Finite Group Databasebeta

← #26217004

Subgroups — #26217004

Order 12032.

1590 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C211yesmaximal, characteristic
2C2×#15689158C212yesmaximal, complemented
3C2×C22⋊C8×D47C211yesmaximal, characteristic
4#20245770C211yesmaximal, characteristic
5#20243588C212yesmaximal, complemented
6#20243586C212yesmaximal, complemented
7#20243583C211yesmaximal, characteristic, complemented
8#20243576C211yesmaximal, characteristic, complemented
9#20243575C211yesmaximal, characteristic, complemented
10#20243103C212yesmaximal, complemented
11C47×#1853C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×C8×D47C2212yes—
14C2×#13093982—21no—
15C2×#13093982—21no—
16C2×#13093982—28no—
17C2×#13093982C2211yescharacteristic
18C2×#13093982C2211yescharacteristic
19C2×#13093982C2212yes—
20C2×#13093982C2212yes—
21C22×C4⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4—21no—
23C22×C4×Dic47—21no—
24#15689158—28no—
25C2×#13093957C2212yescomplemented
26C2×#13093957C2212yescomplemented
27C2×#13093956C2212yescomplemented
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×(C2×D47)⋊C8C2212yes—
30C22⋊C8×D47C418yescomplemented
31#15688985—21no—
32#15688983C2211yescharacteristic
33#15688980C2211yescharacteristic
34#15688980C2211yescharacteristic
35#15688978—21no—
36C22⋊C4×Dic47—21no—
37#15688970—21no—
38#15688886C2212yescomplemented
39#15688885C2212yescomplemented
40#15688885C2212yescomplemented
41C22×C4⋊C4×C47C2211yescharacteristic
42C2×#106×C47C2212yescomplemented
43C2×C22⋊C8×C47C2211yescharacteristic
44C47×#380C2211yescharacteristic
45C47×#340C2212yescomplemented
46C24×D47D411yescharacteristic
47C23×Dic47—21no—
48C23×Dic47D411yescharacteristic
49C22×C4×D47—24no—
50C22×C4×D47—24no—
51C22×C4×D47C2×C414yes—
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C22×C4×D47Q814yes—
55C22×C4×D47C2311yescharacteristic
56C22×C4×D47C2311yescharacteristic
57C22×C47⋊C8C2312yes—
58C2×C8×D47—24no—
59C2×C8×D47—24no—
60C2×C8×D47C2×C418yescomplemented
61#13093982—28no—
62#13093982—28no—
63#13093982—24no—
64#13093982—24no—
65#13093982—24no—
66#13093982—24no—
67#13093982—24no—
68#13093982D418yes—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—24no—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2312yes—
74C2×C22⋊Dic47—21no—
75C2×(C2×D47)⋊C4—28no—
76C2×(C2×D47)⋊C4—22no—
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×C4×Dic47—28no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87#13093957—24no—
88#13093957—24no—
89#13093956—24no—
90C22⋊(C47⋊C8)C2×C414yes—
91(C2×D47)⋊C8C2×C418yescomplemented
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C23×C4×C47—21no—
96C23×C4×C47C2311yescharacteristic
97C22×C8×C47C2312yes—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—24no—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2312yes—
103C2×C22⋊C4×C47—21no—
104#106×C47—24no—
105C22⋊C8×C47C2×C414yes—
106#95×C47—21no—
107C24×C47C2×D411yescharacteristic
108C23×D47—22no—
109C23×D47—22no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—41no—
113C23×D47—41no—
114C23×D47C4⋊C414yes—
115C23×D47C2×D411yescharacteristic
116C23×D47C2×D411yescharacteristic
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—24no—
120C22×C4×C47—22no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×Q812yes—
128C22×C4×C47C2411yescharacteristic
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—24no—
132C22×Dic47—22no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—42no—
136C22×Dic47—42no—
137C22×Dic47C4⋊C414yes—
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—22no—
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—216no—
147C2×C4×D47—216no—
148C2×C4×D47C4⋊C414yes—
149C2×C4×D47C4⋊C414yes—
150C2×C4×D47C22×C412yes—
151C2×C4×D47C22×C412yes—
152C2×C4×D47C2×D414yes—
153C2×C4×D47C2×Q812yes—
154C2×C4×D47C2×Q812yes—
155C2×C4×D47#4114yes—
156C2×C8×C47—22no—
157C2×C8×C47—22no—
158C2×C8×C47C22×C414yes—
159C4⋊C4×C47—24no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47C2×D414yes—
164C22⋊C4×C47—42no—
165C22⋊Dic47—42no—
166(C2×D47)⋊C4—28no—
167(C2×D47)⋊C4—28no—
168(C2×D47)⋊C4—42no—
169(C2×D47)⋊C4—42no—
170(C2×D47)⋊C4—42no—
171(C2×D47)⋊C4—42no—
172C4⋊Dic47—24no—
173C4⋊Dic47—22no—
174C4⋊Dic47—22no—
175C4⋊Dic47—22no—
176C4⋊Dic47C2×D414yes—
177C4×Dic47—28no—
178C4×Dic47—28no—
179C4×Dic47—42no—
180C4×Dic47—42no—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8C22×C414yes—
184C8×D47—216no—
185C23×C47—21no—
186C23×C47—21no—
187C23×C47—21no—
188C23×C47—21no—
189C23×C47C2×C4⋊C412yes—
190C23×C47#13512yes—
191C23×C47#13512yes—
192C23×C47C22×D411yescharacteristic
193C22×D47—21no—
194C22×D47—21no—
195C22×D47—21no—
196C22×D47—21no—
197C22×D47—21no—
198C22×D47—21no—
199C22×D47—21no—
200C22×D47—21no—
201C22×D47—21no—
202C22×D47—21no—
203C22×D47—28no—
204C22×D47—28no—
205C22×D47—44no—
206C22×D47—44no—
207C22×D47—44no—
208C22×D47—44no—
209C22×D47—44no—
210C22×D47C2×C4⋊C412yes—
211C22×D47C2×C4⋊C412yes—
212C22×D47#12012yes—
213C22×D47#12312yes—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—48no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C2×C4⋊C412yes—
229C2×C4×C47C23×C411yescharacteristic
230C2×C4×C47C22×D412yes—
231C2×C4×C47C22×Q811yescharacteristic
232C2×C4×C47C2×#4112yes—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—28no—
236C2×Dic47—24no—
237C2×Dic47—48no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47C2×C4⋊C412yes—
247C2×Dic47C2×C4⋊C412yes—
248C2×Dic47#12012yes—
249C2×Dic47#12312yes—
250C4×D47—28no—
251C4×D47—24no—
252C4×D47—24no—
253C4×D47—28no—
254C4×D47C4×D418yes—
255C4×D47C22⋊Q818yes—
256C8×C47—24no—
257C47⋊C8—24no—
258#20843—471nomaximal, Sylow
259C22×C47—22no—
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—22no—
263C22×C47—22no—
264C22×C47—22no—
265C22×C47#42714yescomplemented
266C22×C47C22×C4⋊C411yescharacteristic
267C22×C47C2×#12011yescharacteristic
268C22×C47C2×#12311yescharacteristic
269C22×C47C2×#13511yescharacteristic
270C22×C47C2×#13511yescharacteristic
271C22×C47#57511yescharacteristic
272C22×C47#57511yescharacteristic
273C2×D47—22no—
274C2×D47—22no—
275C2×D47—22no—
276C2×D47—22no—
277C2×D47—22no—
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—22no—
282C2×D47—416no—
283C2×D47—41no—
284C2×D47—41no—
285C2×D47—41no—
286C2×D47—41no—
287C2×D47#38514yes—
288C4×C47—22no—
289C4×C47—44no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47C2×C4×D412yes—
293C4×C47C2×C22⋊Q812yes—
294Dic47—22no—
295Dic47—44no—
296Dic47—81no—
297Dic47—81no—
298Dic47#38514yes—
299C22×#117—471no—
300C2×#427—472no—
301C22×C22⋊C8—471no—
302#2280—471no—
303#1854—472no—
304#1854—472no—
305#1853—471no—
306#1853D4711yescharacteristic, complemented
307#1852—471no—
308#1852—471no—
309#1735—472no—
310C2×C47—24no—
311C2×C47C2×#38511yescharacteristic
312C2×C47C2×#42711yescharacteristic
313C2×C47#291111yescharacteristic
314C2×C47#300211yescharacteristic
315C2×C47#300211yescharacteristic
316C2×C47#309111yescharacteristic
317C2×C47#309111yescharacteristic
318D47—24no—
319D47—42no—
320C24×C4—471no—
321C23×C8—472no—
322C2×#117—472no—
323C2×#117—472no—
324C2×#117—471no—
325C2×#117—471no—
326C2×#117—948no—
327C2×#117—941no—
328C2×#117—941no—
329C22×C4⋊C4—471no—
330C22×C4⋊C4C2×D4711yescharacteristic
331C22×C22⋊C4—941no—
332C22×C42—941no—
333#427—948no—
334C2×#107—472no—
335C2×#107—472no—
336C2×#106—472no—
337C2×#106C2×D4712yescomplemented
338C2×C22⋊C8—471no—
339C2×C22⋊C8—472no—
340C2×C22⋊C8—478no—
341C2×C22⋊C8C2×D4711yescharacteristic
342#381—941no—
343#380—471no—
344#380—471no—
345#380—471no—
346#380C2×D4711yescharacteristic
347#379—941no—
348C4×C22⋊C4—941no—
349C4×C22⋊C4—941no—
350#340—472no—
351#340—472no—
352#340—472no—
353#340C2×D4712yescomplemented
354C47#2084311yescharacteristic, complemented, Sylow
355C25—471no—
356C23×C4—21no—
357C23×C4—471no—
358C23×C4—471no—
359C23×C4—474no—
360C23×C4—471no—
361C23×C4—471no—
362C23×C4—474no—
363C23×C4—471no—
364C23×C4—944no—
365C23×C4—944no—
366C23×C4—941no—
367C23×C4C22×D4711yescharacteristic
368C22×C8—472no—
369C22×C8—478no—
370C22×C8—944no—
371C22×C8—944no—
372C22×C8C22×D4712yes—
373#117—478no—
374#117—944no—
375#117—944no—
376#117—948no—
377#117—948no—
378#117—944no—
379#117—944no—
380#117—944no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—472no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—944no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4C22×D4711yescharacteristic
389C2×C4⋊C4C22×D4711yescharacteristic
390C2×C4⋊C4C22×D4712yes—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—942no—
393C2×C22⋊C4—942no—
394C2×C22⋊C4—948no—
395C2×C22⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C42—942no—
401C2×C42—942no—
402C2×C42—948no—
403C2×C42—941no—
404C2×C42—941no—
405#107—944no—
406#107—944no—
407#106—24no—
408#106—944no—
409C22⋊C8—474no—
410C22⋊C8—478no—
411C22⋊C8C4×D4714yes—
412#95—21no—
413#95—941no—
414#95—941no—
415#95—941no—
416C24—471no—
417C24—471no—
418C24—474no—
419C24—942no—
420C24—942no—
421C24—942no—
422C24—942no—
423C24—1881no—
424C24—1881no—
425C24D4×D4711yescharacteristic
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—471no—
435C22×C4—472no—
436C22×C4—474no—
437C22×C4—472no—
438C22×C4—474no—
439C22×C4—474no—
440C22×C4—471no—
441C22×C4—474no—
442C22×C4—474no—
443C22×C4—472no—
444C22×C4—472no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4—9416no—
448C22×C4—9416no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—944no—
456C22×C4—942no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—1882no—
460C22×C4—1882no—
461C22×C4C2×C4×D4712yes—
462C22×C4D4×D4711yescharacteristic
463C22×C4Q8×D4712yes—
464C22×C4C23×D4711yescharacteristic
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—474no—
468C2×C8—9416no—
469C2×C8—942no—
470C2×C8—942no—
471C2×C8C2×C4×D4714yes—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—474no—
477C4⋊C4—944no—
478C4⋊C4—942no—
479C4⋊C4—942no—
480C4⋊C4—942no—
481C4⋊C4D4×D4714yes—
482C22⋊C4—42no—
483C22⋊C4—948no—
484C22⋊C4—948no—
485C22⋊C4—1882no—
486C22⋊C4—1882no—
487C22⋊C4—1882no—
488C22⋊C4—1882no—
489C22⋊C4—1882no—
490C42—948no—
491C42—948no—
492C42—1882no—
493C42—1882no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—472no—
499C23—472no—
500C23—472no—
501C23—472no—
502C23—948no—
503C23—941no—
504C23—941no—
505C23—941no—
506C23—941no—
507C23—941no—
508C23—941no—
509C23—941no—
510C23—941no—
511C23—941no—
512C23—941no—
513C23—948no—
514C23—1884no—
515C23—1884no—
516C23—1884no—
517C23—1884no—
518C23—1884no—
519C23C4⋊C4×D4712yes—
520C23#1309404512yes—
521C23#1309404512yes—
522C23C2×D4×D4711yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—48no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—472no—
538C2×C4—472no—
539C2×C4—472no—
540C2×C4—478no—
541C2×C4—478no—
542C2×C4—472no—
543C2×C4—948no—
544C2×C4—948no—
545C2×C4—948no—
546C2×C4—941no—
547C2×C4—941no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—944no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1888no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4C4⋊C4×D4712yes—
561C2×C4C22×C4×D4711yescharacteristic
562C2×C4C2×D4×D4712yes—
563C2×C4C2×Q8×D4711yescharacteristic
564C2×C4#41×D4712yes—
565C8—24no—
566C8—944no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—474no—
574C22—942no—
575C22—942no—
576C22—942no—
577C22—942no—
578C22—942no—
579C22—942no—
580C22—942no—
581C22—942no—
582C22—942no—
583C22—18816no—
584C22—1881no—
585C22—1881no—
586C22—1881no—
587C22—1881no—
588C22#1568915814yescomplemented
589C22C2×C4⋊C4×D4711yescharacteristic
590C22#120×D4711yescharacteristic
591C22#123×D4711yescharacteristic
592C22C2×#1309404511yescharacteristic
593C22C2×#1309404511yescharacteristic
594C22#1568991911yescharacteristic
595C22#1568992211yescharacteristic
596C4—22no—
597C4—44no—
598C4—81no—
599C4—81no—
600C4—474no—
601C4—942no—
602C4—3761no—
603C4—3761no—
604C4—1884no—
605C4C4×D4×D4712yes—
606C4C22⋊Q8×D4712yes—
607C2—24no—
608C2—944no—
609C2—1882no—
610C2#385×D4711yescharacteristic
611C2C2×#1568915811yescharacteristic
612C2#2025197511yescharacteristic
613C2#2025260511yescharacteristic
614C2#2025260711yescharacteristic
615C2#2025329811yescharacteristic
616C2#2025330211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1853C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1853D47
hypocenterC47#20843
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#15689158C2semidirect
5. #20243588C2semidirect
6. #20243586C2semidirect
7. #20243583C2semidirect
8. #20243576C2semidirect
9. #20243575C2semidirect
10. #20243103C2semidirect
11. C47×#1853C2semidirect
25. C2×#13093957C22semidirect
26. C2×#13093957C22semidirect
27. C2×#13093956C22semidirect
30. C22⋊C8×D47C4semidirect
38. #15688886C22semidirect
39. #15688885C22semidirect
40. #15688885C22semidirect
42. C2×#106×C47C22semidirect
45. C47×#340C22semidirect
60. C2×C8×D47C2×C4semidirect
91. (C2×D47)⋊C8C2×C4semidirect
265. C22×C47#427semidirect
306. #1853D47semidirect
337. C2×#106C2×D47semidirect
353. #340C2×D47semidirect
354. C47#20843semidirect
588. C22#15689158semidirect

Maximal subgroups

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

subgroupindex
C22×#130939822
C2×#156891582
C2×C22⋊C8×D472
#202457702
#202435882
#202435862
#202435832
#202435762
#202435752
#202431032
C47×#18532
#2084347