Finite Group Databasebeta

← #26186923

Subgroups — #26186923

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253988C211yesmaximal, characteristic
2#20252539C211yesmaximal, characteristic
3#20242295C211yesmaximal, characteristic, complemented
4#20242288C211yesmaximal, characteristic, complemented
5#20242283C211yesmaximal, characteristic, complemented
6#20242278C211yesmaximal, characteristic, complemented
7#20242205C211yesmaximal, characteristic, complemented
8#20242198C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625336C211yesmaximal, characteristic, complemented
11#20242156C211yesmaximal, characteristic, complemented
12#20241846C211yesmaximal, characteristic
13#20241843C211yesmaximal, characteristic, complemented
14#20241669C211yesmaximal, characteristic, complemented
15C47×#2985C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689529C411yescharacteristic
18#15689515C411yescharacteristic
19#15689491C411yescharacteristic
20#15689485C411yescharacteristic
21#15689379C411yescharacteristic
22#15689379C411yescharacteristic
23#15689371C411yescharacteristic
24#15689371C411yescharacteristic
25#15689253C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625337C2211yescharacteristic
28C4×#10625337C2211yescharacteristic
29C4×#10625336C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31#15689202C2211yescharacteristic
32#15689198—21no—
33#15689197—21no—
34C8×D188C2211yescharacteristic
35#15689183—21no—
36#15689148—21no—
37#15689147C2211yescharacteristic
38C4×#10625329C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46Q8⋊(C47⋊C8)C2211yescharacteristic
47Q8⋊(C47⋊C8)C2211yescharacteristic
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54C8×C47⋊C8C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C47×#533C2211yescharacteristic
57C47×#446—21no—
58C47×#446—21no—
59C47×#446C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C8×Q8×C47C2211yescharacteristic
63C47×#433—21no—
64C47×#433—21no—
65C47×#432C2211yescharacteristic
66C47×#431C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329C2×C411yescharacteristic
73C2×#10625329C2×C411yescharacteristic
74C2×#10625324—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77#13094018—21no—
78#13094016C2×C411yescharacteristic
79#13094012C2×C411yescharacteristic
80#13094007—21no—
81#13094003C2×C411yescharacteristic
82#13093998C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×D188C2311yescharacteristic
85C4×C22⋊D47—21no—
86#13093981—21no—
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91C4⋊(C47⋊C8)—21no—
92C4⋊(C47⋊C8)C2311yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94Dic47⋊C8—21no—
95Dic47⋊C8—21no—
96#13093948C2×C411yescharacteristic
97#13093948C2×C411yescharacteristic
98#13093948C2×C411yescharacteristic
99#13093948C2×C411yescharacteristic
100#13093947C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093944C2×C411yescharacteristic
103#13093944C2×C411yescharacteristic
104(C2×D47)⋊C8—21no—
105(C2×D47)⋊C8—21no—
106#13093935C2×C411yescharacteristic
107#13093935C2×C411yescharacteristic
108#13093934—21no—
109C4×C47⋊C8—21no—
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
114C8×Dic47—21no—
115C4⋊Q8×C47C2×C411yescharacteristic
116C4⋊Q8×C47C2×C411yescharacteristic
117#125×C47—21no—
118C22⋊Q8×C47—21no—
119C22⋊Q8×C47C2×C411yescharacteristic
120C22⋊Q8×C47C2×C411yescharacteristic
121C4×Q8×C47—21no—
122C4×Q8×C47C2311yescharacteristic
123C4×Q8×C47C2311yescharacteristic
124#117×C47—21no—
125C2×C42×C47C2311yescharacteristic
126C4⋊C8×C47—21no—
127C4⋊C8×C47—21no—
128C4⋊C8×C47—21no—
129C4⋊C8×C47—21no—
130C4⋊C8×C47D411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47D411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137#97×C47—21no—
138#97×C47—21no—
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×Q8×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C2×C22⋊D47—21no—
151C2×D188C22×C411yescharacteristic
152C2×C4×D47—21no—
153C2×Dic94C22×C411yescharacteristic
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47C2×D411yescharacteristic
157C2×C8×C47C2×D411yescharacteristic
158C2×C8×C47C2×D411yescharacteristic
159C2×C8×C47C2×D411yescharacteristic
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47C22×C411yescharacteristic
168C4⋊C4×C47C22×C411yescharacteristic
169C22⋊C4×C47—21no—
170C22⋊C4×C47—21no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47C22×C411yescharacteristic
174C42×C47C2×D411yescharacteristic
175C42×C47#4111yescharacteristic
176C42×C47C2411yescharacteristic
177C22⋊Dic47—21no—
178#10625337—22no—
179#10625337—22no—
180#10625336—22no—
181#10625336—22no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47C22×C411yescharacteristic
187C4⋊Dic47C22×C411yescharacteristic
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192C4×Dic47—21no—
193#10625329—22no—
194#10625329—22no—
195#10625329—81no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—42no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205#10625324—81no—
206C8×D47—81no—
207C23×C47C4×D411yescharacteristic
208C22×D47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—81no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—41no—
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C23×C411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C22⋊D47—81no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233D188—21no—
234D188—21no—
235C4×D47—41no—
236C4×D47—41no—
237Dic94—21no—
238Dic94—21no—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C47⋊C8—22no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—41no—
249C47⋊C8—41no—
250C47⋊C8—41no—
251C47⋊C8#13112yes—
252C47⋊C8#13112yes—
253#17969—471nomaximal, Sylow
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47C2×C4×D411yescharacteristic
258C2×D47—41no—
259C2×D47—41no—
260C2×D47—41no—
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47C2×#13111yescharacteristic
270C4×C47C2×#13111yescharacteristic
271C4×C47#57711yescharacteristic
272C4×C47#57811yescharacteristic
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276#3172—471no—
277#2993—471no—
278#2985D4711yescharacteristic, complemented
279#1593—471no—
280#1592—471no—
281#1591—471no—
282#1590—471no—
283#1579—471no—
284SD16⋊C8—471no—
285C8×Q16—471no—
286C8×SD16—471no—
287#1569—471no—
288#1494—471no—
289#1493—471no—
290C8×M16—471no—
291C2×C47—41no—
292C2×C47#293111yescharacteristic
293C2×C47#294711yescharacteristic
294C2×C47#295611yescharacteristic
295D47—81no—
296#533C2×D4711yescharacteristic
297#529—471no—
298#501—471no—
299#497—471no—
300#491—471no—
301#489—471no—
302#470—471no—
303#470—471no—
304#468—471no—
305#468—471no—
306#446—21no—
307#446—21no—
308#446—471no—
309#446C2×D4711yescharacteristic
310#446C2×D4711yescharacteristic
311C8×Q8—471no—
312C8×Q8C2×D4711yescharacteristic
313C8×Q8C2×D4711yescharacteristic
314C4×Q16—471no—
315C4×Q16—471no—
316C4×SD16—471no—
317C4×SD16—471no—
318#436—471no—
319#436—941no—
320#435—941no—
321C8×D4—471no—
322#433—21no—
323#433—21no—
324#433—941no—
325#432C2×D4711yescharacteristic
326#431C2×D4711yescharacteristic
327#424—941no—
328#423—471no—
329C4×M16—471no—
330C2×C4×C8—471no—
331#335—471no—
332#335—471no—
333#334—471no—
334#334—471no—
335Q8⋊C8—471no—
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341D4⋊C8—471no—
342D4⋊C8—471no—
343#322—471no—
344#322—471no—
345C82—471no—
346C82—471no—
347C47#1796911yescharacteristic, complemented, Sylow
348C2×Q16—471no—
349C2×Q16—471no—
350C2×SD16—471no—
351C2×SD16—471no—
352C2×M16—471no—
353C2×M16—471no—
354C2×M16—941no—
355C2×M16—941no—
356C22×C8—941no—
357C22×C8—941no—
358C4⋊Q8C4×D4711yescharacteristic
359C4⋊Q8C4×D4711yescharacteristic
360#126—941no—
361#125—21no—
362#125—471no—
363#124—471no—
364#123—941no—
365C22⋊Q8—21no—
366C22⋊Q8—471no—
367C22⋊Q8C4×D4711yescharacteristic
368C22⋊Q8C4×D4711yescharacteristic
369#121—471no—
370C4×Q8—21no—
371C4×Q8—471no—
372C4×Q8C22×D4711yescharacteristic
373C4×Q8C22×D4711yescharacteristic
374C4×D4—471no—
375C4×D4—941no—
376#117—21no—
377#117—941no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8C22⋊D4711yescharacteristic
393C4⋊C8C22⋊D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396#103—471no—
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#102—471no—
403#102—471no—
404C22⋊C8—21no—
405C22⋊C8—941no—
406C22⋊C8—941no—
407C22⋊C8C22⋊D4711yescharacteristic
408C22⋊C8C22⋊D4711yescharacteristic
409#97—21no—
410#97—21no—
411#97—21no—
412#97—471no—
413#97—471no—
414#97—941no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C2×Q8—21no—
426C2×Q8—471no—
427C2×Q8C2×C4×D4711yescharacteristic
428C2×Q8C2×C4×D4711yescharacteristic
429C2×D4—471no—
430C2×D4—941no—
431C22×C4—941no—
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4#1062535011yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435Q16—942no—
436Q16—942no—
437SD16—942no—
438SD16—942no—
439M16—942no—
440M16—942no—
441M16—3761no—
442M16—3761no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—471no—
446C2×C8—471no—
447C2×C8—471no—
448C2×C8—471no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—3761no—
454C2×C8—1882no—
455C2×C8C2×C22⋊D4711yescharacteristic
456C2×C8C2×C22⋊D4711yescharacteristic
457C2×C8C2×C22⋊D4711yescharacteristic
458C2×C8C2×C22⋊D4711yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—471no—
467C4⋊C4—471no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4C2×C4×D4711yescharacteristic
473C4⋊C4C2×C4×D4711yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—21no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42#1062535011yescharacteristic
486C42C2×C22⋊D4711yescharacteristic
487C42C23×D4711yescharacteristic
488C23—941no—
489C23C4×C22⋊D4711yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—941no—
496Q8—941no—
497D4—941no—
498D4—941no—
499D4—3761no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—1881no—
513C2×C4—1881no—
514C2×C4C4×C22⋊D4711yescharacteristic
515C2×C4C4×C22⋊D4711yescharacteristic
516C2×C4C4×C22⋊D4711yescharacteristic
517C2×C4C22×C4×D4711yescharacteristic
518C2×C4C22×C22⋊D4711yescharacteristic
519C2×C4C2×#1062535011yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—472no—
527C8—472no—
528C8—942no—
529C8—941no—
530C8—941no—
531C8—1881no—
532C8—1881no—
533C8—1881no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—1881no—
538C22—1881no—
539C22—1881no—
540C22C2×C4×C22⋊D4711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—1881no—
550C4—1881no—
551C4—1881no—
552C4#131×D4711yescharacteristic
553C4#131×D4711yescharacteristic
554C4#1568993111yescharacteristic
555C4#1568993811yescharacteristic
556C2—41no—
557C2—3761no—
558C2#2025209811yescharacteristic
559C2#2025223111yescharacteristic
560C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2985C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#2985D47
hypocenterC47#17969
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #20242295C2semidirect
4. #20242288C2semidirect
5. #20242283C2semidirect
6. #20242278C2semidirect
7. #20242205C2semidirect
8. #20242198C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625336C2semidirect
11. #20242156C2semidirect
13. #20241843C2semidirect
14. #20241669C2semidirect
15. C47×#2985C2semidirect
278. #2985D47semidirect
347. C47#17969semidirect

Maximal subgroups

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

subgroupindex
#202539882
#202525392
#202422952
#202422882
#202422832
#202422782
#202422052
#202421982
C8×#106253372
C8×#106253362
#202421562
#202418462
#202418432
#202416692
C47×#29852
#1796947