Finite Group Databasebeta

← #26220611

Subgroups — #26220611

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689223C211yesmaximal, characteristic
2#20245865C211yesmaximal, 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
12#20243221C211yesmaximal, characteristic, complemented
13#20243213C211yesmaximal, characteristic
14C4×#13093935C211yesmaximal, characteristic, complemented
15C47×#2293C211yesmaximal, 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×#13093935C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689029C2211yescharacteristic
35#15689029C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689007—21no—
39#15689007—21no—
40C4×Dic47⋊C4—21no—
41C4×C4⋊Dic47C2211yescharacteristic
42#15688969—21no—
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C2×#117×C47—21no—
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C47×#388—21no—
56C47×#388—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47—21no—
59C43×C47C2211yescharacteristic
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#13093935—22no—
90#13093935C2×C414yes—
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—
104#117×C47—44no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C42×C47—21no—
116C2×C42×C47D411yescharacteristic
117C2×C42×C47D411yescharacteristic
118C2×C42×C47D411yescharacteristic
119C2×C42×C47D411yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126C24×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47C22×C412yes—
133C22×C4×C47—21no—
134C22×C4×C47—24no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2411yescharacteristic
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94C22×C412yes—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—42no—
162C4⋊C4×C47—42no—
163C4⋊C4×C47C22×C412yes—
164C22⋊C4×C47—24no—
165C22⋊C4×C47—42no—
166C22⋊C4×C47—42no—
167C22⋊C4×C47—42no—
168C22⋊C4×C47—42no—
169C42×C47—22no—
170C42×C47—22no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—41no—
176C42×C47—41no—
177C42×C47—42no—
178C42×C47C22×C412yes—
179C42×C47#4112yes—
180#10625335—28no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47C22×C412yes—
187Dic47⋊C4—24no—
188Dic47⋊C4—42no—
189Dic47⋊C4—42no—
190C4×Dic47—24no—
191C4×Dic47—42no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C412yes—
199C2×C47⋊C8C22×C412yes—
200C2×C47⋊C8#4112yes—
201C2×C47⋊C8#4112yes—
202C2×C47⋊C8#4112yes—
203C2×C47⋊C8#4112yes—
204C23×C47—22no—
205C23×C47—41no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47C22×D411yescharacteristic
212D4×C47—22no—
213D4×C47—22no—
214D4×C47—41no—
215D4×C47—41no—
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—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—48no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47C4×D412yes—
241C2×C4×C47C4×D412yes—
242C2×C4×C47AGL(1,ℤ/8)12yes—
243C2×C4×C47#13712yes—
244C2×C4×C47C23×C411yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262Dic94—22no—
263Dic94—22no—
264Dic94—41no—
265Dic94—41no—
266C47⋊C8—22no—
267C47⋊C8—22no—
268C47⋊C8—22no—
269C47⋊C8#11714yescomplemented
270#21288—471nomaximal, Sylow
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47C2×C4×D411yescharacteristic
279C22×C47#53211yescharacteristic
280C22×C47#53211yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C47C2×#13711yescharacteristic
283C22×C47#57511yescharacteristic
284C22×C47#57511yescharacteristic
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—22no—
288C4×C47—22no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—42no—
292C4×C47—81no—
293C4×C47—81no—
294C4×C47C2×#11711yescharacteristic
295C4×C47C4×#4111yescharacteristic
296C4×C47#52911yescharacteristic
297C4×C47#52911yescharacteristic
298Dic47—42no—
299Dic47—42no—
300Dic47—81no—
301Dic47—81no—
302C2×#440—471no—
303#2295—471no—
304#2293D4711yescharacteristic
305#1973—471no—
306#1968—471no—
307#1943—471no—
308#1942—471no—
309#1936—471no—
310#1935—471no—
311#1934—471no—
312#1933—471no—
313#1776—471no—
314#1763—471no—
315#1762—471no—
316C4×#97—471no—
317C2×C47—82no—
318C2×C47#229311yescharacteristic
319C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
320C2×C47C4×#13711yescharacteristic
321C2×C47#318011yescharacteristic
322C2×C47#318111yescharacteristic
323C2×C47#318211yescharacteristic
324C2×C47#318311yescharacteristic
325C22×SD16—471no—
326C2×C4×Q8—471no—
327C2×C4×D4C2×D4711yescharacteristic
328C2×#117—21no—
329#440—478no—
330C2×#107—471no—
331C2×#107—471no—
332C2×#106—471no—
333C2×#103—471no—
334C2×#103—471no—
335C2×#103—471no—
336C2×#102—471no—
337C2×#102—471no—
338C2×#102—471no—
339C2×#97—471no—
340C2×#97—471no—
341C2×#97—471no—
342C2×#97—471no—
343C2×C4×C8—471no—
344C2×C4×C8—471no—
345#391—471no—
346#391—471no—
347#390C2×D4711yescharacteristic
348#390C2×D4711yescharacteristic
349#389—471no—
350#389—471no—
351#389C2×D4711yescharacteristic
352#389C2×D4711yescharacteristic
353#388—21no—
354#388—21no—
355#387—941no—
356#387—941no—
357C4×C4⋊C4—471no—
358C4×C4⋊C4—941no—
359C4×C4⋊C4C2×D4711yescharacteristic
360C4×C22⋊C4—21no—
361#376—941no—
362C43C2×D4711yescharacteristic
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#340—471no—
369C47#2128811yescharacteristic, complemented, Sylow
370C22×Q8—471no—
371C22×D4C22×D4711yescharacteristic
372C23×C4—21no—
373C2×SD16—474no—
374C2×SD16—942no—
375C2×SD16—942no—
376C22×C8—471no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8—471no—
380C4×Q8—474no—
381C4×Q8—942no—
382C4×D4—22no—
383C4×D4C4×D4714yes—
384#117—44no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4C22×D4711yescharacteristic
394C2×C4⋊C4C22×D4711yescharacteristic
395C2×C4⋊C4C22×D4711yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—941no—
403C2×C42—941no—
404C2×C42C22⋊D4711yescharacteristic
405C2×C42C22⋊D4711yescharacteristic
406C2×C42C22⋊D4711yescharacteristic
407C2×C42C22⋊D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409C2×C42C22×D4711yescharacteristic
410C2×C42C22×D4711yescharacteristic
411#107—474no—
412#107—942no—
413#106—942no—
414#103—474no—
415#103—942no—
416#103—942no—
417#102—474no—
418#102—942no—
419#102—942no—
420#97—474no—
421#97—942no—
422#97—942no—
423#97—942no—
424C4×C8—942no—
425C4×C8—942no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—941no—
430#95—941no—
431#95—941no—
432#95—941no—
433#95—941no—
434#95—941no—
435#95—941no—
436C24—21no—
437C2×Q8—472no—
438C2×Q8—941no—
439C2×Q8—941no—
440C2×Q8—941no—
441C2×Q8—941no—
442C2×Q8—941no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C2×C4×D4712yes—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C2×C22⋊D4711yescharacteristic
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C23×D4711yescharacteristic
466SD16—948no—
467C2×C8—472no—
468C2×C8—472no—
469C2×C8—472no—
470C2×C8—472no—
471C2×C8—472no—
472C2×C8—472no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—472no—
487C4⋊C4—944no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—1882no—
494C4⋊C4—1882no—
495C4⋊C4C2×C4×D4712yes—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42—42no—
510C42—944no—
511C42—1882no—
512C42C2×C4×D4712yes—
513C42#1062535012yes—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D4711yescharacteristic
522Q8—942no—
523Q8—942no—
524Q8—1881no—
525Q8—1881no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—48no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4C4×C22⋊D4712yes—
567C2×C4C4×C22⋊D4712yes—
568C2×C4#1309405012yes—
569C2×C4#1309405412yes—
570C2×C4C22×C4×D4711yescharacteristic
571C2×C4#41×D4711yescharacteristic
572C2×C4#41×D4711yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#41×D4711yescharacteristic
575C2×C4C2×#1062535011yescharacteristic
576C8—474no—
577C8—942no—
578C8—942no—
579C8—942no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C4×C22⋊D4711yescharacteristic
588C22#1568966911yescharacteristic
589C22#1568966911yescharacteristic
590C22C2×#1309405011yescharacteristic
591C22C2×#1309405411yescharacteristic
592C22#1568992111yescharacteristic
593C22#1568992111yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—42no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—3761no—
604C4—3761no—
605C4—1882no—
606C4—1882no—
607C4#117×D4711yescharacteristic
608C4#1568959111yescharacteristic
609C4#1568965111yescharacteristic
610C4#1568965111yescharacteristic
611C2—82no—
612C2#2024584711yescharacteristic
613C2C4×#1309405011yescharacteristic
614C2C4×#1309405411yescharacteristic
615C2#2025408011yescharacteristic
616C2#2025409811yescharacteristic
617C2#2025410211yescharacteristic
618C2#2025411111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2293C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenter#2293D47
hypocenterC47#21288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #20245865C2semidirect
5. #20244123C2semidirect
6. #20244118C2semidirect
8. #20244077C2semidirect
10. #20244063C2semidirect
11. #20243286C2semidirect
12. #20243221C2semidirect
14. C4×#13093935C2semidirect
18. #15689223C4semidirect
269. C47⋊C8#117semidirect
369. C47#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#156892232
#202458652
#202442682
#202442412
#202441232
#202441182
#202440882
#202440772
#202440742
#202440632
#202432862
#202432212
#202432132
C4×#130939352
C47×#22932
#2128847