Finite Group Databasebeta

← #26138482

Subgroups — #26138482

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×#15688990C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic47C211yesmaximal, characteristic
3#20241649C212yesmaximal, complemented
4#20241648C212yesmaximal, complemented
5#20241614C211yesmaximal, characteristic, complemented
6#20241613C211yesmaximal, characteristic, complemented
7#20241612C211yesmaximal, characteristic, complemented
8#20241611C211yesmaximal, characteristic
9#20241611C212yesmaximal
10#20241611C212yesmaximal
11C22×#95×C47C211yesmaximal, characteristic
12C22×C22⋊Dic47C2212yes—
13C22×C22⋊Dic47C2211yescharacteristic
14C22×C22⋊Dic47C2211yescharacteristic
15C22×C4×Dic47C2211yescharacteristic
16C22×C4×Dic47C2211yescharacteristic
17#15688990—24no—
18C4×C22⋊Dic47C418yescomplemented
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⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C24×C4×C47C2212yes—
33C24×C4×C47C2211yescharacteristic
34C2×#95×C47—24no—
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2212yes—
37C2×#95×C47C2211yescharacteristic
38C23×Dic47C2312yes—
39C23×Dic47C2312yes—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C2×C22⋊Dic47—24no—
45C2×C22⋊Dic47—22no—
46C2×C22⋊Dic47—22no—
47C2×C22⋊Dic47—24no—
48C2×C22⋊Dic47—24no—
49C2×C22⋊Dic47—24no—
50C2×C22⋊Dic47C2×C414yes—
51C2×C22⋊Dic47C2×C414yes—
52C2×C4×Dic47—22no—
53C2×C4×Dic47—22no—
54C2×C4×Dic47—42no—
55C2×C4×Dic47C2×C414yescomplemented
56C2×C4×Dic47C2×C414yescomplemented
57C47⋊#95—24no—
58C47⋊#95—24no—
59C47⋊#95—22no—
60C47⋊#95—24no—
61C47⋊#95—24no—
62C47⋊#95—22no—
63C47⋊#95—42no—
64C47⋊#95—42no—
65C47⋊#95—42no—
66C47⋊#95—42no—
67C47⋊#95—42no—
68C47⋊#95C2×C414yescomplemented
69C47⋊#95C2×C414yescomplemented
70C25×C47C2311yescharacteristic
71C23×C4×C47—24no—
72C23×C4×C47—24no—
73C23×C4×C47—24no—
74C23×C4×C47—22no—
75C23×C4×C47—24no—
76C23×C4×C47—22no—
77C23×C4×C47—24no—
78C23×C4×C47—24no—
79C23×C4×C47—42no—
80C23×C4×C47—42no—
81C23×C4×C47—42no—
82C23×C4×C47C2×C414yes—
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2312yes—
85C23×C4×C47C2312yes—
86C23×C4×C47C2311yescharacteristic
87#95×C47—24no—
88#95×C47—22no—
89#95×C47D414yes—
90C24×C47—21no—
91C24×C47—21no—
92C24×C47—22no—
93C24×C47—22no—
94C24×C47—21no—
95C24×C47—21no—
96C24×C47C22×C412yes—
97C24×C47#4114yes—
98C24×C47#4114yes—
99C24×C47#4112yes—
100C24×C47#4112yes—
101C24×C47C2411yescharacteristic
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—216no—
105C22×C4×C47—28no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
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—28no—
123C22×C4×C47—44no—
124C22×C4×C47—48no—
125C22×C4×C47—48no—
126C22×C4×C47—48no—
127C22×C4×C47—48no—
128C22×C4×C47—48no—
129C22×C4×C47—48no—
130C22×C4×C47—48no—
131C22×C4×C47—48no—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C22×C412yes—
134C22×C4×C47C2×D414yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47#4114yes—
137C22×C4×C47#4112yes—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47C22×C412yes—
171C22×Dic47C22×C412yes—
172C22×Dic47C22×C412yes—
173C22×Dic47C22×C412yes—
174C22⋊Dic47—28no—
175C22⋊Dic47—28no—
176C22⋊Dic47—48no—
177C4×Dic47—28no—
178C4×Dic47—44no—
179C23×C47—22no—
180C23×C47—22no—
181C23×C47—22no—
182C23×C47—22no—
183C23×C47—24no—
184C23×C47—24no—
185C23×C47—24no—
186C23×C47—24no—
187C23×C47—24no—
188C23×C47—22no—
189C23×C47—22no—
190C23×C47—24no—
191C23×C47—24no—
192C23×C47—24no—
193C23×C47—24no—
194C23×C47—22no—
195C23×C47—22no—
196C23×C47—24no—
197C23×C47#11714yes—
198C23×C47#11714yes—
199C23×C47#11714yes—
200C23×C47#12618yes—
201C23×C47#12618yes—
202C23×C47C23×C411yescharacteristic
203C23×C47C22×D411yescharacteristic
204C23×C47C2×#4112yes—
205C23×C47C2×#4111yescharacteristic
206C23×C47C2×#4112yes—
207C23×C47C2×#4111yescharacteristic
208C23×C47C2×#4112yes—
209C23×C47C2×#4111yescharacteristic
210C23×C47H(5,𝔽2)12yes—
211C23×C47H(5,𝔽2)11yescharacteristic
212C23×C472−1+411yescharacteristic
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—24no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—416no—
227C2×C4×C47—432no—
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—42no—
237C2×C4×C47—42no—
238C2×C4×C47C4×D414yes—
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—22no—
250C2×Dic47—22no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—42no—
258C2×Dic47—41no—
259C2×Dic47—41no—
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—
273C2×Dic47—42no—
274C2×Dic47—42no—
275#13901—471nomaximal, Sylow
276C22×C47—24no—
277C22×C47—24no—
278C22×C47—24no—
279C22×C47—24no—
280C22×C47—24no—
281C22×C47—28no—
282C22×C47—28no—
283C22×C47—28no—
284C22×C47—28no—
285C22×C47—24no—
286C22×C47#38318yescomplemented
287C22×C47C2×#11711yescharacteristic
288C22×C47C2×#11711yescharacteristic
289C22×C47C2×#11711yescharacteristic
290C22×C47C2×C4×D411yescharacteristic
291C22×C47C4×#4111yescharacteristic
292C22×C47#51811yescharacteristic
293C22×C47#52011yescharacteristic
294C22×C47#52512yes—
295C22×C47C2×#12612yes—
296C22×C47C2×#12612yes—
297C22×C47#52912yes—
298C22×C47#53812yes—
299C22×C47#53912yes—
300C22×C47#54612yes—
301C22×C47#54611yescharacteristic
302C22×C47#54811yescharacteristic
303C22×C47#55112yes—
304C22×C47#55112yes—
305C22×C47#55112yes—
306C22×C47#55212yes—
307C22×C47#55211yescharacteristic
308C22×C47#55311yescharacteristic
309C22×C47#55312yes—
310C4×C47—24no—
311C4×C47—42no—
312C4×C47—44no—
313C4×C47—44no—
314Dic47—42no—
315Dic47—42no—
316Dic47—42no—
317Dic47—42no—
318Dic47—82no—
319Dic47—82no—
320C2×#383—471no—
321C2×C4×C22⋊C4—471no—
322C22×#95D4711yescharacteristic
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×C47—28no—
332C2×C47C2×#38311yescharacteristic
333C2×C47#229011yescharacteristic
334C2×C47#231811yescharacteristic
335C2×C47#234211yescharacteristic
336C2×C47#234311yescharacteristic
337C2×C47#235211yescharacteristic
338C2×C47#235311yescharacteristic
339C2×C47#248012yes—
340C2×C47#248112yes—
341C2×C47#249312yes—
342C2×C47#251012yes—
343C24×C4C2×D4712yes—
344C24×C4C2×D4711yescharacteristic
345C22×C22⋊C4—471no—
346C22×C22⋊C4—471no—
347C22×C22⋊C4—472no—
348C22×C42—471no—
349C22×C42—471no—
350#383—944no—
351C4×C22⋊C4—478no—
352C2×#95—24no—
353C2×#95—471no—
354C2×#95—471no—
355C2×#95—471no—
356C2×#95—472no—
357C2×#95—472no—
358C2×#95—471no—
359C2×#95—472no—
360C2×#95—472no—
361C2×#95—472no—
362C2×#95—472no—
363C2×#95—472no—
364C2×#95—472no—
365C2×#95—472no—
366C2×#95C2×D4711yescharacteristic
367C2×#95C2×D4712yes—
368C2×#95C2×D4711yescharacteristic
369C47#1390111yescharacteristic, complemented, Sylow
370C25C22×D4711yescharacteristic
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—471no—
383C23×C4—471no—
384C23×C4—471no—
385C23×C4—471no—
386C23×C4—472no—
387C23×C4—472no—
388C23×C4C4×D4714yes—
389C23×C4C22×D4711yescharacteristic
390C23×C4C22×D4712yes—
391C23×C4C22×D4712yes—
392C23×C4C22×D4711yescharacteristic
393C2×C22⋊C4—474no—
394C2×C22⋊C4—474no—
395C2×C22⋊C4—944no—
396C2×C22⋊C4—942no—
397C2×C22⋊C4—942no—
398C2×C22⋊C4—944no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4—944no—
401C2×C42—474no—
402C2×C42—474no—
403C2×C42—942no—
404C2×C42—942no—
405C2×C42—1882no—
406#95—24no—
407#95—22no—
408#95—474no—
409#95—474no—
410#95—944no—
411#95—944no—
412#95—942no—
413#95—944no—
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—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24C2×C4×D4712yes—
429C24#1062535014yes—
430C24#1062535214yes—
431C24#1062535212yes—
432C24#1062535412yes—
433C24C23×D4711yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—28no—
455C22×C4—44no—
456C22×C4—48no—
457C22×C4—48no—
458C22×C4—48no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—472no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4C2×C4×D4712yes—
501C22×C4C2×C4×D4712yes—
502C22×C4#1062535014yes—
503C22×C4#1062535012yes—
504C22×C4C2×C22⋊D4714yes—
505C22×C4C2×C22⋊D4712yes—
506C22⋊C4—948no—
507C22⋊C4—948no—
508C22⋊C4—1888no—
509C42—948no—
510C42—1884no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—24no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23#1309398014yes—
530C23#1309398114yes—
531C23#1309398214yes—
532C23#1309401718yes—
533C23#1309401918yes—
534C23C22×C4×D4711yescharacteristic
535C23C22×C22⋊D4711yescharacteristic
536C23C2×#1062535212yes—
537C23C2×#1062535211yescharacteristic
538C23C2×#1062535011yescharacteristic
539C23C2×#1062535012yes—
540C23C2×#1062535012yes—
541C23C2×#1062535411yescharacteristic
542C23#1309406912yes—
543C23#1309406911yescharacteristic
544C23#1309407211yescharacteristic
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—416no—
559C2×C4—432no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
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—942no—
580C2×C4—942no—
581C2×C4—942no—
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—1882no—
596C2×C4—1881no—
597C2×C4—1881no—
598C2×C4—1882no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1882no—
604C2×C4—1882no—
605C2×C4—1882no—
606C2×C4C4×C22⋊D4714yes—
607C22—24no—
608C22—24no—
609C22—24no—
610C22—24no—
611C22—28no—
612C22—28no—
613C22—28no—
614C22—24no—
615C22—28no—
616C22—24no—
617C22#1568899018yescomplemented
618C22C2×#1309398011yescharacteristic
619C22C2×#1309398111yescharacteristic
620C22C2×#1309398211yescharacteristic
621C22C2×C4×C22⋊D4711yescharacteristic
622C22C4×#1062535011yescharacteristic
623C22#1568959611yescharacteristic
624C22#1568960411yescharacteristic
625C22#1568963412yes—
626C22C2×#1309401712yes—
627C22C2×#1309401912yes—
628C22#1568965712yes—
629C22#1568971112yes—
630C22#1568972012yes—
631C22#1568976711yescharacteristic
632C22#1568976712yes—
633C22#1568978411yescharacteristic
634C22#1568979912yes—
635C22#1568979912yes—
636C22#1568979912yes—
637C22#1568980811yescharacteristic
638C22#1568980812yes—
639C22#1568982111yescharacteristic
640C22#1568982112yes—
641C4—24no—
642C4—44no—
643C4—44no—
644C4—42no—
645C4—3762no—
646C4—3762no—
647C4—1882no—
648C4—1882no—
649C4—1882no—
650C4—1882no—
651C2—28no—
652C2C2×#1568899011yescharacteristic
653C2#2024583111yescharacteristic
654C2#2024602211yescharacteristic
655C2#2024623311yescharacteristic
656C2#2024624411yescharacteristic
657C2#2024631311yescharacteristic
658C2#2024632411yescharacteristic
659C2#2024762812yes—
660C2#2024764312yes—
661C2#2024777312yes—
662C2#2024794812yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×#95D47
hypocenterC47#13901
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C2×#15688990C2semidirect
3. #20241649C2semidirect
4. #20241648C2semidirect
5. #20241614C2semidirect
6. #20241613C2semidirect
7. #20241612C2semidirect
18. C4×C22⋊Dic47C4semidirect
55. C2×C4×Dic47C2×C4semidirect
56. C2×C4×Dic47C2×C4semidirect
68. C47⋊#95C2×C4semidirect
69. C47⋊#95C2×C4semidirect
286. C22×C47#383semidirect
369. C47#13901semidirect
617. C22#15688990semidirect

Maximal subgroups

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

subgroupindex
C2×#156889902
C2×C4×C22⋊Dic472
#202416492
#202416482
#202416142
#202416132
#202416122
#202416112
C22×#95×C472
#1390147