Finite Group Databasebeta

← #26289066

Subgroups — #26289066

Order 12032.

762 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246424C211yesmaximal, characteristic
2#20244792C211yesmaximal, characteristic, complemented
3#20244759C211yesmaximal, characteristic, complemented
4#20244577C211yesmaximal, characteristic
5#20244577C211yesmaximal, characteristic
6#20244149C211yesmaximal, characteristic, complemented
7#20244113C211yesmaximal, characteristic, complemented
8#20243996C211yesmaximal, characteristic, complemented
9#20243977C211yesmaximal, characteristic, complemented
10#20243973C211yesmaximal, characteristic, complemented
11#20243634C211yesmaximal, characteristic, complemented
12#20243585C211yesmaximal, characteristic, complemented
13#20243480C211yesmaximal, characteristic, complemented
14C4×#13093944C211yesmaximal, characteristic, complemented
15C47×#2496C211yesmaximal, characteristic, complemented
16C2×#13093998C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×#13093944C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689025C2211yescharacteristic
32#15689023—21no—
33#15689021C2211yescharacteristic
34#15689012—21no—
35#15688999—21no—
36C4×C4⋊Dic47C2211yescharacteristic
37#15688970—21no—
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#126×C47—21no—
49C47×#400—21no—
50C47×#397—21no—
51C47×#389C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#387—21no—
54C47×#384C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C22⋊D47—21no—
61C22×C4×D47—21no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13093998—22no—
67#13093998—22no—
68C4×D188—22no—
69C4×D188—41no—
70#13093983—22no—
71#13093983—41no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×C22⋊Dic47—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83#13093957—22no—
84#13093955—22no—
85#13093955—22no—
86#13093955—41no—
87C4⋊(C47⋊C8)—22no—
88#13093944—22no—
89#13093944—22no—
90#13093944—22no—
91#13093944—41no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)—41no—
94C4×C47⋊C8—41no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C23×C4×C47C2311yescharacteristic
98#126×C47—44no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47D411yescharacteristic
110C2×C22⋊C4×C47D411yescharacteristic
111C2×C42×C47—21no—
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47D411yescharacteristic
120#95×C47D411yescharacteristic
121C24×C47C2×D411yescharacteristic
122C23×D47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C2×C22⋊D47—24no—
140C2×C22⋊D47—81no—
141C2×C22⋊D47—81no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188#4112yes—
151C2×C4×D47—42no—
152C2×C4×D47—42no—
153C2×C4×D47—81no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—42no—
163C4⋊C4×C47—42no—
164C4⋊C4×C47—42no—
165C4⋊C4×C47—42no—
166C22⋊C4×C47—22no—
167C22⋊C4×C47—22no—
168C22⋊C4×C47—42no—
169C22⋊C4×C47—42no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—42no—
175C22⋊Dic47—42no—
176(C2×D47)⋊C4—24no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—42no—
179(C2×D47)⋊C4—81no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47#4112yes—
185C4⋊Dic47#4112yes—
186Dic47⋊C4—81no—
187C4×Dic47—42no—
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⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8#4112yes—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47C22×D411yescharacteristic
209C22×D47—22no—
210C22×D47—41no—
211C22×D47—41no—
212C22×D47—41no—
213C22×D47—41no—
214C22×D47—41no—
215C22×D47—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—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—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47#13512yes—
246C2×C4×C47AGL(1,ℤ/8)12yes—
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47H(5,𝔽2)11yescharacteristic
252C2×C4×C472−1+411yescharacteristic
253C22⋊D47—84no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263D188—22no—
264D188—22no—
265D188—41no—
266D188—41no—
267C4×D47—84no—
268C47⋊C8—22no—
269C47⋊C8—41no—
270C47⋊C8—41no—
271C47⋊C8—41no—
272#27039—471nomaximal, Sylow
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47#52511yescharacteristic
281C22×C47#54611yescharacteristic
282C22×C47#54711yescharacteristic
283C22×C47C2×#13511yescharacteristic
284C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C47#57711yescharacteristic
286C22×C47#57711yescharacteristic
287C2×D47—42no—
288C2×D47—42no—
289C2×D47—42no—
290C2×D47—81no—
291C2×D47—81no—
292C2×D47—81no—
293C2×D47—81no—
294C4×C47—22no—
295C4×C47—22no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47—81no—
300C4×C47—81no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47#52911yescharacteristic
304C4×C47#53911yescharacteristic
305C4×C47#55311yescharacteristic
306C4×C47#55611yescharacteristic
307Dic47—42no—
308Dic47—42no—
309Dic47—81no—
310#2496D4711yescharacteristic, complemented
311#2363—471no—
312#2071—471no—
313#2065—471no—
314#2034—471no—
315#2034—471no—
316#1948—471no—
317#1941—471no—
318#1923—471no—
319#1921—471no—
320#1920—471no—
321#1862—471no—
322#1854—471no—
323#1825—471no—
324C4×#102—471no—
325C2×C47—81no—
326C2×C47#246611yescharacteristic
327C2×C47#310611yescharacteristic
328C2×C47#312311yescharacteristic
329C2×C47#330411yescharacteristic
330C2×C47#330611yescharacteristic
331C2×C47#333711yescharacteristic
332C2×C47#335411yescharacteristic
333D47—82no—
334C2×#126—21no—
335C2×#121—471no—
336C2×C4×D4—471no—
337C2×#117—471no—
338C2×#107—471no—
339C2×#106—471no—
340C2×#106—471no—
341C2×#106—471no—
342C2×C4⋊C8—471no—
343C2×#102—471no—
344C2×#102—471no—
345C2×#102—471no—
346C2×#102—471no—
347C2×C22⋊C8—471no—
348C2×C22⋊C8—471no—
349C2×C4×C8—471no—
350#400—21no—
351#397—21no—
352#390—471no—
353#390—941no—
354#389—471no—
355#389C2×D4711yescharacteristic
356#389C2×D4711yescharacteristic
357#388—941no—
358#387—21no—
359#386—941no—
360#384C2×D4711yescharacteristic
361#380C2×D4711yescharacteristic
362#380C2×D4711yescharacteristic
363C4×C4⋊C4—471no—
364C4×C4⋊C4C2×D4711yescharacteristic
365C4×C22⋊C4—941no—
366C4×C22⋊C4C2×D4711yescharacteristic
367#340—471no—
368#340—471no—
369#340—471no—
370#340—471no—
371#340—471no—
372#340—471no—
373#340—471no—
374#340—471no—
375#336—471no—
376#336—471no—
377C47#2703911yescharacteristic, complemented, Sylow
378C22×D4—471no—
379C22×D4—941no—
380C23×C4—941no—
381C23×C4C22×D4711yescharacteristic
382C22×C8—471no—
383C22×C8—471no—
384C22×C8—471no—
385C22×C8—471no—
386#126—44no—
387#121—942no—
388#121—942no—
389C4×D4—942no—
390C4×D4—1881no—
391#117—942no—
392#117—1881no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—941no—
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C22⋊C4—941no—
411C2×C22⋊C4—941no—
412C2×C22⋊C4C22⋊D4711yescharacteristic
413C2×C22⋊C4C22⋊D4711yescharacteristic
414C2×C42—21no—
415C2×C42—941no—
416C2×C42—941no—
417C2×C42C22×D4711yescharacteristic
418C2×C42C22×D4711yescharacteristic
419#107—942no—
420#106—942no—
421#106—942no—
422#106—1881no—
423C4⋊C8—942no—
424#102—942no—
425#102—942no—
426#102—942no—
427#102—1881no—
428C22⋊C8—942no—
429C22⋊C8—1881no—
430C4×C8—1881no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—941no—
437#95—941no—
438#95C22⋊D4711yescharacteristic
439#95C22⋊D4711yescharacteristic
440C24—941no—
441C24C2×C22⋊D4711yescharacteristic
442C2×D4—472no—
443C2×D4—944no—
444C2×D4—941no—
445C2×D4—941no—
446C2×D4—941no—
447C2×D4—941no—
448C2×D4—941no—
449C2×D4—3761no—
450C2×D4—3761no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—3761no—
465C22×C4—1882no—
466C22×C4—1882no—
467C22×C4C2×C22⋊D4711yescharacteristic
468C22×C4C2×C22⋊D4711yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471C22×C4C2×C22⋊D4711yescharacteristic
472C22×C4C23×D4711yescharacteristic
473C2×C8—472no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—472no—
498C4⋊C4—472no—
499C4⋊C4—941no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4—941no—
503C4⋊C4—3761no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—944no—
509C22⋊C4—3761no—
510C22⋊C4—1882no—
511C22⋊C4—1882no—
512C22⋊C4—1882no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—3761no—
519C42—1882no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—942no—
528C23—1881no—
529C23—1881no—
530C23—1881no—
531C23—1881no—
532C23—1881no—
533C23—1881no—
534C23C22×C22⋊D4711yescharacteristic
535D4—942no—
536D4—942no—
537D4—3764no—
538D4—1881no—
539D4—1881no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—3764no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4—1881no—
575C2×C4—1881no—
576C2×C4—1881no—
577C2×C4—1881no—
578C2×C4—1881no—
579C2×C4#1309404412yes—
580C2×C4#1309405012yes—
581C2×C4#41×D4711yescharacteristic
582C2×C4#41×D4711yescharacteristic
583C2×C4#41×D4711yescharacteristic
584C2×C4#41×D4711yescharacteristic
585C2×C4#1309407011yescharacteristic
586C2×C4#1309407111yescharacteristic
587C8—942no—
588C8—1881no—
589C8—1881no—
590C8—1881no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—3761no—
599C22—3761no—
600C22—3761no—
601C22—3761no—
602C22—1882no—
603C22—1882no—
604C22—1882no—
605C22#1568963011yescharacteristic
606C22#1568976111yescharacteristic
607C22#1568977211yescharacteristic
608C22C2×#1309404411yescharacteristic
609C22C2×#1309405011yescharacteristic
610C22#1568993111yescharacteristic
611C22#1568993111yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—3761no—
622C4—1882no—
623C4—1882no—
624C4#1568965611yescharacteristic
625C4#1568971411yescharacteristic
626C4#1568982411yescharacteristic
627C4#1568984011yescharacteristic
628C2—81no—
629C2—3762no—
630C2#2024742011yescharacteristic
631C2#2025344211yescharacteristic
632C2#2025363511yescharacteristic
633C2#2025532111yescharacteristic
634C2#2025534311yescharacteristic
635C2#2025576711yescharacteristic
636C2#2025598311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2496C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenter#2496D47
hypocenterC47#27039
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #20244792C2semidirect
3. #20244759C2semidirect
6. #20244149C2semidirect
7. #20244113C2semidirect
8. #20243996C2semidirect
9. #20243977C2semidirect
10. #20243973C2semidirect
11. #20243634C2semidirect
12. #20243585C2semidirect
13. #20243480C2semidirect
14. C4×#13093944C2semidirect
15. C47×#2496C2semidirect
310. #2496D47semidirect
377. C47#27039semidirect

Maximal subgroups

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

subgroupindex
#202464242
#202447922
#202447592
#202445772
#202441492
#202441132
#202439962
#202439772
#202439732
#202436342
#202435852
#202434802
C4×#130939442
C47×#24962
#2703947