Finite Group Databasebeta

← #26185875

Subgroups — #26185875

Order 12032.

660 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252351C211yesmaximal, characteristic
2C8×Q8×D47C211yesmaximal, characteristic, complemented
3C4×#13094053C211yesmaximal, characteristic
4#20242264C211yesmaximal, characteristic, complemented
5#20242261C211yesmaximal, characteristic, complemented
6#20242259C211yesmaximal, characteristic, complemented
7#20242237C211yesmaximal, characteristic, complemented
8#20242235C211yesmaximal, characteristic, complemented
9#20242234C211yesmaximal, characteristic, complemented
10#20242232C211yesmaximal, characteristic, complemented
11#20242139C211yesmaximal, characteristic, complemented
12#20241781C211yesmaximal, characteristic, complemented
13#20241772C211yesmaximal, characteristic
14#20241676C211yesmaximal, characteristic, complemented
15C47×#1588C211yesmaximal, characteristic, complemented
16C2×#13094053C411yescharacteristic
17C4×#10625352C2211yescharacteristic
18C4×Q8×D47C2211yescharacteristic
19#15689253C2211yescharacteristic
20#15689250C2211yescharacteristic
21Q8×C47⋊C8C2211yescharacteristic
22C8×Dic94—21no—
23C8×Dic94C2211yescharacteristic
24#15689247—21no—
25#15689247C2211yescharacteristic
26#15689229C411yescharacteristic
27#15689227C411yescharacteristic
28#15689224C411yescharacteristic
29#15689220C411yescharacteristic
30C4×Dic188C2211yescharacteristic
31C4×#10625337C2211yescharacteristic
32C4×#10625335C2211yescharacteristic
33#15689201C2211yescharacteristic
34#15689197—21no—
35#15689192—21no—
36#15689175C2211yescharacteristic
37#15689174C2211yescharacteristic
38#15689173—21no—
39#15689162C411yescharacteristic
40C4⋊C8×D47—21no—
41C4⋊C8×D47C2211yescharacteristic
42#15689130C411yescharacteristic
43#15689121C411yescharacteristic
44M16×Dic47—21no—
45C4×#10625324C2211yescharacteristic
46C4×C8×D47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688874C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54#15688853C2211yescharacteristic
55#15688853C2211yescharacteristic
56D4⋊(C47⋊C8)C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688845C2211yescharacteristic
59#15688845C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C47×#436C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625352C2×C411yescharacteristic
68C2×Q8×D47C2×C411yescharacteristic
69#13094053—24no—
70C2×Dic188C2×C411yescharacteristic
71C2×#10625337C2×C411yescharacteristic
72C2×#10625335C2×C411yescharacteristic
73C2×#10625329—21no—
74C2×#10625324C2×C411yescharacteristic
75C2×#10625324C2×C411yescharacteristic
76C2×C8×D47—21no—
77C2×C8×D47D411yescharacteristic
78C2×C8×D47D411yescharacteristic
79Q8×Dic47C2×C411yescharacteristic
80C4×Dic94—21no—
81C4×Dic94C2311yescharacteristic
82C4×Dic94C2311yescharacteristic
83#13093989—21no—
84#13093989C2×C411yescharacteristic
85#13093989C2×C411yescharacteristic
86D4×Dic47C2×C411yescharacteristic
87C4×C22⋊D47—21no—
88(C22⋊D47)⋊C4—21no—
89#13093982C2×C411yescharacteristic
90#13093980—21no—
91C4⋊C4×D47—21no—
92C4⋊C4×D47C2×C411yescharacteristic
93C2×C4×Dic47—21no—
94C42×D47—21no—
95C42×D47C2311yescharacteristic
96#13093958C2×C411yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108#13093949C2×C411yescharacteristic
109#13093949C2×C411yescharacteristic
110#13093948C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093945C2×C411yescharacteristic
114C22⋊(C47⋊C8)—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117#13093934—21no—
118#13093934—21no—
119#13093934C2×C411yescharacteristic
120#13093934C2×C411yescharacteristic
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
130C2×SD16×C47C2×C411yescharacteristic
131C2×M16×C47—21no—
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#106×C47C2×C411yescharacteristic
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C2×C22⋊D47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151Q8×D47—22no—
152Q8×D47M1614yescomplemented
153#10625352—22no—
154#10625352—22no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47C22×C411yescharacteristic
158C2×C4×D47C2×D411yescharacteristic
159C2×C4×D47#4111yescharacteristic
160C2×Dic94—21no—
161C2×Dic94C22×C411yescharacteristic
162C2×Dic94C22×C411yescharacteristic
163SD16×C47—22no—
164M16×C47—42no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C22⋊C4×C47—21no—
176C42×C47—21no—
177C42×C47C2411yescharacteristic
178C22⋊Dic47—21no—
179#10625337—22no—
180#10625335—22no—
181(C2×D47)⋊C4—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47C22×C411yescharacteristic
184C4⋊Dic47C22×C411yescharacteristic
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47C22×C411yescharacteristic
197C4×Dic47C2×D411yescharacteristic
198C4×Dic47#4111yescharacteristic
199#10625329—42no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207Dic188—22no—
208#10625324—22no—
209#10625324—22no—
210C8×D47—22no—
211C8×D47—41no—
212C8×D47—42no—
213C23×C47—21no—
214C22×D47C4×D411yescharacteristic
215Q8×C47—21no—
216Q8×C47C2×M1612yes—
217D4×C47—21no—
218D4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47C23×C411yescharacteristic
225C2×C4×C47C22×D411yescharacteristic
226C2×C4×C47C2×#4111yescharacteristic
227C22⋊D47—42no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47C4×D411yescharacteristic
235C2×Dic47C4×D411yescharacteristic
236C2×Dic47C4×D411yescharacteristic
237C4×D47—24no—
238C4×D47—21no—
239C4×D47—21no—
240C4×D47—41no—
241C4×D47—42no—
242C4×D47C2×M1612yes—
243C4×D47#13112yes—
244Dic94—21no—
245Dic94—24no—
246Dic94—21no—
247Dic94—21no—
248Dic94C2×M1612yes—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47—41no—
256C47⋊C8—21no—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262C47⋊C8#13712yescomplemented
263#17870—471nomaximal, Sylow
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47C2×C4×D411yescharacteristic
268C2×D47—21no—
269C2×D47—21no—
270C2×D47#43512yes—
271C4×C47—22no—
272C4×C47—21no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47C22×M1611yescharacteristic
276C4×C47C2×#13111yescharacteristic
277C4×C47C2×#13711yescharacteristic
278C4×C47#57511yescharacteristic
279Dic47—22no—
280Dic47—21no—
281Dic47—21no—
282Dic47—41no—
283Dic47—41no—
284Dic47—41no—
285Dic47#43512yes—
286#2965—471no—
287C2×C8×Q8—471no—
288C4×#137—471no—
289#1588—471no—
290#1588D4711yescharacteristic, complemented
291#1587—471no—
292#1587—471no—
293#1584—471no—
294#1584—471no—
295#1583—471no—
296#1583—471no—
297#1565—471no—
298#1479—471no—
299#1477—471no—
300#1451—471no—
301C2×C47—81no—
302C2×C47C2×#43511yescharacteristic
303C2×C47C4×#13711yescharacteristic
304C2×C47#295511yescharacteristic
305D47—22no—
306C2×#137—471no—
307C4×#41—471no—
308C2×C4×Q8—471no—
309#446—471no—
310#446—471no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—471no—
314C8×Q8—941no—
315C8×Q8—941no—
316C8×Q8C2×D4711yescharacteristic
317#441—471no—
318#441—471no—
319#440—471no—
320#440—471no—
321C4×Q16—471no—
322C4×Q16—471no—
323C4×SD16—471no—
324C4×SD16C2×D4711yescharacteristic
325#436—471no—
326#436C2×D4711yescharacteristic
327#435—941no—
328#435—941no—
329#431—471no—
330#431—471no—
331#431—941no—
332#428—471no—
333C2×C4⋊C8—471no—
334C2×C4⋊C8—941no—
335#419—471no—
336#417—471no—
337C4×M16—471no—
338C4×M16—941no—
339C2×C4×C8—471no—
340C2×C4×C8—941no—
341#335—471no—
342#335C2×D4711yescharacteristic
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8—471no—
349Q8⋊C8—471no—
350Q8⋊C8C2×D4711yescharacteristic
351D4⋊C8—471no—
352D4⋊C8C2×D4711yescharacteristic
353#322—471no—
354#322—471no—
355#322—471no—
356#322C2×D4711yescharacteristic
357C47#1787011yescharacteristic, complemented, Sylow
358C2×#41—471no—
359C22×Q8—471no—
360#137—944no—
361C2×Q16—471no—
362C2×Q16—471no—
363C2×SD16—471no—
364C2×SD16C4×D4711yescharacteristic
365C2×M16—21no—
366C2×M16—471no—
367C2×M16—471no—
368C2×M16—941no—
369C22×C8—471no—
370C22×C8—471no—
371C22×C8—941no—
372C4×Q8—471no—
373C4×Q8—471no—
374C4×Q8—471no—
375C4×Q8—471no—
376C4×Q8—471no—
377C4×Q8—941no—
378C4×Q8—941no—
379C4×Q8C22×D4711yescharacteristic
380C4×D4—471no—
381C4×D4—941no—
382C4×D4—941no—
383C4×D4C22×D4711yescharacteristic
384#117—471no—
385#117—941no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—941no—
388C2×C42—471no—
389C2×C42—941no—
390C2×C42—941no—
391#107—471no—
392#107—471no—
393#106—471no—
394#106C4×D4711yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8—941no—
404C4⋊C8—941no—
405C4⋊C8C22×D4711yescharacteristic
406C4⋊C8C22×D4711yescharacteristic
407#103—471no—
408#103—471no—
409#103—471no—
410#103—471no—
411#103—471no—
412#103C4×D4711yescharacteristic
413#102—471no—
414#102C4×D4711yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419#97—471no—
420#97—471no—
421#97—941no—
422#97—941no—
423C4×C8—21no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8—941no—
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435C4×C8C22×D4711yescharacteristic
436#41—942no—
437#41—942no—
438C2×Q8—474no—
439C2×Q8—471no—
440C2×Q8—471no—
441C2×Q8—941no—
442C2×Q8—942no—
443C2×Q8C2×C4×D4711yescharacteristic
444C2×D4—941no—
445C2×D4C2×C4×D4711yescharacteristic
446C22×C4—21no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454Q16—942no—
455Q16—942no—
456SD16—22no—
457SD16—942no—
458M16—42no—
459M16—942no—
460M16—942no—
461M16—1882no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—471no—
466C2×C8—471no—
467C2×C8—471no—
468C2×C8—471no—
469C2×C8—942no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—1881no—
474C2×C8—1882no—
475C2×C8C2×C4×D4711yescharacteristic
476C2×C8C2×C4×D4711yescharacteristic
477C2×C8D4×D4711yescharacteristic
478C2×C8D4×D4711yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—471no—
481C4⋊C4—471no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4C2×C4×D4711yescharacteristic
489C4⋊C4C2×C4×D4711yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—471no—
495C42—471no—
496C42—471no—
497C42—941no—
498C42—941no—
499C42—941no—
500C42—941no—
501C42—941no—
502C42—941no—
503C42C23×D4711yescharacteristic
504C23—21no—
505C23—471no—
506Q8—21no—
507Q8—472no—
508Q8—944no—
509Q8—941no—
510Q8—941no—
511Q8—941no—
512Q8M16×D4712yes—
513D4—21no—
514D4—21no—
515D4—1882no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—471no—
522C2×C4—472no—
523C2×C4—472no—
524C2×C4—471no—
525C2×C4—471no—
526C2×C4—944no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—1881no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4C22×C4×D4711yescharacteristic
538C2×C4C2×D4×D4711yescharacteristic
539C2×C4#41×D4711yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—472no—
548C8—941no—
549C8—941no—
550C8—941no—
551C8—1881no—
552C8—1881no—
553C8—1881no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—472no—
558C22—941no—
559C22—941no—
560C22C4×D4×D4711yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—472no—
566C4—941no—
567C4—941no—
568C4—942no—
569C4—1881no—
570C4—1881no—
571C4—1881no—
572C4C2×M16×D4711yescharacteristic
573C4#131×D4711yescharacteristic
574C4#137×D4711yescharacteristic
575C4#1568991911yescharacteristic
576C2—81no—
577C2—942no—
578C2#435×D4711yescharacteristic
579C2#2025221011yescharacteristic
580C2#2025228611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1588C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625352C2×C4
cosocleC42×C47C24
hypercenter#1588D47
hypocenterC47#17870
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D47C2semidirect
4. #20242264C2semidirect
5. #20242261C2semidirect
6. #20242259C2semidirect
7. #20242237C2semidirect
8. #20242235C2semidirect
9. #20242234C2semidirect
10. #20242232C2semidirect
11. #20242139C2semidirect
12. #20241781C2semidirect
14. #20241676C2semidirect
15. C47×#1588C2semidirect
152. Q8×D47M16semidirect
262. C47⋊C8#137semidirect
290. #1588D47semidirect
357. C47#17870semidirect

Maximal subgroups

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

subgroupindex
#202523512
C8×Q8×D472
C4×#130940532
#202422642
#202422612
#202422592
#202422372
#202422352
#202422342
#202422322
#202421392
#202417812
#202417722
#202416762
C47×#15882
#1787047