Finite Group Databasebeta

← #26284740

Subgroups — #26284740

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246413C211yesmaximal, characteristic
2#20244710C211yesmaximal, characteristic, complemented
3#20244591C211yesmaximal, characteristic
4#20244536C211yesmaximal, characteristic, complemented
5#20244396C211yesmaximal, characteristic
6#20244346C211yesmaximal, characteristic, complemented
7#20244081C211yesmaximal, characteristic, complemented
8#20244026C211yesmaximal, characteristic, complemented
9#20244003C211yesmaximal, characteristic
10#20243980C211yesmaximal, characteristic, complemented
11#20243732C211yesmaximal, characteristic, complemented
12#20243701C211yesmaximal, characteristic
13#20243480C211yesmaximal, characteristic
14#20243221C211yesmaximal, characteristic, complemented
15C47×#2489C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C2×#13094003C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093947C2211yescharacteristic
26C2×#13093947C2211yescharacteristic
27C2×#13093947C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31#15689029C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689017—21no—
34#15689011—21no—
35#15689005—21no—
36C4×C4⋊Dic47C2211yescharacteristic
37#15688974—21no—
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#125×C47C2211yescharacteristic
49C2×C22⋊Q8×C47C2211yescharacteristic
50C47×#400—21no—
51C47×#397—21no—
52C47×#391C2211yescharacteristic
53C47×#391C2211yescharacteristic
54C47×#388—21no—
55C47×#382—21no—
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×Dic94C2311yescharacteristic
60C2×#10625337—22no—
61C2×#10625337—41no—
62C2×#10625337—41no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094003—22no—
68#13094003—22no—
69C4×Dic94—22no—
70C4×Dic94—41no—
71#13093983—22no—
72#13093983—41no—
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84#13093957—22no—
85C4⋊(C47⋊C8)—41no—
86#13093948—22no—
87#13093948—22no—
88#13093948—41no—
89#13093947—22no—
90#13093947—22no—
91#13093947—41no—
92C22⋊(C47⋊C8)—41no—
93C22⋊(C47⋊C8)—41no—
94#13093935—41no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C22×Q8×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101#125×C47—22no—
102#125×C47—41no—
103C22⋊Q8×C47—22no—
104C22⋊Q8×C47—41no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47D411yescharacteristic
114C2×C22⋊C4×C47D411yescharacteristic
115C2×C42×C47—21no—
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47D411yescharacteristic
125#95×C47D411yescharacteristic
126C24×C47C2×D411yescharacteristic
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2411yescharacteristic
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94#4112yes—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—42no—
165C4⋊C4×C47—42no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47#4112yes—
168C22⋊C4×C47—41no—
169C22⋊C4×C47—41no—
170C22⋊C4×C47—42no—
171C22⋊C4×C47—42no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—42no—
177C22⋊Dic47—24no—
178C22⋊Dic47—42no—
179#10625337—44no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47#4112yes—
185C4⋊Dic47#4112yes—
186Dic47⋊C4—24no—
187Dic47⋊C4—42no—
188Dic47⋊C4—42no—
189C4×Dic47—42no—
190C4×Dic47—42no—
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⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47C22×D411yescharacteristic
212Q8×C47—41no—
213Q8×C47—41no—
214Q8×C47—41no—
215Q8×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—22no—
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—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
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—41no—
246C2×C4×C47—41no—
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47H(5,𝔽2)11yescharacteristic
252C2×C4×C47H(5,𝔽2)11yescharacteristic
253C2×Dic47—22no—
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—
263C2×Dic47—41no—
264C2×Dic47—41no—
265Dic94—22no—
266Dic94—22no—
267Dic94—41no—
268Dic94—41no—
269C47⋊C8—41no—
270C47⋊C8—41no—
271C47⋊C8—41no—
272C47⋊C8—41no—
273#26749—471nomaximal, Sylow
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47#52511yescharacteristic
282C22×C47#54611yescharacteristic
283C22×C47#54611yescharacteristic
284C22×C47#57511yescharacteristic
285C22×C47#57511yescharacteristic
286C22×C47#57811yescharacteristic
287C22×C47#57811yescharacteristic
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—42no—
293C4×C47—41no—
294C4×C47—81no—
295C4×C47—81no—
296C4×C47—81no—
297C4×C47#52911yescharacteristic
298C4×C47#53811yescharacteristic
299C4×C47#55511yescharacteristic
300C4×C47#55911yescharacteristic
301Dic47—42no—
302Dic47—42no—
303Dic47—42no—
304Dic47—81no—
305#2489D4711yescharacteristic
306#2362—471no—
307#2056—471no—
308#2036—471no—
309#2026—471no—
310#2001—471no—
311#1989—471no—
312#1935—471no—
313#1928—471no—
314#1924—471no—
315#1921—471no—
316#1878—471no—
317#1873—471no—
318#1825—471no—
319#1763—471no—
320C2×C47—81no—
321C2×C47#245911yescharacteristic
322C2×C47#311111yescharacteristic
323C2×C47#312711yescharacteristic
324C2×C47#331311yescharacteristic
325C2×C47#331511yescharacteristic
326C2×C47#331511yescharacteristic
327C2×C47#332711yescharacteristic
328C22×Q16—471no—
329C2×#125C2×D4711yescharacteristic
330C2×C22⋊Q8—471no—
331C2×C22⋊Q8C2×D4711yescharacteristic
332C2×C4×Q8—471no—
333C2×#117—471no—
334C2×#107—471no—
335C2×C4⋊C8—471no—
336C2×#103—471no—
337C2×#103—471no—
338C2×#103—471no—
339C2×#103—471no—
340C2×#103—471no—
341C2×#103—471no—
342C2×C22⋊C8—471no—
343C2×C22⋊C8—471no—
344C2×#97—471no—
345#400—21no—
346#397—21no—
347#391—471no—
348#391C2×D4711yescharacteristic
349#391C2×D4711yescharacteristic
350#389—471no—
351#388—21no—
352#388—941no—
353#388—941no—
354#387—941no—
355#382—21no—
356#380C2×D4711yescharacteristic
357C4×C4⋊C4—471no—
358C4×C4⋊C4—941no—
359C4×C4⋊C4C2×D4711yescharacteristic
360C4×C22⋊C4C2×D4711yescharacteristic
361#340—471no—
362#340—471no—
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#2674911yescharacteristic, complemented, Sylow
372C22×Q8—471no—
373C22×Q8C22×D4711yescharacteristic
374C23×C4C22×D4711yescharacteristic
375C2×Q16—942no—
376C2×Q16—1881no—
377C2×Q16—1881no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382#125—22no—
383#125—41no—
384C22⋊Q8—22no—
385C22⋊Q8—41no—
386C22⋊Q8—942no—
387C22⋊Q8—942no—
388C4×Q8—942no—
389C4×Q8—1881no—
390#117—942no—
391#117—1881no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—941no—
407C2×C22⋊C4—941no—
408C2×C22⋊C4C22⋊D4711yescharacteristic
409C2×C22⋊C4C22⋊D4711yescharacteristic
410C2×C42—21no—
411C2×C42—941no—
412C2×C42—941no—
413C2×C42—941no—
414C2×C42C22×D4711yescharacteristic
415C2×C42C22×D4711yescharacteristic
416#107—942no—
417C4⋊C8—1881no—
418#103—942no—
419#103—942no—
420#103—942no—
421#103—942no—
422#103—1881no—
423#103—1881no—
424C22⋊C8—1881no—
425C22⋊C8—1881no—
426#97—1881no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—941no—
434#95—941no—
435#95—941no—
436#95—941no—
437#95C22⋊D4711yescharacteristic
438#95C22⋊D4711yescharacteristic
439C24C2×C22⋊D4711yescharacteristic
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—472no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×Q8—941no—
451C2×Q8—941no—
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—21no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—941no—
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C2×C22⋊D4711yescharacteristic
468C22×C4C2×C22⋊D4711yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471C22×C4C23×D4711yescharacteristic
472Q16—1884no—
473C2×C8—941no—
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—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—472no—
494C4⋊C4—472no—
495C4⋊C4—944no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4—1882no—
501C4⋊C4—1882no—
502C4⋊C4#1062535212yes—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—944no—
508C22⋊C4—1882no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—1882no—
515C42—1882no—
516C42—1882no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C22×C22⋊D4711yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—942no—
530Q8—942no—
531Q8—1881no—
532Q8—1881no—
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—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
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—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4—1881no—
575C2×C4—1881no—
576C2×C4#41×D4711yescharacteristic
577C2×C4#41×D4711yescharacteristic
578C2×C4#41×D4711yescharacteristic
579C2×C4C2×#1062535211yescharacteristic
580C2×C4#1309406911yescharacteristic
581C2×C4#1309407011yescharacteristic
582C8—1881no—
583C8—1881no—
584C8—1881no—
585C8—1881no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1568963011yescharacteristic
594C22#1568976111yescharacteristic
595C22#1568976711yescharacteristic
596C22#1568992111yescharacteristic
597C22#1568992111yescharacteristic
598C22#1568993811yescharacteristic
599C22#1568993811yescharacteristic
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4—3761no—
610C4—1882no—
611C4—1882no—
612C4—1882no—
613C4#1568965211yescharacteristic
614C4#1568970711yescharacteristic
615C4#1568983511yescharacteristic
616C4#1568985511yescharacteristic
617C2—81no—
618C2#2024732111yescharacteristic
619C2#2025349111yescharacteristic
620C2#2025368311yescharacteristic
621C2#2025545411yescharacteristic
622C2#2025547811yescharacteristic
623C2#2025548411yescharacteristic
624C2#2025565011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2489C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2489D47
hypocenterC47#26749
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2489

Complements

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

NH ≅ G/Ntype
2. #20244710C2semidirect
4. #20244536C2semidirect
6. #20244346C2semidirect
7. #20244081C2semidirect
8. #20244026C2semidirect
10. #20243980C2semidirect
11. #20243732C2semidirect
14. #20243221C2semidirect
371. C47#26749semidirect

Maximal subgroups

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

subgroupindex
#202464132
#202447102
#202445912
#202445362
#202443962
#202443462
#202440812
#202440262
#202440032
#202439802
#202437322
#202437012
#202434802
#202432212
C47×#24892
#2674947