Finite Group Databasebeta

← #26185862

Subgroups — #26185862

Order 12032.

748 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252353C211yesmaximal, characteristic, complemented
2C4×#13094051C211yesmaximal, characteristic
3C8×D4×D47C211yesmaximal, characteristic, complemented
4#20242251C211yesmaximal, characteristic, complemented
5#20242249C211yesmaximal, characteristic, complemented
6#20242248C211yesmaximal, characteristic, complemented
7#20242246C211yesmaximal, characteristic, complemented
8#20242222C211yesmaximal, characteristic, complemented
9#20242219C211yesmaximal, characteristic, complemented
10#20242217C211yesmaximal, characteristic, complemented
11#20242137C211yesmaximal, characteristic, complemented
12#20241777C211yesmaximal, characteristic, complemented
13#20241774C211yesmaximal, characteristic, complemented
14#20241674C211yesmaximal, characteristic, complemented
15C47×#1582C211yesmaximal, characteristic, complemented
16C2×#13094051C411yescharacteristic
17C22×C8×D47—21no—
18C4×#10625354C2211yescharacteristic
19C4×D4×D47C2211yescharacteristic
20#15689254C2211yescharacteristic, complemented
21#15689234C411yescharacteristic
22#15689232C411yescharacteristic
23#15689226C411yescharacteristic
24#15689224C411yescharacteristic
25C4×#10625336C2211yescharacteristic
26C4×D376C2211yescharacteristic
27C4×#10625334C2211yescharacteristic
28#15689202C2211yescharacteristic, complemented
29#15689200C2211yescharacteristic, complemented
30#15689196—21no—
31#15689193—21no—
32C8×D188C2211yescharacteristic
33D4×C47⋊C8C2211yescharacteristic
34#15689188C2211yescharacteristic
35C8×C22⋊D47—21no—
36(C22⋊D47)⋊C8—21no—
37#15689175—21no—
38#15689175C2211yescharacteristic
39#15689174C2211yescharacteristic
40#15689162C411yescharacteristic
41C4⋊C8×D47C2211yescharacteristic
42#15689126C411yescharacteristic
43#15689123C411yescharacteristic
44C22⋊C8×D47—21no—
45#15689075—21no—
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic, complemented
49#15688875C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
52#15688852C2211yescharacteristic
53#15688852C2211yescharacteristic, complemented
54D4⋊(C47⋊C8)C2211yescharacteristic
55#15688850C2211yescharacteristic
56#15688850C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688844C2211yescharacteristic, complemented
59#15688844C2211yescharacteristic, complemented
60C47×#446C2211yescharacteristic, complemented
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C2×#10625354C2×C411yescharacteristic
68C2×D4×D47C2×C411yescharacteristic
69C22×C4×D47—21no—
70#13094051—24no—
71C2×#10625336C2×C411yescharacteristic
72C2×D376C2×C411yescharacteristic
73C2×#10625334C2×C411yescharacteristic
74C2×#10625324—21no—
75C2×#10625324—21no—
76C2×#10625324C2×C411yescharacteristic
77C2×#10625324C2×C411yescharacteristic
78C22×C47⋊C8—21no—
79C2×C8×D47—21no—
80C2×C8×D47—21no—
81C2×C8×D47—21no—
82C2×C8×D47—44no—
83C2×C8×D47D411yescharacteristic
84C2×C8×D47D411yescharacteristic
85Q8×Dic47C2×C411yescharacteristic
86C4×D188—21no—
87C4×D188C2311yescharacteristic
88C4×D188C2311yescharacteristic
89D4×Dic47C2×C411yescharacteristic
90#13093986—21no—
91#13093986C2×C411yescharacteristic
92#13093986C2×C411yescharacteristic
93C4×C22⋊D47—21no—
94(C22⋊D47)⋊C4—21no—
95#13093982—21no—
96#13093982C2×C411yescharacteristic
97C4⋊C4×D47C2×C411yescharacteristic
98C22⋊C4×D47—21no—
99C42×D47—21no—
100C42×D47C2311yescharacteristic
101#13093958C2×C411yescharacteristic
102#13093957C2×C411yescharacteristic
103#13093955C2×C411yescharacteristic
104C4⋊(C47⋊C8)—21no—
105C4⋊(C47⋊C8)C2311yescharacteristic
106C4⋊(C47⋊C8)C2311yescharacteristic
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093948C2×C411yescharacteristic
110#13093946C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093945C2×C411yescharacteristic
113#13093944C2×C411yescharacteristic
114#13093944C2×C411yescharacteristic
115C22⋊(C47⋊C8)—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121(C2×D47)⋊C8—21no—
122#13093935—21no—
123#13093934C2×C411yescharacteristic
124#13093934C2×C411yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C8×Dic47—21no—
129C8×Dic47D411yescharacteristic
130C8×Dic47D411yescharacteristic
131C2×SD16×C47C2×C411yescharacteristic
132C22×C8×C47—21no—
133C4×Q8×C47C2311yescharacteristic
134C4×D4×C47C2311yescharacteristic
135#106×C47C2×C411yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139#103×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141C22⋊C8×C47—21no—
142#97×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C4×C8×C47C2311yescharacteristic
146C23×D47—21no—
147C2×Q8×C47C22×C411yescharacteristic
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C2×C22⋊D47—21no—
151C22×Dic47—21no—
152#10625354—22no—
153#10625354—22no—
154D4×D47—22no—
155D4×D47M1614yescomplemented
156C2×D188—21no—
157C2×D188C22×C411yescharacteristic
158C2×D188C22×C411yescharacteristic
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—42no—
166C2×C4×D47—42no—
167C2×C4×D47C22×C411yescharacteristic
168C2×C4×D47C2×D411yescharacteristic
169C2×C4×D47#4111yescharacteristic
170SD16×C47—22no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—42no—
175C2×C8×C47C22×C411yescharacteristic
176C2×C8×C47C22×C411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C4⋊C4×C47—21no—
180C4⋊C4×C47C22×C411yescharacteristic
181C4⋊C4×C47C22×C411yescharacteristic
182C22⋊C4×C47—21no—
183C42×C47—21no—
184C42×C47C2411yescharacteristic
185C22⋊Dic47—21no—
186#10625336—22no—
187#10625334—22no—
188(C2×D47)⋊C4—21no—
189(C2×D47)⋊C4—21no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192(C2×D47)⋊C4—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47C22×C411yescharacteristic
195C4⋊Dic47C22×C411yescharacteristic
196Dic47⋊C4—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47C22×C411yescharacteristic
200C4×Dic47C2×D411yescharacteristic
201C4×Dic47#4111yescharacteristic
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—42no—
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210D376—22no—
211#10625324—22no—
212#10625324—22no—
213#10625324—42no—
214#10625324—42no—
215C8×D47—22no—
216C8×D47—41no—
217C8×D47—42no—
218C8×D47—42no—
219C8×D47—42no—
220C23×C47—21no—
221C22×D47—21no—
222C22×D47—24no—
223C22×D47—21no—
224C22×D47—42no—
225C22×D47—42no—
226C22×D47C4×D411yescharacteristic
227Q8×C47—21no—
228Q8×C47—21no—
229D4×C47—21no—
230D4×C47C2×M1612yes—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47C23×C411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C22⋊D47—24no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—42no—
243C2×Dic47C4×D411yescharacteristic
244C2×Dic47C4×D411yescharacteristic
245C2×Dic47C4×D411yescharacteristic
246D188—21no—
247D188—21no—
248D188—21no—
249D188—42no—
250D188C2×M1612yes—
251C4×D47—21no—
252C4×D47—21no—
253C4×D47—41no—
254C4×D47—42no—
255C4×D47—42no—
256C4×D47—42no—
257C4×D47—41no—
258C4×D47—41no—
259C4×D47—41no—
260C4×D47—41no—
261C4×D47—42no—
262C4×D47C2×M1612yes—
263C4×D47#13112yes—
264C8×C47—21no—
265C8×C47—21no—
266C8×C47—21no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270C8×C47AGL(1,ℤ/8)12yescomplemented
271C47⋊C8—21no—
272C47⋊C8—21no—
273C47⋊C8—21no—
274C47⋊C8—21no—
275C47⋊C8—41no—
276C47⋊C8—41no—
277C47⋊C8—41no—
278#17869—471nomaximal, Sylow
279C22×C47—22no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47C2×C4×D411yescharacteristic
283C2×D47—21no—
284C2×D47—21no—
285C2×D47—22no—
286C2×D47—48no—
287C2×D47—41no—
288C2×D47—41no—
289C2×D47—41no—
290C2×D47—41no—
291C2×D47—41no—
292C2×D47#43512yes—
293C4×C47—21no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47C22×M1611yescharacteristic
298C4×C47C2×#13111yescharacteristic
299C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C47#57511yescharacteristic
301Dic47—21no—
302Dic47—21no—
303Dic47—41no—
304Dic47—41no—
305Dic47#43512yes—
306#2965—471no—
307C4×AGL(1,ℤ/8)—471no—
308C2×C8×D4—471no—
309#1586—471no—
310#1586—471no—
311#1585—471no—
312#1585—471no—
313#1582—471no—
314#1582D4711yescharacteristic, complemented
315#1581—471no—
316#1581—471no—
317#1565—471no—
318#1478—471no—
319#1477—471no—
320#1451—471no—
321C2×C47—42no—
322C2×C47C2×#43511yescharacteristic
323C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
324C2×C47#295511yescharacteristic
325D47—22no—
326D47—42no—
327D47—81no—
328C2×AGL(1,ℤ/8)—471no—
329C23×C8—941no—
330C4×#41—471no—
331C2×C4×D4—471no—
332#446—471no—
333#446C2×D4711yescharacteristic, complemented
334#442—471no—
335#442—471no—
336#440—471no—
337#440—471no—
338C4×SD16—471no—
339C4×SD16C2×D4711yescharacteristic
340C4×D8—471no—
341C4×D8—471no—
342#436—471no—
343#436—471no—
344#435—941no—
345#435—941no—
346C8×D4—471no—
347C8×D4—471no—
348C8×D4—471no—
349C8×D4—941no—
350C8×D4—941no—
351C8×D4C2×D4711yescharacteristic
352#431—471no—
353#431—471no—
354#431—941no—
355#428—471no—
356C2×C4⋊C8—471no—
357#418—471no—
358#417—471no—
359C2×C22⋊C8—941no—
360C4×M16—471no—
361C4×M16—941no—
362C2×C4×C8—471no—
363#335—471no—
364#335—471no—
365#334—471no—
366#334C2×D4711yescharacteristic, complemented
367Q8⋊C8—471no—
368Q8⋊C8C2×D4711yescharacteristic, complemented
369D4⋊C8—471no—
370D4⋊C8—471no—
371D4⋊C8—471no—
372D4⋊C8—471no—
373D4⋊C8—471no—
374D4⋊C8C2×D4711yescharacteristic
375#322—471no—
376#322—471no—
377#322—471no—
378#322C2×D4711yescharacteristic, complemented
379C47#1786911yescharacteristic, complemented, Sylow
380C2×#41—471no—
381C22×D4—471no—
382C23×C4—941no—
383AGL(1,ℤ/8)—944no—
384C2×SD16—471no—
385C2×SD16C4×D4711yescharacteristic
386C2×D8—471no—
387C2×D8—471no—
388C2×M16—471no—
389C2×M16—471no—
390C2×M16—941no—
391C2×M16—941no—
392C22×C8—21no—
393C22×C8—471no—
394C22×C8—471no—
395C22×C8—941no—
396C22×C8—941no—
397C22×C8—941no—
398C22×C8—941no—
399C22×C8—1884no—
400C4×Q8—471no—
401C4×Q8C22×D4711yescharacteristic
402C4×D4—471no—
403C4×D4—471no—
404C4×D4—471no—
405C4×D4—471no—
406C4×D4—471no—
407C4×D4—941no—
408C4×D4—941no—
409C4×D4—941no—
410C4×D4—941no—
411C4×D4C22×D4711yescharacteristic
412#117—471no—
413#117—941no—
414C2×C4⋊C4—471no—
415C2×C22⋊C4—941no—
416C2×C42—471no—
417C2×C42—941no—
418#107—471no—
419#107—471no—
420#106—471no—
421#106C4×D4711yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—471no—
424C4⋊C8—471no—
425C4⋊C8—941no—
426C4⋊C8—941no—
427C4⋊C8—941no—
428C4⋊C8C22×D4711yescharacteristic
429C4⋊C8C22×D4711yescharacteristic
430#103—471no—
431#103C4×D4711yescharacteristic
432#102—471no—
433#102—471no—
434#102—471no—
435#102—471no—
436#102—471no—
437#102C4×D4711yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—941no—
440C22⋊C8—941no—
441C22⋊C8—941no—
442C22⋊C8—941no—
443C22⋊C8—941no—
444C22⋊C8—941no—
445C22⋊C8—941no—
446#97—21no—
447#97—471no—
448#97—471no—
449#97—941no—
450C4×C8—471no—
451C4×C8—471no—
452C4×C8—471no—
453C4×C8—471no—
454C4×C8—471no—
455C4×C8—941no—
456C4×C8C22×D4711yescharacteristic
457C4×C8C22×D4711yescharacteristic
458C4×C8C22×D4711yescharacteristic
459C24—941no—
460#41—942no—
461#41—942no—
462C2×Q8C2×C4×D4711yescharacteristic
463C2×D4—474no—
464C2×D4—471no—
465C2×D4—471no—
466C2×D4—941no—
467C2×D4—942no—
468C2×D4—941no—
469C2×D4C2×C4×D4711yescharacteristic
470C22×C4—21no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—1882no—
482C22×C4—1882no—
483SD16—22no—
484SD16—942no—
485D8—942no—
486D8—942no—
487M16—942no—
488M16—942no—
489M16—1882no—
490M16—1882no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—471no—
496C2×C8—471no—
497C2×C8—471no—
498C2×C8—471no—
499C2×C8—942no—
500C2×C8—941no—
501C2×C8—941no—
502C2×C8—941no—
503C2×C8—1881no—
504C2×C8—1882no—
505C2×C8—1882no—
506C2×C8—1882no—
507C2×C8—1882no—
508C2×C8C2×C4×D4711yescharacteristic
509C2×C8C2×C4×D4711yescharacteristic
510C2×C8D4×D4711yescharacteristic
511C2×C8D4×D4711yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—471no—
514C4⋊C4—471no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4C2×C4×D4711yescharacteristic
518C4⋊C4C2×C4×D4711yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—941no—
521C22⋊C4—941no—
522C22⋊C4—941no—
523C22⋊C4—941no—
524C22⋊C4—941no—
525C22⋊C4—941no—
526C42—21no—
527C42—471no—
528C42—471no—
529C42—471no—
530C42—941no—
531C42—941no—
532C42C23×D4711yescharacteristic
533C23—21no—
534C23—471no—
535C23—944no—
536C23—941no—
537C23—941no—
538C23—1882no—
539C23—1882no—
540Q8—21no—
541Q8—21no—
542D4—21no—
543D4—472no—
544D4—944no—
545D4—941no—
546D4—941no—
547D4—941no—
548D4—1882no—
549D4M16×D4712yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—471no—
556C2×C4—472no—
557C2×C4—472no—
558C2×C4—471no—
559C2×C4—471no—
560C2×C4—941no—
561C2×C4—941no—
562C2×C4—941no—
563C2×C4—941no—
564C2×C4—1881no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1881no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4C22×C4×D4711yescharacteristic
575C2×C4C2×D4×D4711yescharacteristic
576C2×C4#41×D4711yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—941no—
584C8—941no—
585C8—941no—
586C8—941no—
587C8—1881no—
588C8—1881no—
589C8—1881no—
590C8#1309405112yescomplemented
591C22—22no—
592C22—41no—
593C22—41no—
594C22—472no—
595C22—941no—
596C22—941no—
597C22—942no—
598C22—1888no—
599C22—1881no—
600C22—1881no—
601C22—1881no—
602C22—1881no—
603C22—1881no—
604C22C4×D4×D4711yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—472no—
610C4—941no—
611C4—941no—
612C4—1881no—
613C4—1881no—
614C4C2×M16×D4711yescharacteristic
615C4#131×D4711yescharacteristic
616C4C2×#1309405111yescharacteristic
617C4#1568992011yescharacteristic
618C2—42no—
619C2—942no—
620C2—3761no—
621C2—1882no—
622C2#435×D4711yescharacteristic
623C2C4×#1309405111yescharacteristic
624C2#2025228811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1582C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094051C4
cosocleC42×C47C24
hypercenter#1582D47
hypocenterC47#17869
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #20252353C2semidirect
3. C8×D4×D47C2semidirect
4. #20242251C2semidirect
5. #20242249C2semidirect
6. #20242248C2semidirect
7. #20242246C2semidirect
8. #20242222C2semidirect
9. #20242219C2semidirect
10. #20242217C2semidirect
11. #20242137C2semidirect
12. #20241777C2semidirect
13. #20241774C2semidirect
14. #20241674C2semidirect
15. C47×#1582C2semidirect
20. #15689254C22semidirect
28. #15689202C22semidirect
29. #15689200C22semidirect
48. #15688876C22semidirect
49. #15688875C22semidirect
50. #15688873C22semidirect
51. Q8⋊(C47⋊C8)C22semidirect
53. #15688852C22semidirect
56. #15688850C22semidirect
57. #15688845C22semidirect
58. #15688844C22semidirect
59. #15688844C22semidirect
60. C47×#446C22semidirect
63. C47×#334C22semidirect
64. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
155. D4×D47M16semidirect
270. C8×C47AGL(1,ℤ/8)semidirect
314. #1582D47semidirect
333. #446C2×D47semidirect
366. #334C2×D47semidirect
368. Q8⋊C8C2×D47semidirect
378. #322C2×D47semidirect
379. C47#17869semidirect
590. C8#13094051semidirect

Maximal subgroups

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

subgroupindex
#202523532
C4×#130940512
C8×D4×D472
#202422512
#202422492
#202422482
#202422462
#202422222
#202422192
#202422172
#202421372
#202417772
#202417742
#202416742
C47×#15822
#1786947