Finite Group Databasebeta

← #26217006

Subgroups — #26217006

Order 12032.

1590 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2C2×#15689161C211yesmaximal, characteristic, complemented
3C2×#15689159C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic
5#20245767C211yesmaximal, characteristic
6#20243590C212yesmaximal, complemented
7#20243588C212yesmaximal, complemented
8#20243582C212yesmaximal, complemented
9#20243577C212yesmaximal, complemented
10#20243104C211yesmaximal, characteristic, complemented
11C47×#1735C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C23×C47⋊C8C2211yescharacteristic
14C2×#13093983C2211yescharacteristic
15C2×#13093983C2211yescharacteristic
16C2×#13093982C2212yes—
17C2×#13093981—21no—
18C2×#13093980—21no—
19#117×D47—24no—
20#117×D47—24no—
21C2×C4⋊C4×D47C2212yes—
22C2×C22⋊C4×D47—21no—
23C2×C42×D47—21no—
24#15689161—24no—
25#15689159—24no—
26C2×#13093958C2212yescomplemented
27C2×#13093957C2212yescomplemented
28C2×#13093956C2212yescomplemented
29C2×#13093955C2212yescomplemented
30C2×(C2×D47)⋊C8C418yescomplemented
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35#15688984—21no—
36#15688980C2212yes—
37#15688980C2212yes—
38#15688978—21no—
39C4×(C2×D47)⋊C4—21no—
40C4×(C2×D47)⋊C4—21no—
41#15688885C2212yescomplemented
42#15688885C2212yescomplemented
43C23×C8×C47C2211yescharacteristic
44C2×#117×C47C2211yescharacteristic
45C2×#117×C47C2211yescharacteristic
46C47×#340C2212yescomplemented
47C47×#340C2212yescomplemented
48C24×D47D411yescharacteristic
49C23×Dic47D411yescharacteristic
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47C2×C414yes—
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47Q814yes—
59C22×C4×D47C2311yescharacteristic
60C22×C4×D47C2311yescharacteristic
61C22×C47⋊C8—22no—
62C22×C47⋊C8—22no—
63C22×C47⋊C8C2×C414yescomplemented
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13093983—22no—
67#13093983—22no—
68#13093983—22no—
69#13093983D414yes—
70#13093982—24no—
71#13093982—24no—
72#13093981—28no—
73#13093980—28no—
74C2×C4⋊Dic47C2312yes—
75C2×C4⋊Dic47C2312yes—
76C2×Dic47⋊C4—22no—
77C4⋊C4×D47—24no—
78C4⋊C4×D47—24no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C22⋊C4×D47—28no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—21no—
88C42×D47—28no—
89#13093958—24no—
90#13093957—24no—
91#13093956—24no—
92#13093955—24no—
93(C2×D47)⋊C8C2×C414yes—
94(C2×D47)⋊C8C2×C414yes—
95(C2×D47)⋊C8C2×C414yescomplemented
96(C2×D47)⋊C8C2×C414yescomplemented
97C47⋊#95—22no—
98C47⋊#95—22no—
99C23×C4×C47C2311yescharacteristic
100C22×C8×C47—22no—
101C22×C8×C47—22no—
102C22×C8×C47C2×C414yescomplemented
103C22×C8×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105#117×C47—22no—
106#117×C47—22no—
107#117×C47—22no—
108#117×C47D414yes—
109C2×C4⋊C4×C47C2312yes—
110C2×C4⋊C4×C47C2312yes—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47—21no—
115C24×C47C2×D411yescharacteristic
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—24no—
119C23×D47—42no—
120C23×D47C4⋊C414yes—
121C23×D47C2×D411yescharacteristic
122C23×D47C2×D411yescharacteristic
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×Q812yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×C4×C47C2411yescharacteristic
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47C4⋊C414yes—
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140C2×C4×D47—28no—
141C2×C4×D47—28no—
142C2×C4×D47—22no—
143C2×C4×D47—22no—
144C2×C4×D47—28no—
145C2×C4×D47—28no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—21no—
149C2×C4×D47—21no—
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—28no—
157C2×C4×D47—44no—
158C2×C4×D47—44no—
159C2×C4×D47C4⋊C414yes—
160C2×C4×D47C4⋊C414yes—
161C2×C4×D47C22×C412yes—
162C2×C4×D47C22×C412yes—
163C2×C4×D47C2×Q812yes—
164C2×C4×D47C2×Q812yes—
165C2×C8×C47—28no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47C22×C412yes—
171C2×C8×C47C22×C412yes—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47C2×D414yes—
176C22⋊C4×C47—24no—
177C22⋊C4×C47—42no—
178C42×C47—24no—
179C42×C47—42no—
180C22⋊Dic47—24no—
181C22⋊Dic47—42no—
182(C2×D47)⋊C4—28no—
183(C2×D47)⋊C4—44no—
184(C2×D47)⋊C4—44no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—22no—
188C4⋊Dic47C2×D414yes—
189Dic47⋊C4—28no—
190C4×Dic47—28no—
191C4×Dic47—24no—
192C4×Dic47—42no—
193C2×C47⋊C8—28no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C412yes—
199C2×C47⋊C8C22×C412yes—
200C23×C47—22no—
201C23×C47—22no—
202C23×C47C2×C4⋊C412yes—
203C23×C47#12012yes—
204C23×C47#12312yes—
205C23×C47C22×D411yescharacteristic
206C22×D47—21no—
207C22×D47—21no—
208C22×D47—22no—
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—22no—
212C22×D47—22no—
213C22×D47—28no—
214C22×D47—28no—
215C22×D47—44no—
216C22×D47—48no—
217C22×D47—48no—
218C22×D47C2×C4⋊C412yes—
219C22×D47C2×C4⋊C412yes—
220C22×D47#13514yes—
221C2×C4×C47—24no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47C2×C4⋊C412yes—
228C2×C4×C47C4×D414yes—
229C2×C4×C47C4×D414yes—
230C2×C4×C47#12012yes—
231C2×C4×C47C22⋊Q814yes—
232C2×C4×C47C22⋊Q814yes—
233C2×C4×C47#12312yes—
234C2×C4×C47C23×C411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×Q811yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—28no—
245C2×Dic47—24no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47C2×C4⋊C412yes—
252C2×Dic47C2×C4⋊C412yes—
253C4×D47—22no—
254C4×D47—22no—
255C4×D47—22no—
256C4×D47—22no—
257C4×D47—22no—
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—28no—
262C4×D47—28no—
263C4×D47—416no—
264C8×C47—22no—
265C8×C47—22no—
266C47⋊C8—22no—
267C47⋊C8—22no—
268#20843—471nomaximal, Sylow
269C22×C47—24no—
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—24no—
273C22×C47#38514yes—
274C22×C47C22×C4⋊C411yescharacteristic
275C22×C47C2×#12011yescharacteristic
276C22×C47C2×#12311yescharacteristic
277C22×C47C2×#13512yes—
278C22×C47#57512yes—
279C2×D47—24no—
280C2×D47—22no—
281C2×D47—24no—
282C2×D47—22no—
283C2×D47—22no—
284C2×D47—22no—
285C2×D47—22no—
286C2×D47—416no—
287C2×D47—42no—
288C2×D47—42no—
289C2×D47#42714yescomplemented
290C4×C47—44no—
291C4×C47—82no—
292C4×C47#38514yes—
293C4×C47C2×C4×D411yescharacteristic
294C4×C47C2×C4×D411yescharacteristic
295C4×C47C2×C22⋊Q811yescharacteristic
296C4×C47C2×C22⋊Q811yescharacteristic
297Dic47—22no—
298Dic47—22no—
299Dic47—44no—
300Dic47—82no—
301C22×#117—471no—
302C2×#427—471no—
303C2×#427—471no—
304C22×C22⋊C8—471no—
305#2280—471no—
306#1854—472no—
307#1854—472no—
308#1853—472no—
309#1852—472no—
310#1735—471no—
311#1735D4711yescharacteristic, complemented
312C2×C47—24no—
313C2×C47C2×#38511yescharacteristic
314C2×C47C2×#42711yescharacteristic
315C2×C47#291111yescharacteristic
316C2×C47#300212yes—
317C2×C47#309112yes—
318D47—24no—
319D47—42no—
320C24×C4—471no—
321C23×C8—471no—
322C23×C8C2×D4711yescharacteristic
323C2×#117—471no—
324C2×#117—471no—
325C2×#117—472no—
326C2×#117—941no—
327C2×#117—941no—
328C2×#117—944no—
329C2×#117—944no—
330C2×#117C2×D4711yescharacteristic
331C2×#117C2×D4711yescharacteristic
332C22×C4⋊C4—472no—
333C22×C22⋊C4—941no—
334C22×C42—941no—
335#427—944no—
336#427—944no—
337C2×#107—472no—
338C2×#107—472no—
339C2×#106—472no—
340C2×#106—472no—
341C2×C22⋊C8—478no—
342C2×C22⋊C8—471no—
343C2×C22⋊C8—471no—
344C2×C22⋊C8—471no—
345C2×C22⋊C8—471no—
346#381—941no—
347#380—472no—
348#380—472no—
349#379—941no—
350C4×C22⋊C4—941no—
351C4×C22⋊C4—941no—
352#340—472no—
353#340—472no—
354#340C2×D4712yescomplemented
355#340C2×D4712yescomplemented
356C47#2084311yescharacteristic, complemented, Sylow
357C25—471no—
358C23×C4—471no—
359C23×C4—474no—
360C23×C4—471no—
361C23×C4—471no—
362C23×C4—474no—
363C23×C4—471no—
364C23×C4—471no—
365C23×C4—942no—
366C23×C4—942no—
367C23×C4—942no—
368C23×C4—942no—
369C23×C4—942no—
370C23×C4C22×D4711yescharacteristic
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—474no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—942no—
377C22×C8—942no—
378C22×C8C4×D4714yescomplemented
379C22×C8C22×D4711yescharacteristic
380C22×C8C22×D4711yescharacteristic
381#117—22no—
382#117—22no—
383#117—22no—
384#117—474no—
385#117—948no—
386#117—948no—
387#117—944no—
388#117—942no—
389#117—944no—
390#117—942no—
391#117—942no—
392#117D18814yes—
393C2×C4⋊C4—472no—
394C2×C4⋊C4—472no—
395C2×C4⋊C4—944no—
396C2×C4⋊C4—942no—
397C2×C4⋊C4—944no—
398C2×C4⋊C4C22×D4712yes—
399C2×C4⋊C4C22×D4712yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—948no—
403C2×C22⋊C4—942no—
404C2×C22⋊C4—941no—
405C2×C22⋊C4—942no—
406C2×C22⋊C4—942no—
407C2×C22⋊C4—941no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—948no—
411C2×C42—942no—
412C2×C42—941no—
413C2×C42—941no—
414#107—944no—
415#107—944no—
416#106—944no—
417#106—944no—
418C22⋊C8—474no—
419C22⋊C8—474no—
420C22⋊C8—474no—
421C22⋊C8—474no—
422#95—942no—
423#95—942no—
424C24—471no—
425C24—471no—
426C24—474no—
427C24—944no—
428C24—942no—
429C24—942no—
430C24—1882no—
431C24D4×D4711yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—474no—
435C22×C4—471no—
436C22×C4—471no—
437C22×C4—474no—
438C22×C4—474no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—472no—
442C22×C4—472no—
443C22×C4—948no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—948no—
447C22×C4—948no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—948no—
451C22×C4—948no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—1884no—
465C22×C4—1884no—
466C22×C4C2×C4×D4712yes—
467C22×C4C2×D18812yes—
468C22×C4#1062535012yes—
469C22×C4D4×D4712yes—
470C22×C4D4×D4711yescharacteristic
471C22×C4#1062535212yes—
472C22×C4Q8×D4712yes—
473C22×C4C23×D4711yescharacteristic
474C2×C8—28no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—472no—
480C2×C8—472no—
481C2×C8—948no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—941no—
486C2×C8C2×C4×D4712yes—
487C2×C8C2×C4×D4712yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—474no—
492C4⋊C4—948no—
493C4⋊C4—942no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4C2×D18814yes—
497C22⋊C4—24no—
498C22⋊C4—42no—
499C22⋊C4—948no—
500C22⋊C4—944no—
501C22⋊C4—1884no—
502C22⋊C4—1884no—
503C22⋊C4—1882no—
504C42—24no—
505C42—42no—
506C42—948no—
507C42—944no—
508C42—1882no—
509C23—22no—
510C23—22no—
511C23—472no—
512C23—474no—
513C23—472no—
514C23—948no—
515C23—941no—
516C23—941no—
517C23—942no—
518C23—948no—
519C23—941no—
520C23—941no—
521C23—942no—
522C23—942no—
523C23—1884no—
524C23—1888no—
525C23—1888no—
526C23C4⋊C4×D4712yes—
527C23#1309399412yes—
528C23#1309400612yes—
529C23C2×D4×D4711yescharacteristic
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—472no—
537C2×C4—472no—
538C2×C4—948no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—948no—
544C2×C4—948no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—944no—
554C2×C4—18816no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4C4⋊C4×D4712yes—
561C2×C4(C22⋊D47)⋊C414yes—
562C2×C4C4×D18814yes—
563C2×C4#1309399412yes—
564C2×C4#1309400214yes—
565C2×C4#1309400414yes—
566C2×C4#1309400612yes—
567C2×C4C22×C4×D4711yescharacteristic
568C2×C4C2×D4×D4711yescharacteristic
569C2×C4C22×D18811yescharacteristic
570C2×C4C2×Q8×D4711yescharacteristic
571C2×C4C2×#1062535211yescharacteristic
572C2×C4C2×#1062535011yescharacteristic
573C8—22no—
574C8—22no—
575C8—942no—
576C8—942no—
577C22—22no—
578C22—22no—
579C22—24no—
580C22—24no—
581C22—474no—
582C22—942no—
583C22—942no—
584C22—944no—
585C22—944no—
586C22—942no—
587C22—942no—
588C22—942no—
589C22—18816no—
590C22—1882no—
591C22—1882no—
592C22#1568899714yes—
593C22C2×C4⋊C4×D4711yescharacteristic
594C22C2×#1309399411yescharacteristic
595C22C2×#1309400611yescharacteristic
596C22#135×D4712yes—
597C22#1568992012yes—
598C4—44no—
599C4—82no—
600C4—942no—
601C4—942no—
602C4—3762no—
603C4—1884no—
604C4#1568899714yes—
605C4C2×(C22⋊D47)⋊C411yescharacteristic
606C4C2×C4×D18811yescharacteristic
607C4C2×#1309400211yescharacteristic
608C4C2×#1309400411yescharacteristic
609C2—24no—
610C2—944no—
611C2—1882no—
612C2C2×#1568899711yescharacteristic
613C2#427×D4711yescharacteristic
614C2#2025197611yescharacteristic
615C2#2025260812yes—
616C2#2025329912yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1735C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1735D47
hypocenterC47#20843
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
2. C2×#15689161C2semidirect
3. C2×#15689159C2semidirect
6. #20243590C2semidirect
7. #20243588C2semidirect
8. #20243582C2semidirect
9. #20243577C2semidirect
10. #20243104C2semidirect
11. C47×#1735C2semidirect
26. C2×#13093958C22semidirect
27. C2×#13093957C22semidirect
28. C2×#13093956C22semidirect
29. C2×#13093955C22semidirect
30. C2×(C2×D47)⋊C8C4semidirect
41. #15688885C22semidirect
42. #15688885C22semidirect
46. C47×#340C22semidirect
47. C47×#340C22semidirect
63. C22×C47⋊C8C2×C4semidirect
95. (C2×D47)⋊C8C2×C4semidirect
96. (C2×D47)⋊C8C2×C4semidirect
102. C22×C8×C47C2×C4semidirect
289. C2×D47#427semidirect
311. #1735D47semidirect
354. #340C2×D47semidirect
355. #340C2×D47semidirect
356. C47#20843semidirect
378. C22×C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
C2×#156891612
C2×#156891592
C22×(C2×D47)⋊C82
#202457672
#202435902
#202435882
#202435822
#202435772
#202431042
C47×#17352
#2084347