Finite Group Databasebeta

← #26138484

Subgroups — #26138484

Order 12032.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
2C2×#95×D47C211yesmaximal, characteristic
3#20241649C212yesmaximal, complemented
4#20241648C212yesmaximal, complemented
5#20241615C211yesmaximal, characteristic, complemented
6#20241614C211yesmaximal, characteristic, complemented
7#20241613C211yesmaximal, characteristic, complemented
8(C2×D47)⋊#95C211yesmaximal, characteristic
9(C2×D47)⋊#95C212yesmaximal
10(C2×D47)⋊#95C212yesmaximal
11C2×C47×#383C211yesmaximal, characteristic, complemented
12C23×C4×D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C22×(C2×D47)⋊C4C2212yes—
15C22×(C2×D47)⋊C4C2211yescharacteristic
16C22×(C2×D47)⋊C4C2211yescharacteristic
17C22×C4×Dic47C2211yescharacteristic
18C4×(C2×D47)⋊C4C418yescomplemented
19C2×C47⋊#95C2211yescharacteristic
20C2×C47⋊#95C2212yes—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31#95×D47—24no—
32C22×C42×C47C2211yescharacteristic
33C47×#383—24no—
34C2×#95×C47C2211yescharacteristic
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C2×#95×C47C2211yescharacteristic
38C24×D47C2311yescharacteristic
39C23×Dic47C2312yes—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2312yes—
44C22×C4×D47—24no—
45C22×C4×D47—24no—
46C22×C4×D47—24no—
47C22×C4×D47—22no—
48C22×C4×D47—22no—
49C22×C4×D47—24no—
50C22×C4×D47—24no—
51C22×C4×D47—24no—
52C22×C4×D47—42no—
53C22×C4×D47—42no—
54C22×C4×D47—42no—
55C22×C4×D47C2×C414yes—
56C2×(C2×D47)⋊C4—22no—
57C2×(C2×D47)⋊C4—24no—
58C2×(C2×D47)⋊C4—22no—
59C2×(C2×D47)⋊C4—24no—
60C2×(C2×D47)⋊C4—24no—
61C2×(C2×D47)⋊C4—24no—
62C2×(C2×D47)⋊C4C2×C414yes—
63C2×(C2×D47)⋊C4C2×C414yes—
64C2×C4×Dic47—42no—
65C2×C4×Dic47C2×C414yescomplemented
66C47⋊#95—24no—
67C47⋊#95—22no—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—42no—
72C47⋊#95—42no—
73C47⋊#95—42no—
74C47⋊#95—42no—
75C47⋊#95—42no—
76C47⋊#95C2×C414yescomplemented
77C47⋊#95C2×C414yescomplemented
78C23×C4×C47C2312yes—
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2312yes—
82C23×C4×C47C2311yescharacteristic
83C2×C42×C47—22no—
84C2×C42×C47—22no—
85C2×C42×C47C2×C414yescomplemented
86#95×C47—24no—
87#95×C47—24no—
88#95×C47—22no—
89#95×C47D414yes—
90C24×C47C2411yescharacteristic
91C23×D47—21no—
92C23×D47—21no—
93C23×D47—22no—
94C23×D47—22no—
95C23×D47—21no—
96C23×D47—21no—
97C23×D47C22×C412yes—
98C23×D47#4112yes—
99C23×D47#4114yes—
100C23×D47#4112yes—
101C23×D47#4114yes—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
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×C47C22×C412yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C22×C412yes—
130C22×C4×C47C2×D414yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47#4112yes—
133C22×Dic47—21no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47—22no—
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—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47C22×C412yes—
159C22×Dic47C22×C412yes—
160C22×Dic47C22×C412yes—
161C22×Dic47#4114yes—
162C2×C4×D47—216no—
163C2×C4×D47—28no—
164C2×C4×D47—28no—
165C2×C4×D47—44no—
166C2×C4×D47—48no—
167C2×C4×D47—48no—
168C2×C4×D47—48no—
169C2×C4×D47—48no—
170C2×C4×D47—48no—
171C2×C4×D47—48no—
172C2×C4×D47—48no—
173C2×C4×D47—48no—
174C42×C47—28no—
175(C2×D47)⋊C4—28no—
176(C2×D47)⋊C4—28no—
177(C2×D47)⋊C4—48no—
178C4×Dic47—44no—
179C23×C47C23×C411yescharacteristic
180C23×C47C22×D411yescharacteristic
181C23×C47C2×#4112yes—
182C23×C47C2×#4112yes—
183C23×C47C2×#4111yescharacteristic
184C23×C47C2×#4111yescharacteristic
185C23×C47C2×#4112yes—
186C23×C47C2×#4111yescharacteristic
187C23×C47H(5,𝔽2)12yes—
188C23×C47H(5,𝔽2)11yescharacteristic
189C23×C472−1+411yescharacteristic
190C22×D47—22no—
191C22×D47—22no—
192C22×D47—22no—
193C22×D47—22no—
194C22×D47—24no—
195C22×D47—24no—
196C22×D47—24no—
197C22×D47—24no—
198C22×D47—24no—
199C22×D47—22no—
200C22×D47—22no—
201C22×D47—24no—
202C22×D47—24no—
203C22×D47—24no—
204C22×D47—24no—
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—24no—
208C22×D47#11714yes—
209C22×D47#11714yes—
210C22×D47#11714yes—
211C22×D47#12618yes—
212C22×D47#12618yes—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—42no—
242C2×C4×C47—42no—
243C2×C4×C47C4×D414yes—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
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—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C4×D47—416no—
274C4×D47—432no—
275#13901—471nomaximal, Sylow
276C22×C47C2×#11711yescharacteristic
277C22×C47C2×#11711yescharacteristic
278C22×C47C2×#11711yescharacteristic
279C22×C47C2×C4×D411yescharacteristic
280C22×C47C4×#4111yescharacteristic
281C22×C47#51811yescharacteristic
282C22×C47#52011yescharacteristic
283C22×C47#52512yes—
284C22×C47C2×#12612yes—
285C22×C47C2×#12612yes—
286C22×C47#52912yes—
287C22×C47#53812yes—
288C22×C47#53912yes—
289C22×C47#54612yes—
290C22×C47#54611yescharacteristic
291C22×C47#54811yescharacteristic
292C22×C47#55112yes—
293C22×C47#55112yes—
294C22×C47#55112yes—
295C22×C47#55212yes—
296C22×C47#55211yescharacteristic
297C22×C47#55311yescharacteristic
298C22×C47#55312yes—
299C2×D47—24no—
300C2×D47—24no—
301C2×D47—24no—
302C2×D47—24no—
303C2×D47—24no—
304C2×D47—28no—
305C2×D47—28no—
306C2×D47—28no—
307C2×D47—28no—
308C2×D47—24no—
309C2×D47#38318yescomplemented
310C4×C47—24no—
311C4×C47—42no—
312C4×C47—44no—
313C4×C47—42no—
314C4×C47—82no—
315Dic47—42no—
316Dic47—42no—
317Dic47—42no—
318Dic47—44no—
319Dic47—82no—
320C2×#383D4711yescharacteristic, complemented
321C2×C4×C22⋊C4—471no—
322C22×#95—471no—
323#1443—472no—
324#1443—472no—
325#1434—471no—
326#1434—471no—
327#1434—471no—
328C22⋊#95—472no—
329C22⋊#95—472no—
330C22⋊#95—471no—
331C2×C47C2×#38311yescharacteristic
332C2×C47#229011yescharacteristic
333C2×C47#231811yescharacteristic
334C2×C47#234211yescharacteristic
335C2×C47#234311yescharacteristic
336C2×C47#235211yescharacteristic
337C2×C47#235311yescharacteristic
338C2×C47#248012yes—
339C2×C47#248112yes—
340C2×C47#249312yes—
341C2×C47#251012yes—
342D47—28no—
343C24×C4—471no—
344C24×C4—472no—
345C22×C22⋊C4—471no—
346C22×C22⋊C4—471no—
347C22×C22⋊C4—472no—
348C22×C42—471no—
349C22×C42C2×D4711yescharacteristic
350#383—24no—
351C4×C22⋊C4—478no—
352C2×#95—471no—
353C2×#95—471no—
354C2×#95—471no—
355C2×#95—472no—
356C2×#95—472no—
357C2×#95—471no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95—472no—
361C2×#95—472no—
362C2×#95—472no—
363C2×#95—472no—
364C2×#95—944no—
365C2×#95C2×D4711yescharacteristic
366C2×#95C2×D4712yes—
367C2×#95C2×D4712yes—
368C2×#95C2×D4711yescharacteristic
369C47#1390111yescharacteristic, complemented, Sylow
370C25—471no—
371C23×C4—471no—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—472no—
375C23×C4—474no—
376C23×C4—472no—
377C23×C4—944no—
378C23×C4—944no—
379C23×C4—944no—
380C23×C4—944no—
381C23×C4—944no—
382C23×C4—942no—
383C23×C4—944no—
384C23×C4—942no—
385C23×C4—1882no—
386C23×C4—1882no—
387C23×C4—1882no—
388C23×C4C22×D4712yes—
389C23×C4C22×D4711yescharacteristic
390C23×C4C22×D4711yescharacteristic
391C23×C4C22×D4712yes—
392C23×C4C22×D4711yescharacteristic
393C2×C22⋊C4—474no—
394C2×C22⋊C4—474no—
395C2×C22⋊C4—942no—
396C2×C22⋊C4—944no—
397C2×C22⋊C4—942no—
398C2×C22⋊C4—944no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4—944no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—474no—
404C2×C42—1882no—
405C2×C42C4×D4714yescomplemented
406#95—24no—
407#95—24no—
408#95—22no—
409#95—474no—
410#95—474no—
411#95—944no—
412#95—944no—
413#95—942no—
414#95—944no—
415#95—942no—
416#95—1882no—
417#95—1882no—
418#95—1882no—
419#95—1882no—
420#95—1882no—
421#95C22⋊D4714yes—
422C24—472no—
423C24—472no—
424C24—474no—
425C24—472no—
426C24—474no—
427C24—941no—
428C24—942no—
429C24—941no—
430C24—942no—
431C24—941no—
432C24—941no—
433C24C23×D4711yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—472no—
460C22×C4—472no—
461C22×C4—472no—
462C22×C4—474no—
463C22×C4—948no—
464C22×C4—9416no—
465C22×C4—941no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—941no—
483C22×C4—948no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—1884no—
492C22×C4—1888no—
493C22×C4—1888no—
494C22×C4—1888no—
495C22×C4—1888no—
496C22×C4—1888no—
497C22×C4—1888no—
498C22×C4—1888no—
499C22×C4—1888no—
500C22×C4C2×C4×D4712yes—
501C22×C4C2×C4×D4712yes—
502C22×C4C2×C4×D4712yes—
503C22×C4#1062535012yes—
504C22×C4C2×C22⋊D4714yes—
505C22×C4C2×C22⋊D4712yes—
506C22⋊C4—948no—
507C22⋊C4—948no—
508C22⋊C4—1888no—
509C42—28no—
510C42—1884no—
511C23—474no—
512C23—474no—
513C23—474no—
514C23—478no—
515C23—478no—
516C23—942no—
517C23—944no—
518C23—942no—
519C23—944no—
520C23—944no—
521C23—944no—
522C23—944no—
523C23—942no—
524C23—942no—
525C23—944no—
526C23—942no—
527C23—942no—
528C23—942no—
529C23—942no—
530C23—944no—
531C23—944no—
532C23—944no—
533C23—944no—
534C23C22×C4×D4711yescharacteristic
535C23C22×C22⋊D4711yescharacteristic
536C23#41×D4712yes—
537C23#41×D4711yescharacteristic
538C23#41×D4711yescharacteristic
539C23#41×D4712yes—
540C23#41×D4712yes—
541C23C2×#1062535011yescharacteristic
542C23#1309407012yes—
543C23#1309407011yescharacteristic
544C23#1309407111yescharacteristic
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—944no—
576C2×C4—944no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—944no—
587C2×C4—18816no—
588C2×C4—18832no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1882no—
595C2×C4—1882no—
596C2×C4—1882no—
597C2×C4—1882no—
598C2×C4—1882no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1882no—
604C2×C4—1882no—
605C2×C4—1882no—
606C2×C4C4×C22⋊D4714yes—
607C22—478no—
608C22—944no—
609C22—944no—
610C22—944no—
611C22—944no—
612C22—948no—
613C22—948no—
614C22—948no—
615C22—948no—
616C22—944no—
617C22—944no—
618C22#117×D4711yescharacteristic
619C22#117×D4711yescharacteristic
620C22#117×D4711yescharacteristic
621C22C2×C4×C22⋊D4711yescharacteristic
622C22#1568959111yescharacteristic
623C22#1568959711yescharacteristic
624C22#1568960311yescharacteristic
625C22#1568963012yes—
626C22#126×D4712yes—
627C22#126×D4712yes—
628C22#1568965112yes—
629C22#1568971212yes—
630C22#1568971412yes—
631C22#1568976111yescharacteristic
632C22#1568976112yes—
633C22#1568978011yescharacteristic
634C22#1568979712yes—
635C22#1568979812yes—
636C22#1568979812yes—
637C22#1568980912yes—
638C22#1568981211yescharacteristic
639C22#1568981711yescharacteristic
640C22#1568982412yes—
641C4—24no—
642C4—42no—
643C4—42no—
644C4—44no—
645C4—82no—
646C4—3762no—
647C4—1882no—
648C4—1882no—
649C4—1884no—
650C4—1882no—
651C2—948no—
652C2#383×D4711yescharacteristic
653C2#2024582511yescharacteristic
654C2#2024601911yescharacteristic
655C2#2024623811yescharacteristic
656C2#2024624511yescharacteristic
657C2#2024631811yescharacteristic
658C2#2024632111yescharacteristic
659C2#2024763012yes—
660C2#2024764512yes—
661C2#2024777012yes—
662C2#2024795512yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#383C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#383D47
hypocenterC47#13901
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
3. #20241649C2semidirect
4. #20241648C2semidirect
5. #20241615C2semidirect
6. #20241614C2semidirect
7. #20241613C2semidirect
11. C2×C47×#383C2semidirect
18. C4×(C2×D47)⋊C4C4semidirect
65. C2×C4×Dic47C2×C4semidirect
76. C47⋊#95C2×C4semidirect
77. C47⋊#95C2×C4semidirect
85. C2×C42×C47C2×C4semidirect
309. C2×D47#383semidirect
320. C2×#383D47semidirect
369. C47#13901semidirect
405. C2×C42C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D47)⋊C42
C2×#95×D472
#202416492
#202416482
#202416152
#202416142
#202416132
(C2×D47)⋊#952
C2×C47×#3832
#1390147