Finite Group Databasebeta

← #26138643

Subgroups — #26138643

Order 12032.

1586 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688990C211yesmaximal, characteristic, complemented
2C2×#15688982C211yesmaximal, characteristic
3C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
4#20241646C212yesmaximal, complemented
5#20241636C212yesmaximal
6#20241624C212yesmaximal
7#20241619C212yesmaximal, complemented
8#20241612C211yesmaximal, characteristic, complemented
9(C2×D47)⋊#95C211yesmaximal, characteristic
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C47×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×Dic47⋊C4C2212yes—
14C22×(C2×D47)⋊C4C2212yes—
15C22×(C2×D47)⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2211yescharacteristic
17C22×(C2×D47)⋊C4C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19C22×C4×Dic47C2212yes—
20#15688990—24no—
21#15688982—24no—
22C4×(C2×D47)⋊C4C418yescomplemented
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C22×C42×C47C2211yescharacteristic
34C2×#95×C47C2211yescharacteristic
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C24×D47C2311yescharacteristic
39C23×Dic47C2311yescharacteristic
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C22×C4×D47—22no—
45C22×C4×D47—22no—
46C22×C4×D47—24no—
47C22×C4×D47—42no—
48C22×C4×D47C2×C414yes—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4—24no—
51C2×Dic47⋊C4—42no—
52C2×(C2×D47)⋊C4—22no—
53C2×(C2×D47)⋊C4—22no—
54C2×(C2×D47)⋊C4—24no—
55C2×(C2×D47)⋊C4—24no—
56C2×(C2×D47)⋊C4—24no—
57C2×(C2×D47)⋊C4—24no—
58C2×(C2×D47)⋊C4—24no—
59C2×(C2×D47)⋊C4—42no—
60C2×(C2×D47)⋊C4—42no—
61C2×(C2×D47)⋊C4C2×C414yes—
62C2×(C2×D47)⋊C4C2×C414yes—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—42no—
67C2×C4×Dic47—42no—
68C2×C4×Dic47C2×C414yes—
69C47⋊#95—22no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—42no—
76C47⋊#95C2×C414yes—
77C47⋊#95C2×C414yes—
78C47⋊#95D414yes—
79C23×C4×C47C2312yes—
80C23×C4×C47C2312yes—
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C2×C42×C47—42no—
85C2×C42×C47C2×C414yes—
86#95×C47—22no—
87#95×C47—22no—
88#95×C47—24no—
89#95×C47—42no—
90C24×C47C2411yescharacteristic
91C23×D47—21no—
92C23×D47—22no—
93C23×D47—22no—
94C23×D47—22no—
95C23×D47—21no—
96C23×D47—21no—
97C23×D47—22no—
98C23×D47—21no—
99C23×D47C22×C412yes—
100C23×D47#4112yes—
101C23×D47#4112yes—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
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×C47C22×C412yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47#4114yes—
130C22×C4×C47#4112yes—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—21no—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C412yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C2×D414yes—
160C22×Dic47#4114yes—
161C22×Dic47#4114yes—
162C2×C4×D47—28no—
163C2×C4×D47—28no—
164C2×C4×D47—44no—
165C2×C4×D47—48no—
166C2×C4×D47—48no—
167C42×C47—44no—
168(C2×D47)⋊C4—28no—
169(C2×D47)⋊C4—28no—
170(C2×D47)⋊C4—48no—
171(C2×D47)⋊C4—48no—
172Dic47⋊C4—48no—
173C4×Dic47—28no—
174C4×Dic47—48no—
175C23×C47C23×C411yescharacteristic
176C23×C47C22×D411yescharacteristic
177C23×C47C2×#4112yes—
178C23×C47C2×#4111yescharacteristic
179C23×C47C2×#4111yescharacteristic
180C23×C47C2×#4112yes—
181C23×C47C2×#4112yes—
182C23×C47C2×#4111yescharacteristic
183C23×C47H(5,𝔽2)12yes—
184C23×C47H(5,𝔽2)11yescharacteristic
185C23×C472−1+411yescharacteristic
186C22×D47—22no—
187C22×D47—22no—
188C22×D47—22no—
189C22×D47—22no—
190C22×D47—22no—
191C22×D47—22no—
192C22×D47—24no—
193C22×D47—24no—
194C22×D47—22no—
195C22×D47—22no—
196C22×D47—24no—
197C22×D47—22no—
198C22×D47—24no—
199C22×D47—22no—
200C22×D47—42no—
201C22×D47—42no—
202C22×D47—42no—
203C22×D47—42no—
204C22×D47—42no—
205C22×D47—42no—
206C22×D47—42no—
207C22×D47—42no—
208C22×D47#11714yes—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—24no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47#11714yes—
237C2×C4×C47C4×D414yes—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—42no—
263C2×Dic47—41no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—41no—
268C2×Dic47#11714yes—
269C4×D47—416no—
270#13919—471nomaximal, Sylow
271C22×C47C2×#11711yescharacteristic
272C22×C47C2×#11711yescharacteristic
273C22×C47C2×#11711yescharacteristic
274C22×C47C2×C4×D411yescharacteristic
275C22×C47C4×#4111yescharacteristic
276C22×C47#51811yescharacteristic
277C22×C47#52011yescharacteristic
278C22×C47#52912yes—
279C22×C47#52912yes—
280C22×C47#52912yes—
281C22×C47#53212yes—
282C22×C47#53812yes—
283C22×C47#53912yes—
284C22×C47#54612yes—
285C22×C47#54611yescharacteristic
286C22×C47#54811yescharacteristic
287C22×C47#55112yes—
288C22×C47#55112yes—
289C22×C47#55211yescharacteristic
290C22×C47#55312yes—
291C22×C47#55312yes—
292C22×C47#55311yescharacteristic
293C22×C47#55612yes—
294C2×D47—24no—
295C2×D47—24no—
296C2×D47—24no—
297C2×D47—44no—
298C2×D47—42no—
299C2×D47—44no—
300C2×D47—44no—
301C2×D47—42no—
302C2×D47—42no—
303C2×D47—42no—
304C2×D47—44no—
305C4×C47—24no—
306C4×C47—24no—
307C4×C47—42no—
308C4×C47—82no—
309C4×C47—82no—
310Dic47—24no—
311Dic47—44no—
312Dic47—42no—
313Dic47—42no—
314Dic47—44no—
315C2×#383—471no—
316C2×#380—471no—
317C2×C4×C22⋊C4—471no—
318#1442—472no—
319#1440—472no—
320#1437—472no—
321#1436—472no—
322#1434—471no—
323#1434D4711yescharacteristic, complemented
324C22⋊#95—471no—
325C4×#95—471no—
326C2×C47#228311yescharacteristic
327C2×C47#229311yescharacteristic
328C2×C47#231811yescharacteristic
329C2×C47#234211yescharacteristic
330C2×C47#234711yescharacteristic
331C2×C47#235211yescharacteristic
332C2×C47#235311yescharacteristic
333C2×C47#255912yes—
334C2×C47#256012yes—
335C2×C47#257712yes—
336C2×C47#257812yes—
337D47—44no—
338C24×C4—471no—
339C22×C4⋊C4—472no—
340C22×C22⋊C4—471no—
341C22×C22⋊C4—471no—
342C22×C22⋊C4—472no—
343C22×C22⋊C4—472no—
344C22×C42—471no—
345C22×C42—472no—
346C22×C42C2×D4711yescharacteristic
347#383—944no—
348#380—944no—
349C4×C22⋊C4—478no—
350C2×#95—471no—
351C2×#95—471no—
352C2×#95—471no—
353C2×#95—471no—
354C2×#95—472no—
355C2×#95—472no—
356C2×#95—472no—
357C2×#95—472no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95C2×D4711yescharacteristic
361C2×#95C2×D4711yescharacteristic
362C2×#95C2×D4712yes—
363C2×#95C2×D4712yes—
364C47#1391911yescharacteristic, complemented, Sylow
365C25—471no—
366C23×C4—471no—
367C23×C4—472no—
368C23×C4—471no—
369C23×C4—471no—
370C23×C4—472no—
371C23×C4—474no—
372C23×C4—944no—
373C23×C4—942no—
374C23×C4—942no—
375C23×C4—1882no—
376C23×C4C22×D4712yes—
377C23×C4C22×D4712yes—
378C23×C4C22×D4711yescharacteristic
379C23×C4C22×D4711yescharacteristic
380C23×C4C22×D4711yescharacteristic
381C2×C4⋊C4—944no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—1882no—
384C2×C22⋊C4—474no—
385C2×C22⋊C4—474no—
386C2×C22⋊C4—942no—
387C2×C22⋊C4—942no—
388C2×C22⋊C4—944no—
389C2×C22⋊C4—944no—
390C2×C22⋊C4—944no—
391C2×C22⋊C4—944no—
392C2×C22⋊C4—944no—
393C2×C22⋊C4—1882no—
394C2×C22⋊C4—1882no—
395C2×C42—42no—
396C2×C42—474no—
397C2×C42—942no—
398C2×C42—942no—
399C2×C42—944no—
400C2×C42—1882no—
401C2×C42—1882no—
402C2×C42C4×D4714yes—
403#95—24no—
404#95—22no—
405#95—22no—
406#95—42no—
407#95—474no—
408#95—474no—
409#95—474no—
410#95—944no—
411#95—944no—
412#95—944no—
413#95—944no—
414#95—944no—
415#95—942no—
416#95—1882no—
417C24—472no—
418C24—472no—
419C24—472no—
420C24—941no—
421C24—942no—
422C24—942no—
423C24—942no—
424C24—941no—
425C24—942no—
426C24—941no—
427C24—941no—
428C24C23×D4711yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
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—472no—
453C22×C4—474no—
454C22×C4—472no—
455C22×C4—472no—
456C22×C4—474no—
457C22×C4—474no—
458C22×C4—948no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—942no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—941no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—941no—
484C22×C4—948no—
485C22×C4—1884no—
486C22×C4—1888no—
487C22×C4—1888no—
488C22×C4C2×C4×D4712yes—
489C22×C4C2×C4×D4712yes—
490C22×C4C2×C4×D4712yes—
491C22×C4#1062535014yes—
492C22×C4D4×D4712yes—
493C22×C4#1062535412yes—
494C4⋊C4—1888no—
495C22⋊C4—948no—
496C22⋊C4—948no—
497C22⋊C4—1888no—
498C22⋊C4—1888no—
499C42—44no—
500C42—948no—
501C42—1888no—
502C23—474no—
503C23—942no—
504C23—942no—
505C23—944no—
506C23—942no—
507C23—944no—
508C23—942no—
509C23—942no—
510C23—942no—
511C23—942no—
512C23—942no—
513C23—942no—
514C23—942no—
515C23—944no—
516C23—944no—
517C23—1882no—
518C23—1882no—
519C23—1882no—
520C23—1882no—
521C23—1882no—
522C23—1882no—
523C23—1882no—
524C23—1882no—
525C23C22×C4×D4711yescharacteristic
526C23C2×D4×D4711yescharacteristic
527C23#41×D4712yes—
528C23#41×D4711yescharacteristic
529C23#41×D4711yescharacteristic
530C23#41×D4712yes—
531C23C2×#1062535012yes—
532C23C2×#1062535411yescharacteristic
533C23#1309406912yes—
534C23#1309407011yescharacteristic
535C23#1309407111yescharacteristic
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—474no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—944no—
569C2×C4—944no—
570C2×C4—944no—
571C2×C4—944no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—944no—
579C2×C4—944no—
580C2×C4—18816no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1882no—
584C2×C4—1881no—
585C2×C4—1882no—
586C2×C4—1882no—
587C2×C4—1881no—
588C2×C4—1882no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1882no—
595C2×C4#1309398114yes—
596C2×C4#1309398614yes—
597C22—944no—
598C22—944no—
599C22—944no—
600C22—1882no—
601C22—1882no—
602C22—1884no—
603C22—1884no—
604C22—1884no—
605C22—1884no—
606C22—1882no—
607C22—1882no—
608C22#117×D4711yescharacteristic
609C22#117×D4711yescharacteristic
610C22C2×#1309398111yescharacteristic
611C22C2×#1309398611yescharacteristic
612C22#1568959111yescharacteristic
613C22#1568959611yescharacteristic
614C22#1568960311yescharacteristic
615C22#1568965112yes—
616C22#1568965112yes—
617C22#1568966012yes—
618C22#1568967012yes—
619C22#1568970612yes—
620C22#1568971512yes—
621C22#1568976212yes—
622C22#1568976611yescharacteristic
623C22#1568978111yescharacteristic
624C22#1568980012yes—
625C22#1568980112yes—
626C22#1568981111yescharacteristic
627C22#1568981812yes—
628C22#1568982412yes—
629C22#1568982611yescharacteristic
630C22#1568984012yes—
631C4—24no—
632C4—24no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—944no—
637C4—1882no—
638C4—1882no—
639C4—1884no—
640C4—1884no—
641C2—1884no—
642C2#2024578011yescharacteristic
643C2#2024584911yescharacteristic
644C2#2024601511yescharacteristic
645C2#2024623411yescharacteristic
646C2#2024627611yescharacteristic
647C2#2024631411yescharacteristic
648C2#2024632511yescharacteristic
649C2#2024851912yes—
650C2#2024853412yes—
651C2#2024870912yes—
652C2#2024872412yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1434C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1434D47
hypocenterC47#13919
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#15688990C2semidirect
4. #20241646C2semidirect
7. #20241619C2semidirect
8. #20241612C2semidirect
10. C4×C47⋊#95C2semidirect
11. C47×#1434C2semidirect
22. C4×(C2×D47)⋊C4C4semidirect
323. #1434D47semidirect
364. C47#13919semidirect

Maximal subgroups

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

subgroupindex
C2×#156889902
C2×#156889822
C2×C4×(C2×D47)⋊C42
#202416462
#202416362
#202416242
#202416192
#202416122
(C2×D47)⋊#952
C4×C47⋊#952
C47×#14342
#1391947