Finite Group Databasebeta

← #26220320

Subgroups — #26220320

Order 12032.

1562 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256717C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic, complemented
3C22×#13093951C211yesmaximal, characteristic, complemented
4C22×#13093950C211yesmaximal, characteristic, complemented
5#20251806C211yesmaximal, characteristic, complemented
6#20245870C211yesmaximal, characteristic, complemented
7#20244305C218yesmaximal, complemented
8C2×C47×#421C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689701—22no—
12#15689697C412yescomplemented
13#15689694C412yescomplemented
14#15689690C412yescomplemented
15#15689687C412yescomplemented
16#15689682—22no—
17#15689669C2214yes—
18#15689634—22no—
19#15689630—22no—
20C2×#13093983C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689141—24no—
23C2×#13093952C2214yescomplemented
24C2×#13093951—24no—
25C2×#13093951C2214yescomplemented
26C2×#13093950—24no—
27C2×#13093950C2214yescomplemented
28#15689081—22no—
29#15689078—22no—
30M16×Dic47C2214yescomplemented
31#15689019—22no—
32#15688995—22no—
33C4×Dic47⋊C4C2214yescomplemented
34C22×#41×C47C2211yescharacteristic
35C22×M16×C47C2211yescharacteristic
36C2×#117×C47C2211yescharacteristic
37C47×#421—24no—
38C2×#104×C47C2214yescomplemented
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—22no—
42C2×#10625350—22no—
43C2×#10625350—22no—
44C2×#10625350—22no—
45C2×#10625350C2×C412yes—
46C2×#10625350C2312yes—
47C22×Dic94C2×C411yescharacteristic
48C22×D188C2×C411yescharacteristic
49C22×C22⋊D47—21no—
50C23×Dic47—21no—
51C22×C4×D47—21no—
52C2×#10625329—21no—
53C2×#10625329—22no—
54C2×#10625329D414yescomplemented
55C2×#10625329C2312yes—
56C22×C47⋊C8—21no—
57#13094022C2×C414yescomplemented
58#13094020C2×C414yescomplemented
59#13094013C2×C414yescomplemented
60#13094011C2×C414yescomplemented
61#13094007—24no—
62#13094005—24no—
63#13094003—24no—
64#13094000—24no—
65#13093998—24no—
66#13093996—28no—
67#13093995—24no—
68#13093993—24no—
69#13093992—24no—
70C4×C22⋊D47—28no—
71#13093983C2×C412yes—
72#13093983C2×C412yes—
73#13093983D412yes—
74#13093983D412yes—
75C2×C4⋊Dic47D412yes—
76C2×Dic47⋊C4—24no—
77C2×C22⋊Dic47D412yes—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47C2312yes—
82C2×C4×Dic47C2312yes—
83#13093952—28no—
84#13093951—28no—
85#13093950—28no—
86#13093934—24no—
87C8×Dic47—24no—
88C47⋊#95—24no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—22no—
92C2×#41×C47—22no—
93C2×#41×C47—22no—
94C2×#41×C47—22no—
95C2×#41×C47C2×C412yes—
96C2×#41×C47C2312yes—
97C22×Q8×C47C2×C411yescharacteristic
98C22×D4×C47—21no—
99C22×D4×C47C2×C411yescharacteristic
100C23×C4×C47—21no—
101C23×C4×C47C2311yescharacteristic
102C2×M16×C47—21no—
103C2×M16×C47—22no—
104C2×M16×C47D414yescomplemented
105C2×M16×C47C2312yes—
106C22×C8×C47—21no—
107#117×C47—22no—
108#117×C47—22no—
109C2×C4⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C42×C47C2312yes—
112#104×C47—28no—
113C24×C47—21no—
114C24×C47C2×D411yescharacteristic
115C23×D47—21no—
116#41×C47—24no—
117#41×C47—24no—
118#41×C47—22no—
119#41×C47—22no—
120#41×C47—22no—
121#41×C47—22no—
122#41×C47—42no—
123#41×C47—42no—
124#41×C47—42no—
125#41×C47—42no—
126C2×Q8×C47—21no—
127C2×Q8×C47—22no—
128C2×Q8×C47—22no—
129C2×Q8×C47C22×C412yes—
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47—21no—
133C2×D4×C47—22no—
134C2×D4×C47—22no—
135C2×D4×C47—42no—
136C2×D4×C47—42no—
137C2×D4×C47C22×C412yes—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47#4112yes—
152C22×C4×C47#4112yes—
153C22×C4×C47C2411yescharacteristic
154C2×C22⋊D47—22no—
155C2×C22⋊D47—22no—
156C2×C22⋊D47—28no—
157C2×C22⋊D47—42no—
158C2×C22⋊D47—42no—
159C22×Dic47—21no—
160C22×Dic47—22no—
161C22×Dic47—44no—
162C22×Dic47—42no—
163C22×Dic47C2×D414yes—
164#10625350—24no—
165#10625350—24no—
166#10625350—22no—
167#10625350—22no—
168#10625350—22no—
169#10625350—22no—
170#10625350—42no—
171#10625350—42no—
172#10625350—42no—
173#10625350—42no—
174C2×D188—22no—
175C2×D188—22no—
176C2×D188—21no—
177C2×D188C22×C412yes—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—42no—
181C2×C4×D47—42no—
182C2×Dic94—22no—
183C2×Dic94—22no—
184C2×Dic94—21no—
185C2×Dic94C22×C412yes—
186M16×C47—24no—
187M16×C47—22no—
188M16×C47C2×D414yes—
189C2×C8×C47—24no—
190C2×C8×C47—22no—
191C4⋊C4×C47—42no—
192C22⋊C4×C47—42no—
193C42×C47—22no—
194C42×C47—22no—
195C22⋊Dic47—28no—
196C22⋊Dic47C22⋊C414yes—
197C22⋊Dic47C22⋊C414yes—
198(C2×D47)⋊C4—28no—
199C4⋊Dic47C22⋊C414yes—
200C4⋊Dic47C22⋊C414yes—
201Dic47⋊C4—28no—
202Dic47⋊C4—48no—
203C4×Dic47—22no—
204C4×Dic47—22no—
205C4×Dic47—42no—
206C4×Dic47C22×C414yes—
207C4×Dic47C2×D414yes—
208#10625329—24no—
209#10625329—22no—
210#10625329C2×D414yes—
211C2×C47⋊C8—24no—
212C2×C47⋊C8—22no—
213C23×C47—22no—
214C23×C47—42no—
215C23×C47—42no—
216C23×C47—82no—
217C23×C47C2×C22⋊C411yescharacteristic
218C23×C47C2×C22⋊C411yescharacteristic
219C23×C47#12412yes—
220C23×C47#12712yes—
221C23×C47C22×D411yescharacteristic
222C22×D47—22no—
223C22×D47—42no—
224C22×D47—82no—
225Q8×C47—22no—
226Q8×C47—22no—
227Q8×C47—42no—
228D4×C47—22no—
229D4×C47—22no—
230D4×C47—42no—
231D4×C47—42no—
232D4×C47—44no—
233D4×C47—42no—
234C2×C4×C47—22no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—44no—
239C2×C4×C47—44no—
240C2×C4×C47—42no—
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47C2×C22⋊C411yescharacteristic
243C2×C4×C47C4×D412yes—
244C2×C4×C47C4×D412yes—
245C2×C4×C47C4×D412yes—
246C2×C4×C47C4×D412yes—
247C2×C4×C47#12112yes—
248C2×C4×C47#12112yes—
249C2×C4×C47#12112yes—
250C2×C4×C47#12112yes—
251C2×C4×C47#12412yes—
252C2×C4×C47#12712yes—
253C2×C4×C47C23×C411yescharacteristic
254C2×C4×C47C22×D411yescharacteristic
255C2×C4×C47C22×D411yescharacteristic
256C2×C4×C47C22×D411yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C22⋊D47—42no—
260C22⋊D47—42no—
261C22⋊D47—44no—
262C22⋊D47—88no—
263C2×Dic47—24no—
264C2×Dic47—22no—
265C2×Dic47—44no—
266C2×Dic47—42no—
267C2×Dic47—48no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47C2×C22⋊C418yes—
271D188—22no—
272D188—22no—
273D188—42no—
274C4×D47—42no—
275C4×D47—42no—
276C4×D47—44no—
277Dic94—22no—
278Dic94—22no—
279Dic94—42no—
280C8×C47—24no—
281C47⋊C8—24no—
282#21253—471nomaximal, Sylow
283C22×C47—22no—
284C22×C47—22no—
285C22×C47—22no—
286C22×C47—42no—
287C22×C47—42no—
288C22×C47—44no—
289C22×C47—42no—
290C22×C47—84no—
291C22×C47#39012yes—
292C22×C47#39012yes—
293C22×C47C22×C22⋊C411yescharacteristic
294C22×C47C2×#12411yescharacteristic
295C22×C47C2×#12711yescharacteristic
296C2×D47—44no—
297C2×D47—42no—
298C2×D47—84no—
299C4×C47—42no—
300C4×C47—82no—
301C4×C47#39012yes—
302C4×C47#39012yes—
303C4×C47C2×C4×D411yescharacteristic
304C4×C47C2×C4×D411yescharacteristic
305C4×C47C2×#12111yescharacteristic
306C4×C47C2×#12111yescharacteristic
307Dic47—28no—
308Dic47—44no—
309Dic47—42no—
310#3449—471no—
311C2×#421—471no—
312C2×#421D4711yescharacteristic, complemented
313C22×#104—471no—
314C22×#104—471no—
315#2873—471no—
316#2296—471no—
317#1980—478no—
318C2×C47—21no—
319C2×C47—22no—
320C2×C47—22no—
321C2×C47—21no—
322C2×C47—82no—
323C2×C47C2×#39011yescharacteristic
324C2×C47#290112yes—
325D47—82no—
326C22×#41—471no—
327C22×#41C2×D4711yescharacteristic
328C22×M16—471no—
329C22×M16C2×D4711yescharacteristic
330#537—942no—
331#536—472no—
332#536—472no—
333#535—472no—
334#535—472no—
335#534—942no—
336#532—474no—
337#525—942no—
338#525—942no—
339C2×#117—471no—
340C2×#117C2×D4711yescharacteristic
341C22×C42—471no—
342#421—24no—
343#421—944no—
344C2×#104—474no—
345C2×#104—474no—
346C2×#104—474no—
347C2×#104—944no—
348C2×#104—944no—
349C2×#104C2×D4714yescomplemented
350#405—942no—
351#405—942no—
352C4×M16—474no—
353#389—942no—
354#385—942no—
355C4×C4⋊C4—474no—
356C47#2125311yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—472no—
364C2×#41—472no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—942no—
368C2×#41—942no—
369C2×#41—942no—
370C2×#41—942no—
371C2×#41C4×D4712yes—
372C2×#41C22×D4712yes—
373C22×Q8—471no—
374C22×Q8C4×D4711yescharacteristic
375C22×D4—21no—
376C22×D4—471no—
377C22×D4—941no—
378C22×D4C4×D4711yescharacteristic
379C23×C4—21no—
380C23×C4—941no—
381C23×C4—941no—
382C23×C4C22×D4711yescharacteristic
383C2×M16—21no—
384C2×M16—22no—
385C2×M16—474no—
386C2×M16—472no—
387C2×M16—942no—
388C2×M16—941no—
389C2×M16C22⋊D4714yescomplemented
390C2×M16C22×D4712yes—
391C22×C8—21no—
392C22×C8—941no—
393C4⋊Q8—474no—
394#127—474no—
395#124—474no—
396#124—474no—
397#123—944no—
398#123—944no—
399C22⋊Q8—944no—
400C22⋊Q8—944no—
401#121—944no—
402#121—944no—
403#121—948no—
404#120—944no—
405#120—944no—
406C4×D4—948no—
407#117—22no—
408#117—22no—
409#117—472no—
410#117—472no—
411#117—472no—
412#117—472no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—472no—
415C2×C4⋊C4—944no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—472no—
418C2×C42—472no—
419C2×C42—472no—
420C2×C42—942no—
421C2×C42—942no—
422C2×C42—941no—
423C2×C42C22×D4712yes—
424#104—28no—
425#104—948no—
426#104—948no—
427#104—948no—
428#97—944no—
429C4×C8—944no—
430#95—944no—
431C24—21no—
432C24—941no—
433C24D4×D4711yescharacteristic
434#41—24no—
435#41—24no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440#41—42no—
441#41—42no—
442#41—42no—
443#41—42no—
444#41—944no—
445#41—944no—
446#41—942no—
447#41—942no—
448#41—942no—
449#41—942no—
450#41—1882no—
451#41—1882no—
452#41—1882no—
453#41—1882no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—472no—
458C2×Q8—941no—
459C2×Q8—942no—
460C2×Q8—942no—
461C2×Q8C2×C4×D4712yes—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—472no—
470C2×D4—948no—
471C2×D4—942no—
472C2×D4—942no—
473C2×D4—941no—
474C2×D4—942no—
475C2×D4—942no—
476C2×D4—1882no—
477C2×D4—1882no—
478C2×D4C2×C4×D4712yes—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—474no—
486C22×C4—941no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—1884no—
491C22×C4—1882no—
492C22×C4—1882no—
493C22×C4—1882no—
494C22×C4C2×C4×D4711yescharacteristic
495C22×C4C2×C4×D4711yescharacteristic
496C22×C4#1062535012yes—
497C22×C4D4×D4711yescharacteristic
498C22×C4D4×D4711yescharacteristic
499C22×C4D4×D4711yescharacteristic
500C22×C4D4×D4712yes—
501C22×C4#1062535212yes—
502C22×C4C2×C22⋊D4712yes—
503C22×C4C23×D4711yescharacteristic
504M16—24no—
505M16—22no—
506M16—474no—
507M16—944no—
508M16—942no—
509M16C2×C22⋊D4714yes—
510C2×C8—24no—
511C2×C8—22no—
512C2×C8—944no—
513C2×C8—942no—
514C4⋊C4—42no—
515C4⋊C4—474no—
516C4⋊C4—474no—
517C4⋊C4—948no—
518C4⋊C4—1888no—
519C22⋊C4—42no—
520C22⋊C4—474no—
521C22⋊C4—474no—
522C22⋊C4—948no—
523C22⋊C4—948no—
524C42—22no—
525C42—22no—
526C42—474no—
527C42—474no—
528C42—942no—
529C42—942no—
530C42—1882no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—82no—
535C23—942no—
536C23—3762no—
537C23—1882no—
538C23C22⋊C4×D4711yescharacteristic
539C23C22⋊C4×D4711yescharacteristic
540C23#1309401012yes—
541C23#1309402012yes—
542C23C2×D4×D4711yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—42no—
546Q8—942no—
547Q8—942no—
548Q8—1882no—
549D4—22no—
550D4—22no—
551D4—44no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—942no—
556D4—942no—
557D4—3768no—
558D4—1884no—
559D4—1882no—
560D4—1882no—
561D4—1882no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—478no—
570C2×C4—944no—
571C2×C4—942no—
572C2×C4—1884no—
573C2×C4—1882no—
574C2×C4—1888no—
575C2×C4—1882no—
576C2×C4—1882no—
577C2×C4—1884no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4C22⋊C4×D4711yescharacteristic
581C2×C4C22⋊C4×D4711yescharacteristic
582C2×C4(C22⋊D47)⋊C412yes—
583C2×C4(C22⋊D47)⋊C412yes—
584C2×C4C4×C22⋊D4712yes—
585C2×C4C4×C22⋊D4712yes—
586C2×C4#1309399612yes—
587C2×C4#1309399612yes—
588C2×C4#1309399712yes—
589C2×C4#1309399712yes—
590C2×C4#1309401012yes—
591C2×C4#1309402012yes—
592C2×C4C22×C4×D4711yescharacteristic
593C2×C4C2×D4×D4711yescharacteristic
594C2×C4C2×D4×D4711yescharacteristic
595C2×C4C22×C22⋊D4711yescharacteristic
596C2×C4C2×#1062535211yescharacteristic
597C2×C4C2×#1062535011yescharacteristic
598C8—24no—
599C8—944no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—84no—
608C22—3764no—
609C22—1884no—
610C22—1882no—
611C22#1568902312yes—
612C22#1568902312yes—
613C22C2×C22⋊C4×D4711yescharacteristic
614C22C2×#1309401011yescharacteristic
615C22C2×#1309402011yescharacteristic
616C4—42no—
617C4—82no—
618C4—948no—
619C4—1884no—
620C4—1882no—
621C4#1568902312yes—
622C4#1568902312yes—
623C4C2×(C22⋊D47)⋊C411yescharacteristic
624C4C2×C4×C22⋊D4711yescharacteristic
625C4C2×#1309399611yescharacteristic
626C4C2×#1309399711yescharacteristic
627C2—21no—
628C2—22no—
629C2—22no—
630C2—21no—
631C2—82no—
632C2—3762no—
633C2C2×#1568902311yescharacteristic
634C2#2025193412yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47C22×C22⋊C4
prime radical#20256717C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47#21253
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#15689141C2semidirect
3. C22×#13093951C2semidirect
4. C22×#13093950C2semidirect
5. #20251806C2semidirect
6. #20245870C2semidirect
7. #20244305C2semidirect
8. C2×C47×#421C2semidirect
12. #15689697C4semidirect
13. #15689694C4semidirect
14. #15689690C4semidirect
15. #15689687C4semidirect
23. C2×#13093952C22semidirect
25. C2×#13093951C22semidirect
27. C2×#13093950C22semidirect
30. M16×Dic47C22semidirect
33. C4×Dic47⋊C4C22semidirect
38. C2×#104×C47C22semidirect
54. C2×#10625329D4semidirect
57. #13094022C2×C4semidirect
58. #13094020C2×C4semidirect
59. #13094013C2×C4semidirect
60. #13094011C2×C4semidirect
104. C2×M16×C47D4semidirect
312. C2×#421D47semidirect
349. C2×#104C2×D47semidirect
356. C47#21253semidirect
389. C2×M16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202567172
C2×#156891412
C22×#130939512
C22×#130939502
#202518062
#202458702
#202443052
C2×C47×#4212
#2125347