Finite Group Databasebeta

← #26257647

Subgroups — #26257647

Order 12032.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689415C211yesmaximal, characteristic, complemented
2C2×#15689184C211yesmaximal, characteristic
3#20246070C211yesmaximal, characteristic
4#20244819C211yesmaximal, characteristic
5#20244814C211yesmaximal, characteristic
6#20244591C211yesmaximal, characteristic
7#20244584C211yesmaximal, characteristic
8#20244341C211yesmaximal, characteristic, complemented
9#20244154C211yesmaximal, characteristic, complemented
10#20244128C211yesmaximal, characteristic, complemented
11#20244118C211yesmaximal, characteristic, complemented
12#20244077C211yesmaximal, characteristic, complemented
13#20244063C211yesmaximal, characteristic, complemented
14#20243400C211yesmaximal, characteristic, complemented
15C47×#2628C211yesmaximal, characteristic
16C2×#13094003C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689415—24no—
19#15689184—24no—
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093947C2211yescharacteristic
27C2×#13093947C2211yescharacteristic
28C2×#13093947C2211yescharacteristic
29C2×#13093947C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689029C2211yescharacteristic
35#15689021C2211yescharacteristic
36#15689018—21no—
37#15689017—21no—
38#15689011—21no—
39#15689004—21no—
40#15688983C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50C2×C4⋊Q8×C47C2211yescharacteristic
51C2×#117×C47C2211yescharacteristic
52C47×#400—21no—
53C47×#399—21no—
54C47×#395—21no—
55C47×#393—21no—
56C47×#389C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#382C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#380C2211yescharacteristic
61C22×Dic94C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13094003—22no—
67#13094003—22no—
68C4×Dic94—22no—
69C4×Dic94—22no—
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80#13093957—22no—
81#13093957—22no—
82#13093957—22no—
83#13093955—22no—
84C4⋊(C47⋊C8)—22no—
85C4⋊(C47⋊C8)D414yes—
86#13093947—22no—
87#13093947—22no—
88#13093947—22no—
89#13093947—22no—
90C22⋊(C47⋊C8)—22no—
91C22⋊(C47⋊C8)—22no—
92#13093935—22no—
93C4×C47⋊C8—22no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C22×Q8×C47—21no—
100C23×C4×C47C2311yescharacteristic
101C4⋊Q8×C47—22no—
102C4⋊Q8×C47—22no—
103#117×C47—22no—
104#117×C47—22no—
105C2×C4⋊C4×C47—21no—
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×C4⋊C4×C47C2311yescharacteristic
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47D411yescharacteristic
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126C24×C47C2×D411yescharacteristic
127C2×Q8×C47—42no—
128C2×Q8×C47—81no—
129C2×Q8×C47—81no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×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×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×Dic94#4112yes—
156C4⋊C4×C47—22no—
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—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47—81no—
168C4⋊C4×C47—81no—
169C22⋊C4×C47—22no—
170C22⋊C4×C47—22no—
171C22⋊C4×C47—81no—
172C22⋊C4×C47—81no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47C2×D412yes—
176C42×C47#4112yes—
177C22⋊Dic47—24no—
178C22⋊Dic47—81no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47#4112yes—
185Dic47⋊C4—24no—
186Dic47⋊C4—42no—
187Dic47⋊C4—81no—
188C4×Dic47—42no—
189C4×Dic47—81no—
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⋊C8C2×D412yes—
201C2×C47⋊C8C2×D412yes—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47C22×D411yescharacteristic
210Q8×C47—84no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
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—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
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#12112yes—
241C2×C4×C47#12112yes—
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C472−1+411yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C2×Dic47—22no—
249C2×Dic47—22no—
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—
259C2×Dic47—41no—
260Dic94—22no—
261Dic94—22no—
262Dic94—41no—
263Dic94—41no—
264C47⋊C8—22no—
265C47⋊C8—22no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#24714—471nomaximal, Sylow
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47C2×#12111yescharacteristic
277C22×C47#52511yescharacteristic
278C22×C47#53611yescharacteristic
279C22×C47#57611yescharacteristic
280C22×C47#57711yescharacteristic
281C22×C47#57811yescharacteristic
282C22×C47#57811yescharacteristic
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—81no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47#54711yescharacteristic
293C4×C47#54811yescharacteristic
294C4×C47#55211yescharacteristic
295C4×C47#55611yescharacteristic
296Dic47—42no—
297Dic47—42no—
298Dic47—81no—
299Dic47—81no—
300C2×#477—471no—
301C2×#433—471no—
302#2628D4711yescharacteristic
303#2323—471no—
304#2076—471no—
305#2075—471no—
306#2036—471no—
307#2035—471no—
308#1988—471no—
309#1949—471no—
310#1944—471no—
311#1942—471no—
312#1935—471no—
313#1933—471no—
314#1805—471no—
315C2×C47—81no—
316C2×C47#241511yescharacteristic
317C2×C47#305911yescharacteristic
318C2×C47#306211yescharacteristic
319C2×C47#312111yescharacteristic
320C2×C47#312411yescharacteristic
321C2×C47#324211yescharacteristic
322C2×C47#324311yescharacteristic
323C2×C4⋊Q8C2×D4711yescharacteristic
324C2×C22⋊Q8—471no—
325C2×C4×Q8—471no—
326C2×#117C2×D4711yescharacteristic
327#477—944no—
328#433—944no—
329C2×#107—471no—
330C2×#107—471no—
331C2×#107—471no—
332C2×#106—471no—
333C2×C4⋊C8—471no—
334C2×C4⋊C8—471no—
335C2×#103—471no—
336C2×#103—471no—
337C2×#103—471no—
338C2×#103—471no—
339C2×C22⋊C8—471no—
340C2×C22⋊C8—471no—
341C2×#97—471no—
342C2×C4×C8—471no—
343#400—21no—
344#399—21no—
345#395—21no—
346#393—21no—
347#391—471no—
348#389—471no—
349#389—941no—
350#389C2×D4711yescharacteristic
351#389C2×D4711yescharacteristic
352#388—941no—
353#388—941no—
354#387—941no—
355#382C2×D4711yescharacteristic
356#380—471no—
357#380C2×D4711yescharacteristic
358#380C2×D4711yescharacteristic
359C4×C4⋊C4—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368C47#2471411yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—471no—
371C23×C4C22×D4711yescharacteristic
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8—471no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C22⋊Q8—942no—
379C22⋊Q8—942no—
380C4×Q8—942no—
381C4×Q8—942no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—21no—
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×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4C22⋊D4711yescharacteristic
404C2×C22⋊C4C22⋊D4711yescharacteristic
405C2×C42—941no—
406C2×C42—941no—
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#107—942no—
410#107—942no—
411#107—942no—
412#106—942no—
413C4⋊C8—474no—
414C4⋊C8—942no—
415#103—942no—
416#103—942no—
417#103—942no—
418#103—942no—
419C22⋊C8—942no—
420C22⋊C8—942no—
421#97—942no—
422C4×C8—942no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—941no—
430#95—941no—
431#95—941no—
432#95—941no—
433#95—941no—
434C24C2×C22⋊D4711yescharacteristic
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—472no—
439C2×Q8—941no—
440C2×Q8—941no—
441C2×Q8—941no—
442C2×Q8—941no—
443C2×Q8—941no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C23×D4711yescharacteristic
464C2×C8—472no—
465C2×C8—472no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—472no—
490C4⋊C4—944no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—3761no—
497C4⋊C4—1882no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—944no—
503C22⋊C4—3761no—
504C42—21no—
505C42—21no—
506C42—3761no—
507C42—1882no—
508C42D4×D4712yes—
509C42#1062535212yes—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×C22⋊D4711yescharacteristic
518Q8—84no—
519Q8—942no—
520Q8—942no—
521Q8—1881no—
522Q8—1881no—
523C2×C4—21no—
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—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
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—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—1881no—
555C2×C4—1881no—
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#1309399612yes—
565C2×C4#1309399612yes—
566C2×C4C2×D4×D4711yescharacteristic
567C2×C4#41×D4711yescharacteristic
568C2×C4#41×D4711yescharacteristic
569C2×C4C2×#1062535211yescharacteristic
570C2×C4#1309407211yescharacteristic
571C2×C4#1309407211yescharacteristic
572C8—942no—
573C8—942no—
574C8—1881no—
575C8—1881no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#1309399611yescharacteristic
584C22#1568963011yescharacteristic
585C22#1568969711yescharacteristic
586C22#1568992611yescharacteristic
587C22#1568993411yescharacteristic
588C22#1568993811yescharacteristic
589C22#1568993811yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—3761no—
600C4—3761no—
601C4—1882no—
602C4—1882no—
603C4#1568977511yescharacteristic
604C4#1568978311yescharacteristic
605C4#1568980711yescharacteristic
606C4#1568984411yescharacteristic
607C2—81no—
608C2#2024681811yescharacteristic
609C2#2025304011yescharacteristic
610C2#2025306411yescharacteristic
611C2#2025361111yescharacteristic
612C2#2025364411yescharacteristic
613C2#2025465611yescharacteristic
614C2#2025467111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2628C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2628D47
hypocenterC47#24714
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
1. C2×#15689415C2semidirect
8. #20244341C2semidirect
9. #20244154C2semidirect
10. #20244128C2semidirect
11. #20244118C2semidirect
12. #20244077C2semidirect
13. #20244063C2semidirect
14. #20243400C2semidirect
368. C47#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#156894152
C2×#156891842
#202460702
#202448192
#202448142
#202445912
#202445842
#202443412
#202441542
#202441282
#202441182
#202440772
#202440632
#202434002
C47×#26282
#2471447