Finite Group Databasebeta

← #26187227

Subgroups — #26187227

Order 12032.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252408C211yesmaximal, characteristic, complemented
2#20252393C211yesmaximal, characteristic, complemented
3#20242279C211yesmaximal, characteristic, complemented
4#20242273C211yesmaximal, characteristic, complemented
5#20242239C211yesmaximal, characteristic, complemented
6#20242232C211yesmaximal, characteristic, complemented
7#20242232C211yesmaximal, characteristic, complemented
8#20242218C211yesmaximal, characteristic, complemented
9Q16×C47⋊C8C211yesmaximal, characteristic, complemented
10SD16×C47⋊C8C211yesmaximal, characteristic, complemented
11#20242168C211yesmaximal, characteristic, complemented
12#20241848C211yesmaximal, characteristic, complemented
13#20241770C211yesmaximal, characteristic, complemented
14#20241669C211yesmaximal, characteristic, complemented
15C47×#3102C211yesmaximal, characteristic
16#15689254C2211yescharacteristic
17Q8×C47⋊C8C2211yescharacteristic
18Q8×C47⋊C8C2211yescharacteristic
19Q8×C47⋊C8C2211yescharacteristic
20#15689201—21no—
21#15689201—21no—
22#15689201—21no—
23#15689201C2211yescharacteristic
24#15689201C2211yescharacteristic
25#15689201C2211yescharacteristic
26#15689195—21no—
27D4×C47⋊C8C2211yescharacteristic
28#15689184—21no—
29#15689180—21no—
30#15689180C2211yescharacteristic
31#15689176C2211yescharacteristic
32#15689079—21no—
33C4×#10625329—21no—
34C4×#10625329C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36#15688876C2211yescharacteristic
37#15688876C2211yescharacteristic
38#15688874C2211yescharacteristic
39#15688874C2211yescharacteristic
40Q8⋊(C47⋊C8)C2211yescharacteristic
41Q8⋊(C47⋊C8)C2211yescharacteristic
42Q8⋊(C47⋊C8)C2211yescharacteristic
43Q8⋊(C47⋊C8)C2211yescharacteristic
44D4⋊(C47⋊C8)C2211yescharacteristic
45D4⋊(C47⋊C8)C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48#15688845C2211yescharacteristic
49#15688845C2211yescharacteristic
50C8×C47⋊C8C2211yescharacteristic
51C8×C47⋊C8C2211yescharacteristic
52C47×#529C2211yescharacteristic
53C4×#41×C47C2211yescharacteristic
54C47×#485C411yescharacteristic
55C47×#482C411yescharacteristic
56C47×#479C411yescharacteristic
57C47×#478C411yescharacteristic
58C47×#464C411yescharacteristic
59C47×#463C411yescharacteristic
60C47×#452C411yescharacteristic
61C47×#449C411yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C4×SD16×C47C2211yescharacteristic
64C4×SD16×C47C2211yescharacteristic
65C4×D8×C47C2211yescharacteristic
66C47×#431C2211yescharacteristic
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329D411yescharacteristic
71C2×#10625329D411yescharacteristic
72C22×C47⋊C8—21no—
73C22×C47⋊C8—21no—
74C4⋊(C47⋊C8)—21no—
75C4⋊(C47⋊C8)—21no—
76C4⋊(C47⋊C8)—21no—
77C4⋊(C47⋊C8)—21no—
78C4⋊(C47⋊C8)C2311yescharacteristic
79C4⋊(C47⋊C8)C2311yescharacteristic
80C4⋊(C47⋊C8)C2311yescharacteristic
81C4⋊(C47⋊C8)C2311yescharacteristic
82C22⋊(C47⋊C8)—21no—
83C22⋊(C47⋊C8)—21no—
84C22⋊(C47⋊C8)—21no—
85C22⋊(C47⋊C8)—21no—
86C22⋊(C47⋊C8)—21no—
87C22⋊(C47⋊C8)—21no—
88#13093935—21no—
89#13093935—21no—
90#13093935D411yescharacteristic
91#13093935D411yescharacteristic
92C4×C47⋊C8—21no—
93C4×C47⋊C8—21no—
94C4×C47⋊C8—21no—
95C4×C47⋊C8—21no—
96C4×C47⋊C8—21no—
97C4×C47⋊C8C2311yescharacteristic
98C4×C47⋊C8C2311yescharacteristic
99C4×C47⋊C8C2311yescharacteristic
100C4×C47⋊C8C2311yescharacteristic
101C2×#41×C47C2×C411yescharacteristic
102C2×Q16×C47C2×C411yescharacteristic
103C2×SD16×C47C2×C411yescharacteristic
104C2×SD16×C47C2×C411yescharacteristic
105C2×D8×C47C2×C411yescharacteristic
106#126×C47—21no—
107#125×C47C2×C411yescharacteristic
108#124×C47C2×C411yescharacteristic
109#123×C47—21no—
110C22⋊Q8×C47C2×C411yescharacteristic
111#121×C47C2×C411yescharacteristic
112C4×Q8×C47C2×C411yescharacteristic
113C4×Q8×C47C2311yescharacteristic
114C4×Q8×C47C2311yescharacteristic
115C4×D4×C47—21no—
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47C2×C411yescharacteristic
119C4×D4×C47C2311yescharacteristic
120C4×D4×C47C2311yescharacteristic
121#117×C47—21no—
122#117×C47—21no—
123#117×C47C2×C411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126#107×C47C2×C411yescharacteristic
127#107×C47C2×C411yescharacteristic
128#106×C47C2×C411yescharacteristic
129#106×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47C2×C411yescharacteristic
132#103×C47C2×C411yescharacteristic
133#103×C47C2×C411yescharacteristic
134#103×C47C2×C411yescharacteristic
135#103×C47C2×C411yescharacteristic
136#102×C47C2×C411yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141C22⋊C8×C47C2×C411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—41no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×Q8×C47C22×C411yescharacteristic
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47C22×C411yescharacteristic
151C2×D4×C47C22×C411yescharacteristic
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47#4111yescharacteristic
159Q16×C47—22no—
160SD16×C47—22no—
161SD16×C47—41no—
162D8×C47—41no—
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C22×C411yescharacteristic
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C4⋊C4×C47C22×C411yescharacteristic
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C22⋊C4×C47—21no—
181C22⋊C4×C47—21no—
182C22⋊C4×C47—21no—
183C22⋊C4×C47—21no—
184C22⋊C4×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47C22×C411yescharacteristic
190C42×C47C2×D411yescharacteristic
191C42×C47#4111yescharacteristic
192C42×C47C2411yescharacteristic
193#10625329—22no—
194#10625329—22no—
195#10625329—42no—
196#10625329—42no—
197#10625329—42no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—42no—
205C2×C47⋊C8—42no—
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210C23×C47—21no—
211C23×C47—21no—
212C23×C47C4×D411yescharacteristic
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47#13112yes—
217D4×C47—21no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47—21no—
221D4×C47—42no—
222D4×C47—81no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—41no—
234C2×C4×C47—42no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—81no—
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C4×D411yescharacteristic
243C2×C4×C47C23×C411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C47⋊C8—22no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258C47⋊C8#13512yes—
259C47⋊C8#13512yes—
260#17999—471nomaximal, Sylow
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47C2×C4×D411yescharacteristic
271C4×C47—21no—
272C4×C47—22no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47C2×#13111yescharacteristic
282C4×C47#56811yescharacteristic
283C4×C47C2×#13511yescharacteristic
284C4×C47C2×#13511yescharacteristic
285#3102D4711yescharacteristic
286#2971—471no—
287#2969—471no—
288#1590—471no—
289#1589—471no—
290#1584—471no—
291#1583—471no—
292#1583—471no—
293#1581—471no—
294C8×Q16—471no—
295C8×SD16—471no—
296#1572—471no—
297#1494—471no—
298#1476—471no—
299C8×M16—471no—
300C2×C47—41no—
301C2×C47—81no—
302C2×C47—81no—
303C2×C47#293311yescharacteristic
304C2×C47C4×#13511yescharacteristic
305C2×C47#295611yescharacteristic
306#529C2×D4711yescharacteristic
307C4×#41C2×D4711yescharacteristic
308#485Dic4711yescharacteristic
309#482Dic4711yescharacteristic
310#479Dic4711yescharacteristic
311#478Dic4711yescharacteristic
312#464Dic4711yescharacteristic
313#463Dic4711yescharacteristic
314#452Dic4711yescharacteristic
315#449Dic4711yescharacteristic
316#446—471no—
317C8×Q8—471no—
318C8×Q8—471no—
319C8×Q8—471no—
320C4×Q16C2×D4711yescharacteristic
321C4×SD16C2×D4711yescharacteristic
322C4×SD16C2×D4711yescharacteristic
323C4×D8C2×D4711yescharacteristic
324#436—471no—
325#436—471no—
326#436—471no—
327#436—941no—
328#436—941no—
329#436—941no—
330#435—941no—
331C8×D4—471no—
332#433—941no—
333#432—471no—
334#432—941no—
335#431—471no—
336#431C2×D4711yescharacteristic
337#405—941no—
338C4×M16—471no—
339C4×M16—941no—
340C2×C4×C8—471no—
341#335—471no—
342#335—471no—
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8—471no—
352D4⋊C8—471no—
353#322—471no—
354#322—471no—
355C82—471no—
356C82—471no—
357C47#1799911yescharacteristic, complemented, Sylow
358C2×#41C2×Dic4711yescharacteristic
359C2×Q16C2×Dic4711yescharacteristic
360C2×SD16C2×Dic4711yescharacteristic
361C2×SD16C2×Dic4711yescharacteristic
362C2×D8C2×Dic4711yescharacteristic
363C2×M16—471no—
364C2×M16—471no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C22×C8—941no—
369C22×C8—941no—
370#126—21no—
371#125C2×Dic4711yescharacteristic
372#124C2×Dic4711yescharacteristic
373#123—21no—
374C22⋊Q8C2×Dic4711yescharacteristic
375#121C2×Dic4711yescharacteristic
376C4×Q8C2×Dic4711yescharacteristic
377C4×Q8C22×D4711yescharacteristic
378C4×Q8C22×D4711yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2×Dic4711yescharacteristic
383C4×D4C22×D4711yescharacteristic
384C4×D4C22×D4711yescharacteristic
385#117—21no—
386#117—21no—
387#117C2×Dic4711yescharacteristic
388C2×C42—21no—
389C2×C42C22×D4711yescharacteristic
390#107C2×Dic4711yescharacteristic
391#107C2×Dic4711yescharacteristic
392#106C2×Dic4711yescharacteristic
393#106C2×Dic4711yescharacteristic
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8C2×Dic4711yescharacteristic
403C4⋊C8C2×Dic4711yescharacteristic
404#103C2×Dic4711yescharacteristic
405#103C2×Dic4711yescharacteristic
406#103C2×Dic4711yescharacteristic
407#103C2×Dic4711yescharacteristic
408#102C2×Dic4711yescharacteristic
409#102C2×Dic4711yescharacteristic
410#102C2×Dic4711yescharacteristic
411#102C2×Dic4711yescharacteristic
412C22⋊C8—941no—
413C22⋊C8—941no—
414C22⋊C8—941no—
415C22⋊C8—941no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8C2×Dic4711yescharacteristic
419C22⋊C8C2×Dic4711yescharacteristic
420#97—471no—
421#97—471no—
422#97—941no—
423#97—941no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—941no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8—941no—
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—22no—
436#41—41no—
437C2×Q8C22×Dic4711yescharacteristic
438C2×Q8C22×Dic4711yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×Dic4711yescharacteristic
442C2×D4C22×Dic4711yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4D4×D4711yescharacteristic
448C22×C4#1062535211yescharacteristic
449C22×C4C22×Dic4711yescharacteristic
450Q16—22no—
451SD16—22no—
452SD16—41no—
453D8—41no—
454M16—942no—
455M16—942no—
456M16—1882no—
457M16—1882no—
458M16—1882no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—1882no—
470C2×C8—1882no—
471C2×C8C22×Dic4711yescharacteristic
472C2×C8C22×Dic4711yescharacteristic
473C2×C8C22×Dic4711yescharacteristic
474C2×C8C22×Dic4711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×Dic4711yescharacteristic
482C4⋊C4C22×Dic4711yescharacteristic
483C4⋊C4C22×Dic4711yescharacteristic
484C4⋊C4C22×Dic4711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42D4×D4711yescharacteristic
498C42#1062535211yescharacteristic
499C42C22×Dic4711yescharacteristic
500C42C23×D4711yescharacteristic
501C23—21no—
502C23—21no—
503C23D4×Dic4711yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8#1309403112yes—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—81no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4D4×Dic4711yescharacteristic
532C2×C4D4×Dic4711yescharacteristic
533C2×C4D4×Dic4711yescharacteristic
534C2×C4C23×Dic4711yescharacteristic
535C2×C4C2×D4×D4711yescharacteristic
536C2×C4C2×#1062535211yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—472no—
542C8—472no—
543C8—942no—
544C8—941no—
545C8—941no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C8—1881no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×D4×Dic4711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4C2×#1309403111yescharacteristic
572C4#1568989011yescharacteristic
573C4#135×D4711yescharacteristic
574C4#135×D4711yescharacteristic
575C2—41no—
576C2—81no—
577C2—81no—
578C2#2025211511yescharacteristic
579C2#135×Dic4711yescharacteristic
580C2#2025229811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#3102C2
socleC22×C47C2×C4×D4
prime radicalC47×#449C4
cosocleC42×C47C24
hypercenter#3102D47
hypocenterC47#17999
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #20252408C2semidirect
2. #20252393C2semidirect
3. #20242279C2semidirect
4. #20242273C2semidirect
5. #20242239C2semidirect
6. #20242232C2semidirect
7. #20242232C2semidirect
8. #20242218C2semidirect
9. Q16×C47⋊C8C2semidirect
10. SD16×C47⋊C8C2semidirect
11. #20242168C2semidirect
12. #20241848C2semidirect
13. #20241770C2semidirect
14. #20241669C2semidirect
357. C47#17999semidirect

Maximal subgroups

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

subgroupindex
#202524082
#202523932
#202422792
#202422732
#202422392
#202422322
#202422182
Q16×C47⋊C82
SD16×C47⋊C82
#202421682
#202418482
#202417702
#202416692
C47×#31022
#1799947