Finite Group Databasebeta

← #26121806

Subgroups — #26121806

Order 12032.

1204 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256589C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic
3C2×#15689141C211yesmaximal, characteristic
4C2×#15688893C211yesmaximal, characteristic, complemented
5#20243097C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C47×#1740C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689604—22no—
12#15689603—22no—
13#15689600C412yescomplemented
14#15689597C412yescomplemented
15#15689596—22no—
16C4×#10625350—22no—
17#15689591—22no—
18C2×#13093983C2211yescharacteristic
19#117×D47—22no—
20#15689141—22no—
21#15689141—22no—
22#15689141—22no—
23#15689141C414yescomplemented
24C2×#13093952—22no—
25C2×#13093952C414yescomplemented
26#15688893—22no—
27#15688882—22no—
28#15688879—22no—
29C2×#117×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C47×#342—22no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350C2×C412yes—
40C2×#10625350C2×C412yes—
41C2×#10625350D412yes—
42C2×#10625350D412yes—
43C2×#10625350D412yes—
44C2×#10625350Q812yes—
45C22×Dic94C2×C411yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47—21no—
48C22×C4×D47—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329C2×C412yescomplemented
60C2×#10625329C2×C412yescomplemented
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63C4×Dic94—24no—
64#13093989—24no—
65C4×D188—24no—
66#13093986—24no—
67C4×C22⋊D47—28no—
68(C22⋊D47)⋊C4—28no—
69#13093983—21no—
70#13093983—21no—
71#13093983C2×C412yes—
72#13093983D412yes—
73#13093982—24no—
74#13093981—24no—
75#13093980—24no—
76C2×C4⋊Dic47—21no—
77C4⋊C4×D47—24no—
78C2×C22⋊Dic47—21no—
79C22⋊C4×D47—24no—
80C2×C4×Dic47D412yes—
81C42×D47—24no—
82#13093952—28no—
83#13093952—28no—
84C23×C4×C47C2311yescharacteristic
85#117×C47—21no—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47—21no—
93#117×C47—21no—
94#117×C47C2×C412yes—
95#117×C47C2×C412yescomplemented
96#117×C47D412yes—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47D412yes—
103C2×C42×C47—21no—
104C2×C42×C47—21no—
105C2×C42×C47C2×C412yescomplemented
106C24×C47C2×D411yescharacteristic
107C23×D47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—41no—
111C22×C4×C47C22×C411yescharacteristic
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×Q811yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47—22no—
131C22×Dic47—21no—
132C22×Dic47—22no—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—22no—
143#10625350—22no—
144#10625350—22no—
145#10625350C22⋊C414yes—
146#10625350C22⋊C414yes—
147#10625350C4⋊C414yes—
148#10625350C4⋊C414yes—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188C4212yes—
153C2×D188C22⋊C412yes—
154C2×D188C4⋊C412yes—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—28no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94C4212yes—
166C2×Dic94C22⋊C412yes—
167C2×Dic94C4⋊C412yes—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—41no—
172C4⋊C4×C47—41no—
173C4⋊C4×C47—41no—
174C22⋊C4×C47—22no—
175C22⋊C4×C47—22no—
176C22⋊C4×C47—41no—
177C22⋊C4×C47—41no—
178C22⋊C4×C47—41no—
179C22⋊C4×C47C22⋊C414yes—
180C42×C47—22no—
181C42×C47—22no—
182C42×C47—22no—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—41no—
186C22⋊Dic47—22no—
187C22⋊Dic47—22no—
188(C2×D47)⋊C4—28no—
189C4⋊Dic47—22no—
190C4⋊Dic47—22no—
191Dic47⋊C4—28no—
192C4×Dic47—28no—
193C4×Dic47—22no—
194C4×Dic47C22⋊C414yes—
195#10625329—22no—
196#10625329—22no—
197#10625329—22no—
198#10625329—22no—
199#10625329—41no—
200#10625329—41no—
201#10625329—41no—
202#10625329—41no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—41no—
206C2×C47⋊C8—41no—
207C2×C47⋊C8—41no—
208C2×C47⋊C8—41no—
209C23×C47—81no—
210C23×C47C2×C22⋊C411yescharacteristic
211C23×C47C4×D411yescharacteristic
212C23×C47C4×D411yescharacteristic
213C23×C47#12011yescharacteristic
214C23×C47#12011yescharacteristic
215C23×C47#12111yescharacteristic
216C23×C47C22⋊Q811yescharacteristic
217C22×D47—22no—
218C22×D47—22no—
219C22×D47—22no—
220C22×D47—82no—
221C2×C4×C47—24no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—82no—
225C2×C4×C47—82no—
226C2×C4×C47—82no—
227C2×C4×C47C2×C4211yescharacteristic
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C22⋊C411yescharacteristic
230C2×C4×C47C2×C22⋊C411yescharacteristic
231C2×C4×C47C2×C22⋊C411yescharacteristic
232C2×C4×C47C2×C4⋊C411yescharacteristic
233C2×C4×C47C2×C4⋊C411yescharacteristic
234C2×C4×C47C2×C4⋊C411yescharacteristic
235C2×C4×C47#11711yescharacteristic
236C2×C4×C47#11711yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C4×D411yescharacteristic
243C2×C4×C47#12011yescharacteristic
244C2×C4×C47#12011yescharacteristic
245C2×C4×C47#12111yescharacteristic
246C2×C4×C47#12111yescharacteristic
247C2×C4×C47#12111yescharacteristic
248C2×C4×C47C22⋊Q811yescharacteristic
249C2×C4×C47C22⋊Q811yescharacteristic
250C2×C4×C47C22⋊Q811yescharacteristic
251C2×C4×C47#12311yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12311yescharacteristic
254C2×C4×C47#12311yescharacteristic
255C22⋊D47—24no—
256C22⋊D47—24no—
257C22⋊D47—24no—
258C22⋊D47—24no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—24no—
263C2×Dic47—82no—
264D188—22no—
265D188—22no—
266D188—22no—
267D188#9514yes—
268C4×D47—24no—
269C4×D47—24no—
270C4×D47—24no—
271C4×D47—24no—
272C4×D47—88no—
273Dic94—22no—
274Dic94—22no—
275Dic94—22no—
276Dic94#9514yes—
277C47⋊C8—42no—
278C47⋊C8—42no—
279#10783—471nomaximal, Sylow
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47C4×C22⋊C411yescharacteristic
288C22×C47#37911yescharacteristic
289C22×C47#38011yescharacteristic
290C22×C47#38511yescharacteristic
291C22×C47#38511yescharacteristic
292C22×C47#38611yescharacteristic
293C22×C47#38611yescharacteristic
294C2×D47—24no—
295C2×D47—44no—
296C2×D47—82no—
297C2×D47—82no—
298C4×C47—44no—
299C4×C47—82no—
300C4×C47—82no—
301C4×C47C2×#9511yescharacteristic
302C4×C47C4×C22⋊C411yescharacteristic
303C4×C47#38011yescharacteristic
304C4×C47#38111yescharacteristic
305C4×C47#38511yescharacteristic
306C4×C47#38511yescharacteristic
307C4×C47#38611yescharacteristic
308C4×C47#38611yescharacteristic
309Dic47—24no—
310Dic47—44no—
311#3428—471no—
312C2×#421—471no—
313C2×#421—471no—
314C2×#344—471no—
315#1740D4711yescharacteristic, complemented
316#1733—471no—
317C2×H(3,ℤ/4)—471no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47C22⋊#9511yescharacteristic
326D47—44no—
327C22×#41—471no—
328C22×M16—471no—
329C22×M16—471no—
330#520—942no—
331#520—942no—
332#519—472no—
333#518—472no—
334#518—942no—
335C4×#41—942no—
336C4×#41—942no—
337C2×#117—471no—
338C2×#117—942no—
339C2×#117C2×D4711yescharacteristic
340C2×#117C2×D4711yescharacteristic
341C2×#117C2×D4711yescharacteristic
342#421—474no—
343#421—942no—
344#421—942no—
345#421—942no—
346C2×#104—474no—
347C2×#104—942no—
348#344—942no—
349#342—22no—
350#339—942no—
351H(3,ℤ/4)—942no—
352C47#1078311yescharacteristic, complemented, Sylow
353C2×#41—472no—
354C2×#41—472no—
355C2×#41—472no—
356C2×#41—472no—
357C2×#41—472no—
358C2×#41—472no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C22×Q8—471no—
366C22×D4—471no—
367C22×D4—941no—
368C23×C4—941no—
369C23×C4C22×D4711yescharacteristic
370C2×M16—472no—
371C2×M16—472no—
372C2×M16—941no—
373C2×M16—941no—
374C2×M16—941no—
375C2×M16—941no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16—941no—
381C2×M16—941no—
382C22×C8—941no—
383C22×C8—941no—
384C4×Q8—944no—
385C4×Q8—944no—
386C4×D4—944no—
387C4×D4—944no—
388C4×D4—948no—
389C4×D4—948no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—472no—
400#117—472no—
401#117—944no—
402#117—944no—
403#117—941no—
404#117—941no—
405#117—944no—
406#117C4×D4712yes—
407#117C4×D4712yescomplemented
408#117D18812yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—944no—
413C2×C4⋊C4—941no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—944no—
418C2×C22⋊C4C22⋊D4712yes—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—472no—
422C2×C42—944no—
423C2×C42C4×D4712yescomplemented
424#104—948no—
425#104—948no—
426C24—941no—
427C24C2×C22⋊D4711yescharacteristic
428#41—474no—
429#41—474no—
430#41—474no—
431#41—474no—
432#41—942no—
433#41—942no—
434#41—942no—
435#41—942no—
436#41—942no—
437#41—942no—
438#41—942no—
439#41—942no—
440#41—942no—
441#41—942no—
442#41—942no—
443#41—942no—
444C2×Q8—472no—
445C2×Q8—472no—
446C2×Q8—472no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×D4—472no—
451C2×D4—472no—
452C2×D4—472no—
453C2×D4—942no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4—942no—
458C2×D4—942no—
459C2×D4—941no—
460C2×D4—941no—
461C2×D4—941no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—41no—
465C22×C4—948no—
466C22×C4—941no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4C2×C4×D4711yescharacteristic
475C22×C4C2×C4×D4711yescharacteristic
476C22×C4C2×C4×D4711yescharacteristic
477C22×C4C2×D18811yescharacteristic
478C22×C4#1062535011yescharacteristic
479C22×C4#1062535011yescharacteristic
480C22×C4D4×D4711yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4D4×D4711yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4711yescharacteristic
485C22×C4#1062535211yescharacteristic
486C22×C4Q8×D4711yescharacteristic
487C22×C4#1062535411yescharacteristic
488M16—942no—
489M16—942no—
490M16—942no—
491M16—942no—
492M16—1881no—
493M16—1881no—
494M16—1881no—
495M16—1881no—
496C2×C8—942no—
497C2×C8—942no—
498C2×C8—1881no—
499C2×C8—1881no—
500C2×C8—1881no—
501C2×C8—1881no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—948no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—948no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C22⋊C4(C2×D47)⋊C414yes—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—41no—
526C42—474no—
527C42—948no—
528C42—942no—
529C23—81no—
530C23—942no—
531C23—942no—
532C23—942no—
533C23—3762no—
534C23C2×(C2×D47)⋊C411yescharacteristic
535C23C4×C22⋊D4711yescharacteristic
536C23C4×C22⋊D4711yescharacteristic
537C23#1309399211yescharacteristic
538C23#1309399211yescharacteristic
539C23#1309399511yescharacteristic
540C23#1309400011yescharacteristic
541Q8—474no—
542Q8—942no—
543Q8—942no—
544Q8—942no—
545D4—474no—
546D4—944no—
547D4—944no—
548D4—944no—
549D4—944no—
550D4—942no—
551D4—942no—
552D4—942no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—942no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—944no—
563C2×C4—944no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—944no—
567C2×C4—3768no—
568C2×C4—3762no—
569C2×C4C42×D4711yescharacteristic
570C2×C4C22⋊C4×D4711yescharacteristic
571C2×C4C22⋊C4×D4711yescharacteristic
572C2×C4C22⋊C4×D4711yescharacteristic
573C2×C4C22⋊C4×D4711yescharacteristic
574C2×C4C4⋊C4×D4711yescharacteristic
575C2×C4C4⋊C4×D4711yescharacteristic
576C2×C4C4⋊C4×D4711yescharacteristic
577C2×C4#1309398111yescharacteristic
578C2×C4#1309398211yescharacteristic
579C2×C4(C22⋊D47)⋊C411yescharacteristic
580C2×C4(C22⋊D47)⋊C411yescharacteristic
581C2×C4#1309398611yescharacteristic
582C2×C4#1309398611yescharacteristic
583C2×C4C4×D18811yescharacteristic
584C2×C4C4×D18811yescharacteristic
585C2×C4#1309399411yescharacteristic
586C2×C4#1309399411yescharacteristic
587C2×C4#1309399711yescharacteristic
588C2×C4#1309399711yescharacteristic
589C2×C4#1309399911yescharacteristic
590C2×C4#1309400211yescharacteristic
591C2×C4#1309400211yescharacteristic
592C2×C4#1309400411yescharacteristic
593C2×C4#1309400611yescharacteristic
594C2×C4#1309400611yescharacteristic
595C2×C4#1309400911yescharacteristic
596C2×C4#1309400911yescharacteristic
597C8—1882no—
598C8—1882no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—944no—
607C22—3762no—
608C22—3762no—
609C22—1884no—
610C22C4×(C2×D47)⋊C411yescharacteristic
611C22#1568897811yescharacteristic
612C22#1568898011yescharacteristic
613C22#1568899411yescharacteristic
614C22#1568899411yescharacteristic
615C22#1568899911yescharacteristic
616C22#1568899911yescharacteristic
617C4—44no—
618C4—82no—
619C4—82no—
620C4—944no—
621C4—1884no—
622C4#95×D4711yescharacteristic
623C4#1568897011yescharacteristic
624C4#1568898211yescharacteristic
625C4#1568898511yescharacteristic
626C4#1568899711yescharacteristic
627C4#1568899711yescharacteristic
628C4#1568900111yescharacteristic
629C4#1568900111yescharacteristic
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—1884no—
638C2(C2×D47)⋊#9511yescharacteristic
subgroupG/H
centerC4#15689001
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1740C2
socleC2×C47C22⋊#95
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1740D47
hypocenterC47#10783
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
4. C2×#15688893C2semidirect
5. #20243097C2semidirect
6. C2×#15688879C2semidirect
7. C47×#1740C2semidirect
13. #15689600C4semidirect
14. #15689597C4semidirect
23. #15689141C4semidirect
25. C2×#13093952C4semidirect
59. C2×#10625329C2×C4semidirect
60. C2×#10625329C2×C4semidirect
95. #117×C47C2×C4semidirect
105. C2×C42×C47C2×C4semidirect
315. #1740D47semidirect
352. C47#10783semidirect
407. #117C4×D47semidirect
423. C2×C42C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202565892
C2×#156891412
C2×#156888932
#202430972
C2×#156888792
C47×#17402
#1078347