Finite Group Databasebeta

← #26186929

Subgroups — #26186929

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#20253995C211yesmaximal, characteristic
2#20252537C211yesmaximal, characteristic
3#20252485C211yesmaximal, characteristic, complemented
4#20242294C211yesmaximal, characteristic, complemented
5#20242287C211yesmaximal, characteristic, complemented
6#20242282C211yesmaximal, characteristic, complemented
7#20242281C211yesmaximal, characteristic, complemented
8#20242204C211yesmaximal, characteristic, complemented
9#20242197C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242191C211yesmaximal, characteristic, complemented
12#20242156C211yesmaximal, characteristic, complemented
13#20241844C211yesmaximal, characteristic, complemented
14C8×#10625329C211yesmaximal, characteristic, complemented
15C47×#1494C211yesmaximal, characteristic
16#15689680C2211yescharacteristic
17#15689533C411yescharacteristic
18#15689518C411yescharacteristic
19#15689493C411yescharacteristic
20#15689482C411yescharacteristic
21#15689379C411yescharacteristic
22#15689379C411yescharacteristic
23#15689367C411yescharacteristic
24#15689367C411yescharacteristic
25#15689254C2211yescharacteristic
26#15689251—21no—
27#15689251—21no—
28#15689250C2211yescharacteristic
29#15689250C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31#15689247C2211yescharacteristic
32#15689247C2211yescharacteristic
33C4×#10625337C2211yescharacteristic
34C4×#10625337C2211yescharacteristic
35C4×#10625335C2211yescharacteristic
36C4×#10625335C2211yescharacteristic
37#15689201—21no—
38#15689201C2211yescharacteristic
39#15689195—21no—
40D4×C47⋊C8C2211yescharacteristic
41#15689184—21no—
42#15689181—21no—
43#15689181—21no—
44#15689176C2211yescharacteristic
45#15689150—21no—
46#15689147C2211yescharacteristic
47C4×#10625329C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
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×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329C2×C411yescharacteristic
74C2×#10625329C2×C411yescharacteristic
75C22×C47⋊C8—21no—
76#13094024C2×C411yescharacteristic
77#13094024C2×C411yescharacteristic
78#13094016—21no—
79#13094003—21no—
80#13094003C2×C411yescharacteristic
81#13094003C2×C411yescharacteristic
82C4×Dic94—21no—
83C4×Dic94C2311yescharacteristic
84C4×Dic94C2311yescharacteristic
85#13093983—21no—
86#13093957C2×C411yescharacteristic
87#13093957C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)—21no—
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)D411yescharacteristic
94C4⋊(C47⋊C8)D411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093947C2×C411yescharacteristic
105#13093947C2×C411yescharacteristic
106#13093947C2×C411yescharacteristic
107#13093945C2×C411yescharacteristic
108#13093945C2×C411yescharacteristic
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)D411yescharacteristic
112C22⋊(C47⋊C8)D411yescharacteristic
113#13093935—21no—
114#13093935C2×C411yescharacteristic
115#13093935C2×C411yescharacteristic
116#13093934—21no—
117#13093934—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×Dic94—21no—
152C2×Dic94C22×C411yescharacteristic
153C2×Dic94C22×C411yescharacteristic
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—42no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47C22×C411yescharacteristic
164C4⋊C4×C47C22×C411yescharacteristic
165C22⋊C4×C47—21no—
166C22⋊C4×C47—21no—
167C22⋊C4×C47—21no—
168C22⋊C4×C47—21no—
169C22⋊C4×C47—21no—
170C42×C47—21no—
171C42×C47C22×C411yescharacteristic
172C42×C47C2×D411yescharacteristic
173C42×C47#4111yescharacteristic
174C42×C47C2411yescharacteristic
175C22⋊Dic47—21no—
176C22⋊Dic47—21no—
177#10625337—22no—
178#10625337—22no—
179#10625335—22no—
180#10625335—22no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47C22×C411yescharacteristic
185C4⋊Dic47C22×C411yescharacteristic
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192#10625329—22no—
193#10625329—22no—
194#10625329—81no—
195#10625329—81no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—81no—
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C23×C47—21no—
208C23×C47C4×D411yescharacteristic
209Q8×C47—21no—
210Q8×C47—21no—
211D4×C47—21no—
212D4×C47—21no—
213D4×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—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234Dic94—21no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—81no—
239C8×C47—22no—
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C47⋊C8—21no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—21no—
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×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47C2×C4×D411yescharacteristic
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47C2×#13111yescharacteristic
269C4×C47C2×#13111yescharacteristic
270C4×C47#57711yescharacteristic
271C4×C47#57811yescharacteristic
272Dic47—41no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276#3172—471no—
277#2993—471no—
278#2985—471no—
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#1494D4711yescharacteristic
289#1493—471no—
290C8×M16—471no—
291C2×C47—41no—
292C2×C47—81no—
293C2×C47#293111yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47#295611yescharacteristic
296#533—471no—
297#529C2×D4711yescharacteristic
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—471no—
307#446—471no—
308#446—471no—
309#446—941no—
310#446—941no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—471no—
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—941no—
323#433—941no—
324#433—941no—
325#432C2×D4711yescharacteristic
326#431—471no—
327#424—941no—
328#423—471no—
329C4×M16—471no—
330C2×C4×C8C2×D4711yescharacteristic
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⋊C8C2×D4711yescharacteristic
340Q8⋊C8C2×D4711yescharacteristic
341D4⋊C8C2×D4711yescharacteristic
342D4⋊C8C2×D4711yescharacteristic
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—21no—
357C22×C8—941no—
358C4⋊Q8—471no—
359C4⋊Q8—471no—
360#126—21no—
361#125—941no—
362#125C4×D4711yescharacteristic
363#124C4×D4711yescharacteristic
364#123—21no—
365C22⋊Q8—471no—
366C22⋊Q8—471no—
367C22⋊Q8—941no—
368C22⋊Q8C4×D4711yescharacteristic
369#121C4×D4711yescharacteristic
370C4×Q8—471no—
371C4×Q8—471no—
372C4×Q8—941no—
373C4×Q8C22×D4711yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4711yescharacteristic
376#117—21no—
377#117—941no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—471no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
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—471no—
406C22⋊C8—471no—
407C22⋊C8—941no—
408C22⋊C8—941no—
409#97—21no—
410#97—471no—
411#97—471no—
412#97—941no—
413#97—941no—
414#97—941no—
415C4×C8—21no—
416C4×C8—471no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C2×Q8—471no—
426C2×Q8—471no—
427C2×Q8—941no—
428C2×Q8C2×C4×D4711yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D4711yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4D4×D4711yescharacteristic
434C22×C4#1062535211yescharacteristic
435Q16—942no—
436Q16—942no—
437SD16—942no—
438SD16—942no—
439M16—942no—
440M16—942no—
441M16—3761no—
442M16—3761no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—471no—
449C2×C8—471no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—3761no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—471no—
464C4⋊C4—471no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
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—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—941no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42D4×D4711yescharacteristic
486C42#1062535211yescharacteristic
487C42C23×D4711yescharacteristic
488C23—21no—
489C23(C22⋊D47)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—941no—
493Q8—941no—
494Q8—941no—
495Q8—941no—
496Q8—3761no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4(C22⋊D47)⋊C411yescharacteristic
515C2×C4(C22⋊D47)⋊C411yescharacteristic
516C2×C4(C22⋊D47)⋊C411yescharacteristic
517C2×C4C22×C4×D4711yescharacteristic
518C2×C4C2×D4×D4711yescharacteristic
519C2×C4C2×#1062535211yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—472no—
525C8—472no—
526C8—941no—
527C8—941no—
528C8—941no—
529C8—941no—
530C8—941no—
531C8—941no—
532C8—1881no—
533C8—1881no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×(C22⋊D47)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—1881no—
549C4—1881no—
550C4—1881no—
551C4—1881no—
552C4#131×D4711yescharacteristic
553C4#131×D4711yescharacteristic
554C4#1568993011yescharacteristic
555C4#1568993711yescharacteristic
556C2—41no—
557C2—81no—
558C2#2025209611yescharacteristic
559C2#2025223411yescharacteristic
560C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1494C2
socleC22×C47C2×C4×D4
prime radical#121×C47C2×C4
cosocleC42×C47C24
hypercenter#1494D47
hypocenterC47#17969
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
3. #20252485C2semidirect
4. #20242294C2semidirect
5. #20242287C2semidirect
6. #20242282C2semidirect
7. #20242281C2semidirect
8. #20242204C2semidirect
9. #20242197C2semidirect
10. #20242192C2semidirect
11. #20242191C2semidirect
12. #20242156C2semidirect
13. #20241844C2semidirect
14. C8×#10625329C2semidirect
347. C47#17969semidirect

Maximal subgroups

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

subgroupindex
#202539952
#202525372
#202524852
#202422942
#202422872
#202422822
#202422812
#202422042
#202421972
#202421922
#202421912
#202421562
#202418442
C8×#106253292
C47×#14942
#1796947