Finite Group Databasebeta

← #26217637

Subgroups — #26217637

Order 12032.

2234 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094052C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic, complemented
3C2×#15689125C211yesmaximal, characteristic, complemented
4C2×#15689129C211yesmaximal, characteristic, complemented
5#20245878C211yesmaximal, characteristic, complemented
6#20243735C214yesmaximal, complemented
7#20243721C214yesmaximal, complemented
8#20243108C211yesmaximal, characteristic, complemented
9C47×#1728C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C23×D188C2211yescharacteristic
12C23×C4×D47—21no—
13C2×#13094052—24no—
14C2×#13094052—24no—
15C2×#13094052C418yescomplemented
16C22×#10625325C2212yes—
17C22×D376C2212yes—
18C2×C4×D188—24no—
19C2×C4×D188—24no—
20C2×C4×D188—22no—
21C2×C4×D188C2214yes—
22C2×#13093983C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×(C2×D47)⋊C4—21no—
25#15689129—24no—
26#15689125—24no—
27C2×#13093949C2212yescomplemented
28C2×#13093946C2214yes—
29C2×#13093946C2212yescomplemented
30#15689029C2212yescomplemented
31#15689025C2212yescomplemented
32#15689002—21no—
33#15689002—21no—
34C4×(C2×D47)⋊C4—22no—
35#15688886C2214yescomplemented
36C22×M16×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C47×#336C2214yescomplemented
40C24×D47—21no—
41C2×#10625350—22no—
42C2×#10625350—22no—
43C2×#10625350—22no—
44C2×#10625350—22no—
45C2×#10625350—22no—
46C2×#10625350C2×C414yescomplemented
47C22×Dic94C2311yescharacteristic
48C22×D188—21no—
49C22×D188—22no—
50C22×D188—22no—
51C22×D188—22no—
52C22×D188C2×C414yes—
53C22×D188D414yes—
54C22×D188D414yes—
55C22×D188C2311yescharacteristic
56C22×D188C2312yes—
57C22×C22⋊D47—21no—
58C23×Dic47—21no—
59C22×C4×D47—28no—
60C22×C4×D47—21no—
61C22×C4×D47—24no—
62C22×C4×D47—48no—
63#13094052—232no—
64C2×#10625325—24no—
65C2×#10625325—24no—
66C2×#10625325C2×C418yescomplemented
67C2×D376—24no—
68C2×D376—24no—
69C2×D376C2×C418yescomplemented
70C4×D188—216no—
71C4×D188—28no—
72C4×D188—28no—
73#13093983—22no—
74#13093983—22no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—22no—
77C2×C4⋊Dic47D414yes—
78C2×C4⋊Dic47C2312yes—
79C2×C4⋊Dic47C2312yes—
80C2×C22⋊Dic47—21no—
81C2×(C2×D47)⋊C4—28no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×C4×Dic47—21no—
86#13093949—24no—
87#13093946—28no—
88#13093946—24no—
89C47⋊#95—22no—
90C47⋊#95—22no—
91C23×C4×C47D411yescharacteristic
92C23×C4×C47D411yescharacteristic
93C23×C4×C47C2311yescharacteristic
94C2×M16×C47—22no—
95C2×M16×C47—22no—
96C2×M16×C47—22no—
97C2×M16×C47—22no—
98C2×M16×C47—22no—
99C2×M16×C47C2×C414yescomplemented
100C22×C8×C47C2312yes—
101C22×C8×C47C2312yes—
102C2×C42×C47—22no—
103C2×C42×C47—22no—
104C2×C42×C47D412yes—
105C2×C42×C47C2312yes—
106C24×C47C2×D411yescharacteristic
107C23×D47—24no—
108C23×D47—24no—
109C23×D47—24no—
110C23×D47—22no—
111C23×D47—21no—
112C23×D47—44no—
113C23×D47—44no—
114C22×C4×C47—22no—
115C22×C4×C47—24no—
116C22×C4×C47—22no—
117C22×C4×C47—42no—
118C22×C4×C47C22×C412yes—
119C22×C4×C47C2×D412yes—
120C22×C4×C47C2×D412yes—
121C22×C4×C47C2×D412yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D412yes—
125C22×C4×C47#4112yes—
126C22×C4×C47#4112yes—
127C22×C4×C47C2411yescharacteristic
128C2×C22⋊D47—24no—
129C2×C22⋊D47—42no—
130C2×C22⋊D47—42no—
131C22×Dic47—24no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—44no—
136#10625350—28no—
137#10625350—28no—
138#10625350—44no—
139#10625350—44no—
140C2×D188—28no—
141C2×D188—24no—
142C2×D188—24no—
143C2×D188—28no—
144C2×D188—24no—
145C2×D188—28no—
146C2×D188—22no—
147C2×D188—22no—
148C2×D188—22no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188C22⋊C4116yescomplemented
155C2×D188C22×C414yes—
156C2×D188C22×C412yescomplemented
157C2×D188C2×D414yes—
158C2×D188C2×D414yes—
159C2×C4×D47—216no—
160C2×C4×D47—24no—
161C2×C4×D47—432no—
162C2×C4×D47—48no—
163C2×C4×D47—42no—
164C2×C4×D47—42no—
165C2×C4×D47—48no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94—21no—
169C2×Dic94—21no—
170C2×Dic94—21no—
171C2×Dic94C22×C412yescomplemented
172M16×C47—28no—
173M16×C47—44no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47C22×C414yescomplemented
180C42×C47—24no—
181C42×C47—22no—
182C42×C47—22no—
183C22⋊Dic47—42no—
184(C2×D47)⋊C4—216no—
185(C2×D47)⋊C4—44no—
186(C2×D47)⋊C4—44no—
187C4⋊Dic47—24no—
188C4⋊Dic47—22no—
189C4⋊Dic47—22no—
190C4⋊Dic47—22no—
191C4⋊Dic47C2×D414yes—
192C4×Dic47—42no—
193D376—216no—
194#10625325—216no—
195C23×C47—22no—
196C23×C47—22no—
197C23×C47C4×D412yes—
198C23×C47#12012yes—
199C23×C47#12112yes—
200C23×C47C22×D411yescharacteristic
201C22×D47—24no—
202C22×D47—24no—
203C22×D47—24no—
204C22×D47—216no—
205C22×D47—22no—
206C22×D47—48no—
207C22×D47—416no—
208C22×D47—48no—
209C22×D47—416no—
210C22×D47—44no—
211C22×D47—44no—
212C22×D47—41no—
213C22×D47—41no—
214C22×D47—42no—
215C22×D47—42no—
216C2×C4×C47—28no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—44no—
223C2×C4×C47C2×C22⋊C414yes—
224C2×C4×C47C4×D414yes—
225C2×C4×C47C4×D412yes—
226C2×C4×C47#12012yes—
227C2×C4×C47#12114yes—
228C2×C4×C47#12112yes—
229C2×C4×C47#12314yes—
230C2×C4×C47AGL(1,ℤ/8)14yescomplemented
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C22⋊D47—48no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—48no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—44no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247D188—22no—
248D188—24no—
249D188—22no—
250D188—24no—
251D188—24no—
252D188—216no—
253D188—41no—
254D188—41no—
255D188C2×C22⋊C418yes—
256C4×D47—432no—
257C4×D47—48no—
258Dic94—22no—
259Dic94—22no—
260Dic94—41no—
261Dic94—41no—
262C8×C47—24no—
263C8×C47—42no—
264#20925—471nomaximal, Sylow
265C22×C47—24no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—24no—
269C22×C47#38614yes—
270C22×C47C2×C4×D411yescharacteristic
271C22×C47C2×#12011yescharacteristic
272C22×C47C2×#12111yescharacteristic
273C22×C47C2×AGL(1,ℤ/8)12yes—
274C22×C47#57512yes—
275C2×D47—28no—
276C2×D47—432no—
277C2×D47—48no—
278C2×D47—44no—
279C2×D47—44no—
280C2×D47—48no—
281C2×D47—44no—
282C2×D47—42no—
283C2×D47—81no—
284C2×D47—81no—
285C2×D47—82no—
286C4×C47—24no—
287C4×C47—42no—
288C4×C47#38614yes—
289C4×C47C22×C22⋊C411yescharacteristic
290C4×C47C2×C4×D411yescharacteristic
291C4×C47C2×#12111yescharacteristic
292C4×C47C2×#12311yescharacteristic
293Dic47—44no—
294Dic47—42no—
295Dic47—82no—
296C22×AGL(1,ℤ/8)—471no—
297C22×C4×D4—471no—
298C2×#417—471no—
299C2×#418—471no—
300#2297—471no—
301#1879—474no—
302#1877—474no—
303#1736—471no—
304#1728D4711yescharacteristic, complemented
305C2×C47—24no—
306C2×C47C2×#38611yescharacteristic
307C2×C47C4×AGL(1,ℤ/8)12yes—
308C2×C47#300311yescharacteristic
309C2×C47#300511yescharacteristic
310C2×C47#303612yes—
311D47—48no—
312D47—82no—
313C22×#41—471no—
314C23×D4—471no—
315C24×C4—941no—
316C2×AGL(1,ℤ/8)—478no—
317C2×AGL(1,ℤ/8)—944no—
318C2×AGL(1,ℤ/8)—944no—
319C22×SD16—472no—
320C22×D8—472no—
321C22×M16C2×D4711yescharacteristic
322C22×M16C2×D4711yescharacteristic
323C2×C4×D4—474no—
324C2×C4×D4—944no—
325C2×C4×D4—944no—
326C2×C4×D4—942no—
327C2×#117—471no—
328C22×C4⋊C4—471no—
329C22×C22⋊C4—941no—
330C22×C42C2×D4711yescharacteristic
331#418—944no—
332#417—944no—
333C2×#103—472no—
334C2×#102—474no—
335C2×#102—472no—
336#391—472no—
337#390—472no—
338#386—941no—
339#386—941no—
340C4×C22⋊C4—942no—
341#340—474no—
342#336C2×D4714yescomplemented
343C47#2092511yescharacteristic, complemented, Sylow
344C25—941no—
345C2×#41—474no—
346C2×#41—942no—
347C2×#41—942no—
348C2×#41—942no—
349C2×#41—942no—
350C2×#41—942no—
351C22×Q8—471no—
352C22×D4—474no—
353C22×D4—474no—
354C22×D4—474no—
355C22×D4—472no—
356C22×D4—471no—
357C22×D4—941no—
358C22×D4—941no—
359C22×D4—942no—
360C22×D4—942no—
361C22×D4—942no—
362C23×C4—948no—
363C23×C4—941no—
364C23×C4—944no—
365C23×C4—941no—
366C23×C4—1888no—
367C23×C4D18811yescharacteristic
368C23×C4D18811yescharacteristic
369C23×C4C22×D4711yescharacteristic
370AGL(1,ℤ/8)—9432no—
371C2×SD16—478no—
372C2×SD16—944no—
373C2×SD16—944no—
374C2×D8—478no—
375C2×D8—944no—
376C2×D8—944no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16C4×D4714yescomplemented
383C22×C8C22×D4712yes—
384C22×C8C22×D4712yes—
385C4×D4—948no—
386C4×D4—948no—
387C4×D4—9416no—
388#117—942no—
389#117—942no—
390C2×C4⋊C4—474no—
391C2×C4⋊C4—472no—
392C2×C4⋊C4—472no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—942no—
395C2×C22⋊C4—948no—
396C2×C22⋊C4—944no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—942no—
399C2×C22⋊C4—942no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—941no—
403C2×C42D18812yes—
404C2×C42C22×D4712yes—
405#103—944no—
406#102—944no—
407#102—948no—
408#95—942no—
409#95—942no—
410C24—944no—
411C24—944no—
412C24—944no—
413C24—942no—
414C24—941no—
415C24—1884no—
416C24—1884no—
417C24C2×D18811yescharacteristic
418#41—948no—
419#41—948no—
420#41—1884no—
421#41—1884no—
422C2×Q8—472no—
423C2×Q8—941no—
424C2×Q8—941no—
425C2×Q8—941no—
426C2×Q8—941no—
427C2×Q8—941no—
428C2×D4—4716no—
429C2×D4—474no—
430C2×D4—472no—
431C2×D4—474no—
432C2×D4—474no—
433C2×D4—944no—
434C2×D4—948no—
435C2×D4—944no—
436C2×D4—944no—
437C2×D4—948no—
438C2×D4—944no—
439C2×D4—948no—
440C2×D4—942no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—942no—
445C2×D4—941no—
446C2×D4—942no—
447C2×D4—941no—
448C2×D4—1882no—
449C2×D4—1882no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4—9416no—
455C22×C4—944no—
456C22×C4—941no—
457C22×C4—942no—
458C22×C4—944no—
459C22×C4—942no—
460C22×C4—18832no—
461C22×C4—1888no—
462C22×C4—1884no—
463C22×C4—1882no—
464C22×C4—1882no—
465C22×C4—1888no—
466C22×C4C2×C4×D4712yes—
467C22×C4C2×D18812yes—
468C22×C4C2×D18812yes—
469C22×C4C2×D18811yescharacteristic
470C22×C4#1062535012yes—
471C22×C4D4×D4712yes—
472C22×C4D4×D4712yes—
473C22×C4D4×D4712yes—
474C22×C4#1062535412yes—
475C22×C4C23×D4711yescharacteristic
476SD16—9416no—
477D8—9416no—
478M16—28no—
479M16—44no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8C2×C4×D4714yescomplemented
486C4⋊C4—474no—
487C4⋊C4—944no—
488C4⋊C4—942no—
489C4⋊C4—942no—
490C4⋊C4—942no—
491C22⋊C4—9416no—
492C22⋊C4—1884no—
493C22⋊C4—1882no—
494C22⋊C4—1884no—
495C42—24no—
496C42—22no—
497C42—22no—
498C42—1882no—
499C23—22no—
500C23—22no—
501C23—9416no—
502C23—944no—
503C23—944no—
504C23—944no—
505C23—942no—
506C23—1888no—
507C23—18816no—
508C23—18816no—
509C23—1888no—
510C23—1881no—
511C23—1881no—
512C23—1882no—
513C23—1882no—
514C23—1884no—
515C23—1884no—
516C23C4×D18812yes—
517C23#1309399412yes—
518C23#1309399912yes—
519C23C22×D18811yescharacteristic
520Q8—942no—
521Q8—942no—
522Q8—1881no—
523Q8—1881no—
524D4—478no—
525D4—9416no—
526D4—942no—
527D4—944no—
528D4—942no—
529D4—944no—
530D4—944no—
531D4—1888no—
532D4—1881no—
533D4—1881no—
534C2×C4—28no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—44no—
541C2×C4—942no—
542C2×C4—944no—
543C2×C4—18832no—
544C2×C4—1882no—
545C2×C4—1882no—
546C2×C4—1882no—
547C2×C4—1888no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1884no—
551C2×C4—1888no—
552C2×C4C22⋊C4×D4714yes—
553C2×C4#1309398614yes—
554C2×C4C4×D18812yes—
555C2×C4#1309399412yes—
556C2×C4#1309399714yes—
557C2×C4#1309399912yes—
558C2×C4#1309400914yes—
559C2×C4#1309405214yescomplemented
560C2×C4C22×C4×D4711yescharacteristic
561C2×C4C2×D4×D4711yescharacteristic
562C2×C4C2×D4×D4711yescharacteristic
563C2×C4C2×D4×D4711yescharacteristic
564C2×C4C2×#1062535011yescharacteristic
565C2×C4C2×#1062535411yescharacteristic
566C8—24no—
567C8—42no—
568C22—24no—
569C22—24no—
570C22—22no—
571C22—22no—
572C22—948no—
573C22—3762no—
574C22—3761no—
575C22—3761no—
576C22—18832no—
577C22—1884no—
578C22—1882no—
579C22—1888no—
580C22—1888no—
581C22—1884no—
582C22—1884no—
583C22#1568900114yes—
584C22C2×C4×D18811yescharacteristic
585C22C2×#1309399411yescharacteristic
586C22C2×#1309399911yescharacteristic
587C22C2×#1309405212yes—
588C22#1568992312yes—
589C4—24no—
590C4—42no—
591C4—3762no—
592C4—1882no—
593C4—1884no—
594C4#1568900114yes—
595C4C2×C22⋊C4×D4711yescharacteristic
596C4C2×#1309398611yescharacteristic
597C4C2×#1309399711yescharacteristic
598C4C2×#1309400911yescharacteristic
599C2—24no—
600C2—3762no—
601C2—1888no—
602C2C2×#1568900111yescharacteristic
603C2C4×#1309405212yes—
604C2#2025261811yescharacteristic
605C2#2025263311yescharacteristic
606C2#2025285412yes—
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1728C2
socleC23×C47C22×D4
prime radicalC22×#13094052C2
cosocleC22×C4×C47C24
hypercenter#1728D47
hypocenterC47#20925
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. C22×C4×D188C2semidirect
3. C2×#15689125C2semidirect
4. C2×#15689129C2semidirect
5. #20245878C2semidirect
6. #20243735C2semidirect
7. #20243721C2semidirect
8. #20243108C2semidirect
9. C47×#1728C2semidirect
15. C2×#13094052C4semidirect
27. C2×#13093949C22semidirect
29. C2×#13093946C22semidirect
30. #15689029C22semidirect
31. #15689025C22semidirect
35. #15688886C22semidirect
39. C47×#336C22semidirect
46. C2×#10625350C2×C4semidirect
66. C2×#10625325C2×C4semidirect
69. C2×D376C2×C4semidirect
99. C2×M16×C47C2×C4semidirect
154. C2×D188C22⋊C4semidirect
156. C2×D188C22×C4semidirect
171. C2×Dic94C22×C4semidirect
179. C2×C8×C47C22×C4semidirect
230. C2×C4×C47AGL(1,ℤ/8)semidirect
304. #1728D47semidirect
342. #336C2×D47semidirect
343. C47#20925semidirect
382. C2×M16C4×D47semidirect
485. C2×C8C2×C4×D47semidirect
559. C2×C4#13094052semidirect

Maximal subgroups

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

subgroupindex
C22×#130940522
C22×C4×D1882
C2×#156891252
C2×#156891292
#202458782
#202437352
#202437212
#202431082
C47×#17282
#2092547