Finite Group Databasebeta

← #26121620

Subgroups — #26121620

Order 12032.

1794 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×#15689598C211yesmaximal, characteristic
2C22×#13093939C211yesmaximal, characteristic
3C2×#15688889C212yesmaximal, complemented
4#20241611C212yesmaximal, complemented
5C2×C47×#386C211yesmaximal, characteristic
6#15689598—24no—
7#15689598—22no—
8#15689598C414yescomplemented
9C2×D4×Dic47—24no—
10C2×#13093983—21no—
11C22×C22⋊Dic47—21no—
12C22×C22⋊Dic47C2212yes—
13C22×C22⋊Dic47C2212yes—
14C2×#13093939—22no—
15C2×#13093939—22no—
16C2×#13093939C414yescomplemented
17C2×C47⋊#95—24no—
18#15688889—24no—
19C23×D4×C47C2211yescharacteristic
20C24×C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47—21no—
22C22×C22⋊C4×C47C2211yescharacteristic
23C47×#386—22no—
24C47×#386C414yescomplemented
25C2×#95×C47—21no—
26C23×Dic47—22no—
27C23×Dic47—22no—
28C23×Dic47D414yes—
29D4×Dic47—216no—
30D4×Dic47—216no—
31#13093983—24no—
32#13093983—24no—
33C2×C4⋊Dic47—22no—
34C2×C22⋊Dic47—22no—
35C2×C22⋊Dic47—24no—
36C2×C22⋊Dic47—24no—
37C2×C22⋊Dic47—22no—
38C2×C22⋊Dic47—22no—
39C2×C22⋊Dic47—22no—
40C2×C22⋊Dic47—22no—
41C2×C22⋊Dic47—22no—
42C2×C22⋊Dic47—22no—
43C2×C22⋊Dic47—22no—
44C2×C22⋊Dic47—22no—
45C2×C22⋊Dic47—22no—
46C2×C22⋊Dic47C2×C414yes—
47C2×C22⋊Dic47C2×C414yescomplemented
48C2×C22⋊Dic47D414yes—
49C2×C4×Dic47—22no—
50#13093939—28no—
51C47⋊#95—48no—
52C25×C47D411yescharacteristic
53C25×C47C2311yescharacteristic
54C22×D4×C47—22no—
55C22×D4×C47—22no—
56C22×D4×C47—22no—
57C22×D4×C47—22no—
58C22×D4×C47C2×C412yes—
59C22×D4×C47C2×C412yes—
60C22×D4×C47C2×C412yes—
61C22×D4×C47D412yes—
62C22×D4×C47D412yes—
63C22×D4×C47Q812yes—
64C23×C4×C47—22no—
65C23×C4×C47—21no—
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47—22no—
69C23×C4×C47—44no—
70C23×C4×C47C2×C412yescomplemented
71C23×C4×C47D411yescharacteristic
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—22no—
74C2×C22⋊C4×C47—24no—
75C2×C22⋊C4×C47—21no—
76C2×C22⋊C4×C47—44no—
77C2×C22⋊C4×C47C2×C412yescomplemented
78#95×C47—24no—
79C24×C47—21no—
80C24×C47—21no—
81C24×C47—21no—
82C24×C47—21no—
83C24×C47—42no—
84C24×C47—42no—
85C24×C47—42no—
86C24×C47—42no—
87C24×C47C22⋊C412yes—
88C24×C47C22⋊C412yes—
89C24×C47C4⋊C412yes—
90C24×C47C22×C411yescharacteristic
91C24×C47C22×C411yescharacteristic
92C24×C47C22×C411yescharacteristic
93C24×C47C2×D411yescharacteristic
94C24×C47C2×D412yes—
95C24×C47C2×D411yescharacteristic
96C24×C47C2×D411yescharacteristic
97C24×C47C2×D412yes—
98C24×C47C2×Q811yescharacteristic
99C24×C47#4112yes—
100C24×C47#4112yes—
101C2×D4×C47—24no—
102C2×D4×C47—24no—
103C2×D4×C47—24no—
104C2×D4×C47—24no—
105C2×D4×C47—24no—
106C2×D4×C47—24no—
107C2×D4×C47—24no—
108C2×D4×C47—24no—
109C2×D4×C47—24no—
110C2×D4×C47—24no—
111C2×D4×C47—24no—
112C2×D4×C47—24no—
113C2×D4×C47C4214yes—
114C2×D4×C47C22⋊C414yes—
115C2×D4×C47C4⋊C414yes—
116C2×D4×C47C4⋊C414yes—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—24no—
122C22×C4×C47—28no—
123C22×C4×C47—22no—
124C22×C4×C47—24no—
125C22×C4×C47—22no—
126C22×C4×C47—44no—
127C22×C4×C47—44no—
128C22×C4×C47—48no—
129C22×C4×C47—44no—
130C22×C4×C47—42no—
131C22×C4×C47—41no—
132C22×C4×C47—42no—
133C22×C4×C47—41no—
134C22×C4×C47—42no—
135C22×C4×C47—42no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47C22⋊C412yes—
139C22×C4×C47C22⋊C412yes—
140C22×C4×C47C4⋊C412yes—
141C22×Dic47—24no—
142C22×Dic47—28no—
143C22×Dic47—24no—
144C22×Dic47—24no—
145C22×Dic47—44no—
146C22×Dic47—44no—
147C22×Dic47—44no—
148C22×Dic47—44no—
149C22×Dic47—42no—
150C22×Dic47—42no—
151C22×Dic47—82no—
152C22×Dic47—82no—
153C22×Dic47C22⋊C418yescomplemented
154C22⋊C4×C47—24no—
155C22⋊C4×C47—48no—
156C22⋊C4×C47—42no—
157C22⋊Dic47—28no—
158C22⋊Dic47—24no—
159C22⋊Dic47—24no—
160C22⋊Dic47—24no—
161C22⋊Dic47—24no—
162C22⋊Dic47—24no—
163C22⋊Dic47—24no—
164C22⋊Dic47—42no—
165C22⋊Dic47—42no—
166C4⋊Dic47—28no—
167C4×Dic47—28no—
168C23×C47—24no—
169C23×C47—22no—
170C23×C47—24no—
171C23×C47—22no—
172C23×C47—22no—
173C23×C47—22no—
174C23×C47—22no—
175C23×C47—22no—
176C23×C47—22no—
177C23×C47—22no—
178C23×C47—41no—
179C23×C47—41no—
180C23×C47—42no—
181C23×C47—42no—
182C23×C47—42no—
183C23×C47—41no—
184C23×C47—42no—
185C23×C47—44no—
186C23×C47—41no—
187C23×C47—42no—
188C23×C47—44no—
189C23×C47—42no—
190C23×C47—42no—
191C23×C47—44no—
192C23×C47—42no—
193C23×C47—44no—
194C23×C47—42no—
195C23×C47—42no—
196C23×C47—82no—
197C23×C47—81no—
198C23×C47—81no—
199C23×C47—82no—
200C23×C47#9514yescomplemented
201C23×C47C2×C4211yescharacteristic
202C23×C47C2×C22⋊C412yes—
203C23×C47C2×C22⋊C411yescharacteristic
204C23×C47C2×C22⋊C411yescharacteristic
205C23×C47C2×C22⋊C411yescharacteristic
206C23×C47C2×C4⋊C411yescharacteristic
207C23×C47C2×C4⋊C411yescharacteristic
208C23×C47C2×C4⋊C411yescharacteristic
209C23×C47#11712yes—
210C23×C47C4×D412yes—
211C23×C47C4×D412yes—
212C23×C47C4×D412yes—
213C23×C47C4×D412yes—
214C23×C47#12011yescharacteristic
215C23×C47#12011yescharacteristic
216C23×C47#12012yes—
217C23×C47#12112yes—
218C23×C47#12112yes—
219C23×C47C22⋊Q812yes—
220C23×C47C22⋊Q812yes—
221C23×C47#12311yescharacteristic
222C23×C47#12311yescharacteristic
223C23×C47#12312yes—
224D4×C47—28no—
225D4×C47—28no—
226D4×C47—28no—
227D4×C47—28no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—24no—
235C2×C4×C47—28no—
236C2×C4×C47—48no—
237C2×C4×C47—42no—
238C2×C4×C47—44no—
239C2×C4×C47—44no—
240C2×C4×C47—42no—
241C2×C4×C47—44no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—82no—
246C2×C4×C47—82no—
247C2×C4×C47#9514yescomplemented
248C2×Dic47—28no—
249C2×Dic47—44no—
250C2×Dic47—44no—
251C2×Dic47—48no—
252C2×Dic47—48no—
253C2×Dic47—44no—
254C2×Dic47—84no—
255C2×Dic47—88no—
256C2×Dic47—82no—
257C2×Dic47—82no—
258C2×Dic47—84no—
259#10745—471nomaximal, Sylow
260C22×C47—24no—
261C22×C47—22no—
262C22×C47—22no—
263C22×C47—24no—
264C22×C47—22no—
265C22×C47—21no—
266C22×C47—22no—
267C22×C47—21no—
268C22×C47—22no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—22no—
272C22×C47—24no—
273C22×C47—24no—
274C22×C47—22no—
275C22×C47—22no—
276C22×C47—24no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—42no—
282C22×C47—42no—
283C22×C47—42no—
284C22×C47—42no—
285C22×C47—42no—
286C22×C47—42no—
287C22×C47—44no—
288C22×C47—44no—
289C22×C47—42no—
290C22×C47—42no—
291C22×C47—44no—
292C22×C47—82no—
293C22×C47—82no—
294C22×C47—82no—
295C22×C47C2×#9511yescharacteristic
296C22×C47C4×C22⋊C412yes—
297C22×C47#37911yescharacteristic
298C22×C47#38012yes—
299C22×C47#38111yescharacteristic
300C22×C47#38511yescharacteristic
301C22×C47#38511yescharacteristic
302C22×C47#38512yes—
303C22×C47#38612yes—
304C22×C47#38611yescharacteristic
305C22×C47#38611yescharacteristic
306C22×C47B(4,𝔽2)12yes—
307C22×C47#45812yes—
308C4×C47—24no—
309C4×C47—44no—
310C4×C47—82no—
311Dic47—48no—
312Dic47—84no—
313C2×#518—471no—
314C22×#99—471no—
315C2×#386D4711yescharacteristic
316C2×#342—472no—
317C22⋊#95—472no—
318C2×C47—22no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—22no—
324C2×C47—22no—
325C2×C47—22no—
326C2×C47—44no—
327C2×C47C22⋊#9511yescharacteristic
328C2×C47#179012yes—
329C2×C47#186712yes—
330C2×C47#188911yescharacteristic
331C2×C47#189011yescharacteristic
332C23×D4C2×D4711yescharacteristic
333C24×C4C2×D4711yescharacteristic
334#518—474no—
335#518—944no—
336#518—942no—
337C2×C4×D4—944no—
338C2×#117—941no—
339C22×C22⋊C4—21no—
340C22×C22⋊C4—472no—
341C22×C22⋊C4—472no—
342C22×C22⋊C4—941no—
343C22×C22⋊C4C2×D4711yescharacteristic
344C2×#99—474no—
345C2×#99—942no—
346C2×#99—942no—
347#386—22no—
348#386Dic4714yescomplemented
349C2×#95—21no—
350C2×#95—944no—
351#342—944no—
352C47#1074511yescharacteristic, complemented, Sylow
353C25C22⋊D4711yescharacteristic
354C25C22×D4711yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4Dic9412yes—
360C22×D4C4×D4712yes—
361C22×D4C4×D4712yes—
362C22×D4D18812yes—
363C22×D4C2×Dic4712yes—
364C22×D4C22⋊D4712yes—
365C23×C4—22no—
366C23×C4—21no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—44no—
371C23×C4—474no—
372C23×C4—942no—
373C23×C4—942no—
374C23×C4C2×Dic4712yescomplemented
375C23×C4C22⋊D4711yescharacteristic
376C4×D4—9416no—
377C4×D4—9416no—
378#117—944no—
379#117—944no—
380C2×C4⋊C4—942no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—474no—
387C2×C22⋊C4—474no—
388C2×C22⋊C4—474no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4—944no—
391C2×C22⋊C4—944no—
392C2×C22⋊C4—942no—
393C2×C22⋊C4—942no—
394C2×C22⋊C4—942no—
395C2×C22⋊C4—942no—
396C2×C22⋊C4—942no—
397C2×C22⋊C4—942no—
398C2×C22⋊C4—942no—
399C2×C22⋊C4—942no—
400C2×C22⋊C4—942no—
401C2×C22⋊C4C2×Dic4712yescomplemented
402C2×C42—942no—
403#99—948no—
404#95—24no—
405#95—1888no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24Dic47⋊C412yes—
415C24(C2×D47)⋊C412yes—
416C24C22⋊Dic4712yes—
417C24C2×Dic9411yescharacteristic
418C24C2×C4×D4711yescharacteristic
419C24C2×C4×D4711yescharacteristic
420C24C2×D18811yescharacteristic
421C24D4×D4712yes—
422C24D4×D4712yes—
423C24#1062535212yes—
424C24#1062535212yes—
425C24C22×Dic4711yescharacteristic
426C24C2×C22⋊D4711yescharacteristic
427C24C2×C22⋊D4711yescharacteristic
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C4×Dic4714yes—
441C2×D4Dic47⋊C414yes—
442C2×D4C4⋊Dic4714yes—
443C2×D4(C2×D47)⋊C414yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—48no—
456C22×C4—42no—
457C22×C4—44no—
458C22×C4—41no—
459C22×C4—42no—
460C22×C4—41no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—478no—
466C22×C4—948no—
467C22×C4—944no—
468C22×C4—944no—
469C22×C4—944no—
470C22×C4—3762no—
471C22×C4—3762no—
472C22×C4—1884no—
473C22×C4—1884no—
474C22×C4—1882no—
475C22×C4—1882no—
476C22×C4—1884no—
477C22×C4—1884no—
478C22×C4Dic47⋊C412yes—
479C22×C4(C2×D47)⋊C412yes—
480C22×C4C22⋊Dic4712yes—
481C4⋊C4—948no—
482C22⋊C4—24no—
483C22⋊C4—48no—
484C22⋊C4—42no—
485C22⋊C4—948no—
486C22⋊C4—944no—
487C22⋊C4—944no—
488C22⋊C4—944no—
489C22⋊C4—944no—
490C22⋊C4—944no—
491C22⋊C4—944no—
492C22⋊C4—1882no—
493C22⋊C4—1882no—
494C42—948no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—42no—
506C23—41no—
507C23—41no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—44no—
513C23—42no—
514C23—44no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—44no—
519C23—44no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—81no—
524C23—81no—
525C23—82no—
526C23—82no—
527C23C47⋊#9514yescomplemented
528C23C2×C4×Dic4711yescharacteristic
529C23C22⋊C4×D4712yes—
530C23C2×(C2×D47)⋊C411yescharacteristic
531C23C2×(C2×D47)⋊C411yescharacteristic
532C23C2×C22⋊Dic4711yescharacteristic
533C23C2×Dic47⋊C411yescharacteristic
534C23C2×Dic47⋊C411yescharacteristic
535C23C2×C4⋊Dic4711yescharacteristic
536C23#1309398012yes—
537C23(C22⋊D47)⋊C412yes—
538C23(C22⋊D47)⋊C412yes—
539C23D4×Dic4712yes—
540C23D4×Dic4712yes—
541C23#1309399211yescharacteristic
542C23#1309399211yescharacteristic
543C23#1309399412yes—
544C23#1309399612yes—
545C23#1309399612yes—
546C23#1309400112yes—
547C23#1309400112yes—
548C23#1309400511yescharacteristic
549C23#1309400511yescharacteristic
550C23#1309400812yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—48no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—948no—
575C2×C4—3762no—
576C2×C4—3762no—
577C2×C4—3764no—
578C2×C4—3764no—
579C2×C4—3768no—
580C2×C4—1888no—
581C2×C4—1884no—
582C2×C4—1884no—
583C2×C4—1884no—
584C2×C4—1888no—
585C2×C4C47⋊#9514yescomplemented
586C22—21no—
587C22—22no—
588C22—22no—
589C22—21no—
590C22—21no—
591C22—22no—
592C22—21no—
593C22—22no—
594C22—22no—
595C22—24no—
596C22—24no—
597C22—22no—
598C22—22no—
599C22—24no—
600C22—22no—
601C22—24no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22—44no—
617C22—44no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×C47⋊#9511yescharacteristic
622C22C22⋊C4×Dic4712yes—
623C22#1568897811yescharacteristic
624C22#1568898112yes—
625C22#1568898411yescharacteristic
626C22#1568899511yescharacteristic
627C22#1568899511yescharacteristic
628C22#1568899812yes—
629C22#1568900012yes—
630C22#1568900311yescharacteristic
631C22#1568900311yescharacteristic
632C22#1568930912yes—
633C22#1568931212yes—
634C4—24no—
635C4—44no—
636C4—82no—
637C4—3764no—
638C4—1888no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2#2024161011yescharacteristic
649C2#2024333512yes—
650C2#2024366812yes—
651C2#2024379711yescharacteristic
652C2#2024380211yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC2×C47×#386C2
socleC23×C47#120
prime radicalC23×D4×C47C22
cosocleC25×C47C23
hypercenterC2×#386D47
hypocenterC47#10745
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#15688889C2semidirect
4. #20241611C2semidirect
8. #15689598C4semidirect
16. C2×#13093939C4semidirect
24. C47×#386C4semidirect
47. C2×C22⋊Dic47C2×C4semidirect
70. C23×C4×C47C2×C4semidirect
77. C2×C22⋊C4×C47C2×C4semidirect
153. C22×Dic47C22⋊C4semidirect
200. C23×C47#95semidirect
247. C2×C4×C47#95semidirect
348. #386Dic47semidirect
352. C47#10745semidirect
374. C23×C4C2×Dic47semidirect
401. C2×C22⋊C4C2×Dic47semidirect
527. C23C47⋊#95semidirect
585. C2×C4C47⋊#95semidirect

Maximal subgroups

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

subgroupindex
C2×#156895982
C22×#130939392
C2×#156888892
#202416112
C2×C47×#3862
#1074547