Finite Group Databasebeta

← #26185880

Subgroups — #26185880

Order 12032.

738 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
1C8×#10625352C211yesmaximal, characteristic, complemented
2C4×#13094048C211yesmaximal, characteristic
3#436×D47C211yesmaximal, characteristic, complemented
4#20242268C211yesmaximal, characteristic, complemented
5#20242264C211yesmaximal, characteristic, complemented
6#20242252C211yesmaximal, characteristic, complemented
7#20242234C211yesmaximal, characteristic, complemented
8#20242230C211yesmaximal, characteristic, complemented
9#20242218C211yesmaximal, characteristic, complemented
10#20242214C211yesmaximal, characteristic, complemented
11#20242137C211yesmaximal, characteristic, complemented
12#20241777C211yesmaximal, characteristic, complemented
13#20241772C211yesmaximal, characteristic, complemented
14#20241676C211yesmaximal, characteristic, complemented
15C47×#1586C211yesmaximal, characteristic, complemented
16C2×#13094048C411yescharacteristic
17C2×M16×D47—21no—
18C4×#10625352C2211yescharacteristic
19C4×D4×D47C2211yescharacteristic
20C8×Dic94C2211yescharacteristic, complemented
21#15689247C2211yescharacteristic, complemented
22#15689235C411yescharacteristic
23#15689232C411yescharacteristic
24#15689222C411yescharacteristic
25#15689220C411yescharacteristic
26C4×#10625325C2211yescharacteristic
27C4×#10625335C2211yescharacteristic
28C4×#10625334C2211yescharacteristic
29#15689202C2211yescharacteristic
30#15689201C2211yescharacteristic
31#15689200C2211yescharacteristic
32#15689199—21no—
33#15689198—21no—
34D4×C47⋊C8C2211yescharacteristic, complemented
35C8×C22⋊D47—21no—
36(C22⋊D47)⋊C8—21no—
37#15689175C2211yescharacteristic
38#15689174C2211yescharacteristic
39#15689173—21no—
40#15689164C411yescharacteristic
41C4⋊C8×D47C2211yescharacteristic
42#15689126C411yescharacteristic
43#15689121C411yescharacteristic
44C22⋊C8×D47—21no—
45C4×#10625324C2211yescharacteristic
46C2×C8×Dic47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic, complemented
49#15688875C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688855C2211yescharacteristic, complemented
52#15688853C2211yescharacteristic, complemented
53#15688852C2211yescharacteristic
54D4⋊(C47⋊C8)C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic, complemented
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59#15688845C2211yescharacteristic, complemented
60C4×D8×C47C2211yescharacteristic
61C47×#436C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic, complemented
63C47×#334C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic, complemented
66C47×#322C2211yescharacteristic, complemented
67C2×#10625352C2×C411yescharacteristic
68C2×D4×D47C2×C411yescharacteristic
69C22×C4×D47—21no—
70#13094048—24no—
71C2×#10625325C2×C411yescharacteristic
72C2×#10625335C2×C411yescharacteristic
73C2×#10625334C2×C411yescharacteristic
74C2×#10625329—21no—
75C2×#10625324—21no—
76C2×#10625324—21no—
77C2×#10625324C2×C411yescharacteristic
78C2×#10625324C2×C411yescharacteristic
79M16×D47—44no—
80C22×C47⋊C8—21no—
81C2×C8×D47—21no—
82C2×C8×D47D411yescharacteristic
83C2×C8×D47D411yescharacteristic
84C4×Dic94C2311yescharacteristic
85#13093989C2×C411yescharacteristic
86C4×D188C2311yescharacteristic
87D4×Dic47C2×C411yescharacteristic
88D4×Dic47C2×C411yescharacteristic
89#13093986C2×C411yescharacteristic
90C4×C22⋊D47—21no—
91C4×C22⋊D47—21no—
92(C22⋊D47)⋊C4—21no—
93(C22⋊D47)⋊C4—21no—
94#13093982C2×C411yescharacteristic
95#13093980—21no—
96C4⋊C4×D47C2×C411yescharacteristic
97C22⋊C4×D47—21no—
98C2×C4×Dic47—21no—
99C42×D47C2311yescharacteristic
100#13093957C2×C411yescharacteristic
101#13093956C2×C411yescharacteristic
102#13093955C2×C411yescharacteristic
103C4⋊(C47⋊C8)C2311yescharacteristic
104C4⋊(C47⋊C8)C2311yescharacteristic
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093949C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093945C2×C411yescharacteristic
113#13093945C2×C411yescharacteristic
114#13093944C2×C411yescharacteristic
115C22⋊(C47⋊C8)—21no—
116C22⋊(C47⋊C8)—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121#13093934C2×C411yescharacteristic
122#13093934C2×C411yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C8×Dic47D411yescharacteristic
130C8×Dic47D411yescharacteristic
131C2×D8×C47C2×C411yescharacteristic
132C2×M16×C47—21no—
133C22×C8×C47—21no—
134C4×D4×C47C2311yescharacteristic
135C4×D4×C47C2311yescharacteristic
136#107×C47C2×C411yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139#102×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141C22⋊C8×C47—21no—
142C22⋊C8×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C4×C8×C47C2311yescharacteristic
146C23×D47—21no—
147C2×D4×C47C22×C411yescharacteristic
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C2×C22⋊D47—21no—
152C2×C22⋊D47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156#10625352—22no—
157#10625352M1614yescomplemented
158D4×D47—22no—
159D4×D47—22no—
160C2×D188C22×C411yescharacteristic
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×C4×D47—42no—
165C2×C4×D47—42no—
166C2×C4×D47C22×C411yescharacteristic
167C2×C4×D47C2×D411yescharacteristic
168C2×C4×D47#4111yescharacteristic
169C2×Dic94C22×C411yescharacteristic
170D8×C47—22no—
171M16×C47—42no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—42no—
176C2×C8×C47C22×C411yescharacteristic
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C4⋊C4×C47C22×C411yescharacteristic
181C4⋊C4×C47C22×C411yescharacteristic
182C22⋊C4×C47—21no—
183C22⋊C4×C47—21no—
184C42×C47C2411yescharacteristic
185C22⋊Dic47—21no—
186C22⋊Dic47—21no—
187#10625335—22no—
188#10625334—22no—
189(C2×D47)⋊C4—21no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192C4⋊Dic47C22×C411yescharacteristic
193C4⋊Dic47C22×C411yescharacteristic
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196Dic47⋊C4—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—21no—
200C4×Dic47C22×C411yescharacteristic
201C4×Dic47C2×D411yescharacteristic
202C4×Dic47#4111yescharacteristic
203#10625329—42no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—42no—
208C2×C47⋊C8C22×C411yescharacteristic
209C2×C47⋊C8C22×C411yescharacteristic
210C2×C47⋊C8C2×D411yescharacteristic
211C2×C47⋊C8C2×D411yescharacteristic
212#10625325—22no—
213#10625324—22no—
214#10625324—22no—
215#10625324—42no—
216#10625324—42no—
217C8×D47—22no—
218C8×D47—41no—
219C8×D47—42no—
220C23×C47—21no—
221C23×C47—21no—
222C22×D47—21no—
223C22×D47—42no—
224C22×D47—42no—
225C22×D47—42no—
226C22×D47C4×D411yescharacteristic
227D4×C47—21no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47C2×M1612yescomplemented
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47C23×C411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C22⋊D47—24no—
241C22⋊D47—42no—
242C2×Dic47—21no—
243C2×Dic47—24no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47C4×D411yescharacteristic
249C2×Dic47C4×D411yescharacteristic
250C2×Dic47C4×D411yescharacteristic
251D188—21no—
252D188—21no—
253C4×D47—21no—
254C4×D47—21no—
255C4×D47—41no—
256C4×D47—42no—
257C4×D47—42no—
258C4×D47—41no—
259C4×D47—41no—
260C4×D47C2×M1612yes—
261C4×D47#13112yes—
262Dic94—21no—
263Dic94C2×M1612yescomplemented
264C8×C47—21no—
265C8×C47—21no—
266C8×C47—21no—
267C8×C47—21no—
268C8×C47—41no—
269C8×C47—41no—
270C8×C47—41no—
271C47⋊C8—21no—
272C47⋊C8—21no—
273C47⋊C8—21no—
274C47⋊C8—41no—
275C47⋊C8—41no—
276C47⋊C8—41no—
277C47⋊C8AGL(1,ℤ/8)12yescomplemented
278#17871—471nomaximal, Sylow
279C22×C47—22no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47C2×C4×D411yescharacteristic
286C2×D47—21no—
287C2×D47—21no—
288C2×D47—41no—
289C2×D47—41no—
290C2×D47—41no—
291C2×D47—84no—
292C2×D47#43512yes—
293C4×C47—21no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47C22×M1611yescharacteristic
297C4×C47C2×#13111yescharacteristic
298C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C47#57511yescharacteristic
300Dic47—22no—
301Dic47—21no—
302Dic47—21no—
303Dic47—41no—
304Dic47—41no—
305Dic47#43512yes—
306C8×#41—471no—
307C4×AGL(1,ℤ/8)—471no—
308C2×#436—471no—
309#1588—471no—
310#1588—471no—
311#1586—471no—
312#1586D4711yescharacteristic, complemented
313#1583—471no—
314#1583—471no—
315#1581—471no—
316#1581—471no—
317#1565—471no—
318#1478—471no—
319#1477—471no—
320#1451—471no—
321C2×C47—42no—
322C2×C47—81no—
323C2×C47C2×#43511yescharacteristic
324C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C47#295511yescharacteristic
326D47—22no—
327D47—81no—
328C2×AGL(1,ℤ/8)—471no—
329C22×M16—941no—
330C4×#41—471no—
331C2×C4×D4—471no—
332C8×Q8—471no—
333C8×Q8—471no—
334#442—471no—
335#442—471no—
336#440—471no—
337#440—471no—
338C4×SD16—471no—
339C4×SD16—471no—
340C4×D8—471no—
341C4×D8C2×D4711yescharacteristic
342#436—471no—
343#436—471no—
344#436—471no—
345#436—941no—
346#436—941no—
347#436C2×D4711yescharacteristic
348C8×D4—471no—
349C8×D4—941no—
350C8×D4—941no—
351C8×D4C2×D4711yescharacteristic, complemented
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—
361C2×C4×C8—471no—
362C2×C4×C8—941no—
363#335—471no—
364#335—471no—
365#334—471no—
366#334C2×D4711yescharacteristic, complemented
367Q8⋊C8—471no—
368Q8⋊C8—471no—
369D4⋊C8—471no—
370D4⋊C8—471no—
371D4⋊C8—471no—
372D4⋊C8—471no—
373D4⋊C8C2×D4711yescharacteristic
374D4⋊C8C2×D4711yescharacteristic, complemented
375#322—471no—
376#322—471no—
377#322—471no—
378#322C2×D4711yescharacteristic, complemented
379C47#1787111yescharacteristic, complemented, Sylow
380C2×#41—471no—
381C22×D4—471no—
382C23×C4—941no—
383AGL(1,ℤ/8)—944no—
384C2×SD16—471no—
385C2×SD16—471no—
386C2×D8—471no—
387C2×D8C4×D4711yescharacteristic
388C2×M16—21no—
389C2×M16—471no—
390C2×M16—471no—
391C2×M16—941no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—1884no—
395C22×C8—21no—
396C22×C8—471no—
397C22×C8—471no—
398C22×C8—941no—
399C22×C8—941no—
400C4×Q8—471no—
401C4×Q8—471no—
402C4×D4—471no—
403C4×D4—471no—
404C4×D4—471no—
405C4×D4—471no—
406C4×D4—941no—
407C4×D4—941no—
408C4×D4—941no—
409C4×D4—941no—
410C4×D4C22×D4711yescharacteristic
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#107C4×D4711yescharacteristic
420#106—471no—
421#106—471no—
422C4⋊C8—471no—
423C4⋊C8—471no—
424C4⋊C8—941no—
425C4⋊C8—941no—
426C4⋊C8—941no—
427C4⋊C8—941no—
428C4⋊C8C22×D4711yescharacteristic
429C4⋊C8C22×D4711yescharacteristic
430#103—471no—
431#103—471no—
432#102—471no—
433#102—471no—
434#102—471no—
435#102—471no—
436#102C4×D4711yescharacteristic
437#102C4×D4711yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—941no—
441C22⋊C8—941no—
442C22⋊C8—941no—
443C22⋊C8—941no—
444C22⋊C8—941no—
445C22⋊C8—941no—
446#97—471no—
447#97—471no—
448C4×C8—471no—
449C4×C8—471no—
450C4×C8—471no—
451C4×C8—471no—
452C4×C8—471no—
453C4×C8—941no—
454C4×C8—941no—
455C4×C8—941no—
456C4×C8C22×D4711yescharacteristic
457C4×C8C22×D4711yescharacteristic
458C4×C8C22×D4711yescharacteristic
459C24—941no—
460#41—474no—
461#41—942no—
462C2×Q8—471no—
463C2×D4—471no—
464C2×D4—942no—
465C2×D4—942no—
466C2×D4—941no—
467C2×D4—941no—
468C2×D4C2×C4×D4711yescharacteristic
469C2×D4C2×C4×D4711yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—471no—
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—942no—
484SD16—942no—
485D8—22no—
486D8—942no—
487M16—42no—
488M16—942no—
489M16—942no—
490M16—1882no—
491M16—1882no—
492M16—1882no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—42no—
497C2×C8—471no—
498C2×C8—471no—
499C2×C8—471no—
500C2×C8—471no—
501C2×C8—942no—
502C2×C8—941no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—1881no—
506C2×C8—1882no—
507C2×C8—1882no—
508C2×C8C2×C4×D4711yescharacteristic
509C2×C8C2×C4×D4711yescharacteristic
510C2×C8D4×D4711yescharacteristic
511C2×C8D4×D4711yescharacteristic
512C4⋊C4—471no—
513C4⋊C4—471no—
514C4⋊C4—941no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4C2×C4×D4711yescharacteristic
518C4⋊C4C2×C4×D4711yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—941no—
522C22⋊C4—941no—
523C22⋊C4—941no—
524C22⋊C4—941no—
525C22⋊C4—941no—
526C42—471no—
527C42—471no—
528C42—471no—
529C42—941no—
530C42—941no—
531C42—941no—
532C42C23×D4711yescharacteristic
533C23—21no—
534C23—21no—
535C23—471no—
536C23—941no—
537C23—1882no—
538C23—1882no—
539C23—1882no—
540Q8—472no—
541Q8—941no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—944no—
546D4—941no—
547D4—941no—
548D4—1882no—
549D4M16×D4712yescomplemented
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—471no—
557C2×C4—472no—
558C2×C4—472no—
559C2×C4—471no—
560C2×C4—471no—
561C2×C4—944no—
562C2×C4—941no—
563C2×C4—941no—
564C2×C4—941no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—1881no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4—1882no—
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—21no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8—472no—
585C8—941no—
586C8—941no—
587C8—941no—
588C8—1881no—
589C8—1881no—
590C8—1881no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—472no—
598C22—941no—
599C22—941no—
600C22—3764no—
601C22—1881no—
602C22—1881no—
603C22—1881no—
604C22C4×D4×D4711yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—472no—
609C4—941no—
610C4—941no—
611C4—942no—
612C4—1881no—
613C4—1881no—
614C4C2×M16×D4711yescharacteristic
615C4#131×D4711yescharacteristic
616C4AGL(1,ℤ/8)×D4711yescharacteristic
617C4#1568991911yescharacteristic
618C2—42no—
619C2—81no—
620C2—942no—
621C2—3761no—
622C2#435×D4711yescharacteristic
623C2#2025219911yescharacteristic
624C2#2025228611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1586C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094048C4
cosocleC42×C47C24
hypercenter#1586D47
hypocenterC47#17871
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. C8×#10625352C2semidirect
3. #436×D47C2semidirect
4. #20242268C2semidirect
5. #20242264C2semidirect
6. #20242252C2semidirect
7. #20242234C2semidirect
8. #20242230C2semidirect
9. #20242218C2semidirect
10. #20242214C2semidirect
11. #20242137C2semidirect
12. #20241777C2semidirect
13. #20241772C2semidirect
14. #20241676C2semidirect
15. C47×#1586C2semidirect
20. C8×Dic94C22semidirect
21. #15689247C22semidirect
34. D4×C47⋊C8C22semidirect
48. #15688876C22semidirect
49. #15688875C22semidirect
50. #15688873C22semidirect
51. #15688855C22semidirect
52. #15688853C22semidirect
55. D4⋊(C47⋊C8)C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688845C22semidirect
62. C8×D4×C47C22semidirect
63. C47×#334C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×#322C22semidirect
157. #10625352M16semidirect
230. D4×C47C2×M16semidirect
263. Dic94C2×M16semidirect
277. C47⋊C8AGL(1,ℤ/8)semidirect
312. #1586D47semidirect
351. C8×D4C2×D47semidirect
366. #334C2×D47semidirect
374. D4⋊C8C2×D47semidirect
378. #322C2×D47semidirect
379. C47#17871semidirect
549. D4M16×D47semidirect

Maximal subgroups

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

subgroupindex
C8×#106253522
C4×#130940482
#436×D472
#202422682
#202422642
#202422522
#202422342
#202422302
#202422182
#202422142
#202421372
#202417772
#202417722
#202416762
C47×#15862
#1787147