Finite Group Databasebeta

← #26218440

Subgroups — #26218440

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689160C211yesmaximal, characteristic
2#20245869C211yesmaximal, characteristic
3C4×#13093982C211yesmaximal, characteristic
4#20243982C211yesmaximal, characteristic, complemented
5#20243976C211yesmaximal, characteristic, complemented
6#20243970C211yesmaximal, characteristic, complemented
7#20243966C211yesmaximal, characteristic, complemented
8#20243964C211yesmaximal, characteristic, complemented
9#20243960C211yesmaximal, characteristic, complemented
10#20243958C211yesmaximal, characteristic, complemented
11#20243103C211yesmaximal, characteristic
12#20243103C211yesmaximal, characteristic
13#20243103C211yesmaximal, characteristic
14#336×D47C211yesmaximal, characteristic
15C47×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×#13093982C2211yescharacteristic
19C2×#13093982C2211yescharacteristic
20C2×#13093982C2211yescharacteristic
21C2×#13093982C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23#15689160C418yescomplemented
24C2×#13093958C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27#15689022C2211yescharacteristic
28#15689021C2211yescharacteristic
29#15689019C2211yescharacteristic
30#15688997—21no—
31#15688994—21no—
32C4⋊C4×Dic47—21no—
33C4⋊C4×Dic47C2211yescharacteristic
34C4⋊C4×Dic47C2211yescharacteristic
35C4×C4⋊Dic47C2211yescharacteristic
36#15688974—21no—
37C4×(C2×D47)⋊C4—21no—
38#15688970—21no—
39#15688968—21no—
40C42×Dic47—21no—
41#15688886C2211yescharacteristic
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×#107×C47C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×C4×D47D411yescharacteristic
61C22×C4×D47D411yescharacteristic
62C22×C4×D47C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C2×C8×D47—22no—
66C2×C8×D47—22no—
67C2×C8×D47—22no—
68C2×C8×D47—22no—
69C2×C8×D47—22no—
70C2×C8×D47C2×C414yes—
71#13093982—22no—
72#13093982—22no—
73#13093982—22no—
74#13093982—22no—
75#13093982—22no—
76#13093982C2×C414yes—
77#13093982C2×C414yes—
78#13093982Q814yes—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—21no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—21no—
97C2×C4×Dic47D411yescharacteristic
98C2×C4×Dic47D411yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C42×D47—22no—
101C42×D47—22no—
102#13093958C2×C414yescomplemented
103#13093955C2×C414yescomplemented
104#13093955C2×C414yescomplemented
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C42×C47—21no—
119C2×C42×C47C2311yescharacteristic
120#107×C47C2×C414yescomplemented
121#95×C47—21no—
122#95×C47—21no—
123C23×D47C2×D411yescharacteristic
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47C2×D411yescharacteristic
136C22×Dic47C2×D411yescharacteristic
137C22×Dic47C2×D411yescharacteristic
138C2×C4×D47—22no—
139C2×C4×D47—22no—
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—41no—
143C2×C4×D47—41no—
144C2×C4×D47C22×C412yes—
145C2×C4×D47C2×Q812yes—
146C2×C4×D47#4112yes—
147C2×C4×D47#4112yes—
148C2×C4×D47#4112yes—
149C2×C4×D47#4112yes—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47C22×C412yes—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—42no—
162C4⋊C4×C47C22×C412yes—
163C4⋊C4×C47C22×C412yes—
164C4⋊C4×C47C2×Q812yes—
165C42×C47—21no—
166C42×C47—21no—
167C42×C47—42no—
168(C2×D47)⋊C4—24no—
169(C2×D47)⋊C4—24no—
170(C2×D47)⋊C4—24no—
171(C2×D47)⋊C4—42no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—42no—
178C4⋊Dic47C22×C412yes—
179C4⋊Dic47C22×C412yes—
180C4⋊Dic47C2×Q812yes—
181Dic47⋊C4—42no—
182Dic47⋊C4—42no—
183C4×Dic47—21no—
184C4×Dic47—21no—
185C4×Dic47—24no—
186C4×Dic47—24no—
187C4×Dic47—24no—
188C4×Dic47—22no—
189C4×Dic47—22no—
190C4×Dic47—42no—
191C4×Dic47—42no—
192C4×Dic47—42no—
193C4×Dic47—42no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8C22×C412yes—
200C8×D47—28no—
201C8×D47—44no—
202C23×C47C22×D411yescharacteristic
203C22×D47—21no—
204C22×D47—21no—
205C22×D47—21no—
206C22×D47—21no—
207C22×D47C4×D412yes—
208C22×D47C22⋊Q812yes—
209C22×D47#12312yes—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47#13512yes—
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×Q811yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47C4×D412yes—
252C2×Dic47C22⋊Q812yes—
253C2×Dic47#12312yes—
254C2×Dic47#13512yes—
255C4×D47—44no—
256C4×D47—44no—
257C4×D47#11714yes—
258C4×D47C4×Q814yes—
259C4×D47#12514yes—
260C4×D47#12614yes—
261C8×C47—22no—
262C8×C47—41no—
263C47⋊C8—22no—
264C47⋊C8—41no—
265#21032—471nomaximal, Sylow
266C22×C47C2×C4×D411yescharacteristic
267C22×C47C2×C22⋊Q811yescharacteristic
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#38714yes—
280C4×C47—22no—
281C4×C47—42no—
282C4×C47—41no—
283C4×C47—42no—
284C4×C47—42no—
285C4×C47—81no—
286C4×C47C2×#11711yescharacteristic
287C4×C47C2×C4×Q811yescharacteristic
288C4×C47C2×#12511yescharacteristic
289C4×C47C2×#12611yescharacteristic
290Dic47—22no—
291Dic47—42no—
292Dic47—41no—
293Dic47—42no—
294Dic47—42no—
295Dic47—81no—
296Dic47#38714yes—
297C2×#427—471no—
298#2296—471no—
299C4×#117—471no—
300#1921—471no—
301#1921D4711yescharacteristic, complemented
302#1920—471no—
303#1920—471no—
304#1919—471no—
305#1919—471no—
306#1918—471no—
307#1918—471no—
308#1735—471no—
309#1735—471no—
310#1735—471no—
311C2×#336—471no—
312C2×C47C2×#38711yescharacteristic
313C2×C47C4×#13511yescharacteristic
314C2×C47#294311yescharacteristic
315C2×C47#307611yescharacteristic
316C2×C47#307611yescharacteristic
317C2×C47#309111yescharacteristic
318C2×C47#309111yescharacteristic
319D47—24no—
320C23×C8—471no—
321C23×C8—471no—
322C2×#117—471no—
323C2×#117—471no—
324C2×#117—471no—
325C2×#117—471no—
326C22×C42—471no—
327#427—478no—
328C2×#107—471no—
329C2×#107C2×D4711yescharacteristic
330C2×#106—471no—
331C2×#106—471no—
332#389—471no—
333#389—471no—
334#389—471no—
335#389C2×D4711yescharacteristic
336#385—941no—
337#385—941no—
338C4×C4⋊C4—471no—
339C4×C4⋊C4—471no—
340C4×C4⋊C4—471no—
341C4×C4⋊C4—941no—
342C4×C4⋊C4—941no—
343C4×C4⋊C4C2×D4711yescharacteristic
344C4×C22⋊C4—941no—
345C4×C22⋊C4—941no—
346#376—941no—
347C43—941no—
348#340—471no—
349#340—471no—
350#340—471no—
351#340—471no—
352#340—471no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340C2×D4711yescharacteristic
358#340C2×D4711yescharacteristic
359#340C2×D4711yescharacteristic
360#336—471no—
361#336—471no—
362#336—471no—
363#336C2×D4711yescharacteristic
364C47#2103211yescharacteristic, complemented, Sylow
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—471no—
368C22×C8—471no—
369C22×C8—474no—
370C22×C8—471no—
371C22×C8—942no—
372C22×C8—942no—
373C22×C8—942no—
374C22×C8—942no—
375C22×C8—942no—
376C22×C8C22×D4711yescharacteristic
377C22×C8C22×D4711yescharacteristic
378#117—474no—
379#117—474no—
380#117—474no—
381#117—942no—
382#117—942no—
383#117—942no—
384#117—942no—
385#117—942no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4C22×D4711yescharacteristic
395C2×C4⋊C4C22×D4711yescharacteristic
396C2×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C22⋊C4—941no—
401C2×C22⋊C4—941no—
402C2×C42—21no—
403C2×C42—471no—
404C2×C42—471no—
405C2×C42—471no—
406C2×C42—942no—
407C2×C42—942no—
408C2×C42—941no—
409C2×C42—941no—
410C2×C42—941no—
411C2×C42—941no—
412C2×C42—941no—
413C2×C42—941no—
414C2×C42—941no—
415C2×C42C22×D4711yescharacteristic
416#107—474no—
417#107C4×D4714yescomplemented
418#106—474no—
419#106—474no—
420#95—21no—
421#95—21no—
422#95—941no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428C24—471no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—471no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—472no—
439C22×C4—472no—
440C22×C4—471no—
441C22×C4—471no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—942no—
449C22×C4—941no—
450C22×C4—1881no—
451C22×C4—1881no—
452C22×C4D4×D4711yescharacteristic
453C22×C4D4×D4711yescharacteristic
454C22×C4C23×D4711yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—472no—
461C2×C8—948no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—1884no—
468C2×C8C2×C4×D4712yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—472no—
476C4⋊C4—472no—
477C4⋊C4—472no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—1882no—
484C4⋊C4—1882no—
485C4⋊C4—1882no—
486C4⋊C4C2×C4×D4712yes—
487C4⋊C4C2×C4×D4712yes—
488C4⋊C4Q8×D4712yes—
489C22⋊C4—944no—
490C22⋊C4—944no—
491C22⋊C4—944no—
492C22⋊C4—1882no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—942no—
497C42—942no—
498C42—944no—
499C42—944no—
500C42—944no—
501C42—941no—
502C42—941no—
503C42—1882no—
504C42—1882no—
505C42—1882no—
506C42—1882no—
507C23—472no—
508C23—472no—
509C23—472no—
510C23—941no—
511C23—941no—
512C23—941no—
513C23—941no—
514C23C2×D4×D4711yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—472no—
533C2×C4—472no—
534C2×C4—472no—
535C2×C4—474no—
536C2×C4—474no—
537C2×C4—474no—
538C2×C4—474no—
539C2×C4—472no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—941no—
546C2×C4—941no—
547C2×C4—941no—
548C2×C4—1884no—
549C2×C4—1884no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4#1309404712yes—
560C2×C4C22×C4×D4711yescharacteristic
561C2×C4C2×Q8×D4711yescharacteristic
562C2×C4#41×D4711yescharacteristic
563C2×C4#41×D4711yescharacteristic
564C2×C4#41×D4711yescharacteristic
565C2×C4#41×D4711yescharacteristic
566C8—22no—
567C8—41no—
568C8—942no—
569C8—1881no—
570C22—474no—
571C22—942no—
572C22—942no—
573C22—942no—
574C22—942no—
575C22—942no—
576C22—942no—
577C22C4×D4×D4711yescharacteristic
578C22C22⋊Q8×D4711yescharacteristic
579C22#123×D4711yescharacteristic
580C22#135×D4711yescharacteristic
581C22C2×#1309404711yescharacteristic
582C22#1568991911yescharacteristic
583C22#1568991911yescharacteristic
584C4—22no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—81no—
590C4—474no—
591C4—942no—
592C4—3761no—
593C4—1882no—
594C4—1882no—
595C4—1881no—
596C4—1882no—
597C4#117×D4711yescharacteristic
598C4C4×Q8×D4711yescharacteristic
599C4#125×D4711yescharacteristic
600C4#126×D4711yescharacteristic
601C2—944no—
602C2#387×D4711yescharacteristic
603C2C4×#1309404711yescharacteristic
604C2#2025218511yescharacteristic
605C2#2025317311yescharacteristic
606C2#2025317911yescharacteristic
607C2#2025330011yescharacteristic
608C2#2025330411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1921C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1921D47
hypocenterC47#21032
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #20243982C2semidirect
5. #20243976C2semidirect
6. #20243970C2semidirect
7. #20243966C2semidirect
8. #20243964C2semidirect
9. #20243960C2semidirect
10. #20243958C2semidirect
15. C47×#1921C2semidirect
23. #15689160C4semidirect
102. #13093958C2×C4semidirect
103. #13093955C2×C4semidirect
104. #13093955C2×C4semidirect
120. #107×C47C2×C4semidirect
301. #1921D47semidirect
364. C47#21032semidirect
417. #107C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891602
#202458692
C4×#130939822
#202439822
#202439762
#202439702
#202439662
#202439642
#202439602
#202439582
#202431032
#336×D472
C47×#19212
#2103247