Finite Group Databasebeta

← #26257541

Subgroups — #26257541

Order 12032.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689423C211yesmaximal, characteristic, complemented
2C2×#15689180C211yesmaximal, characteristic, complemented
3#20251698C211yesmaximal, characteristic, complemented
4#20244824C211yesmaximal, characteristic, complemented
5#20244814C211yesmaximal, characteristic, complemented
6#20244574C211yesmaximal, characteristic
7#20244567C211yesmaximal, characteristic
8#20244345C211yesmaximal, characteristic, complemented
9#20244156C211yesmaximal, characteristic, complemented
10#20244128C211yesmaximal, characteristic, complemented
11#20244123C211yesmaximal, characteristic, complemented
12#20244088C211yesmaximal, characteristic, complemented
13#20244088C211yesmaximal, characteristic, complemented
14#20243398C211yesmaximal, characteristic, complemented
15C4×#121×C47C211yesmaximal, characteristic
16C2×#13094016C2211yescharacteristic
17#15689423—24no—
18#15689180—24no—
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689007—21no—
36#15689007—21no—
37#15688996—21no—
38#15688996—21no—
39#15688989C2211yescharacteristic
40#15688983C2211yescharacteristic
41#15688983C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50C2×#121×C47C2211yescharacteristic
51C2×C4×D4×C47—21no—
52C2×C4×D4×C47C2211yescharacteristic
53C22×C42×C47C2211yescharacteristic
54C47×#390C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#388—21no—
57C47×#386—21no—
58C47×#380C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C4×C22⋊C4×C47—21no—
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13094016—22no—
66#13094016—22no—
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77#13093957—22no—
78#13093957—22no—
79#13093955—22no—
80#13093955—22no—
81C4⋊(C47⋊C8)—22no—
82C4⋊(C47⋊C8)D414yescomplemented
83#13093945—22no—
84#13093945—22no—
85#13093945—22no—
86#13093945—22no—
87C22⋊(C47⋊C8)—22no—
88C22⋊(C47⋊C8)—22no—
89#13093935—22no—
90#13093935—22no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C22×D4×C47—21no—
98C22×D4×C47C2311yescharacteristic
99C23×C4×C47—21no—
100C23×C4×C47D411yescharacteristic
101C23×C4×C47D411yescharacteristic
102C23×C4×C47C2311yescharacteristic
103#121×C47—22no—
104#121×C47—22no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C4×D4×C47—44no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C42×C47—22no—
118C2×C42×C47—22no—
119C2×C42×C47—21no—
120C2×C42×C47D411yescharacteristic
121C2×C42×C47D411yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#95×C47—21no—
125#95×C47—21no—
126#95×C47—21no—
127C24×C47—21no—
128C24×C47C2×D411yescharacteristic
129C2×D4×C47—24no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—42no—
136C2×D4×C47—42no—
137C2×D4×C47#4112yes—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—41no—
151C22×C4×C47—41no—
152C22×C4×C47—41no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2411yescharacteristic
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—42no—
172C4⋊C4×C47#4112yes—
173C22⋊C4×C47—24no—
174C22⋊C4×C47—42no—
175C22⋊C4×C47—42no—
176C22⋊C4×C47—42no—
177C22⋊C4×C47—42no—
178C42×C47—22no—
179C42×C47—22no—
180C42×C47—21no—
181C42×C47—21no—
182C42×C47—42no—
183C42×C47C2×D412yes—
184C42×C47#4112yes—
185C22⋊Dic47—42no—
186C22⋊Dic47—42no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195Dic47⋊C4—42no—
196Dic47⋊C4—42no—
197Dic47⋊C4—42no—
198Dic47⋊C4—42no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8C2×D412yes—
210C2×C47⋊C8C2×D412yes—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—22no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—41no—
221C23×C47—41no—
222C23×C47—41no—
223C23×C47—41no—
224C23×C47AGL(1,ℤ/8)12yes—
225C23×C47C22×D411yescharacteristic
226D4×C47—22no—
227D4×C47—22no—
228D4×C47—48no—
229D4×C47—41no—
230D4×C47—41no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—22no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—44no—
246C2×C4×C47—44no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—84no—
260C2×C4×C47#12112yes—
261C2×C4×C47#12112yes—
262C2×C4×C47C22×D411yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47C2×#4111yescharacteristic
266C2×C4×C472−1+411yescharacteristic
267C2×C4×C472−1+411yescharacteristic
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C47⋊C8—22no—
281C47⋊C8—22no—
282C47⋊C8—41no—
283C47⋊C8—41no—
284#24706—471nomaximal, Sylow
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47—42no—
293C22×C47—42no—
294C22×C47—42no—
295C22×C47—81no—
296C22×C47—81no—
297C22×C47—81no—
298C22×C47—81no—
299C22×C47C2×#12111yescharacteristic
300C22×C47#52511yescharacteristic
301C22×C47#53611yescharacteristic
302C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C47#57511yescharacteristic
304C22×C47#57511yescharacteristic
305C22×C47#57511yescharacteristic
306C4×C47—22no—
307C4×C47—22no—
308C4×C47—42no—
309C4×C47—41no—
310C4×C47—41no—
311C4×C47—41no—
312C4×C47—81no—
313C4×C47—81no—
314C4×C47#54711yescharacteristic
315C4×C47#54811yescharacteristic
316C4×C47#55211yescharacteristic
317C4×C47#55611yescharacteristic
318Dic47—81no—
319Dic47—81no—
320Dic47—81no—
321Dic47—81no—
322C2×#478—471no—
323C2×#432—471no—
324#2851—471no—
325C4×#121D4711yescharacteristic
326#2077—471no—
327#2075—471no—
328#2034—471no—
329#2033—471no—
330#1989—471no—
331#1949—471no—
332#1944—471no—
333#1943—471no—
334#1936—471no—
335#1936—471no—
336#1804—471no—
337C2×C47—42no—
338C2×C47—82no—
339C2×C47#241511yescharacteristic
340C2×C47#305411yescharacteristic
341C2×C47#305511yescharacteristic
342C2×C47#311111yescharacteristic
343C2×C47#311411yescharacteristic
344C2×C47#323411yescharacteristic
345C2×C47#324011yescharacteristic
346C2×#125—471no—
347C2×#121C2×D4711yescharacteristic
348C2×C4×D4—21no—
349C2×C4×D4C2×D4711yescharacteristic
350C22×C42C2×D4711yescharacteristic
351#478—944no—
352#432—944no—
353C2×#107—471no—
354C2×#107—471no—
355C2×#106—471no—
356C2×#106—471no—
357C2×C4⋊C8—471no—
358C2×C4⋊C8—471no—
359C2×#102—471no—
360C2×#102—471no—
361C2×#102—471no—
362C2×#102—471no—
363C2×C22⋊C8—471no—
364C2×C22⋊C8—471no—
365C2×#97—471no—
366C2×#97—471no—
367#390C2×D4711yescharacteristic
368#389—471no—
369#389—471no—
370#389C2×D4711yescharacteristic
371#388—21no—
372#387—941no—
373#387—941no—
374#386—21no—
375#385—941no—
376#385—941no—
377#382—471no—
378#380—471no—
379#380—471no—
380#380C2×D4711yescharacteristic
381C4×C4⋊C4C2×D4711yescharacteristic
382C4×C22⋊C4—21no—
383#340—471no—
384#340—471no—
385#340—471no—
386#340—471no—
387#340—471no—
388#340—471no—
389#340—471no—
390#340—471no—
391C47#2470611yescharacteristic, complemented, Sylow
392C22×D4—21no—
393C22×D4C22×D4711yescharacteristic
394C23×C4—21no—
395C23×C4C22⋊D4711yescharacteristic
396C23×C4C22⋊D4711yescharacteristic
397C23×C4C22×D4711yescharacteristic
398C22×C8—471no—
399C22×C8—471no—
400C22×C8—471no—
401C22×C8—471no—
402#125—942no—
403#125—942no—
404#121—22no—
405#121—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—44no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—471no—
411C2×C4⋊C4—471no—
412C2×C4⋊C4—471no—
413C2×C4⋊C4—471no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4—941no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4C22×D4711yescharacteristic
419C2×C4⋊C4C22×D4711yescharacteristic
420C2×C4⋊C4C22×D4711yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—941no—
427C2×C22⋊C4—941no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—21no—
431C2×C42C22⋊D4711yescharacteristic
432C2×C42C22⋊D4711yescharacteristic
433C2×C42C22×D4711yescharacteristic
434C2×C42C22×D4711yescharacteristic
435#107—942no—
436#107—942no—
437#106—942no—
438#106—942no—
439C4⋊C8—474no—
440C4⋊C8—942no—
441#102—942no—
442#102—942no—
443#102—942no—
444#102—942no—
445C22⋊C8—942no—
446C22⋊C8—942no—
447#97—942no—
448#97—942no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—941no—
453#95—941no—
454#95—941no—
455#95—941no—
456#95—941no—
457#95—941no—
458C24—21no—
459C24C2×C22⋊D4711yescharacteristic
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4#1062535012yes—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4C2×C22⋊D4711yescharacteristic
492C22×C4C2×C22⋊D4711yescharacteristic
493C22×C4C2×C22⋊D4711yescharacteristic
494C22×C4C2×C22⋊D4711yescharacteristic
495C22×C4C2×C22⋊D4711yescharacteristic
496C22×C4C23×D4711yescharacteristic
497C2×C8—472no—
498C2×C8—472no—
499C2×C8—941no—
500C2×C8—941no—
501C2×C8—941no—
502C2×C8—941no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4—941no—
518C4⋊C4—941no—
519C4⋊C4—941no—
520C4⋊C4—941no—
521C4⋊C4—941no—
522C4⋊C4—941no—
523C4⋊C4—1882no—
524C4⋊C4—1882no—
525C4⋊C4—1882no—
526C4⋊C4—1882no—
527C4⋊C4#1062535012yes—
528C22⋊C4—24no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—1882no—
534C22⋊C4—1882no—
535C42—22no—
536C42—22no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42D4×D4712yes—
541C42#1062535212yes—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23#1309405012yes—
556C23C22×C22⋊D4711yescharacteristic
557D4—22no—
558D4—22no—
559D4—48no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—1881no—
592C2×C4—1881no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4—1881no—
596C2×C4—1881no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4#1309399612yes—
604C2×C4#1309399612yes—
605C2×C4C2×D4×D4711yescharacteristic
606C2×C4C2×#1062535211yescharacteristic
607C2×C4C2×#1062535011yescharacteristic
608C2×C4C2×#1062535011yescharacteristic
609C2×C4#1309407111yescharacteristic
610C2×C4#1309407111yescharacteristic
611C8—942no—
612C8—942no—
613C8—1881no—
614C8—1881no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×#1309399611yescharacteristic
630C22#1568963411yescharacteristic
631C22#1568969411yescharacteristic
632C22C2×#1309405011yescharacteristic
633C22#1568992111yescharacteristic
634C22#1568992111yescharacteristic
635C22#1568992111yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—81no—
643C4—81no—
644C4—3761no—
645C4—3761no—
646C4—3761no—
647C4—3761no—
648C4#1568977811yescharacteristic
649C4#1568978211yescharacteristic
650C4#1568981311yescharacteristic
651C4#1568984311yescharacteristic
652C2—42no—
653C2—82no—
654C2#2024681711yescharacteristic
655C2#2025299411yescharacteristic
656C2#2025300311yescharacteristic
657C2#2025349711yescharacteristic
658C2#2025352611yescharacteristic
659C2#2025457411yescharacteristic
660C2#2025462411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×#121×C47C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenterC4×#121D47
hypocenterC47#24706
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#15689423C2semidirect
2. C2×#15689180C2semidirect
3. #20251698C2semidirect
4. #20244824C2semidirect
5. #20244814C2semidirect
8. #20244345C2semidirect
9. #20244156C2semidirect
10. #20244128C2semidirect
11. #20244123C2semidirect
12. #20244088C2semidirect
13. #20244088C2semidirect
14. #20243398C2semidirect
82. C4⋊(C47⋊C8)D4semidirect
391. C47#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#156894232
C2×#156891802
#202516982
#202448242
#202448142
#202445742
#202445672
#202443452
#202441562
#202441282
#202441232
#202440882
#202433982
C4×#121×C472
#2470647