Finite Group Databasebeta

← #26216136

Subgroups — #26216136

Order 12032.

1276 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256589C211yesmaximal, characteristic
2C2×#15689096C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4#20243495C218yesmaximal, complemented
5#20243121C211yesmaximal, characteristic, complemented
6#20243120C211yesmaximal, characteristic, complemented
7#20243120C211yesmaximal, characteristic, complemented
8C47×#1740C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689604—22no—
11#15689603—22no—
12#15689600C412yescomplemented
13#15689597C412yescomplemented
14#15689596C2214yes—
15C4×#10625350—22no—
16#15689591—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20#117×D47C414yescomplemented
21#15689096—22no—
22#15689096—22no—
23#15689096—22no—
24#15689096—22no—
25C2×#13093938C2214yes—
26C2×#13093938C2214yes—
27#15688890C2214yes—
28#15688889C2214yes—
29#15688889C2214yes—
30C2×#117×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C47×#342C2214yes—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350D412yes—
43C2×#10625350D412yes—
44C2×#10625350D412yes—
45C2×#10625350D412yes—
46C22×Dic94C2×C411yescharacteristic
47C22×D188C2×C411yescharacteristic
48C22×C22⋊D47C2312yes—
49C22×C4×D47C2×C412yes—
50C4×Dic94—24no—
51#13093989—24no—
52C4×D188—24no—
53#13093986—24no—
54C4×C22⋊D47—28no—
55(C22⋊D47)⋊C4—28no—
56#13093983—21no—
57#13093983—21no—
58#13093983—21no—
59#13093983—21no—
60#13093983—21no—
61#13093983—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983C2×C412yes—
67#13093983C2×C412yes—
68#13093982—24no—
69#13093981—24no—
70#13093980C2×C418yes—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C4⋊C4×D47—24no—
75C2×C22⋊Dic47C2312yes—
76C2×C22⋊Dic47C2312yes—
77C2×C22⋊Dic47C2312yes—
78C22⋊C4×D47C2×C418yes—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82C42×D47—24no—
83#13093938—28no—
84#13093938—28no—
85C23×C4×C47C2311yescharacteristic
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×C47—21no—
95#117×C47—21no—
96#117×C47C2×C412yes—
97#117×C47C2×C412yes—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C22⋊C4×C47C2312yes—
102C2×C22⋊C4×C47C2312yes—
103C2×C22⋊C4×C47C2312yes—
104C2×C42×C47—21no—
105C2×C42×C47—21no—
106C2×C42×C47—21no—
107C24×C47C2411yescharacteristic
108C23×D47C22×C412yes—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
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×C47#4111yescharacteristic
119C22×C4×C47#4111yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47C2×D414yes—
131C2×C22⋊D47C2×D414yes—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47C22×C412yes—
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#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149#10625350—22no—
150#10625350—22no—
151#10625350—22no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188—21no—
156C2×D188C22⋊C412yes—
157C2×D188C22⋊C412yes—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—28no—
163C2×C4×D47C22⋊C414yes—
164C2×C4×D47C22⋊C414yes—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94—21no—
169C2×Dic94C22⋊C412yes—
170C2×Dic94C22⋊C412yes—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—41no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47—41no—
176C4⋊C4×C47—41no—
177C22⋊C4×C47—22no—
178C22⋊C4×C47—22no—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47C22×C414yes—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—41no—
186C42×C47—41no—
187C42×C47—41no—
188C42×C47—41no—
189C22⋊Dic47—22no—
190C22⋊Dic47—22no—
191C22⋊Dic47—22no—
192C22⋊Dic47—22no—
193C22⋊Dic47—22no—
194C22⋊Dic47C22×C414yes—
195(C2×D47)⋊C4—28no—
196C4⋊Dic47—22no—
197C4⋊Dic47—22no—
198C4⋊Dic47—41no—
199C4⋊Dic47—41no—
200C4⋊Dic47—41no—
201C4⋊Dic47—41no—
202Dic47⋊C4—28no—
203C4×Dic47—22no—
204C4×Dic47—22no—
205C4×Dic47—28no—
206C4×Dic47—41no—
207C4×Dic47—41no—
208C4×Dic47—41no—
209C4×Dic47—41no—
210C23×C47—81no—
211C23×C47C23×C411yescharacteristic
212C23×C47C22×D411yescharacteristic
213C23×C47C22×D411yescharacteristic
214C23×C47C2×#4111yescharacteristic
215C23×C47C2×#4111yescharacteristic
216C23×C47C2×#4111yescharacteristic
217C23×C47C2×#4111yescharacteristic
218C22×D47—22no—
219C22×D47—22no—
220C22×D47—82no—
221C22×D47C2×C22⋊C414yes—
222C2×C4×C47—24no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—82no—
226C2×C4×C47—82no—
227C2×C4×C47—82no—
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C22⋊C411yescharacteristic
230C2×C4×C47C2×C22⋊C411yescharacteristic
231C2×C4×C47C2×C22⋊C411yescharacteristic
232C2×C4×C47#11711yescharacteristic
233C2×C4×C47#11711yescharacteristic
234C2×C4×C47#11711yescharacteristic
235C2×C4×C47#11711yescharacteristic
236C2×C4×C47#11711yescharacteristic
237C2×C4×C47#11711yescharacteristic
238C2×C4×C47#11711yescharacteristic
239C2×C4×C47#11711yescharacteristic
240C2×C4×C47#12311yescharacteristic
241C2×C4×C47#12311yescharacteristic
242C2×C4×C47#12311yescharacteristic
243C2×C4×C47#12311yescharacteristic
244C2×C4×C47#12311yescharacteristic
245C2×C4×C47#12311yescharacteristic
246C2×C4×C47#12311yescharacteristic
247C2×C4×C47#12311yescharacteristic
248C2×C4×C47#12311yescharacteristic
249C2×C4×C47#12311yescharacteristic
250C2×C4×C47#12311yescharacteristic
251C2×C4×C47#12311yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12311yescharacteristic
254C2×C4×C47#12311yescharacteristic
255C2×C4×C47#12311yescharacteristic
256C22⋊D47—24no—
257C22⋊D47—24no—
258C22⋊D47—24no—
259C22⋊D47—24no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—24no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—82no—
266C2×Dic47—82no—
267C2×Dic47—82no—
268C2×Dic47C2×C22⋊C414yes—
269D188—22no—
270D188—22no—
271D188—22no—
272D188—22no—
273C4×D47—24no—
274C4×D47—24no—
275C4×D47—24no—
276C4×D47—24no—
277C4×D47—88no—
278Dic94—22no—
279Dic94—22no—
280Dic94—22no—
281Dic94—22no—
282#20710—471nomaximal, Sylow
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47C22×C22⋊C411yescharacteristic
291C22×C47C2×#11711yescharacteristic
292C22×C47C2×#11711yescharacteristic
293C22×C47C2×#12311yescharacteristic
294C22×C47C2×#12311yescharacteristic
295C22×C47C2×#12311yescharacteristic
296C22×C47C2×#12311yescharacteristic
297C2×D47—24no—
298C2×D47—44no—
299C2×D47—82no—
300C2×D47—82no—
301C4×C47—44no—
302C4×C47—82no—
303C4×C47—82no—
304C4×C47#38111yescharacteristic
305C4×C47#38111yescharacteristic
306C4×C47#38111yescharacteristic
307C4×C47#38111yescharacteristic
308C4×C47#38111yescharacteristic
309C4×C47#38111yescharacteristic
310C4×C47#38111yescharacteristic
311C4×C47#38111yescharacteristic
312Dic47—24no—
313Dic47—44no—
314Dic47—82no—
315Dic47—82no—
316#3428—471no—
317C2×#410—471no—
318C2×#410—471no—
319#1828—478no—
320#1740—471no—
321#1740—471no—
322#1740—471no—
323#1740D4711yescharacteristic, complemented
324C2×C47—21no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47—21no—
331C2×C47C2×#38111yescharacteristic
332D47—44no—
333C22×#41—471no—
334#520—942no—
335#520—942no—
336#519—472no—
337#518—472no—
338#518—474no—
339C4×#41—942no—
340C4×#41—942no—
341C2×#117—471no—
342C2×#117—474no—
343C2×#117—471no—
344C2×#117—471no—
345C2×#117C2×D4711yescharacteristic
346C2×#117C2×D4711yescharacteristic
347C2×#117C2×D4711yescharacteristic
348#410—942no—
349#410—942no—
350#410—942no—
351#410—942no—
352C2×#99—474no—
353C2×#99—474no—
354#342—474no—
355#342—474no—
356#342—474no—
357#342C2×D4714yes—
358C47#2071011yescharacteristic, complemented, Sylow
359C2×#41—472no—
360C2×#41—472no—
361C2×#41—472no—
362C2×#41—472no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C2×#41—941no—
369C2×#41—941no—
370C2×#41—941no—
371C22×Q8—471no—
372C22×D4—472no—
373C22×D4—471no—
374C23×C4—472no—
375C23×C4C22×D4711yescharacteristic
376C4×Q8—944no—
377C4×Q8—944no—
378C4×D4—944no—
379C4×D4—948no—
380C4×D4—944no—
381C4×D4—948no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—472no—
393#117—472no—
394#117—478no—
395#117—944no—
396#117—944no—
397#117—941no—
398#117—941no—
399#117—941no—
400#117—941no—
401#117—941no—
402#117—941no—
403#117—941no—
404#117—941no—
405#117—941no—
406#117—941no—
407#117C4×D4712yes—
408#117C4×D4712yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—944no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C22⋊C4—472no—
417C2×C22⋊C4—478no—
418C2×C22⋊C4—472no—
419C2×C22⋊C4—472no—
420C2×C22⋊C4C22×D4712yes—
421C2×C22⋊C4C22×D4712yes—
422C2×C22⋊C4C22×D4712yes—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—944no—
427C2×C42—941no—
428C2×C42—941no—
429C2×C42—941no—
430#99—948no—
431#99—948no—
432C24—472no—
433C24C23×D4711yescharacteristic
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—
444#41—942no—
445#41—942no—
446#41—942no—
447#41—942no—
448#41—942no—
449#41—942no—
450C2×Q8—472no—
451C2×Q8—472no—
452C2×Q8—941no—
453C2×Q8—941no—
454C2×Q8—941no—
455C2×Q8—941no—
456C2×D4—474no—
457C2×D4—474no—
458C2×D4—472no—
459C2×D4—472no—
460C2×D4—942no—
461C2×D4—942no—
462C2×D4—942no—
463C2×D4—942no—
464C2×D4—941no—
465C2×D4—941no—
466C2×D4—941no—
467C2×D4—941no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—472no—
472C22×C4—474no—
473C22×C4—474no—
474C22×C4—948no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4C2×C4×D4711yescharacteristic
483C22×C4C2×C4×D4711yescharacteristic
484C22×C4#1062535011yescharacteristic
485C22×C4#1062535011yescharacteristic
486C22×C4#1062535011yescharacteristic
487C22×C4#1062535011yescharacteristic
488C22×C4D4×D4711yescharacteristic
489C22×C4D4×D4711yescharacteristic
490C22×C4D4×D4711yescharacteristic
491C22×C4D4×D4711yescharacteristic
492C22×C4#1062535211yescharacteristic
493C22×C4#1062535211yescharacteristic
494C22×C4#1062535411yescharacteristic
495C22×C4#1062535411yescharacteristic
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—948no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—1881no—
506C4⋊C4—1881no—
507C4⋊C4—1881no—
508C4⋊C4—1881no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—474no—
515C22⋊C4—948no—
516C22⋊C4—942no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C22⋊C4C2×C4×D4714yes—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C42—41no—
527C42—41no—
528C42—948no—
529C42—942no—
530C42—942no—
531C42—1881no—
532C42—1881no—
533C42—1881no—
534C42—1881no—
535C23—81no—
536C23—474no—
537C23—942no—
538C23—942no—
539C23—3762no—
540C23C22×C4×D4711yescharacteristic
541C23C2×D4×D4711yescharacteristic
542C23C2×D4×D4711yescharacteristic
543C23C2×#1062535211yescharacteristic
544C23C2×#1062535011yescharacteristic
545C23C2×#1062535011yescharacteristic
546C23C2×#1062535411yescharacteristic
547Q8—942no—
548Q8—942no—
549Q8—942no—
550Q8—942no—
551D4—944no—
552D4—944no—
553D4—944no—
554D4—944no—
555D4—942no—
556D4—942no—
557D4—942no—
558D4—942no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—474no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—944no—
569C2×C4—944no—
570C2×C4—944no—
571C2×C4—944no—
572C2×C4—944no—
573C2×C4—3768no—
574C2×C4—3762no—
575C2×C4—3762no—
576C2×C4—3762no—
577C2×C4—1882no—
578C2×C4—1882no—
579C2×C4C22⋊C4×D4711yescharacteristic
580C2×C4C22⋊C4×D4711yescharacteristic
581C2×C4C22⋊C4×D4711yescharacteristic
582C2×C4C22⋊C4×D4711yescharacteristic
583C2×C4#1309398111yescharacteristic
584C2×C4#1309398111yescharacteristic
585C2×C4#1309398111yescharacteristic
586C2×C4#1309398111yescharacteristic
587C2×C4#1309398211yescharacteristic
588C2×C4#1309398211yescharacteristic
589C2×C4#1309398211yescharacteristic
590C2×C4#1309398211yescharacteristic
591C2×C4#1309400611yescharacteristic
592C2×C4#1309400611yescharacteristic
593C2×C4#1309400611yescharacteristic
594C2×C4#1309400611yescharacteristic
595C2×C4#1309400611yescharacteristic
596C2×C4#1309400611yescharacteristic
597C2×C4#1309400611yescharacteristic
598C2×C4#1309400611yescharacteristic
599C2×C4#1309400911yescharacteristic
600C2×C4#1309400911yescharacteristic
601C2×C4#1309400911yescharacteristic
602C2×C4#1309400911yescharacteristic
603C2×C4#1309400911yescharacteristic
604C2×C4#1309400911yescharacteristic
605C2×C4#1309400911yescharacteristic
606C2×C4#1309400911yescharacteristic
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—944no—
615C22—3762no—
616C22—3762no—
617C22—1884no—
618C22C2×C22⋊C4×D4711yescharacteristic
619C22C2×#1309398111yescharacteristic
620C22C2×#1309398211yescharacteristic
621C22C2×#1309400611yescharacteristic
622C22C2×#1309400611yescharacteristic
623C22C2×#1309400911yescharacteristic
624C22C2×#1309400911yescharacteristic
625C4—44no—
626C4—82no—
627C4—82no—
628C4—944no—
629C4—3762no—
630C4—3762no—
631C4—1884no—
632C4#1568898511yescharacteristic
633C4#1568898511yescharacteristic
634C4#1568898511yescharacteristic
635C4#1568898511yescharacteristic
636C4#1568898511yescharacteristic
637C4#1568898511yescharacteristic
638C4#1568898511yescharacteristic
639C4#1568898511yescharacteristic
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—1884no—
648C2C2×#1568898511yescharacteristic
subgroupG/H
centerC4#15688985
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1740C2
socleC2×C47C2×#381
prime radicalC22×#10625350C22
cosocleC24×C47C24
hypercenter#1740D47
hypocenterC47#20710
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
4. #20243495C2semidirect
5. #20243121C2semidirect
6. #20243120C2semidirect
7. #20243120C2semidirect
8. C47×#1740C2semidirect
12. #15689600C4semidirect
13. #15689597C4semidirect
20. #117×D47C4semidirect
323. #1740D47semidirect
358. C47#20710semidirect

Maximal subgroups

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

subgroupindex
#202565892
C2×#156890962
#202434952
#202431212
#202431202
C47×#17402
#2071047