Finite Group Databasebeta

← #26236143

Subgroups — #26236143

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689223C211yesmaximal, characteristic
2#20246343C211yesmaximal, characteristic, complemented
3#20244268C211yesmaximal, characteristic
4#20244241C211yesmaximal, characteristic
5#20244029C211yesmaximal, characteristic, complemented
6#20244022C211yesmaximal, characteristic, complemented
7#20244012C211yesmaximal, characteristic
8#20244005C211yesmaximal, characteristic
9#20243557C211yesmaximal, characteristic, complemented
10#20243400C211yesmaximal, characteristic, complemented
11#20243388C211yesmaximal, characteristic
12#20243286C211yesmaximal, characteristic, complemented
13C4×#13093957C211yesmaximal, characteristic, complemented
14#20243263C211yesmaximal, characteristic, complemented
15C47×#2357C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689223C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093947C2211yescharacteristic
26C2×#13093947C2211yescharacteristic
27C2×#13093947C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689029C2211yescharacteristic
35#15689029C2211yescharacteristic
36#15689010—21no—
37#15689010—21no—
38#15688993C2211yescharacteristic
39#15688988—21no—
40C4⋊C4×Dic47—21no—
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#388—21no—
53C47×#388—21no—
54C47×#382C2211yescharacteristic
55C47×#381—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47—21no—
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⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79#13093957—22no—
80#13093957—41no—
81#13093957C2×C414yes—
82#13093955—22no—
83#13093955—41no—
84C4⋊(C47⋊C8)—22no—
85#13093947—41no—
86#13093947—41no—
87#13093947C2×C414yes—
88#13093945—41no—
89#13093945—41no—
90#13093945C2×C414yes—
91#13093935—22no—
92#13093935C2×C414yes—
93C4×C47⋊C8—22no—
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×C47D411yescharacteristic
105C2×C4⋊C4×C47D411yescharacteristic
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×C47—21no—
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
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—22no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—41no—
162C4⋊C4×C47C22×C412yes—
163C22⋊C4×C47—24no—
164C22⋊C4×C47—42no—
165C22⋊C4×C47—42no—
166C22⋊C4×C47—81no—
167C22⋊C4×C47—81no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—81no—
173C42×C47—81no—
174C42×C47C22×C412yes—
175C42×C47#4112yes—
176#10625335—28no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—42no—
183C4⋊Dic47—81no—
184C4⋊Dic47C22×C412yes—
185Dic47⋊C4—24no—
186C4×Dic47—24no—
187C4×Dic47—81no—
188C4×Dic47—81no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8C22×C412yes—
198C2×C47⋊C8C22×C412yes—
199C2×C47⋊C8#4112yes—
200C2×C47⋊C8#4112yes—
201C23×C47—22no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47—41no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47C22×D411yescharacteristic
209D4×C47—22no—
210D4×C47—22no—
211D4×C47—41no—
212D4×C47—41no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
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—21no—
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—41no—
237C2×C4×C47—84no—
238C2×C4×C47C4×D412yes—
239C2×C4×C47C4×D412yes—
240C2×C4×C47#13712yes—
241C2×C4×C47C23×C411yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47H(5,𝔽2)11yescharacteristic
246C2×C4×C472−1+411yescharacteristic
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259Dic94—22no—
260Dic94—22no—
261Dic94—41no—
262Dic94—41no—
263C47⋊C8—22no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8#11714yes—
267#22819—471nomaximal, Sylow
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47—81no—
274C22×C47—81no—
275C22×C47C2×C4×D411yescharacteristic
276C22×C47#54711yescharacteristic
277C22×C47#55011yescharacteristic
278C22×C47C2×#13711yescharacteristic
279C22×C47#57511yescharacteristic
280C22×C47#57611yescharacteristic
281C22×C47#57711yescharacteristic
282C4×C47—22no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—42no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47C2×#11711yescharacteristic
292C4×C47#52011yescharacteristic
293C4×C47#55511yescharacteristic
294C4×C47#55611yescharacteristic
295Dic47—42no—
296Dic47—42no—
297Dic47—81no—
298Dic47—81no—
299C2×#440—471no—
300#2357D4711yescharacteristic
301#2355—471no—
302#1973—471no—
303#1968—471no—
304#1928—471no—
305#1927—471no—
306#1926—471no—
307#1925—471no—
308#1847—471no—
309#1805—471no—
310#1802—471no—
311#1776—471no—
312C4×#107—471no—
313#1771—471no—
314C2×C47—82no—
315C2×C47#235411yescharacteristic
316C2×C47C4×#13711yescharacteristic
317C2×C47#294611yescharacteristic
318C2×C47#334611yescharacteristic
319C2×C47#335011yescharacteristic
320C2×C47#340011yescharacteristic
321C2×C47#340311yescharacteristic
322C22×SD16—471no—
323C2×C4×Q8—471no—
324C2×C4×D4C2×D4711yescharacteristic
325#440—478no—
326C2×#107—471no—
327C2×#107—471no—
328C2×#107—471no—
329C2×#106—471no—
330C2×#106—471no—
331C2×C4⋊C8—471no—
332C2×#103—471no—
333C2×#103—471no—
334C2×#103—471no—
335C2×#102—471no—
336C2×#102—471no—
337C2×#102—471no—
338C2×#97—471no—
339C2×#97—471no—
340C2×C4×C8—471no—
341#391—471no—
342#391—471no—
343#390C2×D4711yescharacteristic
344#390C2×D4711yescharacteristic
345#388—21no—
346#388—21no—
347#387—941no—
348#387—941no—
349#384—471no—
350#382—941no—
351#382C2×D4711yescharacteristic
352#381—21no—
353C4×C4⋊C4—471no—
354C4×C4⋊C4—471no—
355C4×C4⋊C4—941no—
356C4×C4⋊C4C2×D4711yescharacteristic
357C4×C4⋊C4C2×D4711yescharacteristic
358C4×C4⋊C4C2×D4711yescharacteristic
359C4×C22⋊C4—21no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#336—471no—
365#336—471no—
366C47#2281911yescharacteristic, complemented, Sylow
367C22×Q8—471no—
368C22×D4C22×D4711yescharacteristic
369C23×C4—21no—
370C2×SD16—474no—
371C2×SD16—942no—
372C2×SD16—942no—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—471no—
377C4×Q8—474no—
378C4×Q8—942no—
379C4×D4—22no—
380C4×D4C4×D4714yes—
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×C4⋊C4C22×D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—941no—
400C2×C42—941no—
401C2×C42—941no—
402C2×C42C22×D4711yescharacteristic
403C2×C42C22×D4711yescharacteristic
404C2×C42C22×D4711yescharacteristic
405#107—474no—
406#107—942no—
407#107—1881no—
408#106—942no—
409#106—1881no—
410C4⋊C8—942no—
411#103—474no—
412#103—1881no—
413#103—1881no—
414#102—474no—
415#102—1881no—
416#102—1881no—
417#97—474no—
418#97—942no—
419C4×C8—942no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95—941no—
430#95C22⋊D4711yescharacteristic
431#95C22⋊D4711yescharacteristic
432C24—21no—
433C2×Q8—472no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×C4×D4712yes—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C23×D4711yescharacteristic
462SD16—948no—
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—
473C2×C8—941no—
474C2×C8—941no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—472no—
483C4⋊C4—944no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—3761no—
490C4⋊C4—1882no—
491C4⋊C4C2×C4×D4712yes—
492C22⋊C4—24no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—81no—
502C42—81no—
503C42—944no—
504C42—3761no—
505C42—3761no—
506C42C2×C4×D4712yes—
507C42#1062535012yes—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×C22⋊D4711yescharacteristic
516Q8—942no—
517Q8—942no—
518Q8—1881no—
519Q8—1881no—
520D4—22no—
521D4—22no—
522D4—41no—
523D4—41no—
524C2×C4—21no—
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—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4C4×C22⋊D4712yes—
562C2×C4C4×C22⋊D4712yes—
563C2×C4#1309405412yes—
564C2×C4C22×C4×D4711yescharacteristic
565C2×C4#41×D4711yescharacteristic
566C2×C4#41×D4711yescharacteristic
567C2×C4C2×#1062535011yescharacteristic
568C2×C4#1309407011yescharacteristic
569C2×C4#1309407111yescharacteristic
570C8—474no—
571C8—942no—
572C8—1881no—
573C8—1881no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×C4×C22⋊D4711yescharacteristic
582C22#1568977211yescharacteristic
583C22#1568979211yescharacteristic
584C22C2×#1309405411yescharacteristic
585C22#1568992111yescharacteristic
586C22#1568992611yescharacteristic
587C22#1568993411yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—3761no—
598C4—3761no—
599C4—1882no—
600C4—1882no—
601C4#117×D4711yescharacteristic
602C4#1568960311yescharacteristic
603C4#1568983611yescharacteristic
604C4#1568984111yescharacteristic
605C2—82no—
606C2#2024633811yescharacteristic
607C2C4×#1309405411yescharacteristic
608C2#2025222011yescharacteristic
609C2#2025587311yescharacteristic
610C2#2025592711yescharacteristic
611C2#2025644111yescharacteristic
612C2#2025647211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2357C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenter#2357D47
hypocenterC47#22819
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #20246343C2semidirect
5. #20244029C2semidirect
6. #20244022C2semidirect
9. #20243557C2semidirect
10. #20243400C2semidirect
12. #20243286C2semidirect
13. C4×#13093957C2semidirect
14. #20243263C2semidirect
18. #15689223C4semidirect
366. C47#22819semidirect

Maximal subgroups

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

subgroupindex
C2×#156892232
#202463432
#202442682
#202442412
#202440292
#202440222
#202440122
#202440052
#202435572
#202434002
#202433882
#202432862
C4×#130939572
#202432632
C47×#23572
#2281947