Finite Group Databasebeta

← #26218044

Subgroups — #26218044

Order 12032.

1954 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C2×#15689141C212yesmaximal, complemented
3C2×#15689087C211yesmaximal, characteristic, complemented
4#20243836C214yesmaximal, complemented
5#20243831C214yesmaximal, complemented
6#20243098C212yesmaximal, complemented
7C22×#117×C47C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2212yes—
10#15689634—22no—
11#15689634—21no—
12#15689634—21no—
13#15689634C414yescomplemented
14#15689634C2212yes—
15#15689634C2212yes—
16C2×#13094007—21no—
17C2×#13094003C412yescomplemented
18C2×#13093998C412yescomplemented
19C2×#13093993—21no—
20C2×C4×C22⋊D47—22no—
21C2×#13093983C2211yescharacteristic
22#15689141—28no—
23C2×#13093952C2218yescomplemented
24#15689087—22no—
25#15689087C2212yescomplemented
26#15689087C2212yescomplemented
27C2×C22⋊(C47⋊C8)—22no—
28#15688883C2218yescomplemented
29C24×C4×C47C2211yescharacteristic
30C2×#117×C47—21no—
31C2×#117×C47—21no—
32C2×#117×C47—28no—
33C2×#117×C47C2212yes—
34C2×#117×C47C2212yescomplemented
35C22×C4⋊C4×C47—21no—
36C22×C22⋊C4×C47—21no—
37C22×C42×C47C2212yescomplemented
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—24no—
41C2×#10625350—24no—
42C2×#10625350C2×C412yescomplemented
43C2×#10625350C2312yes—
44C22×Dic94C2×C411yescharacteristic, complemented
45C22×D188C2×C411yescharacteristic, complemented
46C22×C22⋊D47—22no—
47C22×C22⋊D47—21no—
48C22×C4×D47—21no—
49C2×#10625329—22no—
50C2×#10625329—24no—
51C2×#10625329—24no—
52C2×#10625329C2314yes—
53C22×C47⋊C8—22no—
54#13094007—24no—
55#13094007—22no—
56#13094007—22no—
57#13094003—22no—
58#13094003—22no—
59#13094003C2×C414yes—
60#13094003C2×C414yescomplemented
61#13093998—22no—
62#13093998—22no—
63#13093998C2×C414yes—
64#13093998C2×C414yescomplemented
65#13093993—24no—
66#13093993—22no—
67#13093993—22no—
68C4×C22⋊D47—24no—
69C4×C22⋊D47—24no—
70C4×C22⋊D47—24no—
71C4×C22⋊D47—24no—
72#13093983—21no—
73#13093983—21no—
74#13093983C2×C412yescomplemented
75#13093983C2312yes—
76C2×C4⋊Dic47C2×C412yescomplemented
77C2×Dic47⋊C4—22no—
78C2×C22⋊Dic47—22no—
79C2×C22⋊Dic47—21no—
80C2×(C2×D47)⋊C4—22no—
81C2×C4×Dic47—21no—
82#13093952—216no—
83C22⋊(C47⋊C8)—24no—
84C22⋊(C47⋊C8)—24no—
85C25×C47D411yescharacteristic
86C23×C4×C47—24no—
87C23×C4×C47—24no—
88C23×C4×C47—22no—
89C23×C4×C47C2×C412yes—
90C23×C4×C47C2×C412yes—
91C23×C4×C47D411yescharacteristic
92C23×C4×C47D411yescharacteristic
93C23×C4×C47D411yescharacteristic
94C23×C4×C47D412yes—
95C23×C4×C47D412yes—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99#117×C47—28no—
100#117×C47—28no—
101#117×C47—24no—
102#117×C47—28no—
103#117×C47D418yescomplemented
104C2×C4⋊C4×C47—28no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—22no—
107C2×C22⋊C4×C47—28no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47—28no—
112C2×C42×C47C2314yes—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—44no—
116C24×C47C22⋊C412yes—
117C24×C47C22⋊C412yes—
118C24×C47C2×D411yescharacteristic
119C24×C47C2×D411yescharacteristic
120C24×C47C2×D411yescharacteristic
121C23×D47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—28no—
125C22×C4×C47—28no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—28no—
129C22×C4×C47—28no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—28no—
137C22×C4×C47—24no—
138C22×C4×C47—48no—
139C22×C4×C47C22⋊C412yes—
140C22×C4×C47C22⋊C412yes—
141C22×C4×C47C22⋊C412yes—
142C22×C4×C47C22⋊C412yes—
143C22×C4×C47C22⋊C412yes—
144C22×C4×C47C22⋊C412yes—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C22×C412yes—
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D412yes—
152C22×C4×C47C2×D412yes—
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D414yes—
157C22×C4×C47#4114yes—
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—24no—
160C2×C22⋊D47—24no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—48no—
164C2×C22⋊D47—42no—
165C2×C22⋊D47—42no—
166C22×Dic47—22no—
167C22×Dic47—21no—
168#10625350—28no—
169#10625350—24no—
170#10625350—24no—
171#10625350—42no—
172#10625350—44no—
173#10625350—42no—
174C2×D188—24no—
175C2×D188—21no—
176C2×D188C22×C412yes—
177C2×C4×D47—22no—
178C2×C4×D47—22no—
179C2×C4×D47—44no—
180C2×Dic94—24no—
181C2×Dic94—21no—
182C2×Dic94C22×C412yes—
183C4⋊C4×C47—28no—
184C4⋊C4×C47—28no—
185C22⋊C4×C47—28no—
186C22⋊C4×C47—28no—
187C42×C47—28no—
188C42×C47—24no—
189C42×C47C2×D418yescomplemented
190C22⋊Dic47—22no—
191C22⋊Dic47—24no—
192C22⋊Dic47—24no—
193C22⋊Dic47—22no—
194(C2×D47)⋊C4—24no—
195(C2×D47)⋊C4—24no—
196C4⋊Dic47—22no—
197C4⋊Dic47C22×C414yes—
198Dic47⋊C4—24no—
199Dic47⋊C4—24no—
200C4×Dic47—22no—
201C4×Dic47—22no—
202#10625329—24no—
203#10625329—24no—
204#10625329—44no—
205C2×C47⋊C8—24no—
206C2×C47⋊C8—44no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—24no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—42no—
217C23×C47—42no—
218C23×C47—42no—
219C23×C47—42no—
220C23×C47—48no—
221C23×C47—48no—
222C23×C47C2×C22⋊C412yes—
223C23×C47C2×C22⋊C411yescharacteristic
224C23×C47C2×C22⋊C411yescharacteristic
225C23×C47C2×C22⋊C412yes—
226C23×C47#12012yes—
227C23×C47#12312yes—
228C23×C47C22×D411yescharacteristic
229C22×D47—22no—
230C22×D47—44no—
231C22×D47—42no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—24no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—28no—
247C2×C4×C47—416no—
248C2×C4×C47—48no—
249C2×C4×C47C2×C22⋊C412yes—
250C2×C4×C47C2×C22⋊C412yes—
251C2×C4×C47C2×C22⋊C411yescharacteristic
252C2×C4×C47C2×C22⋊C411yescharacteristic
253C2×C4×C47C4×D414yes—
254C2×C4×C47C4×D414yes—
255C2×C4×C47#12012yes—
256C2×C4×C47#12114yes—
257C2×C4×C47#12114yes—
258C2×C4×C47#12312yes—
259C2×C4×C47C23×C411yescharacteristic
260C2×C4×C47C22×D412yes—
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47C2×#4112yes—
263C22⋊D47—48no—
264C22⋊D47—42no—
265C22⋊D47—42no—
266C22⋊D47—44no—
267C22⋊D47—48no—
268C2×Dic47—24no—
269C2×Dic47—22no—
270C2×Dic47—44no—
271C2×Dic47—42no—
272D188—24no—
273D188—42no—
274C4×D47—44no—
275C4×D47—44no—
276Dic94—24no—
277Dic94—42no—
278C47⋊C8—44no—
279#20979—471nomaximal, Sylow
280C22×C47—24no—
281C22×C47—24no—
282C22×C47—22no—
283C22×C47—22no—
284C22×C47—22no—
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47—22no—
290C22×C47—42no—
291C22×C47—42no—
292C22×C47—48no—
293C22×C47—48no—
294C22×C47—42no—
295C22×C47—42no—
296C22×C47#38612yes—
297C22×C47#38612yes—
298C22×C47#42114yescomplemented
299C22×C47C22×C22⋊C411yescharacteristic
300C22×C47C2×#12011yescharacteristic
301C22×C47C2×#12311yescharacteristic
302C2×D47—44no—
303C2×D47—42no—
304C2×D47—84no—
305C4×C47—22no—
306C4×C47—22no—
307C4×C47—48no—
308C4×C47#38612yes—
309C4×C47#38612yes—
310C4×C47C2×C4×D412yes—
311C4×C47C2×#12112yes—
312Dic47—44no—
313Dic47—42no—
314C2×#525—471no—
315C22×#117D4711yescharacteristic, complemented
316C2×#421—472no—
317C2×#407—471no—
318#1897—474no—
319#1896—474no—
320#1733—472no—
321C2×C47—21no—
322C2×C47—22no—
323C2×C47—21no—
324C2×C47—24no—
325C2×C47—22no—
326C2×C47—42no—
327C2×C47C2×#38611yescharacteristic
328C2×C47C2×#42112yes—
329D47—82no—
330C22×#41—471no—
331C24×C4C2×D4711yescharacteristic
332C22×M16—472no—
333#525—474no—
334#525—472no—
335#525—472no—
336#525—942no—
337#525—941no—
338#525—941no—
339C2×#123—941no—
340C2×C22⋊Q8—472no—
341C2×#121—472no—
342C2×#120—941no—
343C2×C4×D4—942no—
344C2×#117—21no—
345C2×#117—21no—
346C2×#117—28no—
347C2×#117—471no—
348C2×#117C2×D4712yes—
349C2×#117C2×D4712yescomplemented
350C22×C4⋊C4—21no—
351C22×C22⋊C4—21no—
352C22×C42C2×D4712yescomplemented
353#421—948no—
354C2×#104—478no—
355#407—472no—
356#407—472no—
357#407—942no—
358C2×C22⋊C8—942no—
359#339—478no—
360C47#2097911yescharacteristic, complemented, Sylow
361C25C22⋊D4711yescharacteristic
362C2×#41—472no—
363C2×#41—472no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—944no—
367C2×#41—944no—
368C22×Q8—471no—
369C22×D4—471no—
370C22×D4—942no—
371C22×D4—941no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—941no—
376C23×C4C4×D4712yes—
377C23×C4C4×D4712yes—
378C23×C4D18812yes—
379C23×C4D18812yes—
380C23×C4C22⋊D4711yescharacteristic
381C23×C4C22⋊D4711yescharacteristic
382C23×C4C22⋊D4711yescharacteristic
383C23×C4C22×D4711yescharacteristic
384C23×C4C22×D4711yescharacteristic
385C23×C4C22×D4711yescharacteristic
386C2×M16—474no—
387C2×M16—942no—
388C2×M16—944no—
389C2×M16—944no—
390C22×C8—942no—
391#123—944no—
392#123—942no—
393#123—942no—
394C22⋊Q8—474no—
395C22⋊Q8—474no—
396C22⋊Q8—942no—
397C22⋊Q8—942no—
398#121—474no—
399#121—474no—
400#121—942no—
401#121—942no—
402#120—944no—
403#120—942no—
404#120—942no—
405C4×D4—944no—
406C4×D4—944no—
407C4×D4—944no—
408C4×D4—944no—
409#117—28no—
410#117—28no—
411#117—24no—
412#117—28no—
413#117—472no—
414#117—472no—
415#117—941no—
416#117—941no—
417#117C22⋊D4718yescomplemented
418C2×C4⋊C4—28no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—472no—
422C2×C4⋊C4—942no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—942no—
427C2×C22⋊C4—941no—
428C2×C22⋊C4—942no—
429C2×C42—22no—
430C2×C42—28no—
431C2×C42—941no—
432C2×C42C22×D4714yes—
433#104—9416no—
434C22⋊C8—944no—
435C22⋊C8—944no—
436C24—22no—
437C24—22no—
438C24—44no—
439C24—941no—
440C24(C2×D47)⋊C412yes—
441C24(C2×D47)⋊C412yes—
442C24C2×C22⋊D4711yescharacteristic
443C24C2×C22⋊D4711yescharacteristic
444C24C2×C22⋊D4711yescharacteristic
445#41—948no—
446#41—944no—
447#41—944no—
448#41—1882no—
449#41—1884no—
450#41—1882no—
451C2×Q8—472no—
452C2×Q8—941no—
453C2×Q8—944no—
454C2×D4—472no—
455C2×D4—944no—
456C2×D4—944no—
457C2×D4—942no—
458C2×D4—942no—
459C2×D4—941no—
460C2×D4—944no—
461C2×D4—1888no—
462C2×D4—1882no—
463C2×D4—1882no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—28no—
479C22×C4—24no—
480C22×C4—48no—
481C22×C4—942no—
482C22×C4—941no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—1884no—
486C22×C4(C2×D47)⋊C412yes—
487C22×C4(C2×D47)⋊C412yes—
488C22×C4(C2×D47)⋊C412yes—
489C22×C4(C2×D47)⋊C412yes—
490C22×C4(C2×D47)⋊C412yes—
491C22×C4(C2×D47)⋊C412yes—
492C22×C4C2×C4×D4712yes—
493C22×C4C2×C4×D4712yes—
494C22×C4C2×C4×D4711yescharacteristic
495C22×C4C2×C4×D4711yescharacteristic
496C22×C4C2×D18812yes—
497C22×C4C2×D18812yes—
498C22×C4C2×D18811yescharacteristic
499C22×C4C2×D18811yescharacteristic
500C22×C4#1062535014yes—
501C22×C4C2×C22⋊D4711yescharacteristic
502C22×C4C2×C22⋊D4711yescharacteristic
503C22×C4C2×C22⋊D4711yescharacteristic
504C22×C4C2×C22⋊D4714yes—
505C22×C4C23×D4711yescharacteristic
506M16—944no—
507M16—944no—
508M16—1884no—
509C2×C8—944no—
510C2×C8—1884no—
511C4⋊C4—28no—
512C4⋊C4—28no—
513C4⋊C4—474no—
514C4⋊C4—944no—
515C4⋊C4—944no—
516C4⋊C4—942no—
517C22⋊C4—28no—
518C22⋊C4—28no—
519C22⋊C4—942no—
520C22⋊C4—944no—
521C22⋊C4—944no—
522C22⋊C4—942no—
523C22⋊C4—944no—
524C22⋊C4—944no—
525C42—28no—
526C42—24no—
527C42—942no—
528C42—942no—
529C42C2×C22⋊D4718yescomplemented
530C23—21no—
531C23—21no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—21no—
536C23—21no—
537C23—24no—
538C23—24no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—48no—
544C23—48no—
545C23—942no—
546C23—1884no—
547C23—1882no—
548C23C2×(C2×D47)⋊C412yes—
549C23C2×(C2×D47)⋊C411yescharacteristic
550C23C2×(C2×D47)⋊C411yescharacteristic
551C23C2×(C2×D47)⋊C412yes—
552C23#1309399312yes—
553C23#1309400712yes—
554C23C22×C22⋊D4711yescharacteristic
555Q8—944no—
556Q8—1882no—
557D4—944no—
558D4—1888no—
559D4—1884no—
560D4—1882no—
561D4—1882no—
562D4—1888no—
563D4—1882no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—28no—
579C2×C4—416no—
580C2×C4—48no—
581C2×C4—944no—
582C2×C4—942no—
583C2×C4—1884no—
584C2×C4—1882no—
585C2×C4—1884no—
586C2×C4—1884no—
587C2×C4C2×(C2×D47)⋊C412yes—
588C2×C4C2×(C2×D47)⋊C412yes—
589C2×C4C2×(C2×D47)⋊C411yescharacteristic
590C2×C4C2×(C2×D47)⋊C411yescharacteristic
591C2×C4C4×C22⋊D4714yes—
592C2×C4C4×C22⋊D4714yes—
593C2×C4#1309399312yes—
594C2×C4#1309399814yes—
595C2×C4#1309399814yes—
596C2×C4#1309400712yes—
597C2×C4C22×C4×D4711yescharacteristic
598C2×C4C22×C22⋊D4712yes—
599C2×C4C22×D18811yescharacteristic
600C2×C4C2×#1062535012yes—
601C8—1884no—
602C22—24no—
603C22—24no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—42no—
613C22—42no—
614C22—48no—
615C22—48no—
616C22—42no—
617C22—42no—
618C22—3764no—
619C22—1884no—
620C22—1882no—
621C22#1568900212yes—
622C22#1568900212yes—
623C22#1568914114yescomplemented
624C22C22×(C2×D47)⋊C411yescharacteristic
625C22C2×#1309399311yescharacteristic
626C22C2×#1309400711yescharacteristic
627C4—22no—
628C4—22no—
629C4—48no—
630C4—1884no—
631C4—1882no—
632C4#1568900212yes—
633C4#1568900212yes—
634C4C2×C4×C22⋊D4712yes—
635C4C2×#1309399812yes—
636C2—21no—
637C2—21no—
638C2—24no—
639C2—22no—
640C2—22no—
641C2—42no—
642C2—3762no—
643C2C2×#1568900211yescharacteristic
644C2C2×#1568914112yes—
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#117×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC22×#117D47
hypocenterC47#20979
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#15689141C2semidirect
3. C2×#15689087C2semidirect
4. #20243836C2semidirect
5. #20243831C2semidirect
6. #20243098C2semidirect
7. C22×#117×C47C2semidirect
13. #15689634C4semidirect
17. C2×#13094003C4semidirect
18. C2×#13093998C4semidirect
23. C2×#13093952C22semidirect
25. #15689087C22semidirect
26. #15689087C22semidirect
28. #15688883C22semidirect
34. C2×#117×C47C22semidirect
37. C22×C42×C47C22semidirect
42. C2×#10625350C2×C4semidirect
44. C22×Dic94C2×C4semidirect
45. C22×D188C2×C4semidirect
60. #13094003C2×C4semidirect
64. #13093998C2×C4semidirect
74. #13093983C2×C4semidirect
76. C2×C4⋊Dic47C2×C4semidirect
103. #117×C47D4semidirect
189. C42×C47C2×D4semidirect
298. C22×C47#421semidirect
315. C22×#117D47semidirect
349. C2×#117C2×D47semidirect
352. C22×C42C2×D47semidirect
360. C47#20979semidirect
417. #117C22⋊D47semidirect
529. C42C2×C22⋊D47semidirect
623. C22#15689141semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×#156891412
C2×#156890872
#202438362
#202438312
#202430982
C22×#117×C472
#2097947