Finite Group Databasebeta

← #26185939

Subgroups — #26185939

Order 12032.

650 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252495C211yesmaximal, characteristic
2#20252470C211yesmaximal, characteristic, complemented
3C4×#13094053C211yesmaximal, characteristic
4#20242262C211yesmaximal, characteristic, complemented
5#20242261C211yesmaximal, characteristic, complemented
6#20242242C211yesmaximal, characteristic, complemented
7#20242237C211yesmaximal, characteristic, complemented
8#20242236C211yesmaximal, characteristic, complemented
9#20242225C211yesmaximal, characteristic, complemented
10#20242224C211yesmaximal, characteristic, complemented
11#20242139C211yesmaximal, characteristic, complemented
12#20241767C211yesmaximal, characteristic
13Q8⋊C8×D47C211yesmaximal, characteristic, complemented
14#20241674C211yesmaximal, characteristic, complemented
15C47×#1585C211yesmaximal, characteristic, complemented
16C2×#13094053C411yescharacteristic
17C4×#10625352C2211yescharacteristic
18C4×Q8×D47C2211yescharacteristic
19#15689254C2211yescharacteristic
20#15689253C2211yescharacteristic
21#15689252—21no—
22#15689251—21no—
23#15689250C2211yescharacteristic
24C8×Dic94C2211yescharacteristic
25#15689247C2211yescharacteristic
26#15689229C411yescharacteristic
27#15689227C411yescharacteristic
28#15689224C411yescharacteristic
29#15689220C411yescharacteristic
30C4×Dic188C2211yescharacteristic
31C4×#10625337C2211yescharacteristic
32C4×#10625335C2211yescharacteristic
33D4×C47⋊C8C2211yescharacteristic
34C8×C22⋊D47—21no—
35(C22⋊D47)⋊C8—21no—
36#15689179—21no—
37#15689178—21no—
38#15689175C2211yescharacteristic
39#15689174C2211yescharacteristic
40#15689173—21no—
41#15689162C411yescharacteristic
42C2×Dic47⋊C8—21no—
43C4⋊C8×D47C2211yescharacteristic
44#15689130C411yescharacteristic
45#15689121C411yescharacteristic
46C4×#10625324C2211yescharacteristic
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#15688844C2211yescharacteristic
59#15688844C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
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×#10625324C2×C411yescharacteristic
74C2×#10625324C2×C411yescharacteristic
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78Q8×Dic47C2×C411yescharacteristic
79C4×Dic94—21no—
80C4×Dic94C2311yescharacteristic
81C4×Dic94C2311yescharacteristic
82#13093989—21no—
83#13093989C2×C411yescharacteristic
84#13093989C2×C411yescharacteristic
85D4×Dic47C2×C411yescharacteristic
86C4×C22⋊D47—21no—
87(C22⋊D47)⋊C4—21no—
88#13093982C2×C411yescharacteristic
89#13093980—21no—
90C4⋊C4×D47—21no—
91C4⋊C4×D47C2×C411yescharacteristic
92C2×C4×Dic47—21no—
93C42×D47—21no—
94C42×D47C2311yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093955C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8D411yescharacteristic
107Dic47⋊C8D411yescharacteristic
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)⋊C8D411yescharacteristic
117(C2×D47)⋊C8D411yescharacteristic
118#13093935—21no—
119#13093934—21no—
120#13093934—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×Dic47—21no—
130C2×SD16×C47C2×C411yescharacteristic
131C22×C8×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—
141#97×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×D47—22no—
153#10625352—22no—
154#10625352M1614yes—
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—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—81no—
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
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—81no—
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—42no—
211C8×D47—81no—
212C23×C47—21no—
213C22×D47C4×D411yescharacteristic
214Q8×C47—21no—
215Q8×C47—21no—
216D4×C47—21no—
217D4×C47C2×M1612yes—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47C23×C411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C2×C4×C47C2×#4111yescharacteristic
226C22⋊D47—24no—
227C2×Dic47—21no—
228C2×Dic47—24no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—81no—
233C2×Dic47C4×D411yescharacteristic
234C2×Dic47C4×D411yescharacteristic
235C2×Dic47C4×D411yescharacteristic
236C4×D47—21no—
237C4×D47—21no—
238C4×D47—41no—
239C4×D47—42no—
240C4×D47—81no—
241C4×D47C2×M1612yes—
242C4×D47#13112yes—
243Dic94—21no—
244Dic94—21no—
245Dic94—21no—
246Dic94—42no—
247Dic94C2×M1612yes—
248C8×C47—22no—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—41no—
254C8×C47—41no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262#17876—471nomaximal, Sylow
263C22×C47—22no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47C2×C4×D411yescharacteristic
267C2×D47—21no—
268C2×D47—21no—
269C2×D47#43512yes—
270C4×C47—21no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47C22×M1611yescharacteristic
275C4×C47C2×#13111yescharacteristic
276C4×C47#57711yescharacteristic
277C4×C47#57811yescharacteristic
278Dic47—22no—
279Dic47—21no—
280Dic47—21no—
281Dic47—41no—
282Dic47—41no—
283Dic47—41no—
284Dic47#43512yes—
285#2988—471no—
286#2983—471no—
287C4×#137—471no—
288#1587—471no—
289#1587—471no—
290#1585—471no—
291#1585D4711yescharacteristic, complemented
292#1584—471no—
293#1584—471no—
294#1582—471no—
295#1582—471no—
296#1565—471no—
297#1476—471no—
298C2×Q8⋊C8—471no—
299#1451—471no—
300C2×C47—42no—
301C2×C47C2×#43511yescharacteristic
302C2×C47#294711yescharacteristic
303C2×C47#295611yescharacteristic
304D47—22no—
305C2×#137—471no—
306C4×#41—471no—
307C2×C4×Q8—471no—
308#446—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313#446C2×D4711yescharacteristic
314C8×Q8—471no—
315C8×Q8—471no—
316#441—471no—
317#441—471no—
318#440—471no—
319#440—471no—
320C4×Q16—471no—
321C4×Q16—471no—
322C4×SD16—471no—
323C4×SD16C2×D4711yescharacteristic
324C8×D4—471no—
325C8×D4—941no—
326C8×D4—941no—
327C8×D4C2×D4711yescharacteristic
328#432—941no—
329#432—941no—
330#431—471no—
331#431—471no—
332#431—941no—
333#428—471no—
334C2×C4⋊C8—471no—
335C2×C4⋊C8—941no—
336#419—471no—
337#417—471no—
338C4×M16—471no—
339C2×C4×C8—471no—
340#335—471no—
341#335C2×D4711yescharacteristic
342#334—471no—
343#334—471no—
344Q8⋊C8—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8—471no—
349Q8⋊C8C2×D4711yescharacteristic
350D4⋊C8—471no—
351D4⋊C8C2×D4711yescharacteristic
352#322—471no—
353#322—471no—
354#322—471no—
355#322C2×D4711yescharacteristic
356C47#1787611yescharacteristic, complemented, Sylow
357C2×#41—471no—
358C22×Q8—471no—
359#137—944no—
360C2×Q16—471no—
361C2×Q16—471no—
362C2×SD16—471no—
363C2×SD16C4×D4711yescharacteristic
364C2×M16—471no—
365C2×M16—471no—
366C22×C8—21no—
367C22×C8—941no—
368C22×C8—941no—
369C22×C8—941no—
370C4×Q8—471no—
371C4×Q8—471no—
372C4×Q8—471no—
373C4×Q8—471no—
374C4×Q8—471no—
375C4×Q8—941no—
376C4×Q8—941no—
377C4×Q8C22×D4711yescharacteristic
378C4×D4—471no—
379C4×D4—941no—
380C4×D4—941no—
381C4×D4C22×D4711yescharacteristic
382#117—471no—
383#117—941no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—941no—
386C2×C42—471no—
387C2×C42—941no—
388C2×C42—941no—
389#107—471no—
390#107—471no—
391#106—471no—
392#106C4×D4711yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—471no—
395C4⋊C8—471no—
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⋊C8C22×D4711yescharacteristic
405C4⋊C8C22×D4711yescharacteristic
406#103—471no—
407#103—471no—
408#103—471no—
409#103—471no—
410#103—471no—
411#103C4×D4711yescharacteristic
412#102—471no—
413#102C4×D4711yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—471no—
416C22⋊C8—471no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419#97—21no—
420#97—471no—
421#97—471no—
422#97—941no—
423#97—941no—
424#97—941no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—941no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—474no—
436#41—942no—
437C2×Q8—471no—
438C2×Q8—471no—
439C2×Q8—941no—
440C2×Q8—942no—
441C2×Q8—942no—
442C2×Q8C2×C4×D4711yescharacteristic
443C2×D4—941no—
444C2×D4C2×C4×D4711yescharacteristic
445C22×C4—21no—
446C22×C4—471no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453Q16—942no—
454Q16—942no—
455SD16—22no—
456SD16—942no—
457M16—942no—
458M16—942no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—471no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—3761no—
471C2×C8—3761no—
472C2×C8—1882no—
473C2×C8C2×C4×D4711yescharacteristic
474C2×C8C2×C4×D4711yescharacteristic
475C2×C8D4×D4711yescharacteristic
476C2×C8D4×D4711yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—471no—
479C4⋊C4—471no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4C2×C4×D4711yescharacteristic
487C4⋊C4C2×C4×D4711yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C42—21no—
492C42—471no—
493C42—471no—
494C42—471no—
495C42—941no—
496C42—941no—
497C42—941no—
498C42—941no—
499C42—941no—
500C42—941no—
501C42C23×D4711yescharacteristic
502C23—21no—
503C23—471no—
504Q8—21no—
505Q8—21no—
506Q8—472no—
507Q8—941no—
508Q8—941no—
509Q8—941no—
510Q8—1882no—
511D4—21no—
512D4—944no—
513D4M16×D4712yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—471no—
520C2×C4—472no—
521C2×C4—472no—
522C2×C4—471no—
523C2×C4—471no—
524C2×C4—944no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—3761no—
532C2×C4—3761no—
533C2×C4—1881no—
534C2×C4—1882no—
535C2×C4C22×C4×D4711yescharacteristic
536C2×C4C2×D4×D4711yescharacteristic
537C2×C4#41×D4711yescharacteristic
538C8—22no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—941no—
546C8—941no—
547C8—941no—
548C8—941no—
549C8—1881no—
550C8—1881no—
551C8—1881no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—472no—
556C22—941no—
557C22—941no—
558C22C4×D4×D4711yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—472no—
564C4—941no—
565C4—941no—
566C4—942no—
567C4—1881no—
568C4—1881no—
569C4—1881no—
570C4C2×M16×D4711yescharacteristic
571C4#131×D4711yescharacteristic
572C4#1568993311yescharacteristic
573C4#1568993911yescharacteristic
574C2—42no—
575C2—942no—
576C2#435×D4711yescharacteristic
577C2#2025222811yescharacteristic
578C2#2025229311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1585C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625352C2×C4
cosocleC42×C47C24
hypercenter#1585D47
hypocenterC47#17876
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #20252470C2semidirect
4. #20242262C2semidirect
5. #20242261C2semidirect
6. #20242242C2semidirect
7. #20242237C2semidirect
8. #20242236C2semidirect
9. #20242225C2semidirect
10. #20242224C2semidirect
11. #20242139C2semidirect
13. Q8⋊C8×D47C2semidirect
14. #20241674C2semidirect
15. C47×#1585C2semidirect
291. #1585D47semidirect
356. C47#17876semidirect

Maximal subgroups

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

subgroupindex
#202524952
#202524702
C4×#130940532
#202422622
#202422612
#202422422
#202422372
#202422362
#202422252
#202422242
#202421392
#202417672
Q8⋊C8×D472
#202416742
C47×#15852
#1787647