Finite Group Databasebeta

← #26186813

Subgroups — #26186813

Order 12032.

630 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253952C211yesmaximal, characteristic
2#20252364C211yesmaximal, characteristic, complemented
3#20252357C211yesmaximal, characteristic, complemented
4#20242282C211yesmaximal, characteristic, complemented
5#20242281C211yesmaximal, characteristic, complemented
6#20242275C211yesmaximal, characteristic, complemented
7#20242270C211yesmaximal, characteristic, complemented
8#20242192C211yesmaximal, characteristic, complemented
9#20242191C211yesmaximal, characteristic, complemented
10#20242185C211yesmaximal, characteristic, complemented
11#20242180C211yesmaximal, characteristic, complemented
12#20242149C211yesmaximal, characteristic, complemented
13#20241849C211yesmaximal, characteristic, complemented
14C2×C8×C47⋊C8C211yesmaximal, characteristic, complemented
15C47×#1494C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689522C411yescharacteristic
18#15689505C411yescharacteristic
19#15689480C411yescharacteristic
20#15689477C411yescharacteristic
21#15689362C411yescharacteristic
22#15689357C411yescharacteristic
23#15689354C411yescharacteristic
24#15689350C411yescharacteristic
25#15689254C2211yescharacteristic
26#15689250C2211yescharacteristic
27Q8×C47⋊C8C2211yescharacteristic
28#15689247C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625334C2211yescharacteristic
33#15689201C2211yescharacteristic
34#15689200C2211yescharacteristic
35#15689195—21no—
36#15689191—21no—
37D4×C47⋊C8—21no—
38D4×C47⋊C8C2211yescharacteristic
39#15689188C2211yescharacteristic
40(C22⋊D47)⋊C8—21no—
41#15689185—21no—
42#15689184—21no—
43#15689180C2211yescharacteristic
44#15689080—21no—
45#15689079—21no—
46C2×C4×C47⋊C8C2211yescharacteristic
47C2×C4×C47⋊C8C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56C8×C47⋊C8C2211yescharacteristic
57C8×C47⋊C8C2211yescharacteristic
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×#10625337C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625324—21no—
73C22×C47⋊C8—21no—
74C22×C47⋊C8C2×C411yescharacteristic
75C22×C47⋊C8C2×C411yescharacteristic
76C22×C47⋊C8D411yescharacteristic
77C22×C47⋊C8D411yescharacteristic
78C2×C8×D47—21no—
79#13094018—21no—
80#13094016C2×C411yescharacteristic
81#13094012C2×C411yescharacteristic
82#13094007—21no—
83#13094003C2×C411yescharacteristic
84#13093998C2×C411yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×D188C2311yescharacteristic
87C4×C22⋊D47—21no—
88#13093981—21no—
89#13093957C2×C411yescharacteristic
90#13093957C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92#13093955C2×C411yescharacteristic
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)—21no—
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—
110(C2×D47)⋊C8—21no—
111(C2×D47)⋊C8—21no—
112#13093935—21no—
113#13093935—21no—
114#13093934—21no—
115C4×C47⋊C8—21no—
116C4×C47⋊C8C2×C411yescharacteristic
117C4×C47⋊C8C2×C411yescharacteristic
118C4×C47⋊C8D411yescharacteristic
119C4×C47⋊C8D411yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
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—
152C2×D188C22×C411yescharacteristic
153C2×C4×D47—21no—
154C2×Dic94C22×C411yescharacteristic
155C2×C8×C47—24no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47C22×C411yescharacteristic
165C4⋊C4×C47C22×C411yescharacteristic
166C22⋊C4×C47—21no—
167C22⋊C4×C47—21no—
168C22⋊C4×C47—21no—
169C22⋊C4×C47—21no—
170C22⋊C4×C47—21no—
171C42×C47—21no—
172C42×C47C22×C411yescharacteristic
173C42×C47C2×D411yescharacteristic
174C42×C47#4111yescharacteristic
175C42×C47C2411yescharacteristic
176C22⋊Dic47—21no—
177#10625337—22no—
178#10625336—22no—
179#10625335—22no—
180#10625334—22no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185C4⋊Dic47C22×C411yescharacteristic
186C4⋊Dic47C22×C411yescharacteristic
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192#10625329—42no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
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—
209C8×D47—42no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212C22×D47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—42no—
218C2×C4×C47—22no—
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—21no—
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—41no—
241C4×D47—41no—
242Dic94—21no—
243Dic94—21no—
244C8×C47—22no—
245C8×C47—22no—
246C8×C47—41no—
247C8×C47—41no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8#13112yes—
255C47⋊C8#13112yes—
256C47⋊C8#13512yes—
257C47⋊C8#13512yes—
258#17959—471nomaximal, Sylow
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47#44312yes—
265C22×C47C2×C4×D411yescharacteristic
266C2×D47—41no—
267C2×D47—41no—
268C2×D47—41no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47C2×#13111yescharacteristic
277C4×C47C2×#13111yescharacteristic
278C4×C47C2×#13511yescharacteristic
279C4×C47C2×#13511yescharacteristic
280Dic47—41no—
281Dic47—41no—
282Dic47—41no—
283#3168—471no—
284#2966—471no—
285#2966—471no—
286#1591—471no—
287#1590—471no—
288#1590—471no—
289#1589—471no—
290C8×Q16—471no—
291C8×SD16—471no—
292C8×SD16—471no—
293C8×D8—471no—
294#1568—471no—
295#1494—471no—
296#1494D4711yescharacteristic, complemented
297C2×C82—471no—
298C2×C47—22no—
299C2×C47—81no—
300C2×C47#293111yescharacteristic
301C2×C47C4×#13511yescharacteristic
302C2×C47C2×#44311yescharacteristic
303D47—81no—
304#529—471no—
305#529C2×D4711yescharacteristic
306#499—471no—
307#495—471no—
308#488—471no—
309#488—471no—
310#467—471no—
311#466—471no—
312#465—471no—
313#465—471no—
314#446—471no—
315#446—471no—
316C8×Q8—471no—
317C8×Q8—471no—
318C4×Q16—471no—
319C4×SD16—471no—
320C4×SD16—471no—
321C4×D8—471no—
322#436—471no—
323#436—471no—
324#435—941no—
325#435—941no—
326C8×D4—471no—
327C8×D4—471no—
328C8×D4—941no—
329C8×D4—941no—
330#433—941no—
331#433—941no—
332#432—471no—
333#432C2×D4711yescharacteristic
334#405—941no—
335#405—941no—
336C2×C4×C8—471no—
337C2×C4×C8—471no—
338C2×C4×C8C2×D4711yescharacteristic
339#335—471no—
340#335—471no—
341#334—471no—
342#334—471no—
343Q8⋊C8—471no—
344Q8⋊C8—471no—
345Q8⋊C8C2×D4711yescharacteristic
346Q8⋊C8C2×D4711yescharacteristic
347D4⋊C8—471no—
348D4⋊C8—471no—
349D4⋊C8C2×D4711yescharacteristic
350D4⋊C8C2×D4711yescharacteristic
351C82—471no—
352C82—471no—
353C82—471no—
354C82—471no—
355C47#1795911yescharacteristic, complemented, Sylow
356C2×Q16—471no—
357C2×SD16—471no—
358C2×SD16—471no—
359C2×D8—471no—
360C2×M16—941no—
361C2×M16—941no—
362C22×C8—21no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—471no—
366C22×C8—471no—
367C22×C8—941no—
368C22×C8—941no—
369#126—21no—
370#126—941no—
371#125—471no—
372#125C4×D4711yescharacteristic
373#124—471no—
374#124C4×D4711yescharacteristic
375#123—21no—
376#123—941no—
377C22⋊Q8—471no—
378C22⋊Q8C4×D4711yescharacteristic
379#121—471no—
380#121C4×D4711yescharacteristic
381C4×Q8—471no—
382C4×Q8C22×D4711yescharacteristic
383C4×D4—21no—
384C4×D4—471no—
385C4×D4—941no—
386C4×D4C22×D4711yescharacteristic
387#117—21no—
388#117—941no—
389C2×C42C22×D4711yescharacteristic
390#107—471no—
391#107—471no—
392#106—471no—
393#106—471no—
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—941no—
397C4⋊C8—941no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8C22×D4711yescharacteristic
401C4⋊C8C22×D4711yescharacteristic
402#103—471no—
403#103—471no—
404#103—471no—
405#103—471no—
406#102—471no—
407#102—471no—
408#102—471no—
409#102—471no—
410C22⋊C8—21no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413C22⋊C8—941no—
414C22⋊C8—941no—
415C22⋊C8—941no—
416#97—21no—
417#97—941no—
418#97—941no—
419#97—941no—
420C4×C8—21no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8C22×D4711yescharacteristic
432C4×C8C22×D4711yescharacteristic
433C2×Q8—471no—
434C2×Q8C2×C4×D4711yescharacteristic
435C2×D4—21no—
436C2×D4—471no—
437C2×D4—941no—
438C2×D4C2×C4×D4711yescharacteristic
439C22×C4—21no—
440C22×C4—941no—
441C22×C4C2×C4×D4711yescharacteristic
442C22×C4D4×D4711yescharacteristic
443C22×C4#1062535211yescharacteristic
444Q16—942no—
445SD16—942no—
446SD16—942no—
447D8—942no—
448M16—1882no—
449M16—1882no—
450C2×C8—24no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—942no—
464C2×C8—942no—
465C2×C8—942no—
466C2×C8—942no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—1882no—
470C2×C8—1882no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—471no—
476C4⋊C4—471no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4C2×C4×D4711yescharacteristic
482C4⋊C4C2×C4×D4711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—941no—
495C42C2×C4×D4711yescharacteristic
496C42D4×D4711yescharacteristic
497C42#1062535211yescharacteristic
498C42C23×D4711yescharacteristic
499C23—21no—
500C23—941no—
501C23(C22⋊D47)⋊C411yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—941no—
505Q8—941no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—941no—
510D4—941no—
511D4—1882no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4(C22⋊D47)⋊C411yescharacteristic
528C2×C4(C22⋊D47)⋊C411yescharacteristic
529C2×C4(C22⋊D47)⋊C411yescharacteristic
530C2×C4C22×C4×D4711yescharacteristic
531C2×C4C2×D4×D4711yescharacteristic
532C2×C4C2×#1062535211yescharacteristic
533C8—22no—
534C8—22no—
535C8—41no—
536C8—41no—
537C8—472no—
538C8—472no—
539C8—472no—
540C8—472no—
541C8—941no—
542C8—941no—
543C8—941no—
544C8—941no—
545C8—1881no—
546C8—1881no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—1881no—
553C22—1881no—
554C22—1881no—
555C22#1568923712yes—
556C22C2×(C22⋊D47)⋊C411yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—1881no—
565C4—1881no—
566C4—1881no—
567C4#131×D4711yescharacteristic
568C4#131×D4711yescharacteristic
569C4#135×D4711yescharacteristic
570C4#135×D4711yescharacteristic
571C2—22no—
572C2—81no—
573C2—3761no—
574C2#2025209611yescharacteristic
575C2#2025215611yescharacteristic
576C2C2×#1568923711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1494C2
socleC22×C47C2×C4×D4
prime radical#15689357C4
cosocleC42×C47C24
hypercenter#1494D47
hypocenterC47#17959
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. #20252364C2semidirect
3. #20252357C2semidirect
4. #20242282C2semidirect
5. #20242281C2semidirect
6. #20242275C2semidirect
7. #20242270C2semidirect
8. #20242192C2semidirect
9. #20242191C2semidirect
10. #20242185C2semidirect
11. #20242180C2semidirect
12. #20242149C2semidirect
13. #20241849C2semidirect
14. C2×C8×C47⋊C8C2semidirect
15. C47×#1494C2semidirect
296. #1494D47semidirect
355. C47#17959semidirect

Maximal subgroups

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

subgroupindex
#202539522
#202523642
#202523572
#202422822
#202422812
#202422752
#202422702
#202421922
#202421912
#202421852
#202421802
#202421492
#202418492
C2×C8×C47⋊C82
C47×#14942
#1795947