Finite Group Databasebeta

← #26187475

Subgroups — #26187475

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253470C211yesmaximal, characteristic
2#20252550C211yesmaximal, characteristic
3#20252475C211yesmaximal, characteristic, complemented
4#20242286C211yesmaximal, characteristic, complemented
5#20242280C211yesmaximal, characteristic, complemented
6#20242268C211yesmaximal, characteristic, complemented
7#20242261C211yesmaximal, characteristic, complemented
8#20242261C211yesmaximal, characteristic, complemented
9#20242247C211yesmaximal, characteristic, complemented
10C8×Dic188C211yesmaximal, characteristic, complemented
11C8×#10625325C211yesmaximal, characteristic, complemented
12#20242173C211yesmaximal, characteristic, complemented
13#20241849C211yesmaximal, characteristic
14C2×#15688855C211yesmaximal, characteristic, complemented
15C47×#1450C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689454C411yescharacteristic
19#15689437C411yescharacteristic
20#15689431C411yescharacteristic
21#15689431C411yescharacteristic
22#15689346C411yescharacteristic
23#15689346C411yescharacteristic
24#15689281C411yescharacteristic
25#15689264C411yescharacteristic
26#15689253C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689253C2211yescharacteristic
29#15689252—21no—
30#15689252—21no—
31C8×Dic94C2211yescharacteristic
32C8×Dic94C2211yescharacteristic
33C8×Dic94C2211yescharacteristic
34C4×Dic188C2211yescharacteristic
35C4×Dic188C2211yescharacteristic
36C4×#10625325C2211yescharacteristic
37C4×#10625325C2211yescharacteristic
38#15689202C2211yescharacteristic
39#15689191—21no—
40C8×D188C2211yescharacteristic
41(C22⋊D47)⋊C8—21no—
42#15689183—21no—
43#15689180C2211yescharacteristic
44#15689177—21no—
45#15689173—21no—
46#15689148—21no—
47C2×C4⋊(C47⋊C8)C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688874C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688855C2211yescharacteristic
57#15688855C2211yescharacteristic
58#15688852C2211yescharacteristic
59#15688852C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C82×C47C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625324—21no—
73C22×C47⋊C8—21no—
74C2×C8×D47—21no—
75#13094018—21no—
76#13094016C2×C411yescharacteristic
77#13094012C2×C411yescharacteristic
78#13094007—21no—
79#13094003C2×C411yescharacteristic
80#13093998C2×C411yescharacteristic
81C4×Dic94—21no—
82C4×Dic94—21no—
83C4×Dic94C2×C411yescharacteristic
84C4×Dic94C2×C411yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×Dic94C2311yescharacteristic
87C4×Dic94C2311yescharacteristic
88C4×D188C2311yescharacteristic
89C4×C22⋊D47—21no—
90#13093981—21no—
91C2×C4⋊Dic47C2×C411yescharacteristic
92C2×Dic47⋊C4—21no—
93C2×C4×Dic47—21no—
94#13093958C2×C411yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093956C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093949C2×C411yescharacteristic
113#13093949C2×C411yescharacteristic
114#13093949C2×C411yescharacteristic
115#13093946C2×C411yescharacteristic
116#13093946C2×C411yescharacteristic
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120#13093935—21no—
121#13093934—21no—
122#13093934—21no—
123#13093934—21no—
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C22×C8×C47—21no—
128C2×C42×C47C2311yescharacteristic
129C4⋊C8×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47D411yescharacteristic
133C22⋊C8×C47C2×C411yescharacteristic
134C22⋊C8×C47C2×C411yescharacteristic
135C22⋊C8×C47D411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137C4×C8×C47—21no—
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C2×D188C22×C411yescharacteristic
151C2×C4×D47—21no—
152C2×Dic94—22no—
153C2×Dic94—21no—
154C2×Dic94—41no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158C2×C8×C47—24no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C2×C8×C47C2×D411yescharacteristic
169C42×C47C22×C411yescharacteristic
170C42×C47C2×D411yescharacteristic
171C42×C47#4111yescharacteristic
172C42×C47C2411yescharacteristic
173C22⋊Dic47—21no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176(C2×D47)⋊C4—21no—
177(C2×D47)⋊C4—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47C22×C411yescharacteristic
180C4⋊Dic47C22×C411yescharacteristic
181C4⋊Dic47C22×C411yescharacteristic
182C4⋊Dic47C22×C411yescharacteristic
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—81no—
201Dic188—22no—
202Dic188—41no—
203#10625325—22no—
204#10625325—41no—
205#10625324—81no—
206C8×D47—81no—
207C23×C47C4×D411yescharacteristic
208C22×D47—21no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C23×C411yescharacteristic
218C2×C4×C47C22×D411yescharacteristic
219C2×C4×C47C2×#4111yescharacteristic
220C22⋊D47—42no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230D188—21no—
231D188—21no—
232C4×D47—41no—
233C4×D47—41no—
234Dic94—21no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—42no—
240Dic94#13112yes—
241C8×C47—22no—
242C8×C47—22no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—21no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#18017—471nomaximal, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47#44312yes—
259C22×C47C2×C4×D411yescharacteristic
260C2×D47—41no—
261C2×D47—41no—
262C2×D47—41no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47C2×#13111yescharacteristic
268C4×C47#56811yescharacteristic
269C4×C47#57711yescharacteristic
270C4×C47#57811yescharacteristic
271Dic47—22no—
272Dic47—41no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278#3108—471no—
279#2994—471no—
280#2984—471no—
281#1591—471no—
282#1590—471no—
283#1588—471no—
284#1587—471no—
285#1587—471no—
286#1585—471no—
287C8×Q16—471no—
288C8×SD16—471no—
289#1573—471no—
290#1494—471no—
291C2×Q8⋊C8—471no—
292#1450D4711yescharacteristic, complemented
293C2×C47—22no—
294C2×C47#293311yescharacteristic
295C2×C47#294711yescharacteristic
296C2×C47C2×#44311yescharacteristic
297D47—81no—
298#529—471no—
299C2×C4×Q8—471no—
300#483—471no—
301#480—471no—
302#479—471no—
303#479—471no—
304#464—471no—
305#464—471no—
306#451—471no—
307#448—471no—
308#446—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8—471no—
316C4×Q16—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16—471no—
320#436—471no—
321#435—941no—
322C8×D4—471no—
323C8×D4—941no—
324#433—941no—
325#432—471no—
326#432—941no—
327#431—941no—
328#431C2×D4711yescharacteristic
329#431C2×D4711yescharacteristic
330#424—941no—
331C2×C4⋊C8—471no—
332C2×C4×C8C2×D4711yescharacteristic
333#335—471no—
334#335—471no—
335#334—471no—
336#334—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8—471no—
343D4⋊C8—471no—
344D4⋊C8—471no—
345#322C2×D4711yescharacteristic
346#322C2×D4711yescharacteristic
347C82C2×D4711yescharacteristic
348C82C2×D4711yescharacteristic
349C47#1801711yescharacteristic, complemented, Sylow
350C22×Q8—471no—
351C2×Q16—471no—
352C2×Q16—471no—
353C2×SD16—471no—
354C2×SD16—471no—
355C2×M16—941no—
356C22×C8—21no—
357C22×C8—941no—
358C22×C8—941no—
359#126—941no—
360#125—471no—
361#124—471no—
362#123—941no—
363C22⋊Q8—471no—
364#121—471no—
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—471no—
370C4×Q8—941no—
371C4×Q8—941no—
372C4×D4—471no—
373C4×D4—941no—
374#117—941no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—941no—
377C2×C42—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⋊C8C4×D4711yescharacteristic
395C4⋊C8C4×D4711yescharacteristic
396C4⋊C8D18811yescharacteristic
397C4⋊C8D18811yescharacteristic
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#102—471no—
405#102—471no—
406C22⋊C8—941no—
407C22⋊C8—941no—
408C22⋊C8—941no—
409C22⋊C8C4×D4711yescharacteristic
410C22⋊C8C4×D4711yescharacteristic
411C22⋊C8D18811yescharacteristic
412C22⋊C8D18811yescharacteristic
413#97—941no—
414#97—941no—
415#97—941no—
416#97—941no—
417C4×C8—21no—
418C4×C8—941no—
419C4×C8—941no—
420C4×C8—941no—
421C4×C8C22×D4711yescharacteristic
422C4×C8C22×D4711yescharacteristic
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427C2×Q8—471no—
428C2×Q8—471no—
429C2×Q8—471no—
430C2×Q8—942no—
431C2×Q8—941no—
432C2×Q8—1881no—
433C2×D4—471no—
434C2×D4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4C2×D18811yescharacteristic
440C22×C4#1062535011yescharacteristic
441Q16—942no—
442Q16—1881no—
443SD16—942no—
444SD16—1881no—
445M16—3761no—
446C2×C8—24no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—3761no—
454C2×C8—3761no—
455C2×C8C2×C4×D4711yescharacteristic
456C2×C8C2×C4×D4711yescharacteristic
457C2×C8C2×C4×D4711yescharacteristic
458C2×C8C2×C4×D4711yescharacteristic
459C2×C8C2×D18811yescharacteristic
460C2×C8C2×D18811yescharacteristic
461C2×C8C2×D18811yescharacteristic
462C2×C8C2×D18811yescharacteristic
463C4⋊C4—471no—
464C4⋊C4—471no—
465C4⋊C4—471no—
466C4⋊C4—471no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42—941no—
485C42—941no—
486C42C2×C4×D4711yescharacteristic
487C42C2×D18811yescharacteristic
488C42#1062535011yescharacteristic
489C42C23×D4711yescharacteristic
490C23—941no—
491C23C4×D18811yescharacteristic
492Q8—472no—
493Q8—941no—
494Q8—941no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—1882no—
499D4—941no—
500D4—941no—
501D4—1882no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—1882no—
515C2×C4—1882no—
516C2×C4—1881no—
517C2×C4—1881no—
518C2×C4C4×D18811yescharacteristic
519C2×C4C4×D18811yescharacteristic
520C2×C4C4×D18811yescharacteristic
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C22×D18811yescharacteristic
523C2×C4C2×#1062535011yescharacteristic
524C8—22no—
525C8—22no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—1881no—
535C8—1881no—
536C8—1881no—
537C8—1881no—
538C22—21no—
539C22—21no—
540C22—1881no—
541C22—1881no—
542C22—1881no—
543C22#1568924112yes—
544C22C2×C4×D18811yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—942no—
550C4—1881no—
551C4—1881no—
552C4—1881no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4#131×D4711yescharacteristic
557C4#1568988811yescharacteristic
558C4#1568993511yescharacteristic
559C4#1568994011yescharacteristic
560C2—22no—
561C2—3761no—
562C2#2025211611yescharacteristic
563C2#2025223311yescharacteristic
564C2C2×#1568924111yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1450C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#1450D47
hypocenterC47#18017
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
3. #20252475C2semidirect
4. #20242286C2semidirect
5. #20242280C2semidirect
6. #20242268C2semidirect
7. #20242261C2semidirect
8. #20242261C2semidirect
9. #20242247C2semidirect
10. C8×Dic188C2semidirect
11. C8×#10625325C2semidirect
12. #20242173C2semidirect
14. C2×#15688855C2semidirect
15. C47×#1450C2semidirect
292. #1450D47semidirect
349. C47#18017semidirect

Maximal subgroups

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

subgroupindex
#202534702
#202525502
#202524752
#202422862
#202422802
#202422682
#202422612
#202422472
C8×Dic1882
C8×#106253252
#202421732
#202418492
C2×#156888552
C47×#14502
#1801747