Finite Group Databasebeta

← #26121674

Subgroups — #26121674

Order 12032.

1192 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#20256589C211yesmaximal, characteristic
2C2×#15689105C211yesmaximal, characteristic
3#20251832C211yesmaximal, characteristic
4C2×#15688895C211yesmaximal, characteristic, complemented
5C2×#15688895C211yesmaximal, characteristic, complemented
6C2×#15688893C211yesmaximal, characteristic, complemented
7C2×C47×#344C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689604—22no—
12#15689603—22no—
13#15689600—21no—
14#15689597—21no—
15#15689596C414yes—
16C4×#10625350—22no—
17#15689591—22no—
18C2×#13093983C2211yescharacteristic
19#117×D47—22no—
20#15689105—22no—
21#15689105C414yescomplemented
22C2×#13093942—21no—
23C2×#13093940—21no—
24#15689091C414yescomplemented
25#15689089—22no—
26#15689086—22no—
27#15688895—22no—
28#15688895—22no—
29#15688893—22no—
30C22×M16×C47C2211yescharacteristic
31C22×M16×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C47×#344—22no—
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×#10625350C2×C412yes—
43C2×#10625350C2×C412yes—
44C2×#10625350D412yes—
45C2×#10625350Q812yes—
46C22×Dic94D411yescharacteristic
47C22×D188D411yescharacteristic
48C22×C22⋊D47C2×C412yes—
49C22×C4×D47D412yes—
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×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329C2×C412yescomplemented
62C22×C47⋊C8—21no—
63C22×C47⋊C8C2×C412yescomplemented
64C4×Dic94—24no—
65#13093989—24no—
66C4×D188—24no—
67#13093986—24no—
68C4×C22⋊D47—28no—
69(C22⋊D47)⋊C4—28no—
70#13093983—21no—
71#13093983—21no—
72#13093983D412yes—
73#13093983D412yes—
74#13093982—24no—
75#13093981—24no—
76#13093980—24no—
77C2×C4⋊Dic47—21no—
78C4⋊C4×D47—24no—
79C2×C22⋊Dic47C2×C412yes—
80C22⋊C4×D47—24no—
81C2×C4×Dic47—21no—
82C42×D47—24no—
83#13093942—24no—
84#13093940—24no—
85(C2×D47)⋊C8—28no—
86C23×C4×C47C2311yescharacteristic
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47C2×C412yescomplemented
98C2×M16×C47C2×C412yescomplemented
99C22×C8×C47—21no—
100C22×C8×C47—21no—
101#117×C47—21no—
102#117×C47—21no—
103#117×C47D412yes—
104#117×C47D412yes—
105C2×C4⋊C4×C47—21no—
106C2×C22⋊C4×C47C2×C412yes—
107C2×C42×C47—21no—
108C24×C47C22×C411yescharacteristic
109C23×D47C22⋊C412yes—
110C22×C4×C47—22no—
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
124C22×C4×C47#4111yescharacteristic
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47C4214yes—
130C2×C22⋊D47C4⋊C414yes—
131C22×Dic47—22no—
132C22×Dic47C22⋊C412yes—
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#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
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—28no—
160C2×C4×D47C22⋊C414yes—
161C2×C4×D47C4⋊C414yes—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94C22⋊C412yes—
167C2×Dic94C4⋊C412yes—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—41no—
173M16×C47—41no—
174M16×C47—41no—
175M16×C47—41no—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—41no—
179C2×C8×C47—41no—
180C2×C8×C47—41no—
181C2×C8×C47—41no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47C22⋊C414yes—
186C42×C47—22no—
187C42×C47—22no—
188C22⋊Dic47—22no—
189C22⋊Dic47C22⋊C414yes—
190(C2×D47)⋊C4—28no—
191C4⋊Dic47—22no—
192C4⋊Dic47—22no—
193Dic47⋊C4—28no—
194C4×Dic47—28no—
195C4×Dic47—22no—
196C4×Dic47—22no—
197#10625329—22no—
198#10625329—22no—
199#10625329—41no—
200#10625329—41no—
201#10625329—41no—
202#10625329—41no—
203#10625329—41no—
204#10625329—41no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C2×C47⋊C8—41no—
210C2×C47⋊C8—41no—
211C23×C47—81no—
212C23×C47C2×C4211yescharacteristic
213C23×C47C2×C22⋊C411yescharacteristic
214C23×C47C2×C22⋊C411yescharacteristic
215C23×C47C2×C22⋊C411yescharacteristic
216C23×C47C2×C4⋊C411yescharacteristic
217C23×C47#11711yescharacteristic
218C23×C47#11711yescharacteristic
219C22×D47—22no—
220C22×D47—22no—
221C22×D47—82no—
222C22×D47#9514yes—
223C2×C4×C47—24no—
224C2×C4×C47—82no—
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C4⋊C411yescharacteristic
228C2×C4×C47C2×C4⋊C411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C4×D411yescharacteristic
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47#12011yescharacteristic
238C2×C4×C47#12011yescharacteristic
239C2×C4×C47#12011yescharacteristic
240C2×C4×C47#12011yescharacteristic
241C2×C4×C47#12111yescharacteristic
242C2×C4×C47#12111yescharacteristic
243C2×C4×C47#12111yescharacteristic
244C2×C4×C47#12111yescharacteristic
245C2×C4×C47C22⋊Q811yescharacteristic
246C2×C4×C47C22⋊Q811yescharacteristic
247C2×C4×C47C22⋊Q811yescharacteristic
248C2×C4×C47C22⋊Q811yescharacteristic
249C2×C4×C47#12311yescharacteristic
250C2×C4×C47#12311yescharacteristic
251C2×C4×C47#12311yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C22⋊D47—24no—
254C22⋊D47—24no—
255C22⋊D47—24no—
256C22⋊D47—24no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—24no—
260C2×Dic47—82no—
261C2×Dic47#9514yes—
262D188—22no—
263D188—22no—
264D188—22no—
265D188—22no—
266C4×D47—24no—
267C4×D47—24no—
268C4×D47—24no—
269C4×D47—24no—
270C4×D47—88no—
271Dic94—22no—
272Dic94—22no—
273Dic94—22no—
274Dic94—22no—
275C8×C47—42no—
276C8×C47—42no—
277C47⋊C8—42no—
278C47⋊C8—42no—
279#10756—471nomaximal, Sylow
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47C2×#9511yescharacteristic
288C22×C47C4×C22⋊C411yescharacteristic
289C22×C47C4×C22⋊C411yescharacteristic
290C22×C47#37911yescharacteristic
291C22×C47#38011yescharacteristic
292C22×C47#38011yescharacteristic
293C22×C47#38111yescharacteristic
294C2×D47—24no—
295C2×D47—44no—
296C2×D47—44no—
297C2×D47—82no—
298C4×C47—44no—
299C4×C47#38511yescharacteristic
300C4×C47#38511yescharacteristic
301C4×C47#38511yescharacteristic
302C4×C47#38511yescharacteristic
303C4×C47#38611yescharacteristic
304C4×C47#38611yescharacteristic
305C4×C47#38611yescharacteristic
306C4×C47#38611yescharacteristic
307Dic47—24no—
308Dic47—44no—
309#3428—471no—
310C2×#413—471no—
311#2879—471no—
312C2×#344—471no—
313C2×#344—471no—
314C2×#344—471no—
315C2×#344D4711yescharacteristic, complemented
316C2×C47—21no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47C22⋊#9511yescharacteristic
324D47—44no—
325C22×#41—471no—
326C22×M16—471no—
327C22×M16—471no—
328C22×M16C2×D4711yescharacteristic
329C22×M16C2×D4711yescharacteristic
330#520—942no—
331#520—942no—
332#519—941no—
333#518—474no—
334#518—941no—
335C4×#41—942no—
336C4×#41—942no—
337C2×#117—471no—
338C2×#117—942no—
339C2×#117C2×D4711yescharacteristic
340#413—474no—
341#413—942no—
342C2×#101—941no—
343C2×#100—941no—
344#408—474no—
345#408—942no—
346#407—942no—
347#344—22no—
348#344—942no—
349#344—942no—
350#344—942no—
351C47#1075611yescharacteristic, complemented, Sylow
352C2×#41—472no—
353C2×#41—472no—
354C2×#41—472no—
355C2×#41—472no—
356C2×#41—941no—
357C2×#41—941no—
358C2×#41—941no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C22×Q8—471no—
365C22×D4—472no—
366C22×D4—471no—
367C23×C4—472no—
368C23×C4C22×D4711yescharacteristic
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—472no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16—941no—
390C2×M16—941no—
391C2×M16C4×D4712yescomplemented
392C2×M16C4×D4712yescomplemented
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—472no—
396C22×C8—941no—
397C4×Q8—944no—
398C4×Q8—944no—
399C4×D4—944no—
400C4×D4—948no—
401C4×D4—944no—
402C4×D4—948no—
403#117—21no—
404#117—21no—
405#117—472no—
406#117—472no—
407#117—944no—
408#117—944no—
409#117—944no—
410#117—941no—
411#117—941no—
412#117D18812yes—
413#117C22⋊D4712yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—944no—
416C2×C4⋊C4—941no—
417C2×C22⋊C4—472no—
418C2×C22⋊C4—944no—
419C2×C22⋊C4C4×D4712yes—
420C2×C42—21no—
421C2×C42—944no—
422C2×C42—941no—
423#101—944no—
424#100—944no—
425C22⋊C8—948no—
426C24—472no—
427C24C2×C4×D4711yescharacteristic
428#41—942no—
429#41—942no—
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—
442#41—942no—
443#41—942no—
444C2×Q8—472no—
445C2×Q8—472no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×D4—474no—
451C2×D4—474no—
452C2×D4—472no—
453C2×D4—472no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4—942no—
458C2×D4—941no—
459C2×D4—941no—
460C2×D4—941no—
461C2×D4—941no—
462C22×C4—22no—
463C22×C4—472no—
464C22×C4—474no—
465C22×C4—474no—
466C22×C4—948no—
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×D18811yescharacteristic
475C22×C4#1062535011yescharacteristic
476C22×C4#1062535011yescharacteristic
477C22×C4D4×D4711yescharacteristic
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4711yescharacteristic
480C22×C4D4×D4711yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4#1062535211yescharacteristic
483C22×C4Q8×D4711yescharacteristic
484C22×C4#1062535411yescharacteristic
485C22×C4C2×C22⋊D4711yescharacteristic
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—41no—
493M16—41no—
494M16—942no—
495M16—942no—
496M16—1881no—
497M16—1881no—
498M16—1881no—
499M16—1881no—
500M16—1881no—
501M16—1881no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—942no—
509C2×C8—942no—
510C2×C8—942no—
511C2×C8—942no—
512C2×C8—1881no—
513C2×C8—1881no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—948no—
517C4⋊C4—942no—
518C4⋊C4—942no—
519C22⋊C4—22no—
520C22⋊C4—474no—
521C22⋊C4—948no—
522C22⋊C4—942no—
523C22⋊C4(C2×D47)⋊C414yes—
524C42—22no—
525C42—22no—
526C42—948no—
527C42—942no—
528C42—942no—
529C23—81no—
530C23—474no—
531C23—942no—
532C23—942no—
533C23—3762no—
534C23C42×D4711yescharacteristic
535C23C22⋊C4×D4711yescharacteristic
536C23C22⋊C4×D4711yescharacteristic
537C23C2×(C2×D47)⋊C411yescharacteristic
538C23C4⋊C4×D4711yescharacteristic
539C23#1309398111yescharacteristic
540C23#1309398211yescharacteristic
541Q8—942no—
542Q8—942no—
543Q8—942no—
544Q8—942no—
545D4—944no—
546D4—944no—
547D4—944no—
548D4—944no—
549D4—942no—
550D4—942no—
551D4—942no—
552D4—942no—
553C2×C4—24no—
554C2×C4—82no—
555C2×C4—474no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—944no—
559C2×C4—944no—
560C2×C4—944no—
561C2×C4—944no—
562C2×C4—944no—
563C2×C4—3768no—
564C2×C4—3762no—
565C2×C4C22⋊C4×D4711yescharacteristic
566C2×C4C22⋊C4×D4711yescharacteristic
567C2×C4C4⋊C4×D4711yescharacteristic
568C2×C4C4⋊C4×D4711yescharacteristic
569C2×C4(C22⋊D47)⋊C411yescharacteristic
570C2×C4(C22⋊D47)⋊C411yescharacteristic
571C2×C4C4×C22⋊D4711yescharacteristic
572C2×C4C4×C22⋊D4711yescharacteristic
573C2×C4#1309398611yescharacteristic
574C2×C4#1309398611yescharacteristic
575C2×C4C4×D18811yescharacteristic
576C2×C4C4×D18811yescharacteristic
577C2×C4#1309399211yescharacteristic
578C2×C4#1309399211yescharacteristic
579C2×C4#1309399411yescharacteristic
580C2×C4#1309399411yescharacteristic
581C2×C4#1309399511yescharacteristic
582C2×C4#1309399711yescharacteristic
583C2×C4#1309399711yescharacteristic
584C2×C4#1309399911yescharacteristic
585C2×C4#1309400011yescharacteristic
586C2×C4#1309400211yescharacteristic
587C2×C4#1309400211yescharacteristic
588C2×C4#1309400411yescharacteristic
589C2×C4#1309400611yescharacteristic
590C2×C4#1309400611yescharacteristic
591C2×C4#1309400911yescharacteristic
592C2×C4#1309400911yescharacteristic
593C8—42no—
594C8—42no—
595C8—1882no—
596C8—1882no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—944no—
605C22—3762no—
606C22—1884no—
607C22—1884no—
608C22#95×D4711yescharacteristic
609C22#1568897011yescharacteristic
610C22C4×(C2×D47)⋊C411yescharacteristic
611C22#1568897811yescharacteristic
612C22#1568898011yescharacteristic
613C22#1568898211yescharacteristic
614C22#1568898511yescharacteristic
615C4—44no—
616C4—944no—
617C4—1884no—
618C4#1568899411yescharacteristic
619C4#1568899411yescharacteristic
620C4#1568899711yescharacteristic
621C4#1568899711yescharacteristic
622C4#1568899911yescharacteristic
623C4#1568899911yescharacteristic
624C4#1568900111yescharacteristic
625C4#1568900111yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—1884no—
634C2(C2×D47)⋊#9511yescharacteristic
subgroupG/H
centerC4#15689001
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC2×C47C22⋊#95
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47#10756
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#15688895C2semidirect
5. C2×#15688895C2semidirect
6. C2×#15688893C2semidirect
7. C2×C47×#344C2semidirect
21. #15689105C4semidirect
24. #15689091C4semidirect
61. C2×#10625329C2×C4semidirect
63. C22×C47⋊C8C2×C4semidirect
97. C2×M16×C47C2×C4semidirect
98. C2×M16×C47C2×C4semidirect
315. C2×#344D47semidirect
351. C47#10756semidirect
391. C2×M16C4×D47semidirect
392. C2×M16C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202565892
C2×#156891052
#202518322
C2×#156888952
C2×#156888932
C2×C47×#3442
#1075647