Finite Group Databasebeta

← #26187187

Subgroups — #26187187

Order 12032.

618 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#20253412C211yesmaximal, characteristic
2#20252401C211yesmaximal, characteristic, complemented
3#20252391C211yesmaximal, characteristic, complemented
4#20242285C211yesmaximal, characteristic, complemented
5#20242278C211yesmaximal, characteristic, complemented
6#20242227C211yesmaximal, characteristic, complemented
7#20242227C211yesmaximal, characteristic, complemented
8#20242219C211yesmaximal, characteristic, complemented
9C8×#10625336C211yesmaximal, characteristic, complemented
10#20242182C211yesmaximal, characteristic, complemented
11#20242167C211yesmaximal, characteristic, complemented
12#20241847C211yesmaximal, characteristic, complemented
13#20241769C211yesmaximal, characteristic, complemented
14#20241667C211yesmaximal, characteristic, complemented
15C47×#1584C211yesmaximal, characteristic, complemented
16#15689660C2211yescharacteristic
17C4×#10625354C2211yescharacteristic
18#15689463C411yescharacteristic
19#15689450C411yescharacteristic
20#15689432C411yescharacteristic
21#15689426C411yescharacteristic
22#15689347C411yescharacteristic
23#15689341C411yescharacteristic
24#15689284C411yescharacteristic
25#15689271C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689254C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625336C2211yescharacteristic
30C4×D376C2211yescharacteristic
31#15689202—21no—
32#15689202C2211yescharacteristic
33#15689196—21no—
34#15689193—21no—
35#15689193—21no—
36C8×D188C2211yescharacteristic
37#15689188C2211yescharacteristic
38#15689188C2211yescharacteristic
39#15689183—21no—
40#15689179—21no—
41#15689179C2211yescharacteristic
42#15689175C2211yescharacteristic
43#15689174C2211yescharacteristic
44#15689077—21no—
45C4×#10625324C2211yescharacteristic
46#97×D47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51Q8⋊(C47⋊C8)C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53#15688852C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688850C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625354C2×C411yescharacteristic
68C2×#10625336C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×D376C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×#10625324D411yescharacteristic
73C2×#10625324D411yescharacteristic
74C2×C8×D47—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78#13094019—21no—
79#13094015C2×C411yescharacteristic
80#13094013C2×C411yescharacteristic
81#13094009—21no—
82#13094000C2×C411yescharacteristic
83#13093999C2×C411yescharacteristic
84Q8×Dic47C2×C411yescharacteristic
85C4×D188—21no—
86C4×D188—21no—
87C4×D188C2311yescharacteristic
88C4×D188C2311yescharacteristic
89#13093986—21no—
90#13093986C2×C411yescharacteristic
91#13093982—21no—
92#13093982C2×C411yescharacteristic
93#13093981—21no—
94C42×D47—21no—
95C42×D47C2311yescharacteristic
96#13093958C2×C411yescharacteristic
97#13093955C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105#13093948C2×C411yescharacteristic
106#13093948C2×C411yescharacteristic
107#13093946C2×C411yescharacteristic
108#13093946C2×C411yescharacteristic
109#13093944C2×C411yescharacteristic
110#13093944C2×C411yescharacteristic
111(C2×D47)⋊C8—21no—
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8C2×C411yescharacteristic
118(C2×D47)⋊C8C2×C411yescharacteristic
119#13093935—21no—
120#13093935—21no—
121#13093934—21no—
122#13093934D411yescharacteristic
123#13093934D411yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×Q16×C47C2×C411yescharacteristic
130C4×Q8×C47C2311yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132#107×C47C2×C411yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#103×C47C2×C411yescharacteristic
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146#10625354—22no—
147#10625354—41no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188C22×C411yescharacteristic
151C2×D188C22×C411yescharacteristic
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47C22×C411yescharacteristic
157C2×C4×D47C2×D411yescharacteristic
158C2×C4×D47#4111yescharacteristic
159Q16×C47—41no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C42×C47—21no—
172C42×C47—21no—
173C42×C47C2411yescharacteristic
174#10625336—22no—
175#10625336—41no—
176(C2×D47)⋊C4—21no—
177(C2×D47)⋊C4—21no—
178(C2×D47)⋊C4—21no—
179(C2×D47)⋊C4—21no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47C22×C411yescharacteristic
187C4⋊Dic47C22×C411yescharacteristic
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47C22×C411yescharacteristic
193C4×Dic47C2×D411yescharacteristic
194C4×Dic47#4111yescharacteristic
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202D376—22no—
203#10625324—22no—
204#10625324—22no—
205#10625324—42no—
206C8×D47—42no—
207C8×D47—42no—
208C8×D47—42no—
209C8×D47—42no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47C4×D411yescharacteristic
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47C23×C411yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C47C2×#4111yescharacteristic
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47C4×D411yescharacteristic
227C2×Dic47C4×D411yescharacteristic
228C2×Dic47C4×D411yescharacteristic
229D188—21no—
230D188—21no—
231D188—21no—
232D188—42no—
233D188—81no—
234D188#13112yes—
235C4×D47—21no—
236C4×D47—21no—
237C4×D47—21no—
238C4×D47—21no—
239C4×D47—41no—
240C4×D47—42no—
241C4×D47—41no—
242C4×D47—41no—
243C4×D47—41no—
244C4×D47—41no—
245C4×D47—81no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47#13512yes—
253C47⋊C8—22no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259C47⋊C8#13512yes—
260#17996—471nomaximal, Sylow
261C22×C47C2×C4×D411yescharacteristic
262C2×D47—21no—
263C2×D47—22no—
264C2×D47—21no—
265C2×D47—21no—
266C2×D47—41no—
267C2×D47—41no—
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C4×C47—21no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47C2×#13111yescharacteristic
277C4×C47#56811yescharacteristic
278C4×C47C2×#13511yescharacteristic
279C4×C47C2×#13511yescharacteristic
280Dic47—21no—
281Dic47—21no—
282Dic47—21no—
283Dic47—41no—
284Dic47—41no—
285#3102—471no—
286#2970—471no—
287#2969—471no—
288#1591—471no—
289#1590—471no—
290#1584D4711yescharacteristic, complemented
291#1582—471no—
292#1582—471no—
293#1581—471no—
294C8×SD16—471no—
295C8×D8—471no—
296#1572—471no—
297#1494—471no—
298#1476—471no—
299C8×M16—471no—
300C2×C47#293311yescharacteristic
301C2×C47C4×#13511yescharacteristic
302C2×C47#295611yescharacteristic
303D47—41no—
304D47—42no—
305D47—81no—
306#529—471no—
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—
317#446—471no—
318#446C2×D4711yescharacteristic
319C8×Q8C2×D4711yescharacteristic
320C4×Q16C2×D4711yescharacteristic
321C4×SD16—471no—
322C4×SD16—471no—
323C4×D8—471no—
324#436—471no—
325#436—941no—
326#435—941no—
327#435—941no—
328#435—941no—
329C8×D4—471no—
330C8×D4—471no—
331C8×D4—471no—
332#433—941no—
333#432—471no—
334#432—941no—
335#431—471no—
336#431—471no—
337#405—941no—
338C4×M16—471no—
339C2×#97—941no—
340C2×C4×C8—471no—
341#335—471no—
342#335C2×D4711yescharacteristic
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⋊C8—471no—
352D4⋊C8—471no—
353#322—471no—
354#322C2×D4711yescharacteristic
355C82—471no—
356C82—471no—
357C47#1799611yescharacteristic, complemented, Sylow
358C2×#41—471no—
359C2×Q16C4×D4711yescharacteristic
360C2×SD16—471no—
361C2×SD16—471no—
362C2×D8—471no—
363C2×M16—471no—
364C2×M16—471no—
365C2×M16—941no—
366C22×C8—941no—
367C22×C8—941no—
368C22×C8—941no—
369C22×C8—941no—
370#126—941no—
371#125—471no—
372#124—471no—
373#123—941no—
374C22⋊Q8—471no—
375#121—471no—
376C4×Q8—471no—
377C4×Q8C22×D4711yescharacteristic
378C4×Q8C22×D4711yescharacteristic
379C4×D4—471no—
380C4×D4—471no—
381C4×D4—471no—
382C4×D4—941no—
383C4×D4—941no—
384C4×D4—941no—
385#117—471no—
386#117—941no—
387#117—941no—
388C2×C42—471no—
389C2×C42—941no—
390#107—471no—
391#107C4×D4711yescharacteristic
392#106—471no—
393#106—471no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—471no—
399C4⋊C8—471no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8C22×D4711yescharacteristic
403C4⋊C8C22×D4711yescharacteristic
404#103—471no—
405#103—471no—
406#103C4×D4711yescharacteristic
407#103C4×D4711yescharacteristic
408#102—471no—
409#102—471no—
410#102—471no—
411#102—471no—
412C22⋊C8—471no—
413C22⋊C8—471no—
414C22⋊C8—941no—
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—
424#97—941no—
425#97—941no—
426C4×C8—21no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—942no—
436#41—1881no—
437C2×Q8C2×C4×D4711yescharacteristic
438C2×Q8C2×C4×D4711yescharacteristic
439C2×D4—471no—
440C2×D4—471no—
441C2×D4—941no—
442C2×D4—941no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450Q16—41no—
451SD16—942no—
452SD16—1881no—
453D8—942no—
454M16—942no—
455M16—942no—
456M16—1882no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—1882no—
468C2×C8—1882no—
469C2×C8—1882no—
470C2×C8—1882no—
471C2×C8C2×C4×D4711yescharacteristic
472C2×C8C2×C4×D4711yescharacteristic
473C2×C8D4×D4711yescharacteristic
474C2×C8D4×D4711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—471no—
478C4⋊C4—471no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4C2×C4×D4711yescharacteristic
484C4⋊C4C2×C4×D4711yescharacteristic
485C22⋊C4—941no—
486C22⋊C4—941no—
487C22⋊C4—941no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—21no—
495C42—471no—
496C42—471no—
497C42—471no—
498C42—941no—
499C42—941no—
500C42C23×D4711yescharacteristic
501C23—471no—
502C23—941no—
503C23—941no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—472no—
509D4—941no—
510D4—941no—
511D4—941no—
512D4—3761no—
513D4—1882no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—471no—
519C2×C4—471no—
520C2×C4—471no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—3761no—
528C2×C4—1881no—
529C2×C4—1882no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4C22×C4×D4711yescharacteristic
535C2×C4C2×D4×D4711yescharacteristic
536C2×C4#41×D4711yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—472no—
544C8—942no—
545C8—941no—
546C8—941no—
547C8—941no—
548C8—1881no—
549C8—1881no—
550C8#1309404712yes—
551C22—941no—
552C22—941no—
553C22—941no—
554C22—942no—
555C22—1881no—
556C22—1881no—
557C22—1881no—
558C22—1881no—
559C22—1881no—
560C22C4×D4×D4711yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—941no—
567C4—941no—
568C4—941no—
569C4—1881no—
570C4—1881no—
571C4#131×D4711yescharacteristic
572C4#1568988911yescharacteristic
573C4#135×D4711yescharacteristic
574C4C2×#1309404711yescharacteristic
575C2—3761no—
576C2—1881no—
577C2—1882no—
578C2#2025211111yescharacteristic
579C2C4×#1309404711yescharacteristic
580C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1584C2
socleC22×C47C2×C4×D4
prime radical#15689271C4
cosocleC42×C47C24
hypercenter#1584D47
hypocenterC47#17996
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. #20252401C2semidirect
3. #20252391C2semidirect
4. #20242285C2semidirect
5. #20242278C2semidirect
6. #20242227C2semidirect
7. #20242227C2semidirect
8. #20242219C2semidirect
9. C8×#10625336C2semidirect
10. #20242182C2semidirect
11. #20242167C2semidirect
12. #20241847C2semidirect
13. #20241769C2semidirect
14. #20241667C2semidirect
15. C47×#1584C2semidirect
290. #1584D47semidirect
357. C47#17996semidirect

Maximal subgroups

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

subgroupindex
#202534122
#202524012
#202523912
#202422852
#202422782
#202422272
#202422192
C8×#106253362
#202421822
#202421672
#202418472
#202417692
#202416672
C47×#15842
#1799647