
260M16×C43—21no—
261M16×C43C22×C412yescomplemented
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C4⋊C4×C43—22no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C2×D411yescharacteristic
270C4⋊C4×C43C2×D411yescharacteristic
271C22⋊C4×C43—22no—
272C22⋊C4×C43—21no—
273C42×C43—22no—
274C42×C43—21no—
275C42×C43—21no—
276C42×C43C22×C412yescomplemented
277C22⋊Dic43—22no—
278C22⋊Dic43—21no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—41no—
285(C2×D43)⋊C4—41no—
286C4⋊Dic43—22no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—82no—
292C4⋊Dic43C2×D411yescharacteristic
293C4⋊Dic43C2×D411yescharacteristic
294Dic43⋊C4—22no—
295Dic43⋊C4—22no—
296Dic43⋊C4—24no—
297Dic43⋊C4—22no—
298Dic43⋊C4—21no—
299Dic43⋊C4—22no—
300Dic43⋊C4—21no—
301Dic43⋊C4—82no—
302C4×Dic43—22no—
303C4×Dic43—22no—
304C4×Dic43—22no—
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—41no—
310C4×Dic43—41no—
311C4×Dic43C22×C412yescomplemented
312#10621877—21no—
313#10621877—21no—
314#10621877—21no—
315#10621877C22×C412yescomplemented
316C2×C43⋊C8—21no—
317C2×C43⋊C8—21no—
318#10621872—24no—
319#10621872—42no—
320C8×D43—24no—
321C8×D43—42no—
322C23×C43—21no—
323C23×C43C22×D411yescharacteristic
324C22×D43—21no—
325C22×D43—24no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43C4×D412yes—
331C22×D43#12011yescharacteristic
332C22×D43#12011yescharacteristic
333C22×D43C22⋊Q812yes—
334Q8×C43—21no—
335Q8×C43C2×C4⋊C412yes—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—21no—
339D4×C43C2×C4⋊C412yes—
340C2×C4×C43—21no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—21no—
345C2×C4×C43—22no—
346C2×C4×C43—21no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—42no—
350C2×C4×C43—42no—
351C2×C4×C43—41no—
352C2×C4×C43—82no—
353C2×C4×C43C23×C411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×Q811yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C22⋊D43—22no—
360C22⋊D43—22no—
361C22⋊D43—24no—
362C22⋊D43—24no—
363C2×Dic43—21no—
364C2×Dic43—24no—
365C2×Dic43—22no—
366C2×Dic43—21no—
367C2×Dic43—22no—
368C2×Dic43—21no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—41no—
374C2×Dic43—82no—
375C2×Dic43C4×D412yes—
376C2×Dic43#12011yescharacteristic
377C2×Dic43#12011yescharacteristic
378C2×Dic43C22⋊Q812yes—
379D172—24no—
380D172—21no—
381D172C2×C4⋊C412yes—
382C4×D43—24no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—24no—
386C4×D43—42no—
387C4×D43—44no—
388C4×D43—42no—
389C4×D43—82no—
390C4×D43—82no—
391C4×D43—82no—
392C4×D43C2×C4⋊C412yes—
393C4×D43C2×C4⋊C412yes—
394C4×D43C4×D412yes—
395C4×D43C4×D412yes—
396C4×D43C22⋊Q812yes—
397C4×D43C22⋊Q812yes—
398C4×D43#12312yes—
399C4×D43#12312yes—
400Dic86—21no—
401Dic86—24no—
402Dic86C2×C4⋊C412yes—
403C8×C43—22no—
404C8×C43—41no—
405C43⋊C8—22no—
406C43⋊C8—41no—
407#20864—431nomaximal, Sylow
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—22no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43C2×C4×D411yescharacteristic
414C22×C43C2×#12011yescharacteristic
415C22×C43C2×C22⋊Q811yescharacteristic
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—21no—
419C2×D43—21no—
420C2×D43—22no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—48no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43#38512yes—
427C2×D43#38512yes—
428C4×C43—22no—
429C4×C43—42no—
430C4×C43—42no—
431C4×C43—41no—
432C4×C43—41no—
433C4×C43—81no—
434C4×C43C22×C4⋊C411yescharacteristic
435C4×C43C2×C4×D411yescharacteristic
436C4×C43C2×C22⋊Q811yescharacteristic
437C4×C43C2×#12311yescharacteristic
438Dic43—22no—
439Dic43—42no—
440Dic43—42no—
441Dic43—41no—
442Dic43—41no—
443Dic43—81no—
444Dic43#38512yes—
445Dic43#38512yes—
446C2×#520—431no—
447#2911—431no—
448C2×#421—431no—
449#2896—431no—
450#2317—431no—
451#1860—431no—
452#1860—431no—
453#1860—431no—
454#1860D4311yescharacteristic, complemented
455#1859—431no—
456#1859—431no—
457#1859—431no—
458#1859—431no—
459C2×#343—431no—
460#1733—431no—
461C2×C43—21no—
462C2×C43—21no—
463C2×C43—42no—
464C2×C43C2×#38511yescharacteristic
465C2×C43#301911yescharacteristic
466C2×C43#302011yescharacteristic
467D43—22no—
468D43—22no—
469D43—42no—
470C22×#41—431no—
471C22×M16—431no—
472C22×M16—431no—
473#520—431no—
474#520—431no—
475#520—431no—
476#520—861no—
477#520—862no—
478#520—861no—
479#520—861no—
480#520—861no—
481#520C2×D4311yescharacteristic
482C2×C4×Q8—861no—
483C2×C4×D4—862no—
484C2×C4×D4—861no—
485C2×#117—431no—
486C2×#117—431no—
487C2×#117—431no—
488C2×#117—861no—
489C22×C4⋊C4—431no—
490C22×C4⋊C4—861no—
491#428—431no—
492#428—431no—
493#428—431no—
494#428—861no—
495#428—861no—
496#428C2×D4311yescharacteristic, complemented
497#427—861no—
498#427—861no—
499#421—438no—
500C2×#104—431no—
501C2×#104—431no—
502C2×#104—431no—
503C2×#104C2×D4311yescharacteristic
504#419—861no—
505#418—861no—
506#417—431no—
507#417—431no—
508#417—431no—
509#417C2×D4311yescharacteristic
510#416—861no—
511#416—861no—
512#389—862no—
513#385—862no—
514#384—431no—
515#384—431no—
516#382—431no—
517#382C2×D4311yescharacteristic, complemented
518#343—431no—
519#343—431no—
520#343—431no—
521#343C2×D4311yescharacteristic, complemented
522#339—431no—
523#339—431no—
524#339—431no—
525#339C2×D4311yescharacteristic, complemented
526C43#2086411yescharacteristic, complemented, Sylow
527C2×#41—434no—
528C2×#41—434no—
529C2×#41—431no—
530C2×#41—431no—
531C2×#41—431no—
532C2×#41—861no—
533C2×#41—861no—
534C2×#41—862no—
535C2×#41—862no—
536C2×#41C22×D4311yescharacteristic
537C22×Q8—431no—
538C22×D4—431no—
539C22×D4—861no—
540C23×C4—431no—
541C23×C4—432no—
542C23×C4—861no—
543C23×C4—862no—
544C2×M16—431no—
545C2×M16—434no—
546C2×M16—431no—
547C2×M16—861no—
548C2×M16—861no—
549C2×M16—862no—
550C2×M16—862no—
551C2×M16—862no—
552C2×M16C22×D4311yescharacteristic
553C2×M16C22×D4311yescharacteristic
554C22×C8—861no—
555C22×C8—861no—
556C4×Q8—21no—
557C4×Q8—861no—
558C4×Q8—862no—
559C4×Q8—861no—
560C4×Q8—862no—
561C4×Q8—861no—
562C4×D4—21no—
563C4×D4—22no—
564C4×D4—861no—
565C4×D4—862no—
566C4×D4—862no—
567C4×D4—862no—
568C4×D4—862no—
569C4×D4—861no—
570C4×D4—862no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574C4×D4—861no—
575C4×D4—862no—
576#117—21no—
577#117—434no—
578#117—431no—
579#117—431no—
580#117—431no—
581#117—861no—
582#117—862no—
583#117—862no—
584#117—861no—
585#117—862no—
586#117—861no—
587#117—861no—
588#117—861no—
589#117—861no—
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—862no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—862no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4C22×D4311yescharacteristic
614C2×C4⋊C4C22×D4311yescharacteristic
615C2×C22⋊C4—861no—
616C2×C22⋊C4—862no—
617C2×C22⋊C4—861no—
618C2×C22⋊C4—861no—
619C2×C42—431no—
620C2×C42—861no—
621C2×C42—862no—
622C2×C42—861no—
623C2×C42C22×D4311yescharacteristic
624#107—21no—
625#107—861no—
626#107—861no—
627#107—861no—
628#106—21no—
629#106—861no—
630#106—861no—
631#106—861no—
632#104—434no—
633#104—434no—
634#104—434no—
635#104C4×D4314yescomplemented
636#103—21no—
637#103—861no—
638#103—861no—
639#103—861no—
640#102—21no—
641#102—861no—
642#102—861no—
643#102—861no—
644#95—22no—
645#95—862no—
646C24—431no—
647C24—861no—
648#41—21no—
649#41—21no—
650#41—434no—
651#41—434no—
652#41—432no—
653#41—432no—
654#41—864no—
655#41—864no—
656#41—864no—
657#41—864no—
658#41—862no—
659#41—862no—
660#41—861no—
661#41—861no—
662#41C2×C4×D4312yes—
663#41Q8×D4312yes—
664C2×Q8—434no—
665C2×Q8—431no—
666C2×Q8—861no—
667C2×Q8—862no—
668C2×Q8D4×D4311yescharacteristic
669C2×D4—21no—
670C2×D4—434no—
671C2×D4—431no—
672C2×D4—861no—
673C2×D4—862no—
674C2×D4—861no—
675C2×D4—864no—
676C2×D4—864no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4D4×D4311yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—431no—
685C22×C4—432no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—431no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—861no—
695C22×C4—864no—
696C22×C4—864no—
697C22×C4—861no—
698C22×C4—862no—
699C22×C4—862no—
700C22×C4—862no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—862no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—862no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—3442no—
710C22×C4—3444no—
711C22×C4D4×D4312yes—
712C22×C4C23×D4311yescharacteristic
713M16—21no—
714M16—21no—
715M16—21no—
716M16—432no—
717M16—864no—
718M16—861no—
719M16—861no—
720M16—861no—
721M16—1722no—
722M16C2×C4×D4312yescomplemented
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—864no—
726C2×C8—861no—
727C2×C8—861no—
728C2×C8—1722no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—431no—
735C4⋊C4—431no—
736C4⋊C4—862no—
737C4⋊C4—861no—
738C4⋊C4—862no—
739C4⋊C4—861no—
740C4⋊C4—864no—
741C4⋊C4—862no—
742C4⋊C4—862no—
743C4⋊C4—862no—
744C4⋊C4—861no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C4⋊C4—3442no—
749C4⋊C4—3442no—
750C4⋊C4D4×D4311yescharacteristic
751C4⋊C4D4×D4311yescharacteristic
752C22⋊C4—22no—
753C22⋊C4—21no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—864no—
757C22⋊C4—862no—
758C22⋊C4—862no—
759C22⋊C4—862no—
760C22⋊C4—861no—
761C22⋊C4—1721no—
762C22⋊C4—1721no—
763C42—22no—
764C42—21no—
765C42—21no—
766C42—432no—
767C42—861no—
768C42—861no—
769C42—862no—
770C42—862no—
771C42—862no—
772C42—861no—
773C42—861no—
774C42—1721no—
775C42—1721no—
776C42C2×C4×D4312yescomplemented
777C23—21no—
778C23—431no—
779C23—431no—
780C23—432no—
781C23—432no—
782C23—864no—
783C23—861no—
784C23—1721no—
785C23—1721no—
786C23—1722no—
787C23—1722no—
788C23C2×D4×D4311yescharacteristic
789Q8—21no—
790Q8—432no—
791Q8—864no—
792Q8—861no—
793Q8C4⋊C4×D4312yes—
794D4—22no—
795D4—22no—
796D4—21no—
797D4—432no—
798D4—864no—
799D4—864no—
800D4—864no—
801D4—862no—
802D4—862no—
803D4—861no—
804D4C4⋊C4×D4312yes—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—82no—
818C2×C4—432no—
819C2×C4—431no—
820C2×C4—431no—
821C2×C4—432no—
822C2×C4—432no—
823C2×C4—432no—
824C2×C4—432no—
825C2×C4—432no—
826C2×C4—432no—
827C2×C4—432no—
828C2×C4—432no—
829C2×C4—432no—
830C2×C4—864no—
831C2×C4—864no—
832C2×C4—864no—
833C2×C4—861no—
834C2×C4—862no—
835C2×C4—862no—
836C2×C4—862no—
837C2×C4—861no—
838C2×C4—861no—
839C2×C4—862no—
840C2×C4—3442no—
841C2×C4—3442no—
842C2×C4—3442no—
843C2×C4—3442no—
844C2×C4—1724no—
845C2×C4—1722no—
846C2×C4—1722no—
847C2×C4—1722no—
848C2×C4—1721no—
849C2×C4—1721no—
850C2×C4—1721no—
851C2×C4—1722no—
852C2×C4C22×C4×D4311yescharacteristic
853C2×C4C2×D4×D4311yescharacteristic
854C2×C4C2×D4×D4311yescharacteristic
855C2×C4C2×Q8×D4311yescharacteristic
856C2×C4#41×D4311yescharacteristic
857C2×C4#41×D4311yescharacteristic
858C8—22no—
859C8—41no—
860C8—862no—
861C8—1721no—
862C22—21no—
863C22—21no—
864C22—22no—
865C22—41no—
866C22—41no—
867C22—432no—
868C22—432no—
869C22—861no—
870C22—861no—
871C22—861no—
872C22—861no—
873C22—862no—
874C22—1722no—
875C22—1722no—
876C22—1728no—
877C22—1721no—
878C22—1721no—
879C22C4×D4×D4311yescharacteristic
880C22#120×D4311yescharacteristic
881C22C22⋊Q8×D4311yescharacteristic
882C4—22no—
883C4—42no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—81no—
888C4—432no—
889C4—432no—
890C4—862no—
891C4—3441no—
892C4—1722no—
893C4—1721no—
894C4—1722no—
895C4—1721no—
896C4C2×C4⋊C4×D4311yescharacteristic
897C4C4×D4×D4311yescharacteristic
898C4C22⋊Q8×D4311yescharacteristic
899C4#123×D4311yescharacteristic
900C2—21no—
901C2—21no—
902C2—42no—
903C2—862no—
904C2—862no—
905C2—1722no—
906C2#385×D4311yescharacteristic
907C2#1914395311yescharacteristic
908C2#1914395611yescharacteristic
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
hypocenterC43#20864
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. #19143182C2semidirect
5. #19137220C2semidirect
6. #19134827C2semidirect
7. #19134826C2semidirect
8. #19134825C2semidirect
9. #19134824C2semidirect
10. #19134823C2semidirect
11. #19134822C2semidirect
12. #19134821C2semidirect
13. #343×D43C2semidirect
14. #19134303C2semidirect
15. C43×#1860C2semidirect
36. #14582942C22semidirect
37. #14582941C22semidirect
39. #14582939C22semidirect
43. #14582914C4semidirect
56. #14582769C22semidirect
57. #14582768C22semidirect
58. #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
95. M16×D43C2×C4semidirect
128. #13063282C2×C4semidirect
163. #13063253C2×C4semidirect
164. #13063252C2×C4semidirect
165. #13063251C2×C4semidirect
187. #104×C43C2×C4semidirect
216. #10621902C4⋊C4semidirect
218. Q8×D43C4⋊C4semidirect
222. #10621900C4⋊C4semidirect
226. D4×D43C4⋊C4semidirect
261. M16×C43C22×C4semidirect
276. C42×C43C22×C4semidirect
311. C4×Dic43C22×C4semidirect
315. #10621877C22×C4semidirect
454. #1860D43semidirect
496. #428C2×D43semidirect
517. #382C2×D43semidirect
521. #343C2×D43semidirect
525. #339C2×D43semidirect
526. C43#20864semidirect
635. #104C4×D43semidirect
722. M16C2×C4×D43semidirect
776. 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
#191431822
C2×#145829142
#191431112
#191372202
#191348272
#191348262
#191348252
#191348242
#191348232
#191348222
#191348212
#343×D432
#191343032
C43×#18602
#2086443