Finite Group Databasebeta

← #26217499

Subgroups — #26217499

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C2×#15689117C212yesmaximal, complemented
3C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
4#20243710C212yesmaximal, complemented
5#20243705C212yesmaximal, complemented
6#20243700C212yesmaximal, complemented
7#20243695C212yesmaximal, complemented
8#20243104C212yesmaximal, complemented
9C22×#117×C47C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C23×C47⋊C8C2212yes—
12#15689634—24no—
13#15689634C418yescomplemented
14C2×#13094007—21no—
15C2×#13094003C2211yescharacteristic
16C2×#13094003C2211yescharacteristic
17C2×#13093998C2211yescharacteristic
18C2×#13093998C2211yescharacteristic
19C2×#13093993—21no—
20C2×C4×C22⋊D47—21no—
21C2×C4×C22⋊D47—21no—
22C2×#13093983C2211yescharacteristic
23#15689117—28no—
24C2×#13093947C2214yescomplemented
25C2×#13093944C2214yescomplemented
26C2×C22⋊(C47⋊C8)—24no—
27C2×C22⋊(C47⋊C8)C2212yes—
28C2×C22⋊(C47⋊C8)C2212yes—
29#15688885C2214yescomplemented
30#15688885C2214yescomplemented
31C24×C4×C47C2211yescharacteristic
32C2×#117×C47—21no—
33C2×#117×C47—21no—
34C2×#117×C47—28no—
35C2×#117×C47C2212yes—
36C2×#117×C47C2212yes—
37C22×C4⋊C4×C47C2212yes—
38C22×C22⋊C4×C47—21no—
39C22×C42×C47—21no—
40C2×#10625350—22no—
41C2×#10625350—24no—
42C2×#10625350—24no—
43C2×#10625350C2×C414yescomplemented
44C22×Dic94C2311yescharacteristic
45C22×D188C2311yescharacteristic
46C22×C22⋊D47—21no—
47C22×C22⋊D47—21no—
48C22×C22⋊D47—21no—
49C22×C4×D47—21no—
50C22×C47⋊C8—24no—
51C22×C47⋊C8—24no—
52C22×C47⋊C8—24no—
53C22×C47⋊C8C2314yes—
54#13094007—28no—
55#13094003—22no—
56#13094003—22no—
57#13094003C2×C414yes—
58#13094003C2×C414yescomplemented
59#13093998—22no—
60#13093998—22no—
61#13093998C2×C414yes—
62#13093998C2×C414yescomplemented
63#13093993—28no—
64C4×C22⋊D47—28no—
65C4×C22⋊D47—28no—
66#13093983—22no—
67#13093983C2×C414yescomplemented
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×C4×Dic47—21no—
78#13093947—28no—
79#13093944—28no—
80C22⋊(C47⋊C8)—24no—
81C22⋊(C47⋊C8)—24no—
82C25×C47D411yescharacteristic
83C23×C4×C47—24no—
84C23×C4×C47—24no—
85C23×C4×C47—22no—
86C23×C4×C47C2×C414yes—
87C23×C4×C47D411yescharacteristic
88C23×C4×C47D411yescharacteristic
89C23×C4×C47D411yescharacteristic
90C23×C4×C47D414yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2311yescharacteristic
94#117×C47—28no—
95#117×C47—28no—
96#117×C47—24no—
97#117×C47—28no—
98#117×C47D418yescomplemented
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—28no—
101C2×C4⋊C4×C47C2314yes—
102C2×C22⋊C4×C47—28no—
103C2×C22⋊C4×C47—22no—
104C2×C22⋊C4×C47—22no—
105C2×C42×C47—28no—
106C2×C42×C47—22no—
107C2×C42×C47—22no—
108C24×C47—22no—
109C24×C47—22no—
110C24×C47—24no—
111C24×C47—42no—
112C24×C47C22⋊C414yes—
113C24×C47C2×D411yescharacteristic
114C24×C47C2×D411yescharacteristic
115C24×C47C2×D411yescharacteristic
116C23×D47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—216no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—216no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—28no—
130C22×C4×C47—24no—
131C22×C4×C47—44no—
132C22×C4×C47—44no—
133C22×C4×C47C22⋊C414yes—
134C22×C4×C47C22⋊C414yes—
135C22×C4×C47C22⋊C414yes—
136C22×C4×C47C22×C412yes—
137C22×C4×C47C22×C412yes—
138C22×C4×C47C22×C412yes—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D412yes—
145C22×C4×C47C2×D414yes—
146C22×C4×C47#4114yes—
147C22×C4×C47C2411yescharacteristic
148C2×C22⋊D47—24no—
149C2×C22⋊D47—24no—
150C2×C22⋊D47—24no—
151C2×C22⋊D47—44no—
152C2×C22⋊D47—42no—
153C2×C22⋊D47—42no—
154C2×C22⋊D47—44no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158#10625350—216no—
159#10625350—48no—
160C2×D188—22no—
161C2×D188—22no—
162C2×D188—21no—
163C2×D188C22×C412yes—
164C2×C4×D47—24no—
165C2×C4×D47—42no—
166C2×C4×D47—42no—
167C2×Dic94—22no—
168C2×Dic94—22no—
169C2×Dic94—21no—
170C2×Dic94C22×C412yes—
171C4⋊C4×C47—28no—
172C4⋊C4×C47—24no—
173C4⋊C4×C47C2×D418yes—
174C22⋊C4×C47—28no—
175C22⋊C4×C47—28no—
176C42×C47—28no—
177C42×C47—28no—
178C22⋊Dic47—24no—
179C22⋊Dic47—24no—
180C22⋊Dic47—24no—
181(C2×D47)⋊C4—24no—
182(C2×D47)⋊C4—24no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47C22×C412yes—
186C4⋊Dic47C22×C412yes—
187Dic47⋊C4—24no—
188Dic47⋊C4—24no—
189C4×Dic47—24no—
190C2×C47⋊C8—24no—
191C2×C47⋊C8—24no—
192C2×C47⋊C8—24no—
193C2×C47⋊C8—48no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47—22no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47—22no—
202C23×C47—22no—
203C23×C47—28no—
204C23×C47—28no—
205C23×C47—44no—
206C23×C47—48no—
207C23×C47—48no—
208C23×C47C2×C22⋊C412yes—
209C23×C47C2×C22⋊C412yes—
210C23×C47C2×C22⋊C412yes—
211C23×C47#12012yes—
212C23×C47#12312yes—
213C23×C47#13514yes—
214C23×C47C22×D411yescharacteristic
215C22×D47—22no—
216C22×D47—41no—
217C22×D47—41no—
218C22×D47—42no—
219C22×D47—42no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—28no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—28no—
230C2×C4×C47—28no—
231C2×C4×C47—28no—
232C2×C4×C47—416no—
233C2×C4×C47—44no—
234C2×C4×C47—44no—
235C2×C4×C47C2×C22⋊C412yes—
236C2×C4×C47C2×C22⋊C412yes—
237C2×C4×C47C2×C22⋊C412yes—
238C2×C4×C47C4×D418yes—
239C2×C4×C47#12012yes—
240C2×C4×C47#12118yes—
241C2×C4×C47#12312yes—
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D412yes—
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C2×#4112yes—
246C22⋊D47—48no—
247C22⋊D47—48no—
248C22⋊D47—48no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256D188—24no—
257D188—42no—
258C4×D47—48no—
259Dic94—24no—
260Dic94—42no—
261C47⋊C8—44no—
262#20908—471nomaximal, Sylow
263C22×C47—24no—
264C22×C47—24no—
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—24no—
269C22×C47—24no—
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—416no—
275C22×C47—42no—
276C22×C47—42no—
277C22×C47#38614yes—
278C22×C47#41614yescomplemented
279C22×C47C22×C22⋊C411yescharacteristic
280C22×C47C2×#12011yescharacteristic
281C22×C47C2×#12311yescharacteristic
282C22×C47C2×#13512yes—
283C22×C47#57512yes—
284C2×D47—42no—
285C2×D47—42no—
286C2×D47—42no—
287C2×D47—82no—
288C2×D47—82no—
289C4×C47—22no—
290C4×C47—22no—
291C4×C47—48no—
292C4×C47#38614yes—
293C4×C47C2×C4×D412yes—
294C4×C47C2×#12112yes—
295Dic47—42no—
296Dic47—42no—
297Dic47—42no—
298C2×#525—471no—
299C22×#117D4711yescharacteristic, complemented
300C2×#416—472no—
301C22×C22⋊C8—471no—
302#1875—472no—
303#1874—472no—
304#1873—472no—
305#1872—472no—
306#1735—472no—
307C2×C47—24no—
308C2×C47—24no—
309C2×C47—42no—
310C2×C47C2×#38611yescharacteristic
311C2×C47C2×#41611yescharacteristic
312C2×C47#289611yescharacteristic
313C2×C47#300212yes—
314C2×C47#309112yes—
315D47—82no—
316C22×#41—471no—
317C24×C4C2×D4711yescharacteristic
318C23×C8—472no—
319#525—478no—
320#525—944no—
321C2×#123—941no—
322C2×C22⋊Q8—471no—
323C2×C22⋊Q8—471no—
324C2×#121—471no—
325C2×#121—471no—
326C2×#120—941no—
327C2×C4×D4—941no—
328C2×C4×D4—941no—
329C2×#117—21no—
330C2×#117—21no—
331C2×#117—28no—
332C2×#117—471no—
333C2×#117C2×D4712yes—
334C2×#117C2×D4712yes—
335C22×C4⋊C4C2×D4712yes—
336C22×C22⋊C4—21no—
337C22×C42—21no—
338#416—948no—
339C2×#103—474no—
340C2×#102—474no—
341C2×C22⋊C8—472no—
342C2×C22⋊C8—472no—
343C2×C22⋊C8—944no—
344#340—474no—
345#340—474no—
346C47#2090811yescharacteristic, complemented, Sylow
347C25C22⋊D4711yescharacteristic
348C2×#41—474no—
349C2×#41—942no—
350C2×#41—944no—
351C2×#41—944no—
352C22×Q8—471no—
353C22×D4—471no—
354C22×D4—941no—
355C22×D4—941no—
356C22×D4—941no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—22no—
360C23×C4—941no—
361C23×C4C4×D4714yes—
362C23×C4D18814yes—
363C23×C4C22⋊D4711yescharacteristic
364C23×C4C22⋊D4711yescharacteristic
365C23×C4C22⋊D4711yescharacteristic
366C23×C4C22×D4711yescharacteristic
367C23×C4C22×D4711yescharacteristic
368C23×C4C22×D4711yescharacteristic
369C22×C8—474no—
370C22×C8—944no—
371C22×C8—944no—
372C22×C8—944no—
373#123—948no—
374C22⋊Q8—474no—
375C22⋊Q8—474no—
376C22⋊Q8—942no—
377C22⋊Q8—942no—
378#121—474no—
379#121—474no—
380#121—942no—
381#121—942no—
382#120—948no—
383C4×D4—948no—
384C4×D4—948no—
385#117—28no—
386#117—28no—
387#117—24no—
388#117—28no—
389#117—474no—
390#117—942no—
391#117C22⋊D4718yescomplemented
392C2×C4⋊C4—22no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4C22×D4714yes—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C22⋊C4—941no—
406C2×C22⋊C4—941no—
407C2×C42—28no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—941no—
411#103—948no—
412#102—948no—
413C22⋊C8—944no—
414C22⋊C8—944no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—42no—
419C24—941no—
420C24(C2×D47)⋊C414yes—
421C24C2×C22⋊D4711yescharacteristic
422C24C2×C22⋊D4711yescharacteristic
423C24C2×C22⋊D4711yescharacteristic
424#41—9416no—
425#41—1888no—
426C2×Q8—472no—
427C2×Q8—941no—
428C2×Q8—942no—
429C2×Q8—942no—
430C2×D4—472no—
431C2×D4—944no—
432C2×D4—944no—
433C2×D4—944no—
434C2×D4—942no—
435C2×D4—941no—
436C2×D4—942no—
437C2×D4—1884no—
438C2×D4—1882no—
439C2×D4—1882no—
440C2×D4—1884no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—216no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—216no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—944no—
461C22×C4—1882no—
462C22×C4—1882no—
463C22×C4(C2×D47)⋊C414yes—
464C22×C4(C2×D47)⋊C414yes—
465C22×C4(C2×D47)⋊C414yes—
466C22×C4C2×C4×D4712yes—
467C22×C4C2×C4×D4712yes—
468C22×C4C2×C4×D4712yes—
469C22×C4C2×D18812yes—
470C22×C4C2×D18812yes—
471C22×C4C2×D18812yes—
472C22×C4#1062535014yes—
473C22×C4C2×C22⋊D4711yescharacteristic
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C2×C22⋊D4714yes—
476C22×C4C2×C22⋊D4711yescharacteristic
477C22×C4C23×D4711yescharacteristic
478C2×C8—944no—
479C2×C8—944no—
480C2×C8—944no—
481C2×C8—1888no—
482C4⋊C4—28no—
483C4⋊C4—24no—
484C4⋊C4—472no—
485C4⋊C4—472no—
486C4⋊C4—944no—
487C4⋊C4—944no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4C2×C22⋊D4718yes—
491C22⋊C4—28no—
492C22⋊C4—28no—
493C22⋊C4—944no—
494C22⋊C4—944no—
495C22⋊C4—944no—
496C22⋊C4—944no—
497C22⋊C4—944no—
498C42—28no—
499C42—28no—
500C42—944no—
501C23—21no—
502C23—21no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—28no—
507C23—21no—
508C23—21no—
509C23—28no—
510C23—22no—
511C23—22no—
512C23—44no—
513C23—48no—
514C23—48no—
515C23—942no—
516C23—1881no—
517C23—1881no—
518C23—1882no—
519C23—1882no—
520C23C2×(C2×D47)⋊C412yes—
521C23C2×(C2×D47)⋊C412yes—
522C23C2×(C2×D47)⋊C412yes—
523C23#1309399312yes—
524C23#1309400712yes—
525C23#1309404414yes—
526C23C22×C22⋊D4711yescharacteristic
527Q8—944no—
528Q8—1882no—
529D4—944no—
530D4—1888no—
531D4—1888no—
532D4—1888no—
533D4—1882no—
534C2×C4—28no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—28no—
540C2×C4—28no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—28no—
546C2×C4—416no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1888no—
557C2×C4C2×(C2×D47)⋊C412yes—
558C2×C4C2×(C2×D47)⋊C412yes—
559C2×C4C2×(C2×D47)⋊C412yes—
560C2×C4C4×C22⋊D4718yes—
561C2×C4#1309399312yes—
562C2×C4#1309399818yes—
563C2×C4#1309400712yes—
564C2×C4C22×C4×D4711yescharacteristic
565C2×C4C22×C22⋊D4712yes—
566C2×C4C22×D18811yescharacteristic
567C2×C4C2×#1062535012yes—
568C8—1884no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—416no—
581C22—42no—
582C22—42no—
583C22—3762no—
584C22—3762no—
585C22—1882no—
586C22—1882no—
587C22—1882no—
588C22#1568900214yes—
589C22#1568911714yescomplemented
590C22C22×(C2×D47)⋊C411yescharacteristic
591C22C2×#1309399311yescharacteristic
592C22C2×#1309400711yescharacteristic
593C22C2×#1309404412yes—
594C22#1568992112yes—
595C4—22no—
596C4—22no—
597C4—48no—
598C4—1882no—
599C4—1882no—
600C4—1882no—
601C4#1568900214yes—
602C4C2×C4×C22⋊D4712yes—
603C4C2×#1309399812yes—
604C2—24no—
605C2—24no—
606C2—42no—
607C2—3762no—
608C2C2×#1568900211yescharacteristic
609C2C2×#1568911711yescharacteristic
610C2#2025190511yescharacteristic
611C2#2025260612yes—
612C2#2025330112yes—
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#117×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC22×#117D47
hypocenterC47#20908
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#15689117C2semidirect
3. C22×C22⋊(C47⋊C8)C2semidirect
4. #20243710C2semidirect
5. #20243705C2semidirect
6. #20243700C2semidirect
7. #20243695C2semidirect
8. #20243104C2semidirect
9. C22×#117×C47C2semidirect
13. #15689634C4semidirect
24. C2×#13093947C22semidirect
25. C2×#13093944C22semidirect
29. #15688885C22semidirect
30. #15688885C22semidirect
43. C2×#10625350C2×C4semidirect
58. #13094003C2×C4semidirect
62. #13093998C2×C4semidirect
67. #13093983C2×C4semidirect
98. #117×C47D4semidirect
278. C22×C47#416semidirect
299. C22×#117D47semidirect
346. C47#20908semidirect
391. #117C22⋊D47semidirect
589. C22#15689117semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×#156891172
C22×C22⋊(C47⋊C8)2
#202437102
#202437052
#202437002
#202436952
#202431042
C22×#117×C472
#2090847