Finite Group Databasebeta

← #25066030

Subgroups — #25066030

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143705C211yesmaximal, characteristic, complemented
2#19143616C211yesmaximal, characteristic, complemented
3C4×#13063352C211yesmaximal, characteristic
4#19133418C211yesmaximal, characteristic, complemented
5#19133417C211yesmaximal, characteristic, complemented
6SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
7#19133405C211yesmaximal, characteristic, complemented
8#19133392C211yesmaximal, characteristic, complemented
9C8×D344C211yesmaximal, characteristic, complemented
10#19133387C211yesmaximal, characteristic, complemented
11#19133344C211yesmaximal, characteristic, complemented
12#19132976C211yesmaximal, characteristic, complemented
13D4⋊C8×D43C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063352C411yescharacteristic
17C4×#10621902C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19Q8×C43⋊C8C2211yescharacteristic, complemented
20#14583010C411yescharacteristic
21#14583008C411yescharacteristic
22#14583002C411yescharacteristic
23#14583000C411yescharacteristic
24C4×#10621884C2211yescharacteristic
25C4×D344C2211yescharacteristic
26C4×#10621882C2211yescharacteristic
27C8×D172—21no—
28C8×D172C2211yescharacteristic
29C8×D172C2211yescharacteristic, complemented
30D4×C43⋊C8C2211yescharacteristic
31#14582964—21no—
32#14582964C2211yescharacteristic
33#14582964C2211yescharacteristic, complemented
34C8×C22⋊D43—21no—
35(C22⋊D43)⋊C8—21no—
36#14582951C2211yescharacteristic
37#14582950—21no—
38#14582950C2211yescharacteristic
39#14582938C411yescharacteristic
40C4⋊C8×D43—21no—
41C4⋊C8×D43C2211yescharacteristic
42#14582902C411yescharacteristic
43#14582899C411yescharacteristic
44C2×(C2×D43)⋊C8—21no—
45C22⋊C8×D43—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
59C8×C43⋊C8C2211yescharacteristic, complemented
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic, complemented
67C2×#10621902C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70#13063352C818yescomplemented
71C2×#10621884C2×C411yescharacteristic
72C2×D344C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74C2×#10621872C2×C411yescharacteristic
75C2×#10621872C2×C411yescharacteristic
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83Q8×Dic43C2×C411yescharacteristic
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86C4×D172C2311yescharacteristic
87D4×Dic43C2×C411yescharacteristic
88#13063287—21no—
89#13063287C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063283—21no—
94#13063283C2×C411yescharacteristic
95C4⋊C4×D43C2×C411yescharacteristic
96C22⋊C4×D43—21no—
97C42×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⋊C8D411yescharacteristic
107Dic43⋊C8D411yescharacteristic
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)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235C2×C411yescharacteristic
123#13063235C2×C411yescharacteristic
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
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—
141C4×C8×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—
151#10621902—22no—
152#10621902C2×C814yescomplemented
153D4×D43—22no—
154D4×D43C2×C814yescomplemented
155C2×D172—21no—
156C2×D172C22×C411yescharacteristic
157C2×D172C22×C411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×C4×D43C22×C411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169SD16×C43C2×C814yescomplemented
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—81no—
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#10621884C2×C814yescomplemented
186#10621882C2×C814yescomplemented
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C22×C411yescharacteristic
194C4⋊Dic43C22×C411yescharacteristic
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43C22×C411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209D344C2×C814yescomplemented
210#10621872—22no—
211#10621872C2×C814yescomplemented
212C8×D43—42no—
213C8×D43—81no—
214C8×D43—81no—
215C8×D43—81no—
216C8×D43—81no—
217C8×D43—81no—
218C23×C43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—24no—
222C22×D43—81no—
223C22×D43—81no—
224C22×D43C4×D411yescharacteristic
225Q8×C43—21no—
226Q8×C43C22×C812yes—
227D4×C43—21no—
228D4×C43C22×C812yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—24no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—81no—
241C2×Dic43C4×D411yescharacteristic
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244D172—24no—
245D172—21no—
246D172—21no—
247D172C22×C812yes—
248D172C22×C812yes—
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—24no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—81no—
258C4×D43—81no—
259C4×D43—81no—
260C4×D43C22×C812yes—
261C4×D43#13112yes—
262C8×C43—22no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43C22×C812yes—
269C43⋊C8—21no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8C22×C812yes—
276#17852—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43C2×C4×D411yescharacteristic
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—84no—
290C2×D43C8×D412yes—
291C4×C43—22no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43C23×C811yescharacteristic
296C4×C43C2×#13111yescharacteristic
297C4×C43#57611yescharacteristic
298C4×C43#57711yescharacteristic
299Dic43—21no—
300Dic43—21no—
301Dic43—41no—
302Dic43—41no—
303Dic43C8×D412yes—
304#2988—431no—
305#2972—431no—
306C4×AGL(1,ℤ/8)—431no—
307#1580—431no—
308#1580—431no—
309SD16⋊C8—431no—
310SD16⋊C8—431no—
311C8×SD16—431no—
312C8×SD16D4311yescharacteristic, complemented
313C8×D8—431no—
314C8×D8—431no—
315#1565—431no—
316#1476—431no—
317C2×D4⋊C8—431no—
318C8×M16—431no—
319C2×C43—42no—
320C2×C43C2×C8×D411yescharacteristic
321C2×C43#294611yescharacteristic
322C2×C43#295611yescharacteristic
323D43—22no—
324D43—42no—
325D43—42no—
326C2×AGL(1,ℤ/8)—431no—
327C4×#41—431no—
328C2×C4×D4—431no—
329C8×Q8—431no—
330C8×Q8C2×D4311yescharacteristic, complemented
331#442—431no—
332#442—431no—
333#440—431no—
334#440—431no—
335C4×SD16—431no—
336C4×SD16C2×D4311yescharacteristic
337C4×D8—431no—
338C4×D8—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342C8×D4—431no—
343C8×D4—431no—
344C8×D4—861no—
345C8×D4—861no—
346C8×D4—861no—
347C8×D4—861no—
348C8×D4C2×D4311yescharacteristic
349#431—431no—
350#431—431no—
351#431—861no—
352#428—431no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—861no—
355#418—431no—
356#417—431no—
357C2×C22⋊C8—861no—
358C2×C22⋊C8—861no—
359C4×M16—431no—
360C2×C4×C8—431no—
361#335—431no—
362#335—431no—
363#334—431no—
364#334C2×D4311yescharacteristic, complemented
365Q8⋊C8—431no—
366Q8⋊C8C2×D4311yescharacteristic, complemented
367D4⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372D4⋊C8C2×D4311yescharacteristic
373#322—431no—
374#322—431no—
375C82—431no—
376C82C2×D4311yescharacteristic, complemented
377C43#1785211yescharacteristic, complemented, Sylow
378C2×#41—431no—
379C22×D4—431no—
380C23×C4—861no—
381AGL(1,ℤ/8)—438no—
382C2×SD16—431no—
383C2×SD16C4×D4311yescharacteristic
384C2×D8—431no—
385C2×D8—431no—
386C2×M16—431no—
387C2×M16—431no—
388C22×C8—21no—
389C22×C8—861no—
390C22×C8—861no—
391C22×C8—861no—
392C22×C8—861no—
393C22×C8—861no—
394C22×C8—861no—
395C22×C8—861no—
396C4×Q8—431no—
397C4×Q8C22×D4311yescharacteristic
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—431no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4C22×D4311yescharacteristic
408#117—431no—
409#117—861no—
410C2×C4⋊C4—431no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413C2×C42—861no—
414#107—431no—
415#107—431no—
416#106—431no—
417#106C4×D4311yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425C4⋊C8C22×D4311yescharacteristic
426C4⋊C8C22×D4311yescharacteristic
427#103—431no—
428#103C4×D4311yescharacteristic
429#102—431no—
430#102—431no—
431#102—431no—
432#102—431no—
433#102—431no—
434#102C4×D4311yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—431no—
437C22⋊C8—431no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444#97—431no—
445#97—431no—
446C4×C8—21no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—861no—
451C4×C8—861no—
452C4×C8—861no—
453C4×C8C22×D4311yescharacteristic
454C4×C8C22×D4311yescharacteristic
455C4×C8C22×D4311yescharacteristic
456C24—861no—
457#41—434no—
458#41—862no—
459C2×Q8C2×C4×D4311yescharacteristic
460C2×D4—434no—
461C2×D4—431no—
462C2×D4—431no—
463C2×D4—861no—
464C2×D4—862no—
465C2×D4—861no—
466C2×D4C2×C4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—3441no—
479C22×C4—3441no—
480SD16—434no—
481SD16C8×D4314yescomplemented
482D8—434no—
483D8—434no—
484M16—434no—
485M16—862no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—3441no—
498C2×C8—3441no—
499C2×C8—3441no—
500C2×C8—3441no—
501C2×C8—3441no—
502C2×C8—3441no—
503C2×C8—1722no—
504C2×C8C2×C4×D4311yescharacteristic
505C2×C8C2×C4×D4311yescharacteristic
506C2×C8D4×D4311yescharacteristic
507C2×C8D4×D4311yescharacteristic
508C4⋊C4—21no—
509C4⋊C4—431no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4C2×C4×D4311yescharacteristic
514C4⋊C4C2×C4×D4311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—861no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—861no—
521C22⋊C4—861no—
522C42—21no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—861no—
527C42—861no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—431no—
531C23—864no—
532C23—861no—
533C23—861no—
534C23—3441no—
535C23—3441no—
536Q8—21no—
537Q8C2×C8×D4312yes—
538D4—21no—
539D4—432no—
540D4—432no—
541D4—864no—
542D4—864no—
543D4—861no—
544D4—861no—
545D4C2×C8×D4312yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—431no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—431no—
555C2×C4—431no—
556C2×C4—864no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—3441no—
562C2×C4—3441no—
563C2×C4—3441no—
564C2×C4—3441no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C8—22no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—432no—
580C8—861no—
581C8—861no—
582C8—861no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C8C2×C8×D4312yes—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—432no—
591C22—861no—
592C22—861no—
593C22—862no—
594C22—862no—
595C22—3444no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22—1721no—
600C22C4×D4×D4311yescharacteristic
601C4—21no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—432no—
606C4—861no—
607C4—861no—
608C4—1721no—
609C4—1721no—
610C4C22×C8×D4311yescharacteristic
611C4#131×D4311yescharacteristic
612C4#1458370111yescharacteristic
613C4#1458370511yescharacteristic
614C2—42no—
615C2—862no—
616C2—1722no—
617C2—1722no—
618C2C8×D4×D4311yescharacteristic
619C2#1914342211yescharacteristic
620C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC8×SD16×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063352C4
cosocleC42×C43C24
hypercenterC8×SD16D43
hypocenterC43#17852
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
1. #19143705C2semidirect
2. #19143616C2semidirect
4. #19133418C2semidirect
5. #19133417C2semidirect
6. SD16⋊(C43⋊C8)C2semidirect
7. #19133405C2semidirect
8. #19133392C2semidirect
9. C8×D344C2semidirect
10. #19133387C2semidirect
11. #19133344C2semidirect
12. #19132976C2semidirect
13. D4⋊C8×D43C2semidirect
14. C8×#10621872C2semidirect
15. C8×SD16×C43C2semidirect
19. Q8×C43⋊C8C22semidirect
29. C8×D172C22semidirect
33. #14582964C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582649C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. #14582628C22semidirect
56. #14582626C22semidirect
57. #14582621C22semidirect
58. #14582620C22semidirect
59. C8×C43⋊C8C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#334C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C82×C43C22semidirect
70. #13063352C8semidirect
152. #10621902C2×C8semidirect
154. D4×D43C2×C8semidirect
169. SD16×C43C2×C8semidirect
185. #10621884C2×C8semidirect
186. #10621882C2×C8semidirect
209. D344C2×C8semidirect
211. #10621872C2×C8semidirect
312. C8×SD16D43semidirect
330. C8×Q8C2×D43semidirect
364. #334C2×D43semidirect
366. Q8⋊C8C2×D43semidirect
376. C82C2×D43semidirect
377. C43#17852semidirect
481. SD16C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191437052
#191436162
C4×#130633522
#191334182
#191334172
SD16⋊(C43⋊C8)2
#191334052
#191333922
C8×D3442
#191333872
#191333442
#191329762
D4⋊C8×D432
C8×#106218722
C8×SD16×C432
#1785243