Finite Group Databasebeta

← #26223958

Subgroups — #26223958

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689423C211yesmaximal, characteristic
2C4×#13094016C211yesmaximal, characteristic, complemented
3#20244345C211yesmaximal, characteristic, complemented
4#20244156C211yesmaximal, characteristic, complemented
5#20243973C211yesmaximal, characteristic, complemented
6#20243959C211yesmaximal, characteristic, complemented
7#20243649C211yesmaximal, characteristic
8#20243635C211yesmaximal, characteristic
9#20243398C211yesmaximal, characteristic
10#20243286C211yesmaximal, characteristic, complemented
11#20243286C211yesmaximal, characteristic, complemented
12#20243241C211yesmaximal, characteristic, complemented
13#20243213C211yesmaximal, characteristic
14#20243213C211yesmaximal, characteristic
15C42×D4×C47C211yesmaximal, characteristic
16C2×#13094016C2211yescharacteristic
17#15689423C418yescomplemented
18C2×#13093957C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689007—21no—
33#15689007—21no—
34#15688989C2211yescharacteristic
35C4×Dic47⋊C4—21no—
36C4×Dic47⋊C4—21no—
37C4×C4⋊Dic47C2211yescharacteristic
38C4×C4⋊Dic47C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C2×C4×D4×C47C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C22×C42×C47—21no—
53C4×C4⋊C4×C47C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C22⋊C4×C47—21no—
57C4×C22⋊C4×C47—21no—
58C4×C22⋊C4×C47—21no—
59C43×C47C2211yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64#13094016—22no—
65#13094016C2×C414yescomplemented
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×C4×Dic47—21no—
75C2×C4×Dic47—21no—
76#13093957—22no—
77#13093957C2×C414yescomplemented
78#13093955—22no—
79#13093955C2×C414yescomplemented
80C4⋊(C47⋊C8)—22no—
81C4⋊(C47⋊C8)C2×C414yescomplemented
82#13093945—22no—
83#13093945—22no—
84#13093945C2×C414yes—
85#13093945C2×C414yes—
86#13093935—22no—
87#13093935—22no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C22×D4×C47C2311yescharacteristic
95C23×C4×C47—21no—
96C23×C4×C47—21no—
97C23×C4×C47—21no—
98C4×D4×C47—22no—
99C4×D4×C47—22no—
100C4×D4×C47—22no—
101C4×D4×C47—22no—
102C4×D4×C47C2×C414yes—
103C4×D4×C47Q814yes—
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×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47—44no—
114C2×C42×C47D411yescharacteristic
115C2×C42×C47D411yescharacteristic
116C2×C42×C47D411yescharacteristic
117C2×C42×C47D411yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124C24×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47C22×C412yes—
129C2×D4×C47C2×Q812yes—
130C2×D4×C47#4112yes—
131C22×C4×C47—24no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—24no—
136C22×C4×C47—24no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2411yescharacteristic
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47C22×C412yes—
158C4⋊C4×C47C2×Q812yes—
159C4⋊C4×C47#4112yes—
160C22⋊C4×C47—24no—
161C22⋊C4×C47—24no—
162C22⋊C4×C47—24no—
163C42×C47—22no—
164C42×C47—21no—
165C42×C47—21no—
166C42×C47—41no—
167C42×C47—41no—
168C42×C47—41no—
169C42×C47—42no—
170C42×C47—42no—
171C42×C47—42no—
172C42×C47C22×C412yes—
173C42×C47C2×Q812yes—
174C42×C47#4112yes—
175C42×C47#4112yes—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47C22×C412yes—
183C4⋊Dic47C22×C412yes—
184Dic47⋊C4—24no—
185Dic47⋊C4—24no—
186Dic47⋊C4—42no—
187Dic47⋊C4—42no—
188C4×Dic47—42no—
189C4×Dic47—42no—
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⋊C8C22×C412yes—
201C2×C47⋊C8C22×C412yes—
202C23×C47—22no—
203C23×C47—22no—
204C23×C47—22no—
205C23×C47—41no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47C22×D411yescharacteristic
210D4×C47—22no—
211D4×C47—22no—
212D4×C47—22no—
213D4×C47C4×Q814yes—
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—22no—
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—48no—
231C2×C4×C47—48no—
232C2×C4×C47—48no—
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×C47C4×D412yes—
240C2×C4×C47C4×D412yes—
241C2×C4×C47C22⋊Q812yes—
242C2×C4×C47C22⋊Q812yes—
243C2×C4×C47AGL(1,ℤ/8)12yes—
244C2×C4×C47C23×C411yescharacteristic
245C2×C4×C47C22×Q811yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×Dic47—22no—
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—
262C47⋊C8—22no—
263C47⋊C8—22no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266#21617—471nomaximal, Sylow
267C22×C47—24no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47C2×C4×D411yescharacteristic
275C22×C47C2×C22⋊Q811yescharacteristic
276C22×C47#52511yescharacteristic
277C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C47#57511yescharacteristic
279C22×C47#57511yescharacteristic
280C22×C47#57511yescharacteristic
281C4×C47—22no—
282C4×C47—22no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—42no—
287C4×C47—41no—
288C4×C47—42no—
289C4×C47—42no—
290C4×C47C2×C4×Q811yescharacteristic
291C4×C47C4×#4111yescharacteristic
292C4×C47#52911yescharacteristic
293C4×C47#53311yescharacteristic
294Dic47—42no—
295Dic47—42no—
296Dic47—81no—
297Dic47—81no—
298C2×#478—471no—
299C4×#125—471no—
300C42×D4D4711yescharacteristic
301#1989—471no—
302#1949—471no—
303#1920—471no—
304#1918—471no—
305#1864—471no—
306#1862—471no—
307#1804—471no—
308#1776—471no—
309#1776—471no—
310#1767—471no—
311#1762—471no—
312#1762—471no—
313C2×C47—44no—
314C2×C47C4×C22⋊Q811yescharacteristic
315C2×C47#294311yescharacteristic
316C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C47#307711yescharacteristic
318C2×C47#308011yescharacteristic
319C2×C47#311111yescharacteristic
320C2×C47#311411yescharacteristic
321C2×#125—471no—
322C2×C4×D4C2×D4711yescharacteristic
323C2×C4×D4C2×D4711yescharacteristic
324C2×C4×D4C2×D4711yescharacteristic
325C22×C42—21no—
326#478—478no—
327C2×#107—471no—
328C2×#107—471no—
329C2×#106—471no—
330C2×#106—471no—
331C2×C4⋊C8—471no—
332C2×C4⋊C8—471no—
333C2×#102—471no—
334C2×#102—471no—
335C2×#102—471no—
336C2×#102—471no—
337C2×#97—471no—
338C2×#97—471no—
339#389—471no—
340#389—471no—
341#387—941no—
342#387—941no—
343#382—471no—
344C4×C4⋊C4—471no—
345C4×C4⋊C4—471no—
346C4×C4⋊C4—941no—
347C4×C4⋊C4—941no—
348C4×C4⋊C4C2×D4711yescharacteristic
349C4×C4⋊C4C2×D4711yescharacteristic
350C4×C4⋊C4C2×D4711yescharacteristic
351C4×C22⋊C4—21no—
352C4×C22⋊C4—21no—
353C4×C22⋊C4—21no—
354C43C2×D4711yescharacteristic
355#340—471no—
356#340—471no—
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#336—471no—
364#336—471no—
365C47#2161711yescharacteristic, complemented, Sylow
366C22×D4C22×D4711yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C22×C8—471no—
371C22×C8—471no—
372C22×C8—471no—
373C22×C8—471no—
374#125—474no—
375#125—942no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4Dic9414yes—
381C4×D4C4×D4714yes—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4C22×D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C4⋊C4C22×D4711yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—44no—
400C2×C42—941no—
401C2×C42—941no—
402C2×C42C22⋊D4711yescharacteristic
403C2×C42C22⋊D4711yescharacteristic
404C2×C42C22⋊D4711yescharacteristic
405C2×C42C22⋊D4711yescharacteristic
406C2×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#107—474no—
410#107—942no—
411#106—474no—
412#106—942no—
413C4⋊C8—474no—
414C4⋊C8—942no—
415#102—474no—
416#102—474no—
417#102—942no—
418#102—942no—
419#97—942no—
420#97—942no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95—941no—
430C24—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×Dic9412yes—
435C2×D4C2×C4×D4712yes—
436C2×D4#1062535012yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460C2×C8—472no—
461C2×C8—472no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—472no—
476C4⋊C4—472no—
477C4⋊C4—944no—
478C4⋊C4—944no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—1882no—
486C4⋊C4—1882no—
487C4⋊C4C2×Dic9412yes—
488C4⋊C4C2×C4×D4712yes—
489C4⋊C4#1062535012yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C42—22no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42—42no—
500C42—42no—
501C42—42no—
502C42—1882no—
503C42—1882no—
504C42C2×Dic9412yes—
505C42C2×C4×D4712yes—
506C42#1062535012yes—
507C42#1062535012yes—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×C22⋊D4711yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4C4×Dic9414yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4C4×C22⋊D4712yes—
558C2×C4C4×C22⋊D4712yes—
559C2×C4#1309400312yes—
560C2×C4#1309400312yes—
561C2×C4#1309405012yes—
562C2×C4C22×C4×D4711yescharacteristic
563C2×C4C22×Dic9411yescharacteristic
564C2×C4C2×#1062535011yescharacteristic
565C2×C4C2×#1062535011yescharacteristic
566C2×C4C2×#1062535011yescharacteristic
567C2×C4C2×#1062535011yescharacteristic
568C8—942no—
569C8—942no—
570C8—1881no—
571C8—1881no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×C4×C22⋊D4711yescharacteristic
580C22C2×#1309400311yescharacteristic
581C22#1568963411yescharacteristic
582C22C2×#1309405011yescharacteristic
583C22#1568992111yescharacteristic
584C22#1568992111yescharacteristic
585C22#1568992111yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—3761no—
596C4—3761no—
597C4—1882no—
598C4—1882no—
599C4C2×C4×Dic9411yescharacteristic
600C4C4×#1062535011yescharacteristic
601C4#1568965711yescharacteristic
602C4#1568968011yescharacteristic
603C2—44no—
604C2C4×#1309400311yescharacteristic
605C2#2025218611yescharacteristic
606C2C4×#1309405011yescharacteristic
607C2#2025318511yescharacteristic
608C2#2025321011yescharacteristic
609C2#2025349711yescharacteristic
610C2#2025352611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC42×D4×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenterC42×D4D47
hypocenterC47#21617
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C4×#13094016C2semidirect
3. #20244345C2semidirect
4. #20244156C2semidirect
5. #20243973C2semidirect
6. #20243959C2semidirect
10. #20243286C2semidirect
11. #20243286C2semidirect
12. #20243241C2semidirect
17. #15689423C4semidirect
65. #13094016C2×C4semidirect
77. #13093957C2×C4semidirect
79. #13093955C2×C4semidirect
81. C4⋊(C47⋊C8)C2×C4semidirect
365. C47#21617semidirect

Maximal subgroups

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

subgroupindex
C2×#156894232
C4×#130940162
#202443452
#202441562
#202439732
#202439592
#202436492
#202436352
#202433982
#202432862
#202432412
#202432132
C42×D4×C472
#2161747