Finite Group Databasebeta

← #26187391

Subgroups — #26187391

Order 12032.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252408C211yesmaximal, characteristic, complemented
2#20252132C211yesmaximal, characteristic, complemented
3#20242302C211yesmaximal, characteristic, complemented
4#20242273C211yesmaximal, characteristic, complemented
5#20242267C211yesmaximal, characteristic, complemented
6#20242253C211yesmaximal, characteristic, complemented
7#20242232C211yesmaximal, characteristic, complemented
8#20242218C211yesmaximal, characteristic, complemented
9SD16⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C47⋊C8C211yesmaximal, characteristic, complemented
11#20242173C211yesmaximal, characteristic, complemented
12#20241857C211yesmaximal, characteristic, complemented
13#20241775C211yesmaximal, characteristic, complemented
14#20241683C211yesmaximal, characteristic, complemented
15C47×#3106C211yesmaximal, characteristic
16C2×#13094031—21no—
17Q8×C47⋊C8C2211yescharacteristic
18Q8×C47⋊C8C2211yescharacteristic
19#15689201—21no—
20#15689201—21no—
21#15689201C2211yescharacteristic
22#15689201C2211yescharacteristic
23#15689201C2211yescharacteristic
24#15689201C2211yescharacteristic
25#15689195—21no—
26#15689195—21no—
27D4×C47⋊C8C2211yescharacteristic
28D4×C47⋊C8C2211yescharacteristic
29#15689180—21no—
30#15689180C2211yescharacteristic
31#15689176C2211yescharacteristic
32C2×C4⋊(C47⋊C8)C2211yescharacteristic
33#15689090—21no—
34C4×#10625329—21no—
35C4×#10625329C2211yescharacteristic
36#15688876C2211yescharacteristic
37#15688876C2211yescharacteristic
38#15688874C2211yescharacteristic
39#15688874C2211yescharacteristic
40Q8⋊(C47⋊C8)C2211yescharacteristic
41Q8⋊(C47⋊C8)C2211yescharacteristic
42D4⋊(C47⋊C8)C2211yescharacteristic
43D4⋊(C47⋊C8)C2211yescharacteristic
44D4⋊(C47⋊C8)C2211yescharacteristic
45D4⋊(C47⋊C8)C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48#15688845C2211yescharacteristic
49#15688845C2211yescharacteristic
50#15688844C2211yescharacteristic
51C8×C47⋊C8C2211yescharacteristic
52C47×#532C2211yescharacteristic
53C4×#41×C47C2211yescharacteristic
54C47×#482C411yescharacteristic
55C47×#482C411yescharacteristic
56C47×#477C411yescharacteristic
57C47×#476C411yescharacteristic
58C47×#460C411yescharacteristic
59C47×#459C411yescharacteristic
60C47×#449C411yescharacteristic
61C47×#449C411yescharacteristic
62C4×SD16×C47C2211yescharacteristic
63C4×SD16×C47C2211yescharacteristic
64C4×D8×C47C2211yescharacteristic
65C4×D8×C47C2211yescharacteristic
66C47×#431C2211yescharacteristic
67#13094031—44no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329—21no—
72C2×#10625329D411yescharacteristic
73C2×#10625329D411yescharacteristic
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C22×C47⋊C8—21no—
77C4⋊(C47⋊C8)—21no—
78C4⋊(C47⋊C8)—21no—
79C4⋊(C47⋊C8)—21no—
80C4⋊(C47⋊C8)—21no—
81C4⋊(C47⋊C8)C2311yescharacteristic
82C4⋊(C47⋊C8)C2311yescharacteristic
83C4⋊(C47⋊C8)C2311yescharacteristic
84C4⋊(C47⋊C8)C2311yescharacteristic
85C22⋊(C47⋊C8)—21no—
86C22⋊(C47⋊C8)—21no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)—21no—
93#13093935—21no—
94#13093935D411yescharacteristic
95#13093935D411yescharacteristic
96C4×C47⋊C8—21no—
97C4×C47⋊C8—21no—
98C4×C47⋊C8C2311yescharacteristic
99C4×C47⋊C8C2311yescharacteristic
100C4×C47⋊C8C2311yescharacteristic
101C4×C47⋊C8C2311yescharacteristic
102C2×#41×C47—21no—
103C2×#41×C47C2×C411yescharacteristic
104C2×SD16×C47C2×C411yescharacteristic
105C2×SD16×C47C2×C411yescharacteristic
106C2×D8×C47C2×C411yescharacteristic
107C2×D8×C47C2×C411yescharacteristic
108C4⋊Q8×C47C2×C411yescharacteristic
109#127×C47C2×C411yescharacteristic
110#124×C47—21no—
111#121×C47—21no—
112#121×C47C2×C411yescharacteristic
113#121×C47C2×C411yescharacteristic
114C4×Q8×C47C2×C411yescharacteristic
115C4×Q8×C47C2311yescharacteristic
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47—21no—
119C4×D4×C47C2×C411yescharacteristic
120C4×D4×C47C2311yescharacteristic
121C4×D4×C47C2311yescharacteristic
122C4×D4×C47C2311yescharacteristic
123#117×C47—21no—
124#117×C47C2×C411yescharacteristic
125C2×C42×C47—21no—
126C2×C42×C47C2311yescharacteristic
127#107×C47C2×C411yescharacteristic
128#107×C47C2×C411yescharacteristic
129#106×C47C2×C411yescharacteristic
130#106×C47C2×C411yescharacteristic
131C4⋊C8×C47C2×C411yescharacteristic
132C4⋊C8×C47C2×C411yescharacteristic
133#103×C47C2×C411yescharacteristic
134#103×C47C2×C411yescharacteristic
135#102×C47C2×C411yescharacteristic
136#102×C47C2×C411yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141C22⋊C8×C47C2×C411yescharacteristic
142C22⋊C8×C47C2×C411yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145#41×C47—22no—
146#41×C47—41no—
147#41×C47—42no—
148#41×C47—42no—
149C2×Q8×C47—21no—
150C2×Q8×C47C22×C411yescharacteristic
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47C22×C411yescharacteristic
157C2×D4×C47C22×C411yescharacteristic
158C2×D4×C47C22×C411yescharacteristic
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47#4111yescharacteristic
167SD16×C47—22no—
168SD16×C47—22no—
169D8×C47—41no—
170D8×C47—41no—
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C2×C8×C47C22×C411yescharacteristic
174C2×C8×C47C22×C411yescharacteristic
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47C22×C411yescharacteristic
179C4⋊C4×C47C22×C411yescharacteristic
180C4⋊C4×C47C22×C411yescharacteristic
181C4⋊C4×C47C22×C411yescharacteristic
182C22⋊C4×C47—21no—
183C22⋊C4×C47—21no—
184C22⋊C4×C47—21no—
185C22⋊C4×C47—21no—
186C22⋊C4×C47—21no—
187C22⋊C4×C47—21no—
188C22⋊C4×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47C22×C411yescharacteristic
193C42×C47C2×D411yescharacteristic
194C42×C47#4111yescharacteristic
195C42×C47C2411yescharacteristic
196#10625329—22no—
197#10625329—41no—
198#10625329—42no—
199#10625329—42no—
200#10625329—42no—
201#10625329—42no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—42no—
209C2×C47⋊C8—42no—
210C2×C47⋊C8—42no—
211C2×C47⋊C8C2×D411yescharacteristic
212C2×C47⋊C8C2×D411yescharacteristic
213C2×C47⋊C8C2×D411yescharacteristic
214C2×C47⋊C8C2×D411yescharacteristic
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47C4×D411yescharacteristic
219Q8×C47—21no—
220Q8×C47—42no—
221Q8×C47#13112yescomplemented
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—21no—
227D4×C47—21no—
228D4×C47—42no—
229D4×C47—42no—
230D4×C47—42no—
231D4×C47—42no—
232D4×C47—81no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—41no—
243C2×C4×C47—42no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—81no—
251C2×C4×C47C4×D411yescharacteristic
252C2×C4×C47C4×D411yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C23×C411yescharacteristic
255C2×C4×C47C22×D411yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C8×C47—21no—
258C8×C47—21no—
259C8×C47—21no—
260C8×C47—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268C47⋊C8—41no—
269C47⋊C8—41no—
270C47⋊C8AGL(1,ℤ/8)12yes—
271#18011—471nomaximal, Sylow
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47C2×C4×D411yescharacteristic
285C4×C47—21no—
286C4×C47—22no—
287C4×C47—21no—
288C4×C47—21no—
289C4×C47—21no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47C2×#13111yescharacteristic
295C4×C47#56811yescharacteristic
296C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C47#57511yescharacteristic
298#3106D4711yescharacteristic
299#2971—471no—
300#2935—471no—
301#1594—471no—
302#1589—471no—
303#1588—471no—
304#1586—471no—
305#1583—471no—
306#1581—471no—
307SD16⋊C8—471no—
308C8×SD16—471no—
309#1573—471no—
310#1496—471no—
311#1477—471no—
312#1453—471no—
313C2×C47—41no—
314C2×C47—81no—
315C2×C47—81no—
316C2×C47—81no—
317C2×C47#293311yescharacteristic
318C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C47#295711yescharacteristic
320C2×#131—941no—
321#532C2×D4711yescharacteristic
322C4×#41C2×D4711yescharacteristic
323#482Dic4711yescharacteristic
324#482Dic4711yescharacteristic
325#477Dic4711yescharacteristic
326#476Dic4711yescharacteristic
327#460Dic4711yescharacteristic
328#459Dic4711yescharacteristic
329#449Dic4711yescharacteristic
330#449Dic4711yescharacteristic
331C8×Q8—471no—
332C8×Q8—471no—
333C4×SD16C2×D4711yescharacteristic
334C4×SD16C2×D4711yescharacteristic
335C4×D8C2×D4711yescharacteristic
336C4×D8C2×D4711yescharacteristic
337#436—471no—
338#436—471no—
339#436—471no—
340#436—471no—
341#436—941no—
342#436—941no—
343#435—941no—
344#435—941no—
345C8×D4—471no—
346C8×D4—471no—
347#432—471no—
348#432—941no—
349#431—471no—
350#431C2×D4711yescharacteristic
351C2×C4⋊C8—471no—
352#408—941no—
353C4×M16—471no—
354C4×M16—941no—
355#335—471no—
356#335—471no—
357#334—471no—
358#334—471no—
359Q8⋊C8—471no—
360Q8⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364D4⋊C8—471no—
365D4⋊C8—471no—
366D4⋊C8—471no—
367#322—471no—
368#322—471no—
369#322—471no—
370C82—471no—
371C47#1801111yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41C2×Dic4711yescharacteristic
374C2×SD16C2×Dic4711yescharacteristic
375C2×SD16C2×Dic4711yescharacteristic
376C2×D8C2×Dic4711yescharacteristic
377C2×D8C2×Dic4711yescharacteristic
378#131—1884no—
379C2×M16—471no—
380C2×M16—471no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C22×C8—941no—
386C22×C8—941no—
387C22×C8—941no—
388C4⋊Q8C2×Dic4711yescharacteristic
389#127C2×Dic4711yescharacteristic
390#124—21no—
391#121—21no—
392#121C2×Dic4711yescharacteristic
393#121C2×Dic4711yescharacteristic
394C4×Q8C2×Dic4711yescharacteristic
395C4×Q8C22×D4711yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C2×Dic4711yescharacteristic
400C4×D4C22×D4711yescharacteristic
401C4×D4C22×D4711yescharacteristic
402C4×D4C22×D4711yescharacteristic
403#117—21no—
404#117C2×Dic4711yescharacteristic
405C2×C42—21no—
406C2×C42C22×D4711yescharacteristic
407#107C2×Dic4711yescharacteristic
408#107C2×Dic4711yescharacteristic
409#106C2×Dic4711yescharacteristic
410#106C2×Dic4711yescharacteristic
411C4⋊C8—471no—
412C4⋊C8—471no—
413C4⋊C8—471no—
414C4⋊C8—471no—
415C4⋊C8—941no—
416C4⋊C8—941no—
417C4⋊C8—941no—
418C4⋊C8—941no—
419C4⋊C8C2×Dic4711yescharacteristic
420C4⋊C8C2×Dic4711yescharacteristic
421#103C2×Dic4711yescharacteristic
422#103C2×Dic4711yescharacteristic
423#102C2×Dic4711yescharacteristic
424#102C2×Dic4711yescharacteristic
425#102C2×Dic4711yescharacteristic
426#102C2×Dic4711yescharacteristic
427#102C2×Dic4711yescharacteristic
428#102C2×Dic4711yescharacteristic
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437C22⋊C8C2×Dic4711yescharacteristic
438C22⋊C8C2×Dic4711yescharacteristic
439#97—471no—
440#97—471no—
441#97—941no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—471no—
445C4×C8—471no—
446C4×C8—941no—
447C4×C8—941no—
448C4×C8C22×D4711yescharacteristic
449C4×C8C22×D4711yescharacteristic
450#41—22no—
451#41—41no—
452#41—42no—
453#41—42no—
454C2×Q8—21no—
455C2×Q8C22×Dic4711yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4C22×Dic4711yescharacteristic
462C2×D4C22×Dic4711yescharacteristic
463C2×D4C22×Dic4711yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4D4×D4711yescharacteristic
470C22×C4#1062535211yescharacteristic
471C22×C4C22×Dic4711yescharacteristic
472SD16—22no—
473SD16—22no—
474D8—41no—
475D8—41no—
476M16—942no—
477M16—1882no—
478M16—1882no—
479M16—1881no—
480M16—1882no—
481M16—1882no—
482C2×C8—471no—
483C2×C8—471no—
484C2×C8—471no—
485C2×C8—471no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—1882no—
493C2×C8—1882no—
494C2×C8—1882no—
495C2×C8C22×Dic4711yescharacteristic
496C2×C8C22×Dic4711yescharacteristic
497C2×C8C22×Dic4711yescharacteristic
498C2×C8C22×Dic4711yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4C22×Dic4711yescharacteristic
503C4⋊C4C22×Dic4711yescharacteristic
504C4⋊C4C22×Dic4711yescharacteristic
505C4⋊C4C22×Dic4711yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42D4×D4711yescharacteristic
517C42#1062535211yescharacteristic
518C42C22×Dic4711yescharacteristic
519C42C23×D4711yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23D4×Dic4711yescharacteristic
524Q8—21no—
525Q8—42no—
526Q8#1309403112yescomplemented
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—81no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4D4×Dic4711yescharacteristic
557C2×C4D4×Dic4711yescharacteristic
558C2×C4D4×Dic4711yescharacteristic
559C2×C4C23×Dic4711yescharacteristic
560C2×C4C2×D4×D4711yescharacteristic
561C2×C4C2×#1062535211yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—472no—
567C8—941no—
568C8—941no—
569C8—941no—
570C8—1881no—
571C8—1881no—
572C8—1881no—
573C8—1881no—
574C8—1881no—
575C8—1881no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C2×D4×Dic4711yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4C2×#1309403111yescharacteristic
599C4#1568989011yescharacteristic
600C4AGL(1,ℤ/8)×D4711yescharacteristic
601C4#1568991911yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—81no—
606C2#2025211511yescharacteristic
607C2AGL(1,ℤ/8)×Dic4711yescharacteristic
608C2#2025230511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
Fitting, prime radicalC47×#3106C2
socleC22×C47C2×C4×D4
cosocleC42×C47C24
hypercenter#3106D47
hypocenterC47#18011
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #20252408C2semidirect
2. #20252132C2semidirect
3. #20242302C2semidirect
4. #20242273C2semidirect
5. #20242267C2semidirect
6. #20242253C2semidirect
7. #20242232C2semidirect
8. #20242218C2semidirect
9. SD16⋊(C47⋊C8)C2semidirect
10. SD16×C47⋊C8C2semidirect
11. #20242173C2semidirect
12. #20241857C2semidirect
13. #20241775C2semidirect
14. #20241683C2semidirect
221. Q8×C47#131semidirect
371. C47#18011semidirect
526. Q8#13094031semidirect

Maximal subgroups

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

subgroupindex
#202524082
#202521322
#202423022
#202422732
#202422672
#202422532
#202422322
#202422182
SD16⋊(C47⋊C8)2
SD16×C47⋊C82
#202421732
#202418572
#202417752
#202416832
C47×#31062
#1801147