Finite Group Databasebeta

← #26138346

Subgroups — #26138346

Order 12032.

1602 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×#15688987C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic47C211yesmaximal, characteristic
3C2×C4×C22⋊Dic47C211yesmaximal, characteristic
4#20241635C212yesmaximal
5#20241631C212yesmaximal
6#20241619C212yesmaximal, complemented
7#20241614C211yesmaximal, characteristic, complemented
8#20241613C212yesmaximal, complemented
9#20241613C211yesmaximal, characteristic, complemented
10#20241612C211yesmaximal, characteristic, complemented
11C47×C22⋊#95C211yesmaximal, characteristic
12C22×Dic47⋊C4C2212yes—
13C22×C22⋊Dic47C2212yes—
14C22×C22⋊Dic47C2211yescharacteristic
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19#15688987—24no—
20C4×C22⋊Dic47—24no—
21C4×C22⋊Dic47C418yescomplemented
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C24×C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2212yes—
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2211yescharacteristic
37C2×#95×C47C2212yes—
38C23×Dic47C2311yescharacteristic
39C23×Dic47C2311yescharacteristic
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C2×Dic47⋊C4—24no—
45C2×Dic47⋊C4—24no—
46C2×Dic47⋊C4—42no—
47C2×C22⋊Dic47—24no—
48C2×C22⋊Dic47—24no—
49C2×C22⋊Dic47—24no—
50C2×C22⋊Dic47—24no—
51C2×C22⋊Dic47—22no—
52C2×C22⋊Dic47—22no—
53C2×C22⋊Dic47C2×C414yes—
54C2×C22⋊Dic47C2×C414yes—
55C2×C4×Dic47—22no—
56C2×C4×Dic47—22no—
57C2×C4×Dic47—24no—
58C2×C4×Dic47—24no—
59C2×C4×Dic47—42no—
60C2×C4×Dic47—42no—
61C2×C4×Dic47C2×C414yes—
62C2×C4×Dic47C2×C414yes—
63C47⋊#95—22no—
64C47⋊#95—24no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—42no—
69C47⋊#95—42no—
70C47⋊#95—42no—
71C47⋊#95C2×C414yes—
72C47⋊#95C2×C414yes—
73C47⋊#95D414yes—
74C25×C47C2311yescharacteristic
75C23×C4×C47—22no—
76C23×C4×C47—24no—
77C23×C4×C47—22no—
78C23×C4×C47—42no—
79C23×C4×C47C2×C414yes—
80C23×C4×C47C2312yes—
81C23×C4×C47C2312yes—
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C2×C22⋊C4×C47—24no—
85C2×C22⋊C4×C47—42no—
86C2×C22⋊C4×C47—42no—
87#95×C47—22no—
88#95×C47—24no—
89#95×C47—22no—
90C24×C47—21no—
91C24×C47—22no—
92C24×C47—21no—
93C24×C47—21no—
94C24×C47—21no—
95C24×C47—22no—
96C24×C47—21no—
97C24×C47—22no—
98C24×C47—21no—
99C24×C47C22×C412yes—
100C24×C47#4114yes—
101C24×C47C2411yescharacteristic
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—28no—
108C22×C4×C47—28no—
109C22×C4×C47—22no—
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—44no—
124C22×C4×C47—48no—
125C22×C4×C47—48no—
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—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—22no—
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—22no—
151C22×Dic47—21no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—21no—
158C22×Dic47—22no—
159C22×Dic47C22×C412yes—
160C22×Dic47C22×C412yes—
161C22×Dic47C22×C412yes—
162C22×Dic47C22×C412yes—
163C22×Dic47C2×D414yes—
164C22×Dic47#4114yes—
165C22×Dic47#4112yes—
166C22×Dic47#4112yes—
167C22⋊C4×C47—48no—
168C22⋊Dic47—216no—
169C22⋊Dic47—28no—
170C22⋊Dic47—28no—
171Dic47⋊C4—48no—
172C4×Dic47—28no—
173C4×Dic47—44no—
174C4×Dic47—48no—
175C23×C47—22no—
176C23×C47—22no—
177C23×C47—22no—
178C23×C47—22no—
179C23×C47—22no—
180C23×C47—22no—
181C23×C47—24no—
182C23×C47—24no—
183C23×C47—24no—
184C23×C47—24no—
185C23×C47—24no—
186C23×C47—24no—
187C23×C47—42no—
188C23×C47—41no—
189C23×C47—41no—
190C23×C47—42no—
191C23×C47—42no—
192C23×C47—41no—
193C23×C47—42no—
194C23×C47—41no—
195C23×C47—42no—
196C23×C47—42no—
197C23×C47#11714yes—
198C23×C47C23×C411yescharacteristic
199C23×C47C22×D411yescharacteristic
200C23×C47C2×#4111yescharacteristic
201C23×C47C2×#4111yescharacteristic
202C23×C47C2×#4112yes—
203C23×C47C2×#4112yes—
204C23×C47C2×#4111yescharacteristic
205C23×C47C2×#4112yes—
206C23×C47H(5,𝔽2)12yes—
207C23×C47H(5,𝔽2)11yescharacteristic
208C23×C472−1+411yescharacteristic
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—416no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
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#11714yes—
233C2×C4×C47C4×D414yes—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—42no—
269C2×Dic47#11714yes—
270#13888—471nomaximal, Sylow
271C22×C47—24no—
272C22×C47—24no—
273C22×C47—24no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—42no—
277C22×C47—42no—
278C22×C47—44no—
279C22×C47—44no—
280C22×C47—44no—
281C22×C47—44no—
282C22×C47C2×#11711yescharacteristic
283C22×C47C2×#11711yescharacteristic
284C22×C47C2×#11711yescharacteristic
285C22×C47C2×C4×D411yescharacteristic
286C22×C47C4×#4111yescharacteristic
287C22×C47#51811yescharacteristic
288C22×C47#52011yescharacteristic
289C22×C47#52512yes—
290C22×C47#52912yes—
291C22×C47#52912yes—
292C22×C47#52912yes—
293C22×C47#53812yes—
294C22×C47#53912yes—
295C22×C47#54612yes—
296C22×C47#54611yescharacteristic
297C22×C47#54811yescharacteristic
298C22×C47#55112yes—
299C22×C47#55212yes—
300C22×C47#55211yescharacteristic
301C22×C47#55312yes—
302C22×C47#55311yescharacteristic
303C22×C47#55512yes—
304C22×C47#55912yes—
305C4×C47—24no—
306C4×C47—24no—
307C4×C47—82no—
308C4×C47—82no—
309Dic47—24no—
310Dic47—42no—
311Dic47—42no—
312Dic47—44no—
313Dic47—44no—
314Dic47—42no—
315C2×#382—471no—
316C2×C4×C22⋊C4—471no—
317C2×C4×C22⋊C4—471no—
318#1440—472no—
319#1439—472no—
320#1436—472no—
321#1434—471no—
322#1434—472no—
323#1434—471no—
324#1434—471no—
325C22⋊#95D4711yescharacteristic
326C2×C47—44no—
327C2×C47#228311yescharacteristic
328C2×C47#229011yescharacteristic
329C2×C47#231811yescharacteristic
330C2×C47#234211yescharacteristic
331C2×C47#234611yescharacteristic
332C2×C47#235211yescharacteristic
333C2×C47#235711yescharacteristic
334C2×C47#245912yes—
335C2×C47#246012yes—
336C2×C47#251712yes—
337C2×C47#251812yes—
338C24×C4C2×D4711yescharacteristic
339C22×C4⋊C4—472no—
340C22×C22⋊C4—471no—
341C22×C22⋊C4—471no—
342C22×C22⋊C4—472no—
343C22×C22⋊C4C2×D4712yes—
344C22×C42—471no—
345C22×C42—471no—
346C22×C42—472no—
347#382—944no—
348C4×C22⋊C4—478no—
349C4×C22⋊C4—944no—
350C2×#95—471no—
351C2×#95—471no—
352C2×#95—471no—
353C2×#95—472no—
354C2×#95—472no—
355C2×#95—471no—
356C2×#95—472no—
357C2×#95—472no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95—472no—
361C2×#95C2×D4711yescharacteristic
362C2×#95C2×D4712yes—
363C2×#95C2×D4711yescharacteristic
364C47#1388811yescharacteristic, complemented, Sylow
365C25C22×D4711yescharacteristic
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4—471no—
371C23×C4—472no—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—471no—
375C23×C4—472no—
376C23×C4C4×D4714yes—
377C23×C4C22×D4712yes—
378C23×C4C22×D4712yes—
379C23×C4C22×D4711yescharacteristic
380C23×C4C22×D4711yescharacteristic
381C2×C4⋊C4—944no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—1882no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—474no—
388C2×C22⋊C4—474no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4—942no—
391C2×C22⋊C4—944no—
392C2×C22⋊C4—944no—
393C2×C22⋊C4—944no—
394C2×C22⋊C4—944no—
395C2×C42—474no—
396C2×C42—474no—
397C2×C42—942no—
398C2×C42—942no—
399C2×C42—944no—
400C2×C42—944no—
401C2×C42—1882no—
402C2×C42—1882no—
403#95—22no—
404#95—24no—
405#95—22no—
406#95—474no—
407#95—474no—
408#95—474no—
409#95—944no—
410#95—944no—
411#95—944no—
412#95—944no—
413#95—942no—
414#95—1882no—
415#95—1882no—
416#95—1882no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24C2×C4×D4712yes—
427C24#1062535014yes—
428C24C23×D4711yescharacteristic
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—22no—
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—44no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—472no—
454C22×C4—472no—
455C22×C4—472no—
456C22×C4—472no—
457C22×C4—472no—
458C22×C4—472no—
459C22×C4—474no—
460C22×C4—474no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—941no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—941no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—941no—
489C22×C4C2×C4×D4712yes—
490C22×C4C2×C4×D4712yes—
491C22×C4D4×D4712yes—
492C22×C4#1062535214yes—
493C22×C4#1062535212yes—
494C4⋊C4—1888no—
495C22⋊C4—48no—
496C22⋊C4—948no—
497C22⋊C4—9416no—
498C22⋊C4—948no—
499C42—948no—
500C42—1884no—
501C42—1888no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—42no—
523C23—42no—
524C23#1309398114yes—
525C23C22×C4×D4711yescharacteristic
526C23C2×D4×D4711yescharacteristic
527C23#41×D4711yescharacteristic
528C23#41×D4711yescharacteristic
529C23#41×D4712yes—
530C23C2×#1062535212yes—
531C23C2×#1062535211yescharacteristic
532C23C2×#1062535012yes—
533C23#1309406912yes—
534C23#1309406911yescharacteristic
535C23#1309407211yescharacteristic
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—416no—
545C2×C4—42no—
546C2×C4—42no—
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—474no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—944no—
567C2×C4—944no—
568C2×C4—944no—
569C2×C4—944no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—944no—
580C2×C4—944no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4—1882no—
585C2×C4—1882no—
586C2×C4—1882no—
587C2×C4—1882no—
588C2×C4—1882no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1882no—
595C2×C4#1309398014yes—
596C2×C4(C22⋊D47)⋊C414yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—42no—
601C22—44no—
602C22—42no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22#117×D4711yescharacteristic
609C22C2×#1309398011yescharacteristic
610C22C2×#1309398111yescharacteristic
611C22C2×(C22⋊D47)⋊C411yescharacteristic
612C22#1568959111yescharacteristic
613C22#1568959611yescharacteristic
614C22#1568960411yescharacteristic
615C22#1568963212yes—
616C22#1568965312yes—
617C22#1568965312yes—
618C22#1568965312yes—
619C22#1568971112yes—
620C22#1568972012yes—
621C22#1568976012yes—
622C22#1568977011yescharacteristic
623C22#1568978311yescharacteristic
624C22#1568980412yes—
625C22#1568980712yes—
626C22#1568980711yescharacteristic
627C22#1568981812yes—
628C22#1568982011yescharacteristic
629C22#1568983712yes—
630C22#1568985712yes—
631C4—24no—
632C4—24no—
633C4—82no—
634C4—82no—
635C4—944no—
636C4—1882no—
637C4—1884no—
638C4—1884no—
639C4—1882no—
640C4—1882no—
641C2—44no—
642C2#2024578211yescharacteristic
643C2#2024582711yescharacteristic
644C2#2024602211yescharacteristic
645C2#2024623911yescharacteristic
646C2#2024627511yescharacteristic
647C2#2024631011yescharacteristic
648C2#2024635611yescharacteristic
649C2#2024732712yes—
650C2#2024734212yes—
651C2#2024803612yes—
652C2#2024804812yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22⋊#95D47
hypocenterC47#13888
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#15688987C2semidirect
6. #20241619C2semidirect
7. #20241614C2semidirect
8. #20241613C2semidirect
9. #20241613C2semidirect
10. #20241612C2semidirect
21. C4×C22⋊Dic47C4semidirect
364. C47#13888semidirect

Maximal subgroups

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

subgroupindex
C2×#156889872
C2×C4×C22⋊Dic472
#202416352
#202416312
#202416192
#202416142
#202416132
#202416122
C47×C22⋊#952
#1388847