Finite Group Databasebeta

← #26138890

Subgroups — #26138890

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20241650C212yesmaximal, complemented
2#20241637C212yesmaximal
3#20241625C212yesmaximal
4#20241615C211yesmaximal, characteristic, complemented
5#20241615C211yesmaximal, characteristic, complemented
6#20241615C211yesmaximal, characteristic, complemented
7#20241613C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic
9#20241611C211yesmaximal, characteristic
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C22×C22⋊Dic47C2212yes—
13C22×C22⋊Dic47C2212yes—
14C22×C4×Dic47C2212yes—
15C2×C47⋊#95C2211yescharacteristic
16C2×C47⋊#95C2211yescharacteristic
17C2×C47⋊#95C2212yes—
18C2×C47⋊#95C2211yescharacteristic
19C2×C47⋊#95C2211yescharacteristic
20C2×C47⋊#95C2212yes—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C24×C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2211yescharacteristic
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C4×C22⋊C4×C47C418yescomplemented
34C2×#95×C47C2211yescharacteristic
35C2×#95×C47C2211yescharacteristic
36C23×Dic47C2312yes—
37C23×Dic47C2312yes—
38C23×Dic47C2312yes—
39C23×Dic47C2312yes—
40C2×C22⋊Dic47—24no—
41C2×C22⋊Dic47—24no—
42C2×C22⋊Dic47—24no—
43C2×C22⋊Dic47—24no—
44C2×C22⋊Dic47—42no—
45C2×C22⋊Dic47—42no—
46C2×C4×Dic47—24no—
47C2×C4×Dic47—24no—
48C2×C4×Dic47—42no—
49C47⋊#95—22no—
50C47⋊#95—22no—
51C47⋊#95—24no—
52C47⋊#95—22no—
53C47⋊#95—22no—
54C47⋊#95—24no—
55C47⋊#95—24no—
56C47⋊#95—24no—
57C47⋊#95—42no—
58C47⋊#95—42no—
59C47⋊#95—42no—
60C47⋊#95—42no—
61C47⋊#95—42no—
62C25×C47C2311yescharacteristic
63C23×C4×C47—22no—
64C23×C4×C47—22no—
65C23×C4×C47—42no—
66C23×C4×C47—42no—
67C23×C4×C47C2×C414yes—
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C2×C22⋊C4×C47—22no—
75C2×C22⋊C4×C47—22no—
76C2×C22⋊C4×C47—22no—
77C2×C22⋊C4×C47—22no—
78C2×C22⋊C4×C47C2×C414yes—
79C2×C22⋊C4×C47C2×C414yes—
80C2×C42×C47—42no—
81C2×C42×C47—42no—
82C2×C42×C47C2×C414yes—
83C2×C42×C47C2×C414yes—
84#95×C47C2×C414yes—
85#95×C47C2×C414yes—
86C24×C47—21no—
87C24×C47—21no—
88C24×C47—21no—
89C24×C47—21no—
90C24×C47—22no—
91C24×C47—22no—
92C24×C47—22no—
93C24×C47—22no—
94C24×C47C22×C412yes—
95C24×C47#4112yes—
96C24×C47#4112yes—
97C24×C47C2411yescharacteristic
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
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—28no—
119C22×C4×C47—44no—
120C22×C4×C47—44no—
121C22×C4×C47—48no—
122C22×C4×C47—48no—
123C22×C4×C47C22×C412yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47#4112yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47#4114yes—
160C22×Dic47#4114yes—
161C22⋊C4×C47—28no—
162C22⋊C4×C47—28no—
163C42×C47—44no—
164C42×C47—44no—
165C22⋊Dic47—48no—
166C22⋊Dic47—48no—
167C4×Dic47—48no—
168C23×C47—22no—
169C23×C47—22no—
170C23×C47—22no—
171C23×C47—22no—
172C23×C47—22no—
173C23×C47—22no—
174C23×C47—22no—
175C23×C47—22no—
176C23×C47—22no—
177C23×C47—22no—
178C23×C47—24no—
179C23×C47—24no—
180C23×C47—24no—
181C23×C47—24no—
182C23×C47—42no—
183C23×C47—42no—
184C23×C47—42no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47—42no—
189C23×C47—42no—
190C23×C47#11714yes—
191C23×C47C23×C411yescharacteristic
192C23×C47C2×#4112yes—
193C23×C47C2×#4112yes—
194C23×C47C2×#4111yescharacteristic
195C23×C47C2×#4111yescharacteristic
196C23×C47C2×#4111yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47C2×#4111yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47H(5,𝔽2)12yes—
201C23×C47H(5,𝔽2)12yes—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—24no—
209C2×C4×C47—24no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—416no—
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#11714yes—
232C2×C4×C47#11714yes—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—24no—
238C2×Dic47—24no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261#13947—471nomaximal, Sylow
262C22×C47—24no—
263C22×C47—24no—
264C22×C47—24no—
265C22×C47—42no—
266C22×C47—44no—
267C22×C47—44no—
268C22×C47—44no—
269C22×C47—44no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—42no—
273C22×C47C2×#11711yescharacteristic
274C22×C47C2×#11711yescharacteristic
275C22×C47C2×#11711yescharacteristic
276C22×C47C4×#4111yescharacteristic
277C22×C47C4×#4111yescharacteristic
278C22×C47#51811yescharacteristic
279C22×C47#51811yescharacteristic
280C22×C47#52912yes—
281C22×C47#52912yes—
282C22×C47#52911yescharacteristic
283C22×C47#52911yescharacteristic
284C22×C47#52911yescharacteristic
285C22×C47#52911yescharacteristic
286C22×C47#53812yes—
287C22×C47#53812yes—
288C22×C47#55112yes—
289C22×C47#55112yes—
290C22×C47#55112yes—
291C22×C47#55312yes—
292C22×C47#55312yes—
293C22×C47#55312yes—
294C22×C47#55312yes—
295C22×C47#55912yes—
296C4×C47—24no—
297C4×C47—24no—
298C4×C47—42no—
299C4×C47—42no—
300C4×C47—42no—
301C4×C47—42no—
302Dic47—44no—
303Dic47—44no—
304Dic47—82no—
305Dic47—82no—
306C2×C4×C22⋊C4D4711yescharacteristic
307#1443—472no—
308#1440—472no—
309#1437—472no—
310#1434—471no—
311#1434—471no—
312#1434—471no—
313#1434—472no—
314C22⋊#95—471no—
315C22⋊#95—471no—
316C4×#95—471no—
317C2×C47—44no—
318C2×C47#228311yescharacteristic
319C2×C47#229811yescharacteristic
320C2×C47#231211yescharacteristic
321C2×C47#235311yescharacteristic
322C2×C47#235311yescharacteristic
323C2×C47#235311yescharacteristic
324C2×C47#235711yescharacteristic
325C2×C47#257612yes—
326C2×C47#257812yes—
327C2×C47#259512yes—
328C2×C47#259712yes—
329C24×C4C2×D4711yescharacteristic
330C22×C22⋊C4—472no—
331C22×C22⋊C4—472no—
332C22×C22⋊C4C2×D4711yescharacteristic
333C22×C22⋊C4C2×D4711yescharacteristic
334C22×C42—472no—
335C22×C42C2×D4711yescharacteristic
336C22×C42C2×D4711yescharacteristic
337C4×C22⋊C4Dic4718yescomplemented
338C2×#95—471no—
339C2×#95—471no—
340C2×#95—472no—
341C2×#95—471no—
342C2×#95—471no—
343C2×#95—472no—
344C2×#95—472no—
345C2×#95—472no—
346C2×#95—472no—
347C2×#95—472no—
348C2×#95—472no—
349C2×#95—472no—
350C2×#95—472no—
351C2×#95C2×D4711yescharacteristic
352C2×#95C2×D4711yescharacteristic
353C47#1394711yescharacteristic, complemented, Sylow
354C25C22×D4711yescharacteristic
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—472no—
360C23×C4—472no—
361C23×C4—472no—
362C23×C4—472no—
363C23×C4C2×Dic4714yes—
364C23×C4C22×D4711yescharacteristic
365C23×C4C22×D4711yescharacteristic
366C23×C4C22×D4711yescharacteristic
367C23×C4C22×D4711yescharacteristic
368C23×C4C22×D4711yescharacteristic
369C23×C4C22×D4711yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—944no—
375C2×C22⋊C4—944no—
376C2×C22⋊C4—944no—
377C2×C22⋊C4—944no—
378C2×C22⋊C4—1882no—
379C2×C22⋊C4—1882no—
380C2×C22⋊C4C2×Dic4714yes—
381C2×C22⋊C4C2×Dic4714yes—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—944no—
385C2×C42—944no—
386C2×C42—1882no—
387C2×C42C2×Dic4714yes—
388C2×C42C2×Dic4714yes—
389#95—944no—
390#95—944no—
391#95—944no—
392#95—942no—
393#95—942no—
394#95—944no—
395#95—942no—
396#95—942no—
397#95—1882no—
398#95—1882no—
399#95—1882no—
400#95—1882no—
401#95—1882no—
402#95C2×Dic4714yes—
403#95C2×Dic4714yes—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24#1062535012yes—
413C24#1062535012yes—
414C24C22×Dic4712yes—
415C24C23×D4711yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—474no—
442C22×C4—474no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4#1062535012yes—
470C22×C4#1062535012yes—
471C22×C4#1062535012yes—
472C22×C4#1062535012yes—
473C22×C4C22×Dic4712yes—
474C22×C4C22×Dic4712yes—
475C22×C4C22×Dic4712yes—
476C22×C4C22×Dic4712yes—
477C22×C4C22×Dic4712yes—
478C22×C4C22×Dic4712yes—
479C22⋊C4—28no—
480C22⋊C4—28no—
481C22⋊C4—1888no—
482C22⋊C4—1888no—
483C42—44no—
484C42—44no—
485C42—1888no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23#1309398314yes—
509C23C23×Dic4711yescharacteristic
510C23#41×D4712yes—
511C23#41×D4712yes—
512C23C2×#1062535011yescharacteristic
513C23C2×#1062535011yescharacteristic
514C23C2×#1062535011yescharacteristic
515C23C2×#1062535011yescharacteristic
516C23C2×#1062535011yescharacteristic
517C23C2×#1062535011yescharacteristic
518C23#1309406912yes—
519C23#1309406912yes—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—416no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—944no—
550C2×C4—944no—
551C2×C4—944no—
552C2×C4—944no—
553C2×C4—944no—
554C2×C4—944no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4—1882no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4—1882no—
575C2×C4—1882no—
576C2×C4—1882no—
577C2×C4#1309398314yes—
578C2×C4#1309398314yes—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—44no—
586C22—44no—
587C22—42no—
588C22—44no—
589C22—42no—
590C22C2×#1309398311yescharacteristic
591C22C2×#1309398311yescharacteristic
592C22C2×#1309398311yescharacteristic
593C22#41×Dic4711yescharacteristic
594C22#41×Dic4711yescharacteristic
595C22#1568959811yescharacteristic
596C22#1568959811yescharacteristic
597C22#1568965112yes—
598C22#1568965112yes—
599C22#1568965711yescharacteristic
600C22#1568965711yescharacteristic
601C22#1568965711yescharacteristic
602C22#1568965711yescharacteristic
603C22#1568971112yes—
604C22#1568971112yes—
605C22#1568980212yes—
606C22#1568980212yes—
607C22#1568980212yes—
608C22#1568982212yes—
609C22#1568982212yes—
610C22#1568982212yes—
611C22#1568982312yes—
612C22#1568985612yes—
613C4—24no—
614C4—24no—
615C4—42no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—3762no—
620C4—3762no—
621C4—1884no—
622C4—1884no—
623C2—44no—
624C2#2024578611yescharacteristic
625C2#2024588611yescharacteristic
626C2#2024598611yescharacteristic
627C2#2024632811yescharacteristic
628C2#2024632811yescharacteristic
629C2#2024632811yescharacteristic
630C2#2024636111yescharacteristic
631C2#2024868612yes—
632C2#2024871612yes—
633C2#2024890312yes—
634C2#2024893312yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13947
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20241650C2semidirect
4. #20241615C2semidirect
5. #20241615C2semidirect
6. #20241615C2semidirect
7. #20241613C2semidirect
10. C4×C47⋊#95C2semidirect
33. C4×C22⋊C4×C47C4semidirect
337. C4×C22⋊C4Dic47semidirect
353. C47#13947semidirect

Maximal subgroups

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

subgroupindex
#202416502
#202416372
#202416252
#202416152
#202416132
#202416112
C4×C47⋊#952
C2×C4×C22⋊C4×C472
#1394747