Finite Group Databasebeta

← #26220656

Subgroups — #26220656

Order 12032.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689223C211yesmaximal, characteristic
2#20246040C211yesmaximal, characteristic, complemented
3#20244268C211yesmaximal, characteristic
4#20244241C211yesmaximal, characteristic
5#20244123C211yesmaximal, characteristic, complemented
6#20244118C211yesmaximal, characteristic, complemented
7#20244088C211yesmaximal, characteristic
8#20244077C211yesmaximal, characteristic, complemented
9#20244074C211yesmaximal, characteristic
10#20244063C211yesmaximal, characteristic, complemented
11#20243286C211yesmaximal, characteristic, complemented
12C4×#13093947C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic
14#20243075C211yesmaximal, characteristic, complemented
15C47×#2319C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689223C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093947C2211yescharacteristic
23C2×#13093947C2211yescharacteristic
24C2×#13093947C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689029C2211yescharacteristic
35#15689029C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689005—21no—
39#15689005—21no—
40#15688990—21no—
41#15688987—21no—
42C4×C4⋊Dic47C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#388—21no—
56C47×#381—21no—
57C47×#380—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#376C2211yescharacteristic
60C22×Dic94C2311yescharacteristic
61C2×#10625335—22no—
62C2×#10625335—22no—
63C2×#10625335C2×C414yes—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C4×Dic94—22no—
69C4×Dic94C2×C414yes—
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—21no—
78#13093957—22no—
79#13093957C2×C414yes—
80#13093955—22no—
81#13093947—22no—
82#13093947—22no—
83#13093947C2×C414yes—
84#13093945—22no—
85#13093945—22no—
86#13093945C2×C414yes—
87#13093935—22no—
88#13093935—22no—
89#13093935C2×C414yes—
90C4×C47⋊C8—22no—
91C4×C47⋊C8—22no—
92C4×C47⋊C8—22no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×D4×C47C2311yescharacteristic
101C23×C4×C47—21no—
102C4×D4×C47—22no—
103C4×D4×C47C2×C414yes—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C42×C47—21no—
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124#95×C47D411yescharacteristic
125C24×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47C22×C412yes—
132C22×C4×C47—21no—
133C22×C4×C47—24no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—81no—
137C22×C4×C47—81no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2411yescharacteristic
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94C22×C412yes—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—81no—
161C4⋊C4×C47—81no—
162C4⋊C4×C47C22×C412yes—
163C22⋊C4×C47—24no—
164C22⋊C4×C47—81no—
165C22⋊C4×C47—81no—
166C22⋊C4×C47—81no—
167C22⋊C4×C47—81no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—81no—
173C42×C47C22×C412yes—
174C42×C47#4112yes—
175#10625335—28no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47C22×C412yes—
182Dic47⋊C4—24no—
183Dic47⋊C4—81no—
184Dic47⋊C4—81no—
185C4×Dic47—24no—
186C4×Dic47—81no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8C22×C412yes—
194C2×C47⋊C8C22×C412yes—
195C2×C47⋊C8#4112yes—
196C2×C47⋊C8#4112yes—
197C2×C47⋊C8#4112yes—
198C2×C47⋊C8#4112yes—
199C23×C47—22no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47—41no—
206C23×C47C22×D411yescharacteristic
207D4×C47—22no—
208D4×C47—22no—
209D4×C47—41no—
210D4×C47—41no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—22no—
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—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—84no—
237C2×C4×C47C4×D412yes—
238C2×C4×C47C4×D412yes—
239C2×C4×C47C23×C411yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257Dic94—22no—
258Dic94—22no—
259Dic94—41no—
260Dic94—41no—
261C47⋊C8—22no—
262C47⋊C8—22no—
263C47⋊C8—22no—
264C47⋊C8#11714yes—
265#21291—471nomaximal, Sylow
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47C2×C4×D411yescharacteristic
274C22×C47#53211yescharacteristic
275C22×C47#53211yescharacteristic
276C22×C47#57611yescharacteristic
277C22×C47#57711yescharacteristic
278C22×C47#57711yescharacteristic
279C22×C47#57811yescharacteristic
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—42no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47C2×#11711yescharacteristic
290C4×C47C4×#4111yescharacteristic
291C4×C47#52911yescharacteristic
292C4×C47#52911yescharacteristic
293Dic47—42no—
294Dic47—42no—
295Dic47—81no—
296Dic47—81no—
297C2×#440—471no—
298#2320—471no—
299#2319D4711yescharacteristic
300#1973—471no—
301#1968—471no—
302#1943—471no—
303#1942—471no—
304#1936—471no—
305#1935—471no—
306#1934—471no—
307#1933—471no—
308#1776—471no—
309C4×#103—471no—
310C4×#102—471no—
311#1726—471no—
312C2×C47—82no—
313C2×C47#229311yescharacteristic
314C2×C47#294611yescharacteristic
315C2×C47#294711yescharacteristic
316C2×C47#317411yescharacteristic
317C2×C47#317511yescharacteristic
318C2×C47#317811yescharacteristic
319C2×C47#317911yescharacteristic
320C22×SD16—471no—
321C2×C4×Q8—471no—
322C2×C4×D4C2×D4711yescharacteristic
323#440—478no—
324C2×#107—471no—
325C2×#107—471no—
326C2×#106—471no—
327C2×#103—471no—
328C2×#103—471no—
329C2×#103—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×#102—471no—
333C2×#97—471no—
334C2×#97—471no—
335C2×#97—471no—
336C2×C4×C8—471no—
337C2×C4×C8—471no—
338C2×C4×C8—471no—
339#391—471no—
340#391—471no—
341#390C2×D4711yescharacteristic
342#390C2×D4711yescharacteristic
343#389—471no—
344#389—471no—
345#389C2×D4711yescharacteristic
346#389C2×D4711yescharacteristic
347#388—21no—
348#388—21no—
349#387—941no—
350#387—941no—
351#383—941no—
352#382—941no—
353#381—21no—
354#380—21no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4C2×D4711yescharacteristic
357#376C2×D4711yescharacteristic
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364C47#2129111yescharacteristic, complemented, Sylow
365C22×Q8—471no—
366C22×D4C22×D4711yescharacteristic
367C23×C4—21no—
368C2×SD16—474no—
369C2×SD16—942no—
370C2×SD16—942no—
371C22×C8—471no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375C4×Q8—474no—
376C4×Q8—942no—
377C4×D4—22no—
378C4×D4C4×D4714yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—471no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—941no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4C22×D4711yescharacteristic
388C2×C4⋊C4C22×D4711yescharacteristic
389C2×C4⋊C4C22×D4711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—941no—
397C2×C42—941no—
398C2×C42C22×D4711yescharacteristic
399C2×C42C22×D4711yescharacteristic
400C2×C42C22×D4711yescharacteristic
401#107—474no—
402#107—942no—
403#106—942no—
404#103—474no—
405#103—942no—
406#103—942no—
407#102—474no—
408#102—942no—
409#102—942no—
410#97—474no—
411#97—942no—
412#97—942no—
413C4×C8—942no—
414C4×C8—942no—
415C4×C8—942no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—941no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95C22⋊D4711yescharacteristic
427#95C22⋊D4711yescharacteristic
428#95C22⋊D4711yescharacteristic
429#95C22⋊D4711yescharacteristic
430C24—21no—
431C2×Q8—472no—
432C2×Q8—941no—
433C2×Q8—941no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×C4×D4712yes—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460SD16—948no—
461C2×C8—472no—
462C2×C8—472no—
463C2×C8—472no—
464C2×C8—472no—
465C2×C8—472no—
466C2×C8—472no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—472no—
481C4⋊C4—944no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—3761no—
488C4⋊C4—3761no—
489C4⋊C4C2×C4×D4712yes—
490C22⋊C4—24no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—944no—
501C42—3761no—
502C42C2×C4×D4712yes—
503C42#1062535012yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×C22⋊D4711yescharacteristic
512Q8—942no—
513Q8—942no—
514Q8—1881no—
515Q8—1881no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4C4×C22⋊D4712yes—
559C2×C4C4×C22⋊D4712yes—
560C2×C4C22×C4×D4711yescharacteristic
561C2×C4#41×D4711yescharacteristic
562C2×C4#41×D4711yescharacteristic
563C2×C4#41×D4711yescharacteristic
564C2×C4#41×D4711yescharacteristic
565C2×C4C2×#1062535011yescharacteristic
566C8—474no—
567C8—942no—
568C8—942no—
569C8—942no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×C22⋊D4711yescharacteristic
578C22#1568966911yescharacteristic
579C22#1568966911yescharacteristic
580C22#1568992611yescharacteristic
581C22#1568993411yescharacteristic
582C22#1568993411yescharacteristic
583C22#1568993811yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—3761no—
594C4—3761no—
595C4—1882no—
596C4—1882no—
597C4#117×D4711yescharacteristic
598C4#1568959111yescharacteristic
599C4#1568965111yescharacteristic
600C4#1568965111yescharacteristic
601C2—82no—
602C2#2024584711yescharacteristic
603C2#2025222011yescharacteristic
604C2#2025222711yescharacteristic
605C2#2025401011yescharacteristic
606C2#2025402111yescharacteristic
607C2#2025405011yescharacteristic
608C2#2025407311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2319C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenter#2319D47
hypocenterC47#21291
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #20246040C2semidirect
5. #20244123C2semidirect
6. #20244118C2semidirect
8. #20244077C2semidirect
10. #20244063C2semidirect
11. #20243286C2semidirect
12. C4×#13093947C2semidirect
14. #20243075C2semidirect
18. #15689223C4semidirect
364. C47#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#156892232
#202460402
#202442682
#202442412
#202441232
#202441182
#202440882
#202440772
#202440742
#202440632
#202432862
C4×#130939472
C4×#130939452
#202430752
C47×#23192
#2129147