Finite Group Databasebeta

← #26223108

Subgroups — #26223108

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252996C211yesmaximal, characteristic
2C2×#15689238C211yesmaximal, characteristic, complemented
3#20252093C211yesmaximal, characteristic, complemented
4#20252089C211yesmaximal, characteristic, complemented
5C2×#15689075C211yesmaximal, characteristic, complemented
6#20244278C211yesmaximal, characteristic, complemented
7#20244140C211yesmaximal, characteristic, complemented
8#20244094C211yesmaximal, characteristic, complemented
9#20244090C211yesmaximal, characteristic, complemented
10#20243830C211yesmaximal, characteristic, complemented
11#20243828C211yesmaximal, characteristic, complemented
12#20243429C211yesmaximal, characteristic, complemented
13#20243268C211yesmaximal, characteristic, complemented
14#20243232C211yesmaximal, characteristic, complemented
15C47×#1765C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20#15689635C2211yescharacteristic
21#15689630C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23#15689380C412yescomplemented
24#15689375C412yescomplemented
25#15689372C412yescomplemented
26#15689368C412yescomplemented
27#15689238—24no—
28#15689202—22no—
29#15689199—22no—
30#15689196—22no—
31#15689194—22no—
32C2×#13093959C2211yescharacteristic
33C2×#13093959C2211yescharacteristic
34#15689159C2211yescharacteristic
35#15689151C2211yescharacteristic
36#15689150C2211yescharacteristic
37C2×#13093952C2211yescharacteristic
38C2×#13093951C2211yescharacteristic
39C2×#13093950C2211yescharacteristic
40#15689120C2211yescharacteristic
41#15689091C2211yescharacteristic
42#15689090C2211yescharacteristic
43#15689086C2211yescharacteristic
44#15689086C2211yescharacteristic
45#15689078C2211yescharacteristic
46#15689075—24no—
47C2×#13093935C2211yescharacteristic
48C2×C8×Dic47C2211yescharacteristic
49C2×C8×Dic47C2211yescharacteristic
50#15688888C2211yescharacteristic
51#15688884C2211yescharacteristic
52#15688883C2211yescharacteristic
53#15688882C2211yescharacteristic
54C2×#131×C47C2211yescharacteristic
55C2×#104×C47C2211yescharacteristic
56C47×#416C2211yescharacteristic
57C47×#405C2211yescharacteristic
58C2×#97×C47C2211yescharacteristic
59C47×#341C2211yescharacteristic
60C47×#339C2211yescharacteristic
61C2×#10625350C2311yescharacteristic
62C22×C4×D47—21no—
63C22×C4×D47C2311yescharacteristic
64#13094044—22no—
65#13094044—22no—
66C2×#10625337C2×C411yescharacteristic, complemented
67C2×#10625335C2×C411yescharacteristic, complemented
68C2×#10625336C2×C411yescharacteristic, complemented
69C2×#10625334C2×C411yescharacteristic, complemented
70#13094030—22no—
71#13094030—22no—
72C2×#10625329C2311yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625324—22no—
75C2×#10625324—22no—
76C2×#10625324—22no—
77C2×#10625324—22no—
78C2×#10625324—21no—
79C2×#10625324C2×C412yes—
80C2×#10625324C2×C412yes—
81C2×#10625324D412yes—
82C2×#10625324D412yes—
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C2×C8×D47—21no—
86#13094008—21no—
87#13094005—21no—
88#13094004C2×C412yes—
89#13094000C2×C412yes—
90#13093999C2×C412yes—
91#13093995C2×C412yes—
92#13093994—21no—
93#13093992—21no—
94C4×D188—22no—
95C4×C22⋊D47—22no—
96#13093983C2311yescharacteristic
97C2×C4×Dic47—21no—
98C2×C4×Dic47C2311yescharacteristic
99C42×D47—22no—
100C42×D47—22no—
101#13093959—22no—
102#13093959—22no—
103#13093957C2×C412yescomplemented
104#13093955C2×C412yescomplemented
105C4⋊(C47⋊C8)—22no—
106Dic47⋊C8—22no—
107#13093952—22no—
108#13093951—22no—
109#13093950—22no—
110#13093949C2×C412yescomplemented
111#13093946C2×C412yescomplemented
112C22⋊(C47⋊C8)—22no—
113(C2×D47)⋊C8—22no—
114(C2×D47)⋊C8—22no—
115(C2×D47)⋊C8—22no—
116#13093935—22no—
117#13093934—21no—
118C8×Dic47—21no—
119C8×Dic47—22no—
120C8×Dic47D414yescomplemented
121C2×#41×C47C2311yescharacteristic
122#131×C47—22no—
123#131×C47—22no—
124C2×M16×C47—21no—
125C2×M16×C47C2311yescharacteristic
126C2×M16×C47C2311yescharacteristic
127C22×C8×C47—21no—
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130#117×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132#104×C47—22no—
133#103×C47C2×C412yescomplemented
134#102×C47C2×C412yescomplemented
135#97×C47—22no—
136#97×C47—21no—
137C4×C8×C47—21no—
138C23×D47#4111yescharacteristic
139#41×C47—21no—
140#41×C47—21no—
141#41×C47—21no—
142#41×C47—21no—
143C2×Q8×C47C22×C411yescharacteristic
144C2×D4×C47—21no—
145C2×D4×C47C22×C411yescharacteristic
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47C2411yescharacteristic
149C2×C22⋊D47—21no—
150C2×C22⋊D47—22no—
151C22×Dic47—21no—
152C22×Dic47#4111yescharacteristic
153#10625350—21no—
154#10625350—21no—
155#10625350—21no—
156#10625350—21no—
157C2×D188—22no—
158C2×D188C22×C411yescharacteristic
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—24no—
164C2×C4×D47—21no—
165C2×C4×D47—44no—
166C2×C4×D47C22×C412yes—
167C2×C4×D47C2×D412yes—
168C2×Dic94C22×C411yescharacteristic
169M16×C47—21no—
170M16×C47—21no—
171M16×C47—21no—
172M16×C47—21no—
173M16×C47—42no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—42no—
179C2×C8×C47C22×C412yes—
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D412yes—
183C2×C8×C47#4112yes—
184C4⋊C4×C47C22×C412yes—
185C22⋊C4×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47#4112yes—
189C22⋊Dic47—21no—
190C22⋊Dic47—22no—
191#10625337—22no—
192#10625336—22no—
193#10625335—22no—
194#10625334—22no—
195(C2×D47)⋊C4—22no—
196(C2×D47)⋊C4—22no—
197(C2×D47)⋊C4—22no—
198C4⋊Dic47—22no—
199C4⋊Dic47C22×C412yes—
200Dic47⋊C4—22no—
201C4×Dic47—24no—
202C4×Dic47—21no—
203C4×Dic47—21no—
204C4×Dic47C2×D412yes—
205#10625329—21no—
206#10625329—21no—
207#10625329—21no—
208#10625329—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8C22×C411yescharacteristic
214C2×C47⋊C8C22×C411yescharacteristic
215C2×C47⋊C8C2×D412yes—
216C2×C47⋊C8C2×D412yes—
217C2×C47⋊C8#4112yes—
218#10625324—24no—
219#10625324—24no—
220#10625324—24no—
221#10625324—24no—
222#10625324—42no—
223C8×D47—42no—
224C23×C47—21no—
225C23×C47C2×#4111yescharacteristic
226C22×D47—21no—
227C22×D47—21no—
228C22×D47—21no—
229C22×D47—42no—
230C22×D47C4×D412yes—
231Q8×C47—21no—
232Q8×C47—21no—
233D4×C47—21no—
234D4×C47—21no—
235D4×C47—41no—
236D4×C47—41no—
237C2×C4×C47—21no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—42no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47C23×C411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C22⋊D47—41no—
250C22⋊D47—41no—
251C22⋊D47—82no—
252C2×Dic47—24no—
253C2×Dic47—21no—
254C2×Dic47—22no—
255C2×Dic47—21no—
256C2×Dic47—22no—
257C2×Dic47—21no—
258C2×Dic47C4×D412yes—
259D188—21no—
260D188—21no—
261D188—82no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—22no—
265C4×D47—22no—
266C4×D47—48no—
267C4×D47—41no—
268C4×D47—41no—
269Dic94—21no—
270Dic94—21no—
271C8×C47—22no—
272C8×C47—41no—
273C8×C47—41no—
274C8×C47#12112yes—
275C8×C47#12112yes—
276C47⋊C8—22no—
277C47⋊C8—41no—
278C47⋊C8—41no—
279C47⋊C8C4×D412yes—
280C47⋊C8C4×D412yes—
281#21549—471nomaximal, Sylow
282C22×C47—22no—
283C22×C47—42no—
284C22×C47—41no—
285C22×C47C2×C4×D411yescharacteristic
286C22×C47#52511yescharacteristic
287C22×C47#52911yescharacteristic
288C2×D47—22no—
289C2×D47—22no—
290C2×D47—22no—
291C2×D47—42no—
292C2×D47—42no—
293C2×D47—42no—
294C2×D47—41no—
295C4×C47—42no—
296C4×C47—42no—
297C4×C47—41no—
298C4×C47C2×C4×D411yescharacteristic
299C4×C47C4×#4111yescharacteristic
300C4×C47C2×#12111yescharacteristic
301C4×C47#53211yescharacteristic
302Dic47—24no—
303Dic47—22no—
304Dic47—42no—
305Dic47—41no—
306#3054—471no—
307C2×#443—471no—
308#2930—471no—
309#2930—471no—
310C2×C4×M16—471no—
311#1975—471no—
312#1946—471no—
313#1937—471no—
314#1937—471no—
315#1896—471no—
316#1896—471no—
317#1811—471no—
318#1772—471no—
319#1765—471no—
320#1765D4711yescharacteristic, complemented
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—81no—
324C2×C47C4×#12111yescharacteristic
325C2×C47#295612yes—
326D47—42no—
327D47—81no—
328C2×#135—471no—
329C2×#131—471no—
330C2×#131C2×D4711yescharacteristic
331C22×M16—471no—
332C22×M16—471no—
333#525—471no—
334#525—471no—
335C22×C42—471no—
336#470—472no—
337#469—472no—
338#468—472no—
339#468—472no—
340#443—944no—
341#436—942no—
342#436—942no—
343#435—942no—
344#435—942no—
345C2×#108—471no—
346C2×#108—471no—
347#427—471no—
348#424—471no—
349#424—471no—
350C2×#104—471no—
351C2×#104—471no—
352C2×#104—471no—
353C2×#104C2×D4711yescharacteristic
354#416—471no—
355#416C2×D4711yescharacteristic
356#408—471no—
357#408—471no—
358#407—471no—
359#407—471no—
360#405—471no—
361#405C2×D4711yescharacteristic
362C4×M16—944no—
363C2×#97—471no—
364C2×#97C2×D4711yescharacteristic
365C2×C4×C8—471no—
366C2×C4×C8—471no—
367#341—471no—
368#341C2×D4711yescharacteristic
369#339—471no—
370#339—471no—
371#339—471no—
372#339C2×D4711yescharacteristic
373C47#2154911yescharacteristic, complemented, Sylow
374C2×#41—471no—
375C2×#41C22×D4711yescharacteristic
376C23×C4—471no—
377C23×C4—941no—
378#135—942no—
379#135—942no—
380C2×Q16—471no—
381C2×SD16—471no—
382C2×SD16—471no—
383C2×D8—471no—
384#131—22no—
385#131—22no—
386#131—942no—
387#131—942no—
388C2×M16—21no—
389C2×M16—472no—
390C2×M16—472no—
391C2×M16—472no—
392C2×M16—472no—
393C2×M16—471no—
394C2×M16—471no—
395C2×M16—942no—
396C2×M16—942no—
397C2×M16—942no—
398C2×M16—942no—
399C2×M16—941no—
400C2×M16C22×D4711yescharacteristic
401C2×M16C22×D4711yescharacteristic
402C22×C8—21no—
403C22×C8—471no—
404C22×C8—471no—
405C22×C8—941no—
406C22×C8C22×D4711yescharacteristic
407C22×C8C22×D4711yescharacteristic
408#123—941no—
409#123—941no—
410C22⋊Q8—472no—
411C22⋊Q8—472no—
412#121—472no—
413#121—472no—
414#120—941no—
415#120—941no—
416C4×D4—942no—
417C4×D4—942no—
418#117—471no—
419#117C22×D4711yescharacteristic
420C2×C42—471no—
421C2×C42—942no—
422C2×C42—941no—
423C2×C42—942no—
424C2×C42C22×D4711yescharacteristic
425#108—942no—
426#108—942no—
427#107—472no—
428#106—472no—
429C4⋊C8—942no—
430C4⋊C8—942no—
431#104—22no—
432#104—942no—
433#104—942no—
434#104—942no—
435#103—472no—
436#103C4×D4712yescomplemented
437#102—472no—
438#102C4×D4712yescomplemented
439C22⋊C8—942no—
440C22⋊C8—942no—
441C22⋊C8—942no—
442C22⋊C8—942no—
443#97—22no—
444#97—21no—
445#97—942no—
446#97—941no—
447C4×C8—21no—
448C4×C8—474no—
449C4×C8—942no—
450C4×C8—941no—
451C24—471no—
452#41—21no—
453#41—21no—
454#41—21no—
455#41—21no—
456#41—941no—
457#41—941no—
458#41—941no—
459#41—941no—
460C2×Q8—471no—
461C2×Q8C2×C4×D4711yescharacteristic
462C2×D4—21no—
463C2×D4—471no—
464C2×D4—942no—
465C2×D4—942no—
466C2×D4—941no—
467C2×D4C2×C4×D4711yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—471no—
471C22×C4—472no—
472C22×C4—472no—
473C22×C4—944no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—1884no—
481C22×C4C23×D4711yescharacteristic
482Q16—942no—
483SD16—942no—
484SD16—942no—
485D8—942no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—42no—
491M16—944no—
492M16—944no—
493M16—944no—
494M16—944no—
495M16—941no—
496M16—941no—
497M16—941no—
498M16—941no—
499M16—1882no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8—471no—
506C2×C8—471no—
507C2×C8—472no—
508C2×C8—472no—
509C2×C8—472no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—1882no—
515C2×C8C2×C4×D4712yes—
516C2×C8#1062535012yes—
517C2×C8D4×D4712yes—
518C2×C8D4×D4711yescharacteristic
519C2×C8D4×D4711yescharacteristic
520C4⋊C4—472no—
521C4⋊C4—942no—
522C4⋊C4—942no—
523C4⋊C4C2×C4×D4712yes—
524C22⋊C4—21no—
525C22⋊C4—942no—
526C22⋊C4—942no—
527C22⋊C4—942no—
528C22⋊C4—942no—
529C22⋊C4—941no—
530C42—21no—
531C42—21no—
532C42—472no—
533C42—944no—
534C42—941no—
535C42—941no—
536C42#1062535012yes—
537C23—21no—
538C23—472no—
539C23—941no—
540C23—941no—
541C23—941no—
542C23—1882no—
543C23#41×D4711yescharacteristic
544Q8—21no—
545Q8—21no—
546Q8—941no—
547Q8—941no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—941no—
553D4—941no—
554D4—3762no—
555D4—3762no—
556D4—1881no—
557D4—1881no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—472no—
565C2×C4—944no—
566C2×C4—942no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—941no—
575C2×C4—1888no—
576C2×C4—1881no—
577C2×C4—1881no—
578C2×C4C22×C4×D4711yescharacteristic
579C2×C4C2×D4×D4711yescharacteristic
580C2×C4C2×D4×D4711yescharacteristic
581C2×C4#41×D4711yescharacteristic
582C2×C4C2×#1062535011yescharacteristic
583C2×C4C2×#1062535011yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—472no—
588C8—472no—
589C8—942no—
590C8—1881no—
591C8—1881no—
592C8#1309399712yes—
593C8#1309399712yes—
594C22—22no—
595C22—42no—
596C22—41no—
597C22—942no—
598C22—942no—
599C22—942no—
600C22—1882no—
601C22—1882no—
602C22—1882no—
603C22—1881no—
604C22C4×D4×D4711yescharacteristic
605C22#1568963211yescharacteristic
606C22#1568965111yescharacteristic
607C4—42no—
608C4—42no—
609C4—41no—
610C4—944no—
611C4—942no—
612C4—1882no—
613C4—1881no—
614C4C4×D4×D4711yescharacteristic
615C4C4×#1062535011yescharacteristic
616C4C2×#1309399711yescharacteristic
617C4#1568967011yescharacteristic
618C2—21no—
619C2—21no—
620C2—81no—
621C2—3761no—
622C2—1882no—
623C2C4×#1309399711yescharacteristic
624C2#2025229612yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1765C2
socleC22×C47C2×C4×D4
prime radical#20252996C2
cosocleC22×C4×C47C24
hypercenter#1765D47
hypocenterC47#21549
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. C2×#15689238C2semidirect
3. #20252093C2semidirect
4. #20252089C2semidirect
5. C2×#15689075C2semidirect
6. #20244278C2semidirect
7. #20244140C2semidirect
8. #20244094C2semidirect
9. #20244090C2semidirect
10. #20243830C2semidirect
11. #20243828C2semidirect
12. #20243429C2semidirect
13. #20243268C2semidirect
14. #20243232C2semidirect
15. C47×#1765C2semidirect
23. #15689380C4semidirect
24. #15689375C4semidirect
25. #15689372C4semidirect
26. #15689368C4semidirect
66. C2×#10625337C2×C4semidirect
67. C2×#10625335C2×C4semidirect
68. C2×#10625336C2×C4semidirect
69. C2×#10625334C2×C4semidirect
103. #13093957C2×C4semidirect
104. #13093955C2×C4semidirect
110. #13093949C2×C4semidirect
111. #13093946C2×C4semidirect
120. C8×Dic47D4semidirect
133. #103×C47C2×C4semidirect
134. #102×C47C2×C4semidirect
320. #1765D47semidirect
373. C47#21549semidirect
436. #103C4×D47semidirect
438. #102C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202529962
C2×#156892382
#202520932
#202520892
C2×#156890752
#202442782
#202441402
#202440942
#202440902
#202438302
#202438282
#202434292
#202432682
#202432322
C47×#17652
#2154947