Finite Group Databasebeta

← #26123543

Subgroups — #26123543

Order 12032.

1054 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251977C211yesmaximal, characteristic, complemented
2C2×#15689087C211yesmaximal, characteristic
3#20245771C211yesmaximal, characteristic
4#20243098C211yesmaximal, characteristic, complemented
5#20243097C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C47×#2280C211yesmaximal, characteristic
8C22×#10625329C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689166—22no—
13#15689163—22no—
14#15689159—22no—
15#15689087—22no—
16#15689087C414yescomplemented
17C2×C22⋊(C47⋊C8)—22no—
18#15688986—21no—
19#15688983—22no—
20#15688979—21no—
21C4×C22⋊Dic47—22no—
22#15688883—22no—
23#15688882—22no—
24#15688879—22no—
25C24×C4×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C2×#117×C47C2211yescharacteristic
28C47×#381—21no—
29C47×#380—22no—
30C47×#379—21no—
31C4×C22⋊C4×C47—22no—
32C2×#10625329—21no—
33C2×#10625329—21no—
34C2×#10625329—21no—
35C2×#10625329—21no—
36C2×#10625329—21no—
37C2×#10625329—21no—
38C2×#10625329—21no—
39C2×#10625329—21no—
40C2×#10625329—21no—
41C2×#10625329C2×C412yes—
42C2×#10625329C2×C412yes—
43C2×#10625329D412yes—
44C22×C47⋊C8—21no—
45C22×C47⋊C8D412yes—
46#13093983—21no—
47#13093983—21no—
48#13093983—21no—
49#13093983—21no—
50#13093983—21no—
51#13093983—21no—
52#13093983—21no—
53#13093983—21no—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47D412yes—
56C2×C22⋊Dic47—24no—
57C2×C22⋊Dic47—21no—
58C2×C22⋊Dic47—21no—
59C2×C4×Dic47—21no—
60C2×C4×Dic47D412yes—
61#13093957—24no—
62#13093955—24no—
63C22⋊(C47⋊C8)—28no—
64C47⋊#95—24no—
65C25×C47D411yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C23×C4×C47—21no—
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47C2×C412yes—
79C23×C4×C47D411yescharacteristic
80C23×C4×C47Q812yes—
81C23×C4×C47C2311yescharacteristic
82#117×C47—21no—
83#117×C47—21no—
84#117×C47—21no—
85#117×C47—21no—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47D412yes—
92C2×C22⋊C4×C47—24no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47D412yes—
97#95×C47—24no—
98C24×C47—21no—
99C24×C47—21no—
100C24×C47—21no—
101C24×C47—21no—
102C24×C47—21no—
103C24×C47—21no—
104C24×C47—44no—
105C24×C47C4⋊C412yes—
106C24×C47C2×D411yescharacteristic
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—41no—
128C22×C4×C47—41no—
129C22×C4×C47—41no—
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47—41no—
134C22×C4×C47—41no—
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47—41no—
139C22×C4×C47—41no—
140C22×C4×C47—41no—
141C22×C4×C47—41no—
142C22×C4×C47—41no—
143C22×C4×C47C4⋊C412yes—
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×Q811yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×C4×C47#4111yescharacteristic
156C22×C4×C47#4111yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C22×Dic47—22no—
159C22×Dic47—22no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—41no—
163C4⋊C4×C47—41no—
164C22⋊C4×C47—48no—
165C22⋊C4×C47—41no—
166C22⋊C4×C47—41no—
167C22⋊C4×C47—41no—
168C22⋊C4×C47—41no—
169C42×C47—22no—
170C42×C47—22no—
171C42×C47—41no—
172C42×C47—41no—
173C22⋊Dic47—48no—
174C22⋊Dic47—41no—
175C22⋊Dic47—41no—
176C22⋊Dic47—41no—
177C22⋊Dic47—41no—
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180C4⋊Dic47—41no—
181C4⋊Dic47—41no—
182C4×Dic47—22no—
183C4×Dic47—22no—
184C4×Dic47—41no—
185C4×Dic47—41no—
186#10625329—22no—
187#10625329—22no—
188#10625329—22no—
189#10625329—22no—
190#10625329—22no—
191#10625329—22no—
192#10625329—41no—
193#10625329—41no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—41no—
198C2×C47⋊C8—41no—
199C2×C47⋊C8C22⋊C414yescomplemented
200C23×C47—24no—
201C23×C47—24no—
202C23×C47—24no—
203C23×C47—22no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47—44no—
207C23×C47—42no—
208C23×C47—42no—
209C23×C47—42no—
210C23×C47—42no—
211C23×C47—44no—
212C23×C47—44no—
213C23×C47—44no—
214C23×C47—41no—
215C23×C47—41no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47C2×C4⋊C411yescharacteristic
219C23×C47#12011yescharacteristic
220C23×C47#12011yescharacteristic
221C23×C47#12111yescharacteristic
222C23×C47#12111yescharacteristic
223C23×C47#12311yescharacteristic
224C23×C47#12311yescharacteristic
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—44no—
241C2×C4×C47—44no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47C2×C22⋊C411yescharacteristic
245C2×C4×C47#11711yescharacteristic
246C2×C4×C47C4×D411yescharacteristic
247C2×C4×C47C4×D411yescharacteristic
248C2×C4×C47C4×D411yescharacteristic
249C2×C4×C47C4×D411yescharacteristic
250C2×C4×C47#12011yescharacteristic
251C2×C4×C47#12111yescharacteristic
252C2×C4×C47#12111yescharacteristic
253C2×C4×C47#12111yescharacteristic
254C2×C4×C47#12111yescharacteristic
255C2×C4×C47#12111yescharacteristic
256C2×C4×C47#12111yescharacteristic
257C2×C4×C47C22⋊Q811yescharacteristic
258C2×C4×C47C22⋊Q811yescharacteristic
259C2×C4×C47C22⋊Q811yescharacteristic
260C2×C4×C47C22⋊Q811yescharacteristic
261C2×C4×C47C22⋊Q811yescharacteristic
262C2×C4×C47C22⋊Q811yescharacteristic
263C2×C4×C47#12311yescharacteristic
264C2×C4×C47#12311yescharacteristic
265C2×C4×C47#12311yescharacteristic
266C2×C4×C47#12411yescharacteristic
267C2×C4×C47#12411yescharacteristic
268C2×C4×C47#12411yescharacteristic
269C2×C4×C47#12611yescharacteristic
270C2×C4×C47#12611yescharacteristic
271C2×C4×C47#12711yescharacteristic
272C2×Dic47—44no—
273C2×Dic47—44no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C47⋊C8—24no—
277C47⋊C8—42no—
278#11100—471nomaximal, Sylow
279C22×C47—22no—
280C22×C47—22no—
281C22×C47—22no—
282C22×C47—24no—
283C22×C47—24no—
284C22×C47—24no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—44no—
290C22×C47—44no—
291C22×C47—42no—
292C22×C47—42no—
293C22×C47—42no—
294C22×C47—44no—
295C22×C47—42no—
296C22×C47—44no—
297C22×C47#38011yescharacteristic
298C22×C47#38511yescharacteristic
299C22×C47#38511yescharacteristic
300C22×C47#39211yescharacteristic
301C22×C47#39411yescharacteristic
302C22×C47#39411yescharacteristic
303C22×C47#39711yescharacteristic
304C4×C47—42no—
305C4×C47—82no—
306C4×C47—82no—
307C4×C47#38611yescharacteristic
308C4×C47#38811yescharacteristic
309C4×C47#38811yescharacteristic
310C4×C47#39011yescharacteristic
311C4×C47#39311yescharacteristic
312C4×C47#39611yescharacteristic
313C4×C47#39611yescharacteristic
314C4×C47#39911yescharacteristic
315Dic47—82no—
316Dic47—82no—
317#2911—471no—
318C2×#407—471no—
319#2280—471no—
320#2280D4711yescharacteristic
321#1733—471no—
322#1733—471no—
323C2×H(3,ℤ/4)—471no—
324C2×C47—21no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47—44no—
331C2×C47#143911yescharacteristic
332C2×C47#201012yes—
333C24×C4C2×D4711yescharacteristic
334C22×M16—471no—
335C22×M16—471no—
336C2×#117—471no—
337C2×#117—471no—
338C2×#117C2×D4711yescharacteristic
339C2×#117C2×D4711yescharacteristic
340#428—942no—
341#428—942no—
342#427—942no—
343#407—474no—
344#407—942no—
345C2×C22⋊C8—942no—
346#381—21no—
347#381—941no—
348#380—22no—
349#380—942no—
350#379—21no—
351#379—941no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4—942no—
354#339—942no—
355#339—942no—
356H(3,ℤ/4)—942no—
357C47#1110011yescharacteristic, complemented, Sylow
358C25C22⋊D4711yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4Dic9412yes—
372C23×C4C4×D4712yes—
373C23×C4C22⋊D4711yescharacteristic
374C23×C4C22×D4711yescharacteristic
375C2×M16—472no—
376C2×M16—472no—
377C2×M16—472no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C22×C8—472no—
388C22×C8—941no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—941no—
398#117—941no—
399#117—941no—
400#117—941no—
401#117—941no—
402#117—941no—
403#117—941no—
404#117—941no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—472no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4C22⋊D4712yes—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—944no—
413C2×C22⋊C4—941no—
414C2×C22⋊C4—941no—
415C2×C42—21no—
416C2×C42—472no—
417C2×C42—941no—
418C2×C42C22⋊D4712yes—
419#107—944no—
420#106—944no—
421C22⋊C8—948no—
422#95—24no—
423#95—944no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—44no—
431C24Dic47⋊C412yes—
432C24C2×C22⋊D4711yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4Dic47⋊C412yes—
472C22×C4C2×Dic9411yescharacteristic
473C22×C4C2×C4×D4711yescharacteristic
474C22×C4#1062535011yescharacteristic
475C22×C4#1062535011yescharacteristic
476C22×C4D4×D4711yescharacteristic
477C22×C4D4×D4711yescharacteristic
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4711yescharacteristic
480C22×C4#1062535211yescharacteristic
481C22×C4#1062535211yescharacteristic
482C22×C4#1062535211yescharacteristic
483C22×C4#1062535211yescharacteristic
484C22×C4C2×C22⋊D4711yescharacteristic
485C22×C4C2×C22⋊D4711yescharacteristic
486M16—942no—
487M16—942no—
488M16—942no—
489M16—942no—
490M16—942no—
491M16—942no—
492M16—1881no—
493M16—1881no—
494C2×C8—474no—
495C2×C8—942no—
496C2×C8—942no—
497C2×C8—942no—
498C2×C8—1881no—
499C2×C8—1881no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—1881no—
507C4⋊C4—1881no—
508C22⋊C4—48no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—1888no—
514C22⋊C4—1881no—
515C22⋊C4—1881no—
516C22⋊C4—1881no—
517C22⋊C4—1881no—
518C42—22no—
519C42—22no—
520C42—41no—
521C42—41no—
522C42—942no—
523C42—942no—
524C42—1881no—
525C42—1881no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—44no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—44no—
538C23—44no—
539C23—44no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C2×Dic47⋊C411yescharacteristic
545C23#1309399211yescharacteristic
546C23#1309399311yescharacteristic
547C23#1309399611yescharacteristic
548C23#1309399611yescharacteristic
549C23#1309400511yescharacteristic
550C23#1309400711yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—1884no—
571C2×C4—1884no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4C22⋊C4×D4711yescharacteristic
575C2×C4#1309398011yescharacteristic
576C2×C4(C22⋊D47)⋊C411yescharacteristic
577C2×C4(C22⋊D47)⋊C411yescharacteristic
578C2×C4C4×C22⋊D4711yescharacteristic
579C2×C4C4×C22⋊D4711yescharacteristic
580C2×C4#1309399211yescharacteristic
581C2×C4#1309399511yescharacteristic
582C2×C4#1309399511yescharacteristic
583C2×C4#1309399611yescharacteristic
584C2×C4#1309399611yescharacteristic
585C2×C4#1309399711yescharacteristic
586C2×C4#1309399711yescharacteristic
587C2×C4#1309400111yescharacteristic
588C2×C4#1309400111yescharacteristic
589C2×C4#1309400111yescharacteristic
590C2×C4#1309400111yescharacteristic
591C2×C4#1309400311yescharacteristic
592C2×C4#1309400311yescharacteristic
593C2×C4#1309400511yescharacteristic
594C2×C4#1309400611yescharacteristic
595C2×C4#1309400611yescharacteristic
596C2×C4#1309401011yescharacteristic
597C2×C4#1309401011yescharacteristic
598C2×C4#1309401111yescharacteristic
599C2×C4#1309401711yescharacteristic
600C2×C4#1309401711yescharacteristic
601C2×C4#1309402011yescharacteristic
602C8—944no—
603C8—1882no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—24no—
608C22—24no—
609C22—24no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—42no—
621C22—44no—
622C22#1568898111yescharacteristic
623C22#1568899511yescharacteristic
624C22#1568899611yescharacteristic
625C22#1568903111yescharacteristic
626C22#1568903711yescharacteristic
627C22#1568903811yescharacteristic
628C22#1568905111yescharacteristic
629C4—42no—
630C4—82no—
631C4—82no—
632C4—3762no—
633C4—3762no—
634C4#1568899911yescharacteristic
635C4#1568901111yescharacteristic
636C4#1568901711yescharacteristic
637C4#1568902311yescharacteristic
638C4#1568903511yescharacteristic
639C4#1568904611yescharacteristic
640C4#1568904611yescharacteristic
641C4#1568905911yescharacteristic
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—21no—
648C2—44no—
649C2#2024163111yescharacteristic
650C2#2024445312yes—
subgroupG/H
centerC2×C4#13094020
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2280C2
socleC22×C47#392
prime radicalC25×C47D4
cosocleC23×C4×C47C23
hypercenter#2280D47
hypocenterC47#11100
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. #20251977C2semidirect
4. #20243098C2semidirect
5. #20243097C2semidirect
6. C2×#15688879C2semidirect
16. #15689087C4semidirect
199. C2×C47⋊C8C22⋊C4semidirect
357. C47#11100semidirect

Maximal subgroups

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

subgroupindex
#202519772
C2×#156890872
#202457712
#202430982
#202430972
C2×#156888792
C47×#22802
#1110047