Finite Group Databasebeta

← #26187459

Subgroups — #26187459

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253455C211yesmaximal, characteristic
2#20252511C211yesmaximal, characteristic
3#20252486C211yesmaximal, characteristic, complemented
4#20242284C211yesmaximal, characteristic, complemented
5#20242283C211yesmaximal, characteristic, complemented
6#20242261C211yesmaximal, characteristic, complemented
7#20242256C211yesmaximal, characteristic, complemented
8#20242242C211yesmaximal, characteristic, complemented
9SD16×C47⋊C8C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242178C211yesmaximal, characteristic, complemented
12#20241841C211yesmaximal, characteristic, complemented
13#20241767C211yesmaximal, characteristic
14#20241673C211yesmaximal, characteristic, complemented
15C47×#1585C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17C4×#10625352C2211yescharacteristic
18#15689467C411yescharacteristic
19#15689463C411yescharacteristic
20#15689407C411yescharacteristic
21#15689401C411yescharacteristic
22#15689332C411yescharacteristic
23#15689326C411yescharacteristic
24#15689286C411yescharacteristic
25#15689282C411yescharacteristic
26#15689253C2211yescharacteristic
27#15689251—21no—
28#15689250C2211yescharacteristic
29#15689250C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31C8×Dic94C2211yescharacteristic
32#15689247—21no—
33C4×Dic188C2211yescharacteristic
34C4×#10625337C2211yescharacteristic
35C4×#10625335C2211yescharacteristic
36#15689194—21no—
37#15689191—21no—
38D4×C47⋊C8C2211yescharacteristic
39#15689185—21no—
40#15689183—21no—
41#15689177—21no—
42#15689175C2211yescharacteristic
43#15689174C2211yescharacteristic
44#15689174C2211yescharacteristic
45#15689145C2211yescharacteristic
46C2×Dic47⋊C8—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#15688844C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625352C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625324—21no—
72C22×C47⋊C8—21no—
73C2×C8×D47—21no—
74#13094023C2×C411yescharacteristic
75#13094022C2×C411yescharacteristic
76#13094014—21no—
77#13094004C2×C411yescharacteristic
78#13094002—21no—
79#13094000C2×C411yescharacteristic
80C4×Dic94—21no—
81C4×Dic94C2311yescharacteristic
82C4×Dic94C2311yescharacteristic
83#13093989C2×C411yescharacteristic
84D4×Dic47C2×C411yescharacteristic
85C4×C22⋊D47—21no—
86(C22⋊D47)⋊C4—21no—
87#13093982C2×C411yescharacteristic
88#13093981—21no—
89#13093980—21no—
90C2×C4×Dic47—21no—
91C42×D47C2311yescharacteristic
92#13093958C2×C411yescharacteristic
93#13093957C2×C411yescharacteristic
94#13093955C2×C411yescharacteristic
95C4⋊(C47⋊C8)—21no—
96C4⋊(C47⋊C8)C2311yescharacteristic
97C4⋊(C47⋊C8)C2311yescharacteristic
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105Dic47⋊C8D411yescharacteristic
106Dic47⋊C8D411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093949C2×C411yescharacteristic
109#13093948C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093945C2×C411yescharacteristic
113C22⋊(C47⋊C8)—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8C2×C411yescharacteristic
116(C2×D47)⋊C8C2×C411yescharacteristic
117(C2×D47)⋊C8D411yescharacteristic
118(C2×D47)⋊C8D411yescharacteristic
119#13093934—21no—
120#13093934—21no—
121#13093934—21no—
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×SD16×C47C2×C411yescharacteristic
130C22×C8×C47—21no—
131C4×Q8×C47C2311yescharacteristic
132C4×D4×C47C2311yescharacteristic
133#106×C47C2×C411yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139C22⋊C8×C47—21no—
140#97×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47C22×C411yescharacteristic
146C22×C4×C47—21no—
147C2×C22⋊D47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150#10625352—22no—
151#10625352—41no—
152C2×C4×D47C22×C411yescharacteristic
153C2×C4×D47C2×D411yescharacteristic
154C2×C4×D47#4111yescharacteristic
155C2×Dic94—21no—
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158SD16×C47—22no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—81no—
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C4⋊C4×C47—21no—
168C4⋊C4×C47C22×C411yescharacteristic
169C4⋊C4×C47C22×C411yescharacteristic
170C22⋊C4×C47—21no—
171C42×C47—21no—
172C42×C47C2411yescharacteristic
173C22⋊Dic47—21no—
174#10625337—41no—
175#10625335—22no—
176(C2×D47)⋊C4—21no—
177(C2×D47)⋊C4—21no—
178(C2×D47)⋊C4—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47C22×C411yescharacteristic
181C4⋊Dic47C22×C411yescharacteristic
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47C22×C411yescharacteristic
194C4×Dic47C2×D411yescharacteristic
195C4×Dic47#4111yescharacteristic
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—81no—
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204Dic188—41no—
205#10625324—81no—
206C8×D47—24no—
207C23×C47—21no—
208C22×D47C4×D411yescharacteristic
209Q8×C47—21no—
210Q8×C47—21no—
211D4×C47—21no—
212D4×C47#13112yes—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47C23×C411yescharacteristic
219C2×C4×C47C22×D411yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C22⋊D47—42no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—42no—
227C2×Dic47—42no—
228C2×Dic47C4×D411yescharacteristic
229C2×Dic47C4×D411yescharacteristic
230C2×Dic47C4×D411yescharacteristic
231C4×D47—21no—
232C4×D47—21no—
233C4×D47—21no—
234C4×D47—21no—
235C4×D47—22no—
236Dic94—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—21no—
240Dic94—42no—
241C8×C47—22no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C47⋊C8—22no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#18016—471nomaximal, Sylow
256C22×C47—22no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47C2×C4×D411yescharacteristic
260C2×D47—21no—
261C2×D47—21no—
262C2×D47—21no—
263C4×C47—21no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47C2×#13111yescharacteristic
268C4×C47#56811yescharacteristic
269C4×C47#57711yescharacteristic
270C4×C47#57811yescharacteristic
271Dic47—21no—
272Dic47—21no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47#44312yes—
278#3107—471no—
279#2990—471no—
280#2986—471no—
281#1591—471no—
282#1591—471no—
283#1587—471no—
284#1587—471no—
285#1585—471no—
286#1585D4711yescharacteristic, complemented
287C8×SD16—471no—
288C8×SD16—471no—
289#1574—471no—
290#1493—471no—
291#1476—471no—
292#1450—471no—
293C2×C47—42no—
294C2×C47#293311yescharacteristic
295C2×C47#294711yescharacteristic
296C2×C47C2×#44311yescharacteristic
297D47—41no—
298#533—471no—
299C4×#41—471no—
300#485—471no—
301#485—471no—
302#475—471no—
303#474—471no—
304#462—471no—
305#461—471no—
306#452—471no—
307#452—471no—
308#446—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446C2×D4711yescharacteristic
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8—941no—
316C4×Q16—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16C2×D4711yescharacteristic
320#435—941no—
321#435—941no—
322C8×D4—471no—
323C8×D4C2×D4711yescharacteristic
324#433—941no—
325#433—941no—
326#432—941no—
327#431—471no—
328#431—471no—
329#431—471no—
330#423—471no—
331C2×C4⋊C8—941no—
332C2×C4×C8—471no—
333#335—471no—
334#335C2×D4711yescharacteristic
335#334—471no—
336#334—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8C2×D4711yescharacteristic
343D4⋊C8—471no—
344D4⋊C8C2×D4711yescharacteristic
345#322—471no—
346#322C2×D4711yescharacteristic
347C82—471no—
348C82—471no—
349C47#1801611yescharacteristic, complemented, Sylow
350C2×#41—471no—
351C2×Q16—471no—
352C2×Q16—471no—
353C2×SD16—471no—
354C2×SD16C4×D4711yescharacteristic
355C2×M16—941no—
356C22×C8—21no—
357C22×C8—941no—
358C22×C8—941no—
359C4⋊Q8—471no—
360C4⋊Q8—471no—
361#125—941no—
362C22⋊Q8—471no—
363C22⋊Q8—471no—
364C22⋊Q8—941no—
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—471no—
368C4×Q8—941no—
369C4×Q8C22×D4711yescharacteristic
370C4×D4—471no—
371C4×D4—941no—
372C4×D4—941no—
373C4×D4C22×D4711yescharacteristic
374#117—471no—
375#117—941no—
376#117—941no—
377C2×C42—471no—
378C2×C42—941no—
379#107—471no—
380#107—471no—
381#106—471no—
382#106C4×D4711yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8C22×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103C4×D4711yescharacteristic
404#102—471no—
405#102C4×D4711yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—471no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—471no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413#97—21no—
414#97—941no—
415#97—941no—
416#97—941no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427#41—942no—
428#41—1881no—
429C2×Q8—471no—
430C2×Q8—471no—
431C2×Q8—941no—
432C2×Q8C2×C4×D4711yescharacteristic
433C2×D4—941no—
434C2×D4C2×C4×D4711yescharacteristic
435C22×C4—21no—
436C22×C4—471no—
437C22×C4—471no—
438C22×C4—471no—
439C22×C4—941no—
440C22×C4—941no—
441Q16—1881no—
442Q16—1881no—
443SD16—22no—
444SD16—942no—
445M16—3761no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—81no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—944no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—3761no—
459C2×C8C2×C4×D4711yescharacteristic
460C2×C8C2×C4×D4711yescharacteristic
461C2×C8D4×D4711yescharacteristic
462C2×C8D4×D4711yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—471no—
465C4⋊C4—471no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4C2×C4×D4711yescharacteristic
475C4⋊C4C2×C4×D4711yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—471no—
483C42—471no—
484C42—471no—
485C42—941no—
486C42—941no—
487C42—941no—
488C42—941no—
489C42C23×D4711yescharacteristic
490C23—21no—
491C23—471no—
492Q8—21no—
493Q8—21no—
494Q8—941no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—1882no—
499D4—21no—
500D4—1882no—
501D4#1309403212yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—471no—
508C2×C4—471no—
509C2×C4—471no—
510C2×C4—942no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—1882no—
520C2×C4—1882no—
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4#41×D4711yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—942no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—1881no—
537C8—1881no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—941no—
542C22—941no—
543C22—941no—
544C22C4×D4×D4711yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—472no—
550C4—941no—
551C4—941no—
552C4—1881no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4C2×#1309403211yescharacteristic
557C4#1568988811yescharacteristic
558C4#1568993311yescharacteristic
559C4#1568993911yescharacteristic
560C2—42no—
561C2—1881no—
562C2#2025211411yescharacteristic
563C2#2025222811yescharacteristic
564C2#443×D4711yescharacteristic
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#18016
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
3. #20252486C2semidirect
4. #20242284C2semidirect
5. #20242283C2semidirect
6. #20242261C2semidirect
7. #20242256C2semidirect
8. #20242242C2semidirect
9. SD16×C47⋊C8C2semidirect
10. C8×#10625335C2semidirect
11. #20242178C2semidirect
12. #20241841C2semidirect
14. #20241673C2semidirect
15. C47×#1585C2semidirect
286. #1585D47semidirect
349. C47#18016semidirect

Maximal subgroups

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

subgroupindex
#202534552
#202525112
#202524862
#202422842
#202422832
#202422612
#202422562
#202422422
SD16×C47⋊C82
C8×#106253352
#202421782
#202418412
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C47×#15852
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