Finite Group Databasebeta

← #26121815

Subgroups — #26121815

Order 12032.

1186 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic
3C2×#15689122C211yesmaximal, characteristic
4C2×#15688893C211yesmaximal, characteristic, complemented
5C2×#15688892C211yesmaximal, characteristic, complemented
6C2×C47⋊#338C211yesmaximal, characteristic, complemented
7C47×#1736C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9#15689889—22no—
10#15689889—22no—
11#15689889—22no—
12#15689889C414yescomplemented
13C2×#13094032—22no—
14C2×#13094030—22no—
15C22×#10625329C2211yescharacteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×M16×D47—22no—
19#15689141—22no—
20#15689141C414yescomplemented
21C2×#13093952—22no—
22#15689122—22no—
23#15689122—22no—
24C2×#13093947C412yescomplemented
25C2×#13093944C412yescomplemented
26#15688893—22no—
27#15688892—22no—
28C47⋊#338—22no—
29C22×M16×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C47×#340—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—
49#13094032—28no—
50#13094032—28no—
51#13094030—28no—
52#13094030—28no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329C2×C412yes—
68C2×#10625329C2×C412yes—
69C2×#10625329D412yes—
70C2×#10625329D412yes—
71C2×#10625324—24no—
72M16×D47—28no—
73M16×D47—28no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C22×C47⋊C8C2×C412yes—
77C2×C8×D47—24no—
78#13093952—28no—
79#13093947—24no—
80#13093944—24no—
81C23×C4×C47—21no—
82C23×C4×C47C2311yescharacteristic
83C2×M16×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47C2×C412yes—
88C2×M16×C47D412yes—
89C22×C8×C47D412yes—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47—21no—
93#117×C47C2×C412yes—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47C2×C412yes—
101C2×C22⋊C4×C47—21no—
102C2×C42×C47—21no—
103C24×C47#4111yescharacteristic
104C23×D47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—41no—
107C22×C4×C47—41no—
108C22×C4×C47—41no—
109C22×C4×C47—82no—
110C22×C4×C47C22×C411yescharacteristic
111C22×C4×C47C22×C411yescharacteristic
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
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
124C2×C22⋊D47—22no—
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C22×Dic47—21no—
131#10625350—22no—
132#10625350—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#10625350C22⋊C414yes—
144#10625350C22⋊C414yes—
145#10625350C4⋊C414yes—
146#10625350C4⋊C414yes—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188C4212yes—
151C2×D188C22⋊C412yes—
152C2×D188C4⋊C412yes—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94—21no—
162C2×Dic94C4212yes—
163C2×Dic94C22⋊C412yes—
164C2×Dic94C4⋊C412yes—
165M16×C47—22no—
166M16×C47—22no—
167M16×C47—22no—
168M16×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47C22⋊C414yes—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—41no—
176C4⋊C4×C47—41no—
177C4⋊C4×C47—41no—
178C22⋊C4×C47—22no—
179C22⋊C4×C47—41no—
180C42×C47—22no—
181C42×C47—41no—
182#10625329—22no—
183#10625329—22no—
184#10625329—22no—
185#10625329—22no—
186#10625329—22no—
187#10625329—41no—
188#10625329—41no—
189#10625329—41no—
190#10625329—41no—
191#10625329—41no—
192#10625329—41no—
193#10625329C22⋊C414yes—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—22no—
201C2×C47⋊C8—41no—
202C2×C47⋊C8—41no—
203#10625324—216no—
204C8×D47—216no—
205C23×C47—41no—
206C23×C47—41no—
207C23×C47#11711yescharacteristic
208C23×C47C4×D411yescharacteristic
209C23×C47C4×D411yescharacteristic
210C23×C47#12111yescharacteristic
211C23×C47C22⋊Q811yescharacteristic
212C23×C47#12311yescharacteristic
213C23×C47#12311yescharacteristic
214C22×D47—22no—
215C22×D47—22no—
216C22×D47—22no—
217C22×D47—81no—
218C22×D47—81no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—81no—
222C2×C4×C47—81no—
223C2×C4×C47—82no—
224C2×C4×C47—82no—
225C2×C4×C47—82no—
226C2×C4×C47C2×C4211yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
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×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47#12011yescharacteristic
243C2×C4×C47#12011yescharacteristic
244C2×C4×C47#12011yescharacteristic
245C2×C4×C47#12011yescharacteristic
246C2×C4×C47#12111yescharacteristic
247C2×C4×C47#12111yescharacteristic
248C2×C4×C47#12111yescharacteristic
249C2×C4×C47C22⋊Q811yescharacteristic
250C2×C4×C47C22⋊Q811yescharacteristic
251C2×C4×C47C22⋊Q811yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12311yescharacteristic
254C22⋊D47—24no—
255C22⋊D47—24no—
256C22⋊D47—24no—
257C22⋊D47—24no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261D188—22no—
262D188—22no—
263D188—22no—
264D188#9514yes—
265C4×D47—24no—
266C4×D47—24no—
267C4×D47—24no—
268C4×D47—24no—
269Dic94—22no—
270Dic94—22no—
271Dic94—22no—
272Dic94#9514yes—
273C8×C47—24no—
274C47⋊C8—24no—
275C47⋊C8—42no—
276C47⋊C8—42no—
277#10784—471nomaximal, Sylow
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47—21no—
283C22×C47—21no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47C4×C22⋊C411yescharacteristic
289C22×C47#38011yescharacteristic
290C22×C47#38111yescharacteristic
291C22×C47#38511yescharacteristic
292C22×C47#38511yescharacteristic
293C22×C47#38611yescharacteristic
294C22×C47#38611yescharacteristic
295C2×D47—24no—
296C2×D47—42no—
297C2×D47—42no—
298C2×D47—82no—
299C2×D47—82no—
300C4×C47—82no—
301C4×C47—82no—
302C4×C47C2×#9511yescharacteristic
303C4×C47C4×C22⋊C411yescharacteristic
304C4×C47#37911yescharacteristic
305C4×C47#38011yescharacteristic
306C4×C47#38511yescharacteristic
307C4×C47#38511yescharacteristic
308C4×C47#38611yescharacteristic
309C4×C47#38611yescharacteristic
310Dic47—24no—
311C2×#568—471no—
312C2×#421—471no—
313C2×#417—471no—
314C2×#344—471no—
315C2×#343—471no—
316#1736D4711yescharacteristic, complemented
317C2×#338—471no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47C22⋊#9511yescharacteristic
325C2×C47#190211yescharacteristic
326C2×C47#190311yescharacteristic
327D47—44no—
328C22×#41—471no—
329#568—474no—
330#568—942no—
331#568—942no—
332#568—942no—
333C2×#131—942no—
334C2×#131—942no—
335C22×M16—471no—
336C22×M16—471no—
337C22×M16—471no—
338C22×M16—942no—
339C22×M16C2×D4711yescharacteristic
340C2×#117C2×D4711yescharacteristic
341C22×C4⋊C4C2×D4711yescharacteristic
342#421—474no—
343#421—942no—
344C2×#104—942no—
345#417—942no—
346#417—942no—
347C2×#103—472no—
348C2×#102—472no—
349#344—942no—
350#343—942no—
351#340—22no—
352#338—942no—
353C47#1078411yescharacteristic, complemented, Sylow
354C2×#41—472no—
355C2×#41—472no—
356C2×#41—472no—
357C2×#41—472no—
358C2×#41—472no—
359C2×#41—472no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C22×Q8—471no—
367C22×D4—471no—
368C22×D4—941no—
369C23×C4—21no—
370C23×C4—941no—
371C23×C4C22×D4711yescharacteristic
372#131—948no—
373#131—948no—
374#131—948no—
375#131—948no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—472no—
381C2×M16—472no—
382C2×M16—472no—
383C2×M16—472no—
384C2×M16—944no—
385C2×M16—948no—
386C2×M16—948no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16—941no—
390C2×M16—941no—
391C2×M16—941no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16—941no—
396C2×M16—941no—
397C2×M16—941no—
398C2×M16—941no—
399C2×M16—941no—
400C2×M16—941no—
401C2×M16C4×D4712yes—
402C2×M16D18812yes—
403C22×C8—472no—
404C22×C8—944no—
405C22×C8—941no—
406C22×C8—941no—
407C22×C8C22⋊D4712yes—
408#117—21no—
409#117—21no—
410#117—21no—
411#117C4×D4712yes—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4C4×D4712yes—
419C2×C22⋊C4—21no—
420C2×C42—21no—
421#104—948no—
422#103—944no—
423#102—944no—
424C24—941no—
425C24#1062535211yescharacteristic
426#41—474no—
427#41—474no—
428#41—474no—
429#41—474no—
430#41—942no—
431#41—942no—
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—
442C2×Q8—472no—
443C2×Q8—472no—
444C2×Q8—472no—
445C2×Q8—941no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×D4—472no—
449C2×D4—472no—
450C2×D4—472no—
451C2×D4—942no—
452C2×D4—942no—
453C2×D4—942no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4—941no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—82no—
465C22×C4—941no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4C2×C4×D4711yescharacteristic
473C22×C4C2×C4×D4711yescharacteristic
474C22×C4C2×C4×D4711yescharacteristic
475C22×C4C2×D18811yescharacteristic
476C22×C4#1062535011yescharacteristic
477C22×C4#1062535011yescharacteristic
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4711yescharacteristic
480C22×C4D4×D4711yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4D4×D4711yescharacteristic
483C22×C4Q8×D4711yescharacteristic
484C22×C4#1062535411yescharacteristic
485C22×C4C2×C22⋊D4711yescharacteristic
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—474no—
491M16—9416no—
492M16—942no—
493M16—942no—
494M16—942no—
495M16—942no—
496M16—942no—
497M16—1881no—
498M16—1881no—
499M16—1881no—
500M16—1881no—
501M16—1881no—
502M16—1881no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—9416no—
506C2×C8—942no—
507C2×C8—942no—
508C2×C8—942no—
509C2×C8—942no—
510C2×C8—942no—
511C2×C8—942no—
512C2×C8—942no—
513C2×C8—1881no—
514C2×C8—1881no—
515C2×C8(C2×D47)⋊C414yes—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C22⋊C4—22no—
523C22⋊C4—41no—
524C42—22no—
525C42—41no—
526C23—41no—
527C23—41no—
528C23—942no—
529C23—942no—
530C23—942no—
531C23—3761no—
532C23—3761no—
533C23#1309398211yescharacteristic
534C23(C22⋊D47)⋊C411yescharacteristic
535C23(C22⋊D47)⋊C411yescharacteristic
536C23#1309399511yescharacteristic
537C23#1309400411yescharacteristic
538C23#1309400611yescharacteristic
539C23#1309400611yescharacteristic
540Q8—474no—
541Q8—942no—
542Q8—942no—
543Q8—942no—
544D4—474no—
545D4—944no—
546D4—944no—
547D4—944no—
548D4—944no—
549D4—942no—
550D4—942no—
551D4—942no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—81no—
555C2×C4—81no—
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×C4C42×D4711yescharacteristic
567C2×C4C22⋊C4×D4711yescharacteristic
568C2×C4C22⋊C4×D4711yescharacteristic
569C2×C4C22⋊C4×D4711yescharacteristic
570C2×C4C22⋊C4×D4711yescharacteristic
571C2×C4C2×(C2×D47)⋊C411yescharacteristic
572C2×C4C4⋊C4×D4711yescharacteristic
573C2×C4C4⋊C4×D4711yescharacteristic
574C2×C4C4⋊C4×D4711yescharacteristic
575C2×C4#1309398111yescharacteristic
576C2×C4C4×C22⋊D4711yescharacteristic
577C2×C4C4×C22⋊D4711yescharacteristic
578C2×C4#1309398611yescharacteristic
579C2×C4#1309398611yescharacteristic
580C2×C4C4×D18811yescharacteristic
581C2×C4C4×D18811yescharacteristic
582C2×C4#1309399211yescharacteristic
583C2×C4#1309399211yescharacteristic
584C2×C4#1309399411yescharacteristic
585C2×C4#1309399411yescharacteristic
586C2×C4#1309399711yescharacteristic
587C2×C4#1309399711yescharacteristic
588C2×C4#1309399911yescharacteristic
589C2×C4#1309400011yescharacteristic
590C2×C4#1309400211yescharacteristic
591C2×C4#1309400211yescharacteristic
592C2×C4#1309400911yescharacteristic
593C2×C4#1309400911yescharacteristic
594C8—24no—
595C8—944no—
596C8—1882no—
597C8—1882no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—944no—
609C22—3762no—
610C22—3762no—
611C22—1882no—
612C22—1882no—
613C22#1568897011yescharacteristic
614C22#1568898011yescharacteristic
615C22#1568898511yescharacteristic
616C22#1568899711yescharacteristic
617C22#1568899711yescharacteristic
618C22#1568899911yescharacteristic
619C22#1568899911yescharacteristic
620C4—82no—
621C4—82no—
622C4—944no—
623C4#95×D4711yescharacteristic
624C4C4×(C2×D47)⋊C411yescharacteristic
625C4#1568897811yescharacteristic
626C4#1568898211yescharacteristic
627C4#1568899411yescharacteristic
628C4#1568899411yescharacteristic
629C4#1568900111yescharacteristic
630C4#1568900111yescharacteristic
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—1884no—
638C2(C2×D47)⋊#9511yescharacteristic
639C2#2024385811yescharacteristic
640C2#2024386511yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1736C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1736D47
hypocenterC47#10784
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#15688893C2semidirect
5. C2×#15688892C2semidirect
6. C2×C47⋊#338C2semidirect
7. C47×#1736C2semidirect
12. #15689889C4semidirect
20. #15689141C4semidirect
24. C2×#13093947C4semidirect
25. C2×#13093944C4semidirect
316. #1736D47semidirect
353. C47#10784semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156891412
C2×#156891222
C2×#156888932
C2×#156888922
C2×C47⋊#3382
C47×#17362
#1078447