Finite Group Databasebeta

← #26187221

Subgroups — #26187221

Order 12032.

616 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#20253400C211yesmaximal, characteristic
2#20252406C211yesmaximal, characteristic, complemented
3#20242278C211yesmaximal, characteristic, complemented
4#20242271C211yesmaximal, characteristic, complemented
5#20242236C211yesmaximal, characteristic, complemented
6#20242231C211yesmaximal, characteristic, complemented
7#20242229C211yesmaximal, characteristic, complemented
8#20242217C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242166C211yesmaximal, characteristic, complemented
12#20241848C211yesmaximal, characteristic, complemented
13#20241768C211yesmaximal, characteristic, complemented
14M16×C47⋊C8C211yesmaximal, characteristic, complemented
15C47×#2969C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689461C411yescharacteristic
18#15689444C411yescharacteristic
19#15689427C411yescharacteristic
20#15689420C411yescharacteristic
21#15689342C411yescharacteristic
22#15689335C411yescharacteristic
23#15689283C411yescharacteristic
24#15689266C411yescharacteristic
25C8×Dic94C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625337C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625335C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689202C2211yescharacteristic
32#15689202C2211yescharacteristic
33#15689199—21no—
34#15689199—21no—
35#15689180C2211yescharacteristic
36#15689178—21no—
37#15689176C2211yescharacteristic
38#15689075—21no—
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46#15688853C2211yescharacteristic
47#15688853C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688844C2211yescharacteristic
53#15688844C2211yescharacteristic
54C8×C47⋊C8C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C47×#529C2211yescharacteristic
57C47×#446C2211yescharacteristic
58C8×Q8×C47C2211yescharacteristic
59C47×#436—21no—
60C47×#436C2211yescharacteristic
61C47×#435—21no—
62C8×D4×C47C2211yescharacteristic
63C47×#433—21no—
64C47×#431C2211yescharacteristic
65C47×#405—21no—
66C4×M16×C47C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×#10625324—21no—
74C22×C47⋊C8—21no—
75C4×Dic94C2×C411yescharacteristic
76C4×Dic94C2311yescharacteristic
77C4×D188C2×C411yescharacteristic
78C4×D188C2311yescharacteristic
79C4×C22⋊D47—21no—
80C4×C22⋊D47—21no—
81#13093983C2×C411yescharacteristic
82#13093981—21no—
83C42×D47—21no—
84#13093957C2×C411yescharacteristic
85#13093957C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88C4⋊(C47⋊C8)C2×C411yescharacteristic
89C4⋊(C47⋊C8)C2×C411yescharacteristic
90C4⋊(C47⋊C8)C2311yescharacteristic
91C4⋊(C47⋊C8)C2311yescharacteristic
92Dic47⋊C8—21no—
93Dic47⋊C8—21no—
94#13093948C2×C411yescharacteristic
95#13093948C2×C411yescharacteristic
96#13093947C2×C411yescharacteristic
97#13093947C2×C411yescharacteristic
98#13093945C2×C411yescharacteristic
99#13093945C2×C411yescharacteristic
100#13093944C2×C411yescharacteristic
101#13093944C2×C411yescharacteristic
102C22⋊(C47⋊C8)—21no—
103C22⋊(C47⋊C8)C2×C411yescharacteristic
104C22⋊(C47⋊C8)C2×C411yescharacteristic
105(C2×D47)⋊C8—21no—
106(C2×D47)⋊C8—21no—
107#13093935—21no—
108C4×C47⋊C8—21no—
109C4×C47⋊C8C2311yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C8×Dic47—21no—
114C8×Dic47—21no—
115C2×M16×C47—21no—
116C2×M16×C47D411yescharacteristic
117C2×M16×C47D411yescharacteristic
118C22×C8×C47—21no—
119#126×C47—21no—
120#125×C47C2×C411yescharacteristic
121#124×C47C2×C411yescharacteristic
122#123×C47—21no—
123C22⋊Q8×C47C2×C411yescharacteristic
124#121×C47C2×C411yescharacteristic
125C4×Q8×C47C2311yescharacteristic
126C4×D4×C47—21no—
127C4×D4×C47C2311yescharacteristic
128#117×C47—21no—
129C2×C42×C47C2311yescharacteristic
130C4⋊C8×C47—21no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47—21no—
137#97×C47—21no—
138#97×C47D411yescharacteristic
139#97×C47D411yescharacteristic
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47—21no—
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C2×C22⋊D47—21no—
152#10625350—22no—
153#10625350—41no—
154C2×D188C22×C411yescharacteristic
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×Dic94C22×C411yescharacteristic
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—42no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—42no—
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C2×C8×C47C2×D411yescharacteristic
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C42×C47—21no—
181C42×C47C22×C411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47#4111yescharacteristic
184C42×C47C2411yescharacteristic
185C22⋊Dic47—21no—
186#10625337—22no—
187#10625336—41no—
188#10625335—22no—
189#10625334—41no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192C4⋊Dic47C22×C411yescharacteristic
193C4⋊Dic47C22×C411yescharacteristic
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—42no—
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208#10625324—42no—
209#10625324—42no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212C22×D47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—81no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C22⋊D47—42no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238D188—21no—
239D188—21no—
240C4×D47—42no—
241C4×D47—41no—
242C4×D47—41no—
243C4×D47—81no—
244Dic94—21no—
245Dic94#13112yes—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47#13512yes—
251C8×C47#13512yes—
252C47⋊C8—22no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259C47⋊C8—41no—
260#17999—471nomaximal, Sylow
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47C2×C4×D411yescharacteristic
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47C2×#13111yescharacteristic
279C4×C47#56811yescharacteristic
280C4×C47C2×#13511yescharacteristic
281C4×C47C2×#13511yescharacteristic
282Dic47—22no—
283Dic47—41no—
284Dic47—41no—
285#3102—471no—
286#2971—471no—
287#2969D4711yescharacteristic, complemented
288#1590—471no—
289#1589—471no—
290#1584—471no—
291#1583—471no—
292#1583—471no—
293#1581—471no—
294C8×Q16—471no—
295C8×SD16—471no—
296#1572—471no—
297#1494—471no—
298#1476—471no—
299C8×M16—471no—
300C2×C47—41no—
301C2×C47—81no—
302C2×C47#293311yescharacteristic
303C2×C47C4×#13511yescharacteristic
304C2×C47#295611yescharacteristic
305D47—81no—
306#529C2×D4711yescharacteristic
307C4×#41—471no—
308#485—471no—
309#482—471no—
310#479—471no—
311#478—471no—
312#464—471no—
313#463—471no—
314#452—471no—
315#449—471no—
316#446C2×D4711yescharacteristic
317C8×Q8—471no—
318C8×Q8—471no—
319C8×Q8C2×D4711yescharacteristic
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16—471no—
323C4×D8—471no—
324#436—21no—
325#436—471no—
326#436—471no—
327#436—941no—
328#436—941no—
329#436C2×D4711yescharacteristic
330#435—21no—
331C8×D4C2×D4711yescharacteristic
332#433—21no—
333#432—471no—
334#432—941no—
335#431—471no—
336#431C2×D4711yescharacteristic
337#405—21no—
338C4×M16—941no—
339C4×M16C2×D4711yescharacteristic
340C2×C4×C8—471no—
341#335—471no—
342#335—471no—
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8—471no—
352D4⋊C8—471no—
353#322—471no—
354#322—471no—
355C82—471no—
356C82—471no—
357C47#1799911yescharacteristic, complemented, Sylow
358C2×#41—471no—
359C2×Q16—471no—
360C2×SD16—471no—
361C2×SD16—471no—
362C2×D8—471no—
363C2×M16—21no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16C22⋊D4711yescharacteristic
367C2×M16C22⋊D4711yescharacteristic
368C22×C8—21no—
369C22×C8—941no—
370#126—21no—
371#125C4×D4711yescharacteristic
372#124C4×D4711yescharacteristic
373#123—21no—
374C22⋊Q8C4×D4711yescharacteristic
375#121C4×D4711yescharacteristic
376C4×Q8—471no—
377C4×Q8—471no—
378C4×Q8C22×D4711yescharacteristic
379C4×D4—21no—
380C4×D4—471no—
381C4×D4—471no—
382C4×D4—941no—
383C4×D4—941no—
384C4×D4C22×D4711yescharacteristic
385#117—21no—
386#117—471no—
387#117—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390#107—471no—
391#107—471no—
392#106—471no—
393#106—471no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—471no—
399C4⋊C8—471no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8C22×D4711yescharacteristic
403C4⋊C8C22×D4711yescharacteristic
404#103—471no—
405#103—471no—
406#103—471no—
407#103—471no—
408#102—471no—
409#102—471no—
410#102—471no—
411#102—471no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—471no—
416C22⋊C8—471no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—21no—
421#97—941no—
422#97C22⋊D4711yescharacteristic
423#97C22⋊D4711yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8—941no—
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—942no—
436#41—1881no—
437C2×Q8—471no—
438C2×Q8C2×C4×D4711yescharacteristic
439C2×D4—21no—
440C2×D4—471no—
441C2×D4—941no—
442C2×D4C2×C4×D4711yescharacteristic
443C22×C4—21no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4C2×C4×D4711yescharacteristic
448C22×C4#1062535011yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450Q16—942no—
451SD16—942no—
452SD16—1881no—
453D8—1881no—
454M16—22no—
455M16—22no—
456M16—42no—
457M16—1882no—
458M16—1882no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—1882no—
471C2×C8C2×C22⋊D4711yescharacteristic
472C2×C8C2×C22⋊D4711yescharacteristic
473C2×C8C2×C22⋊D4711yescharacteristic
474C2×C8C2×C22⋊D4711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—471no—
480C4⋊C4—471no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4C2×C4×D4711yescharacteristic
484C4⋊C4C2×C4×D4711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—941no—
495C42—941no—
496C42—941no—
497C42C2×C4×D4711yescharacteristic
498C42#1062535011yescharacteristic
499C42C2×C22⋊D4711yescharacteristic
500C42C23×D4711yescharacteristic
501C23—21no—
502C23—941no—
503C23C4×C22⋊D4711yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—472no—
507Q8—941no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—941no—
512D4—941no—
513D4—1882no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—3761no—
528C2×C4—1882no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4C4×C22⋊D4711yescharacteristic
532C2×C4C4×C22⋊D4711yescharacteristic
533C2×C4C4×C22⋊D4711yescharacteristic
534C2×C4C22×C4×D4711yescharacteristic
535C2×C4C22×C22⋊D4711yescharacteristic
536C2×C4C2×#1062535011yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—942no—
542C8—941no—
543C8—941no—
544C8—941no—
545C8—941no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8#1309404412yes—
550C8#1309404412yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—1881no—
558C22—1881no—
559C22—1881no—
560C22C2×C4×C22⋊D4711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—942no—
569C4—1881no—
570C4—1881no—
571C4#131×D4711yescharacteristic
572C4#1568988811yescharacteristic
573C4C2×#1309404411yescharacteristic
574C4C2×#1309404411yescharacteristic
575C2—41no—
576C2—81no—
577C2—3761no—
578C2#2025211011yescharacteristic
579C2C4×#1309404411yescharacteristic
580C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2969C2
socleC22×C47C2×C4×D4
prime radical#15689266C4
cosocleC42×C47C24
hypercenter#2969D47
hypocenterC47#17999
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #20252406C2semidirect
3. #20242278C2semidirect
4. #20242271C2semidirect
5. #20242236C2semidirect
6. #20242231C2semidirect
7. #20242229C2semidirect
8. #20242217C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625335C2semidirect
11. #20242166C2semidirect
12. #20241848C2semidirect
13. #20241768C2semidirect
14. M16×C47⋊C8C2semidirect
15. C47×#2969C2semidirect
287. #2969D47semidirect
357. C47#17999semidirect

Maximal subgroups

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

subgroupindex
#202534002
#202524062
#202422782
#202422712
#202422362
#202422312
#202422292
#202422172
C8×#106253372
C8×#106253352
#202421662
#202418482
#202417682
M16×C47⋊C82
C47×#29692
#1799947