Finite Group Databasebeta

← #25066614

Subgroups — #25066614

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144646C211yesmaximal, characteristic
2#19143569C211yesmaximal, characteristic, complemented
3C8×D4×D43C211yesmaximal, characteristic, complemented
4#19133429C211yesmaximal, characteristic, complemented
5#19133426C211yesmaximal, characteristic, complemented
6#19133424C211yesmaximal, characteristic, complemented
7#19133418C211yesmaximal, characteristic, complemented
8#19133416C211yesmaximal, characteristic, complemented
9#19133410C211yesmaximal, characteristic, complemented
10SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
11#19133377C211yesmaximal, characteristic, complemented
12#19133036C211yesmaximal, characteristic, complemented
13#19133007C211yesmaximal, characteristic, complemented
14#19132881C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C22×C8×D43—21no—
17#14583436C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583233C411yescharacteristic
20#14583219C411yescharacteristic
21#14583198C411yescharacteristic
22#14583197C411yescharacteristic
23#14583117C411yescharacteristic
24#14583116C411yescharacteristic
25#14583048C411yescharacteristic
26#14583034C411yescharacteristic
27Q8×C43⋊C8C2211yescharacteristic, complemented
28C4×#10621884C2211yescharacteristic
29C4×D344C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic, complemented
32#14582972—21no—
33C8×D172C2211yescharacteristic
34D4×C43⋊C8C2211yescharacteristic
35#14582964—21no—
36#14582964C2211yescharacteristic
37#14582964C2211yescharacteristic, complemented
38C8×C22⋊D43—21no—
39(C22⋊D43)⋊C8—21no—
40#14582959—21no—
41#14582955C2211yescharacteristic
42#14582950C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C22⋊C8×D43—21no—
45#14582856—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582628C2211yescharacteristic
53#14582628C2211yescharacteristic, complemented
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic, complemented
57#14582621C2211yescharacteristic, complemented
58#14582620C2211yescharacteristic, complemented
59#14582620C2211yescharacteristic, complemented
60C43×#446C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621884C2×C411yescharacteristic
70C2×D344C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—44no—
80C2×C8×D43D411yescharacteristic
81C2×C8×D43D411yescharacteristic
82#13063320—21no—
83#13063316C2×C411yescharacteristic
84#13063314C2×C411yescharacteristic
85#13063310—21no—
86#13063301C2×C411yescharacteristic
87#13063300C2×C411yescharacteristic
88C4×D172—21no—
89C4×D172C2311yescharacteristic
90C4×D172C2311yescharacteristic
91D4×Dic43C2×C411yescharacteristic
92#13063287C2×C411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95#13063282—21no—
96C4⋊C4×D43C2×C411yescharacteristic
97C22⋊C4×D43—21no—
98C42×D43C2311yescharacteristic
99#13063259C2×C411yescharacteristic
100#13063258C2×C411yescharacteristic
101#13063256C2×C411yescharacteristic
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8C2×C411yescharacteristic
107Dic43⋊C8C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113#13063245C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8C2×C411yescharacteristic
121(C2×D43)⋊C8C2×C411yescharacteristic
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C22×C8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151D4×D43—22no—
152D4×D43—22no—
153C2×D172—21no—
154C2×D172C22×C411yescharacteristic
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165SD16×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621884—22no—
182#10621882—22no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207D344—22no—
208#10621872—42no—
209#10621872—42no—
210C8×D43—22no—
211C8×D43—41no—
212C8×D43—42no—
213C8×D43—42no—
214C8×D43—42no—
215C8×D43—42no—
216C23×C43—21no—
217C22×D43—24no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43C4×D411yescharacteristic
223Q8×C43—21no—
224Q8×C43—21no—
225D4×C43—21no—
226D4×C43#13112yes—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—24no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—42no—
239C2×Dic43C4×D411yescharacteristic
240C2×Dic43C4×D411yescharacteristic
241C2×Dic43C4×D411yescharacteristic
242D172—21no—
243D172—21no—
244D172—21no—
245D172—42no—
246D172#13112yes—
247C4×D43—22no—
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—21no—
252C4×D43—42no—
253C4×D43—42no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—41no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43AGL(1,ℤ/8)12yes—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—21no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#17914—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×C4×D411yescharacteristic
277C2×D43—21no—
278C2×D43—21no—
279C2×D43—22no—
280C2×D43—48no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43#44412yes—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43C2×#13111yescharacteristic
292C4×C43C2×#13111yescharacteristic
293C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C43#57511yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—41no—
299Dic43—41no—
300#3105—431no—
301#2966—431no—
302C2×C8×D4—431no—
303#1582—431no—
304#1582D4311yescharacteristic, complemented
305#1581—431no—
306#1581—431no—
307#1580—431no—
308#1580—431no—
309SD16⋊C8—431no—
310SD16⋊C8—431no—
311#1573—431no—
312#1490—431no—
313#1483—431no—
314#1451—431no—
315C2×C43—42no—
316C2×C43#292911yescharacteristic
317C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C43C2×#44411yescharacteristic
319D43—22no—
320D43—42no—
321D43—81no—
322C23×C8—861no—
323#529—431no—
324C2×C4×D4—431no—
325#484—431no—
326#481—431no—
327#478—431no—
328#478—431no—
329#463—431no—
330#463—431no—
331#450—431no—
332#447—431no—
333#446C2×D4311yescharacteristic, complemented
334C8×Q8—431no—
335C4×SD16—431no—
336C4×SD16C2×D4311yescharacteristic
337C4×D8—431no—
338C4×D8—431no—
339#436—431no—
340#435—861no—
341C8×D4—431no—
342C8×D4—431no—
343C8×D4—431no—
344C8×D4—431no—
345C8×D4—861no—
346C8×D4—861no—
347C8×D4—861no—
348C8×D4C2×D4311yescharacteristic
349#433—861no—
350#432—431no—
351#431—431no—
352C2×C4⋊C8—431no—
353C2×C22⋊C8—861no—
354#405—861no—
355C4×M16—431no—
356C2×C4×C8—431no—
357#335—431no—
358#335—431no—
359#334—431no—
360#334C2×D4311yescharacteristic, complemented
361Q8⋊C8—431no—
362Q8⋊C8C2×D4311yescharacteristic, complemented
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8C2×D4311yescharacteristic
369#322—431no—
370#322—431no—
371#322—431no—
372#322C2×D4311yescharacteristic, complemented
373C43#1791411yescharacteristic, complemented, Sylow
374C22×D4—431no—
375C23×C4—861no—
376C2×SD16—431no—
377C2×SD16C4×D4311yescharacteristic
378C2×D8—431no—
379C2×D8—431no—
380C2×M16—861no—
381C2×M16—861no—
382C22×C8—21no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8—861no—
386C22×C8—861no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C22×C8—1724no—
391#126—861no—
392#125—431no—
393#124—431no—
394#123—861no—
395C22⋊Q8—431no—
396#121—431no—
397C4×Q8C22×D4311yescharacteristic
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4C22×D4311yescharacteristic
406#117—861no—
407C2×C4⋊C4—431no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410#107—431no—
411#107—431no—
412#106—431no—
413#106C4×D4311yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—431no—
424#103C4×D4311yescharacteristic
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429#102—431no—
430#102C4×D4311yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—431no—
433C22⋊C8—431no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#97—21no—
441#97—861no—
442#97—861no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8—861no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C4×C8C22×D4311yescharacteristic
452C24—861no—
453C2×Q8C2×C4×D4311yescharacteristic
454C2×D4—431no—
455C2×D4—431no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—862no—
459C2×D4—862no—
460C2×D4C2×C4×D4311yescharacteristic
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—1722no—
471C22×C4—1722no—
472SD16—22no—
473SD16—862no—
474D8—862no—
475D8—862no—
476M16—1722no—
477M16—1722no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—862no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—1721no—
491C2×C8—1722no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8—1722no—
496C2×C8C2×C4×D4311yescharacteristic
497C2×C8C2×C4×D4311yescharacteristic
498C2×C8D4×D4311yescharacteristic
499C2×C8D4×D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—431no—
502C4⋊C4—431no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4C2×C4×D4311yescharacteristic
508C4⋊C4C2×C4×D4311yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C22⋊C4—861no—
518C42—21no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—431no—
525C23—864no—
526C23—861no—
527C23—861no—
528C23—1722no—
529C23—1722no—
530Q8—21no—
531Q8—21no—
532D4—21no—
533D4—432no—
534D4—864no—
535D4—861no—
536D4—861no—
537D4—861no—
538D4—1722no—
539D4#1306333312yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—431no—
546C2×C4—431no—
547C2×C4—431no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4C22×C4×D4311yescharacteristic
563C2×C4C2×D4×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—861no—
572C8—861no—
573C8—861no—
574C8—861no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8#1306335212yes—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—432no—
583C22—861no—
584C22—861no—
585C22—862no—
586C22—1728no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22C4×D4×D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—861no—
598C4—861no—
599C4—861no—
600C4—1721no—
601C4—1721no—
602C4#131×D4311yescharacteristic
603C4C2×#1306333311yescharacteristic
604C4C2×#1306335211yescharacteristic
605C4#1458369611yescharacteristic
606C2—42no—
607C2—862no—
608C2—3441no—
609C2—1722no—
610C2#1914328611yescharacteristic
611C2C4×#1306335211yescharacteristic
612C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1582C2
socleC22×C43C2×C4×D4
prime radical#14583034C4
cosocleC42×C43C24
hypercenter#1582D43
hypocenterC43#17914
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #19143569C2semidirect
3. C8×D4×D43C2semidirect
4. #19133429C2semidirect
5. #19133426C2semidirect
6. #19133424C2semidirect
7. #19133418C2semidirect
8. #19133416C2semidirect
9. #19133410C2semidirect
10. SD16⋊(C43⋊C8)C2semidirect
11. #19133377C2semidirect
12. #19133036C2semidirect
13. #19133007C2semidirect
14. #19132881C2semidirect
15. C43×#1582C2semidirect
27. Q8×C43⋊C8C22semidirect
31. #14582978C22semidirect
37. #14582964C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582649C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. #14582628C22semidirect
56. #14582626C22semidirect
57. #14582621C22semidirect
58. #14582620C22semidirect
59. #14582620C22semidirect
60. C43×#446C22semidirect
63. C43×#334C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
304. #1582D43semidirect
333. #446C2×D43semidirect
360. #334C2×D43semidirect
362. Q8⋊C8C2×D43semidirect
372. #322C2×D43semidirect
373. C43#17914semidirect

Maximal subgroups

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

subgroupindex
#191446462
#191435692
C8×D4×D432
#191334292
#191334262
#191334242
#191334182
#191334162
#191334102
SD16⋊(C43⋊C8)2
#191333772
#191330362
#191330072
#191328812
C43×#15822
#1791443