Finite Group Databasebeta

← #26257343

Subgroups — #26257343

Order 12032.

808 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689423C211yesmaximal, characteristic
2C2×#15689223C211yesmaximal, characteristic
3#20248579C211yesmaximal, characteristic, complemented
4#20244801C211yesmaximal, characteristic
5#20244791C211yesmaximal, characteristic
6#20244705C211yesmaximal, characteristic
7#20244705C211yesmaximal, characteristic
8#20244356C211yesmaximal, characteristic, complemented
9#20244156C211yesmaximal, characteristic, complemented
10#20244146C211yesmaximal, characteristic, complemented
11#20244112C211yesmaximal, characteristic, complemented
12#20244029C211yesmaximal, characteristic, complemented
13#20244022C211yesmaximal, characteristic, complemented
14#20243390C211yesmaximal, characteristic, complemented
15C47×#2354C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×#13094016C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19#15689423—24no—
20#15689223—24no—
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×#13093947C2211yescharacteristic
28C2×#13093947C2211yescharacteristic
29C2×#13093947C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093935C2211yescharacteristic
34#15689053—21no—
35#15689053—21no—
36#15689029C2211yescharacteristic
37#15689029C2211yescharacteristic
38#15689008—21no—
39#15689008—21no—
40#15688993C2211yescharacteristic
41#15688989C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×C4×D4×C47C2211yescharacteristic
51C2×#117×C47—21no—
52C47×#390C2211yescharacteristic
53C47×#390C2211yescharacteristic
54C47×#388—21no—
55C47×#388—21no—
56C47×#384C2211yescharacteristic
57C47×#380—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C22×Dic94C2311yescharacteristic
62C2×#10625335—22no—
63C2×#10625335—22no—
64C2×#10625335—22no—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69#13094016—22no—
70#13094016—22no—
71C4×Dic94—22no—
72C4×Dic94—22no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×C4×Dic47—21no—
82#13093957—22no—
83#13093957—22no—
84#13093955—22no—
85C4⋊(C47⋊C8)—22no—
86C4⋊(C47⋊C8)—22no—
87C4⋊(C47⋊C8)—22no—
88#13093947—22no—
89#13093947—22no—
90#13093947—22no—
91#13093945—22no—
92#13093945—22no—
93#13093945—22no—
94#13093935—22no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47—21no—
103C4×D4×C47—22no—
104C4×D4×C47D414yes—
105#117×C47—44no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C42×C47—21no—
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#95×C47—21no—
124#95×C47—21no—
125#95×C47D411yescharacteristic
126#95×C47D411yescharacteristic
127C24×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47C2×D412yes—
134C22×C4×C47—21no—
135C22×C4×C47—24no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2411yescharacteristic
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94#4112yes—
157C4⋊C4×C47—22no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—42no—
165C4⋊C4×C47—81no—
166C4⋊C4×C47C2×D412yes—
167C22⋊C4×C47—24no—
168C22⋊C4×C47—42no—
169C22⋊C4×C47—42no—
170C22⋊C4×C47—81no—
171C22⋊C4×C47—81no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—42no—
177C42×C47—42no—
178C42×C47C2×D412yes—
179C42×C47#4112yes—
180#10625335—28no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—42no—
188C4⋊Dic47—42no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191Dic47⋊C4—42no—
192C4×Dic47—42no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8#4112yes—
205C23×C47—22no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47C22×D411yescharacteristic
213D4×C47—22no—
214D4×C47—22no—
215D4×C47—41no—
216D4×C47—41no—
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—22no—
224C2×C4×C47—21no—
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—21no—
232C2×C4×C47—21no—
233C2×C4×C47—48no—
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×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47#12112yes—
243C2×C4×C47#12112yes—
244C2×C4×C47AGL(1,ℤ/8)12yes—
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C472−1+411yescharacteristic
250C2×C4×C472−1+411yescharacteristic
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—
262C2×Dic47—41no—
263Dic94—22no—
264Dic94—22no—
265Dic94—41no—
266Dic94—41no—
267C47⋊C8—22no—
268C47⋊C8—41no—
269C47⋊C8—41no—
270C47⋊C8—41no—
271#24690—471nomaximal, Sylow
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47C2×#12111yescharacteristic
280C22×C47#54711yescharacteristic
281C22×C47#54811yescharacteristic
282C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C47#57511yescharacteristic
284C22×C47#57711yescharacteristic
285C22×C47#57811yescharacteristic
286C4×C47—22no—
287C4×C47—22no—
288C4×C47—22no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—42no—
293C4×C47—81no—
294C4×C47—81no—
295C4×C47#52511yescharacteristic
296C4×C47#53611yescharacteristic
297C4×C47#55211yescharacteristic
298C4×C47#55611yescharacteristic
299Dic47—42no—
300Dic47—81no—
301Dic47—81no—
302Dic47—81no—
303C2×#478—471no—
304C2×#440—471no—
305#2565—471no—
306#2354D4711yescharacteristic
307#2073—471no—
308#2071—471no—
309#2055—471no—
310#2055—471no—
311#1992—471no—
312#1949—471no—
313#1947—471no—
314#1940—471no—
315#1928—471no—
316#1927—471no—
317#1803—471no—
318C2×C47—82no—
319C2×C47#241511yescharacteristic
320C2×C47#303611yescharacteristic
321C2×C47#304611yescharacteristic
322C2×C47#334311yescharacteristic
323C2×C47#334811yescharacteristic
324C2×C47#336811yescharacteristic
325C2×C47#337711yescharacteristic
326C22×SD16—471no—
327C2×#125—471no—
328C2×C4×Q8—471no—
329C2×C4×D4C2×D4711yescharacteristic
330C2×#117—21no—
331#478—944no—
332#440—944no—
333C2×#107—471no—
334C2×#107—471no—
335C2×#106—471no—
336C2×C4⋊C8—471no—
337C2×C4⋊C8—471no—
338C2×C4⋊C8—471no—
339C2×#103—471no—
340C2×#103—471no—
341C2×#103—471no—
342C2×#102—471no—
343C2×#102—471no—
344C2×#102—471no—
345C2×#97—471no—
346#398—941no—
347#398—941no—
348#391—471no—
349#391—471no—
350#390C2×D4711yescharacteristic
351#390C2×D4711yescharacteristic
352#388—21no—
353#388—21no—
354#387—941no—
355#387—941no—
356#384—471no—
357#384C2×D4711yescharacteristic
358#382—471no—
359#380—21no—
360C4×C4⋊C4C2×D4711yescharacteristic
361C4×C4⋊C4C2×D4711yescharacteristic
362C4×C4⋊C4C2×D4711yescharacteristic
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#340—471no—
369#336—471no—
370#336—471no—
371C47#2469011yescharacteristic, complemented, Sylow
372C22×Q8—471no—
373C22×D4C22×D4711yescharacteristic
374C23×C4—21no—
375C2×SD16—942no—
376C2×SD16—942no—
377C2×SD16—942no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382#125—942no—
383#125—942no—
384C4×Q8—942no—
385C4×Q8—942no—
386C4×D4—22no—
387C4×D4D18814yes—
388#117—44no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4C22⋊D4711yescharacteristic
400C2×C4⋊C4C22⋊D4711yescharacteristic
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—941no—
412C2×C42C22×D4711yescharacteristic
413C2×C42C22×D4711yescharacteristic
414C2×C42C22×D4711yescharacteristic
415#107—942no—
416#107—942no—
417#106—942no—
418C4⋊C8—942no—
419C4⋊C8—942no—
420C4⋊C8—942no—
421#103—942no—
422#103—942no—
423#103—942no—
424#102—942no—
425#102—942no—
426#102—942no—
427#97—942no—
428#95—21no—
429#95—21no—
430#95—941no—
431#95—941no—
432#95—941no—
433#95—941no—
434#95—941no—
435#95—941no—
436#95C22⋊D4711yescharacteristic
437#95C22⋊D4711yescharacteristic
438C24—21no—
439C2×Q8—472no—
440C2×Q8—941no—
441C2×Q8—941no—
442C2×Q8—941no—
443C2×Q8—941no—
444C2×Q8—941no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×D18812yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C2×C22⋊D4711yescharacteristic
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C23×D4711yescharacteristic
468SD16—948no—
469C2×C8—472no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—1882no—
497C4⋊C4—1882no—
498C4⋊C4—1882no—
499C4⋊C4—1882no—
500C4⋊C4—1882no—
501C4⋊C4C2×D18812yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C42—1882no—
514C42C2×D18812yes—
515C42#1062535012yes—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×C22⋊D4711yescharacteristic
524Q8—942no—
525Q8—942no—
526Q8—1881no—
527Q8—1881no—
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—48no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—942no—
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×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4#1309399812yes—
570C2×C4#1309399812yes—
571C2×C4#1309405012yes—
572C2×C4C22×D18811yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#41×D4711yescharacteristic
575C2×C4C2×#1062535011yescharacteristic
576C2×C4#1309407111yescharacteristic
577C2×C4#1309407111yescharacteristic
578C8—942no—
579C8—1881no—
580C8—1881no—
581C8—1881no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22C2×#1309399811yescharacteristic
590C22#1568977211yescharacteristic
591C22#1568978011yescharacteristic
592C22C2×#1309405011yescharacteristic
593C22#1568992111yescharacteristic
594C22#1568993411yescharacteristic
595C22#1568993811yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—3761no—
606C4—3761no—
607C4—3761no—
608C4—1882no—
609C4#1568963511yescharacteristic
610C4#1568969911yescharacteristic
611C4#1568981211yescharacteristic
612C4#1568984111yescharacteristic
613C2—82no—
614C2#2024681111yescharacteristic
615C2#2025285211yescharacteristic
616C2#2025293811yescharacteristic
617C2#2025582211yescharacteristic
618C2#2025590311yescharacteristic
619C2#2025611311yescharacteristic
620C2#2025622411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2354C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2354D47
hypocenterC47#24690
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
3. #20248579C2semidirect
8. #20244356C2semidirect
9. #20244156C2semidirect
10. #20244146C2semidirect
11. #20244112C2semidirect
12. #20244029C2semidirect
13. #20244022C2semidirect
14. #20243390C2semidirect
371. C47#24690semidirect

Maximal subgroups

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

subgroupindex
C2×#156894232
C2×#156892232
#202485792
#202448012
#202447912
#202447052
#202443562
#202441562
#202441462
#202441122
#202440292
#202440222
#202433902
C47×#23542
#2469047