Finite Group Databasebeta

← #26187231

Subgroups — #26187231

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#20252405C211yesmaximal, characteristic, complemented
3#20252393C211yesmaximal, characteristic, complemented
4#20242275C211yesmaximal, characteristic, complemented
5#20242270C211yesmaximal, characteristic, complemented
6#20242241C211yesmaximal, characteristic, complemented
7#20242234C211yesmaximal, characteristic, complemented
8#20242228C211yesmaximal, characteristic, complemented
9#20242214C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242191C211yesmaximal, characteristic, complemented
12#20242169C211yesmaximal, characteristic, complemented
13#20241771C211yesmaximal, characteristic, complemented
14C8×#10625329C211yesmaximal, characteristic, complemented
15C47×#1494C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689461C411yescharacteristic
18#15689444C411yescharacteristic
19#15689427C411yescharacteristic
20#15689420C411yescharacteristic
21#15689342C411yescharacteristic
22#15689335C411yescharacteristic
23#15689283C411yescharacteristic
24#15689266C411yescharacteristic
25#15689254C2211yescharacteristic
26Q8×C47⋊C8C2211yescharacteristic
27#15689247C2211yescharacteristic
28#15689247C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625334C2211yescharacteristic
33#15689201—21no—
34#15689201C2211yescharacteristic
35#15689200C2211yescharacteristic
36#15689200C2211yescharacteristic
37#15689198—21no—
38#15689198—21no—
39#15689195—21no—
40D4×C47⋊C8C2211yescharacteristic
41#15689184—21no—
42#15689178—21no—
43#15689176C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689079—21no—
46C4×#10625329C2211yescharacteristic
47#15689075—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#529C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625329—21no—
73C2×#10625329D411yescharacteristic
74C2×#10625329D411yescharacteristic
75C2×#10625324—21no—
76C2×#10625324—21no—
77C22×C47⋊C8—21no—
78C4×Dic94C2×C411yescharacteristic
79C4×Dic94C2311yescharacteristic
80C4×D188C2×C411yescharacteristic
81C4×D188C2311yescharacteristic
82C4×C22⋊D47—21no—
83C4×C22⋊D47—21no—
84#13093983C2×C411yescharacteristic
85#13093981—21no—
86C42×D47—21no—
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91C4⋊(C47⋊C8)—21no—
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)C2×C411yescharacteristic
94C4⋊(C47⋊C8)C2×C411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093947C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)C2×C411yescharacteristic
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114#13093935—21no—
115#13093935D411yescharacteristic
116#13093935D411yescharacteristic
117C4×C47⋊C8—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8C2311yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C22×C8×C47—21no—
126#126×C47—21no—
127#125×C47C2×C411yescharacteristic
128#124×C47C2×C411yescharacteristic
129#123×C47—21no—
130C22⋊Q8×C47C2×C411yescharacteristic
131#121×C47C2×C411yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47—21no—
134C4×D4×C47C2311yescharacteristic
135#117×C47—21no—
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140#97×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
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—42no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47C22×C411yescharacteristic
169C4⋊C4×C47C22×C411yescharacteristic
170C22⋊C4×C47—21no—
171C22⋊C4×C47—21no—
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C42×C47—21no—
176C42×C47C22×C411yescharacteristic
177C42×C47C2×D411yescharacteristic
178C42×C47#4111yescharacteristic
179C42×C47C2411yescharacteristic
180C22⋊Dic47—21no—
181#10625337—22no—
182#10625336—41no—
183#10625335—22no—
184#10625334—41no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194#10625329—22no—
195#10625329—22no—
196#10625329—42no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—42no—
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
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—22no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258C47⋊C8#13512yes—
259C47⋊C8#13512yes—
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#2969—471no—
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#1494D4711yescharacteristic, complemented
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#446—471no—
317C8×Q8—471no—
318C8×Q8—471no—
319C8×Q8—471no—
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16—471no—
323C4×D8—471no—
324#436—471no—
325#436—471no—
326#436—471no—
327#436—941no—
328#436—941no—
329#436—941no—
330#435—941no—
331C8×D4—471no—
332#433—941no—
333#432—941no—
334#432C2×D4711yescharacteristic
335#431—471no—
336#431—471no—
337#405—941no—
338C4×M16—471no—
339C4×M16—941no—
340C2×C4×C8C2×D4711yescharacteristic
341#335—471no—
342#335—471no—
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8C2×D4711yescharacteristic
348Q8⋊C8C2×D4711yescharacteristic
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8C2×D4711yescharacteristic
352D4⋊C8C2×D4711yescharacteristic
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—471no—
364C2×M16—471no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
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—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—941no—
399C4⋊C8—941no—
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—471no—
414C22⋊C8—471no—
415C22⋊C8—941no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—21no—
421#97—471no—
422#97—471no—
423#97—941no—
424C4×C8—21no—
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
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×C4D4×D4711yescharacteristic
449C22×C4#1062535211yescharacteristic
450Q16—942no—
451SD16—942no—
452SD16—1881no—
453D8—1881no—
454M16—942no—
455M16—942no—
456M16—1882no—
457M16—1882no—
458M16—1882no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—471no—
467C2×C8—471no—
468C2×C8—471no—
469C2×C8—471no—
470C2×C8—471no—
471C2×C8—471no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—1882no—
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
498C42D4×D4711yescharacteristic
499C42#1062535211yescharacteristic
500C42C23×D4711yescharacteristic
501C23—21no—
502C23—941no—
503C23(C22⋊D47)⋊C411yescharacteristic
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×C4(C22⋊D47)⋊C411yescharacteristic
532C2×C4(C22⋊D47)⋊C411yescharacteristic
533C2×C4(C22⋊D47)⋊C411yescharacteristic
534C2×C4C22×C4×D4711yescharacteristic
535C2×C4C2×D4×D4711yescharacteristic
536C2×C4C2×#1062535211yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—472no—
542C8—472no—
543C8—941no—
544C8—941no—
545C8—941no—
546C8—941no—
547C8—941no—
548C8—941no—
549C8—1881no—
550C8—1881no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—1881no—
558C22—1881no—
559C22—1881no—
560C22C2×(C22⋊D47)⋊C411yescharacteristic
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
573C4#135×D4711yescharacteristic
574C4#135×D4711yescharacteristic
575C2—41no—
576C2—81no—
577C2—3761no—
578C2#2025211811yescharacteristic
579C2#2025215611yescharacteristic
580C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1494C2
socleC22×C47C2×C4×D4
prime radical#15689266C4
cosocleC42×C47C24
hypercenter#1494D47
hypocenterC47#17999
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #20252405C2semidirect
3. #20252393C2semidirect
4. #20242275C2semidirect
5. #20242270C2semidirect
6. #20242241C2semidirect
7. #20242234C2semidirect
8. #20242228C2semidirect
9. #20242214C2semidirect
10. #20242192C2semidirect
11. #20242191C2semidirect
12. #20242169C2semidirect
13. #20241771C2semidirect
14. C8×#10625329C2semidirect
15. C47×#1494C2semidirect
297. #1494D47semidirect
357. C47#17999semidirect

Maximal subgroups

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

subgroupindex
#202534002
#202524052
#202523932
#202422752
#202422702
#202422412
#202422342
#202422282
#202422142
#202421922
#202421912
#202421692
#202417712
C8×#106253292
C47×#14942
#1799947