Finite Group Databasebeta

← #26187638

Subgroups — #26187638

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253415C211yesmaximal, characteristic
2#20252475C211yesmaximal, characteristic, complemented
3#20242290C211yesmaximal, characteristic, complemented
4#20242276C211yesmaximal, characteristic, complemented
5#20242264C211yesmaximal, characteristic, complemented
6#20242245C211yesmaximal, characteristic, complemented
7#20242229C211yesmaximal, characteristic, complemented
8#20242224C211yesmaximal, characteristic, complemented
9#20242200C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242166C211yesmaximal, characteristic, complemented
12#20241857C211yesmaximal, characteristic
13#20241782C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#2979C211yesmaximal, characteristic
16C2×C4×Dic94C2211yescharacteristic
17#15689439C411yescharacteristic
18#15689439C411yescharacteristic
19#15689405C411yescharacteristic
20#15689405C411yescharacteristic
21#15689320C411yescharacteristic
22#15689320C411yescharacteristic
23#15689261C411yescharacteristic
24#15689261C411yescharacteristic
25#15689253C2211yescharacteristic
26#15689253C2211yescharacteristic
27#15689252—21no—
28#15689252—21no—
29C8×Dic94C2211yescharacteristic
30C8×Dic94C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625335C2211yescharacteristic
33C4×#10625335C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689180C2211yescharacteristic
36#15689177—21no—
37#15689176C2211yescharacteristic
38#15689176C2211yescharacteristic
39#15689173—21no—
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44#15688853C2211yescharacteristic
45#15688853C2211yescharacteristic
46#15688853C2211yescharacteristic
47#15688853C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50D4⋊(C47⋊C8)C2211yescharacteristic
51D4⋊(C47⋊C8)C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54#15688844C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C47×#532C2211yescharacteristic
57C47×#436—21no—
58C47×#436C2211yescharacteristic
59C47×#436C2211yescharacteristic
60C8×D4×C47—21no—
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#431C2211yescharacteristic
64C47×#431C2211yescharacteristic
65C47×#408—21no—
66C47×#408—21no—
67C22×Dic94C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C4×Dic94—21no—
73C4×Dic94—21no—
74C4×Dic94C2×C411yescharacteristic
75C4×Dic94C2×C411yescharacteristic
76C4×Dic94C2311yescharacteristic
77C4×Dic94C2311yescharacteristic
78C2×C4⋊Dic47C2×C411yescharacteristic
79C2×Dic47⋊C4—21no—
80C2×C4×Dic47—21no—
81#13093955C2×C411yescharacteristic
82#13093955C2×C411yescharacteristic
83#13093955C2×C411yescharacteristic
84#13093955C2×C411yescharacteristic
85C4⋊(C47⋊C8)—21no—
86C4⋊(C47⋊C8)C2×C411yescharacteristic
87C4⋊(C47⋊C8)C2×C411yescharacteristic
88C4⋊(C47⋊C8)C2311yescharacteristic
89C4⋊(C47⋊C8)C2311yescharacteristic
90Dic47⋊C8—21no—
91Dic47⋊C8—21no—
92Dic47⋊C8—21no—
93Dic47⋊C8—21no—
94#13093947C2×C411yescharacteristic
95#13093947C2×C411yescharacteristic
96#13093947C2×C411yescharacteristic
97#13093947C2×C411yescharacteristic
98#13093945C2×C411yescharacteristic
99#13093945C2×C411yescharacteristic
100#13093945C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102C22⋊(C47⋊C8)—21no—
103C22⋊(C47⋊C8)—21no—
104C22⋊(C47⋊C8)C2×C411yescharacteristic
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106#13093935—21no—
107#13093934—21no—
108#13093934—21no—
109C4×C47⋊C8C2311yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C8×Dic47—21no—
114C8×Dic47—21no—
115C2×#41×C47—21no—
116C2×M16×C47—21no—
117C2×M16×C47—21no—
118C22×C8×C47—21no—
119C22×C8×C47—21no—
120C4⋊Q8×C47C2×C411yescharacteristic
121#127×C47C2×C411yescharacteristic
122#124×C47—21no—
123#121×C47—21no—
124#121×C47C2×C411yescharacteristic
125#121×C47C2×C411yescharacteristic
126C4×D4×C47—21no—
127C4×D4×C47C2311yescharacteristic
128C4×D4×C47C2311yescharacteristic
129C2×C42×C47C2311yescharacteristic
130C4⋊C8×C47D411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47D411yescharacteristic
140C22⋊C8×C47D411yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—81no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47C22×C411yescharacteristic
152C2×D4×C47C22×C411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C22×Dic47—21no—
159C22×Dic47—21no—
160C2×Dic94—22no—
161C2×Dic94—21no—
162C2×Dic94—41no—
163C2×Dic94C22×C411yescharacteristic
164C2×Dic94C22×C411yescharacteristic
165M16×C47—81no—
166M16×C47—81no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—81no—
170C2×C8×C47—81no—
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C4⋊C4×C47—21no—
176C4⋊C4×C47C22×C411yescharacteristic
177C4⋊C4×C47C22×C411yescharacteristic
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C22⋊C4×C47—21no—
181C22⋊C4×C47—21no—
182C42×C47C22×C411yescharacteristic
183C42×C47C2×D411yescharacteristic
184C42×C47#4111yescharacteristic
185C42×C47C2411yescharacteristic
186#10625335—22no—
187#10625335—22no—
188#10625335—41no—
189#10625335—41no—
190C4⋊Dic47—21no—
191C4⋊Dic47C22×C411yescharacteristic
192C4⋊Dic47C22×C411yescharacteristic
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196Dic47⋊C4—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—21no—
200C4×Dic47—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C22×C411yescharacteristic
209C23×C47—21no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212Q8×C47—81no—
213D4×C47—21no—
214D4×C47—21no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—42no—
218D4×C47—81no—
219D4×C47—81no—
220D4×C47—81no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244Dic94—21no—
245Dic94—21no—
246Dic94—21no—
247Dic94—42no—
248Dic94#13112yes—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—41no—
254C8×C47—41no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263#18030—471nomaximal, Sylow
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—21no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47C2×C4×D411yescharacteristic
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47C2×#13111yescharacteristic
281C4×C47#56811yescharacteristic
282C4×C47#57711yescharacteristic
283C4×C47#57711yescharacteristic
284Dic47—22no—
285Dic47—41no—
286Dic47—41no—
287Dic47—41no—
288#3103—471no—
289#2984—471no—
290#2979D4711yescharacteristic
291#1592—471no—
292#1590—471no—
293#1588—471no—
294#1585—471no—
295#1583—471no—
296#1582—471no—
297SD16⋊C8—471no—
298C8×SD16—471no—
299#1572—471no—
300#1496—471no—
301#1479—471no—
302#1454—471no—
303C2×C47—41no—
304C2×C47—81no—
305C2×C47—81no—
306C2×C47#293311yescharacteristic
307C2×C47#294911yescharacteristic
308C2×C47#295511yescharacteristic
309#532C2×D4711yescharacteristic
310C2×C4×Q8—471no—
311#481—471no—
312#481—471no—
313#475—471no—
314#475—471no—
315#460—471no—
316#460—471no—
317#448—471no—
318#448—471no—
319#446—471no—
320#446—471no—
321#446—941no—
322#446—941no—
323C8×Q8—471no—
324C8×Q8—471no—
325C4×SD16—471no—
326C4×SD16—471no—
327C4×SD16—471no—
328C4×SD16—471no—
329#436—21no—
330#436C2×D4711yescharacteristic
331#436C2×D4711yescharacteristic
332C8×D4—21no—
333C8×D4C2×D4711yescharacteristic
334C8×D4C2×D4711yescharacteristic
335#432—471no—
336#432—941no—
337#431—471no—
338#431—471no—
339#431—941no—
340#431C2×D4711yescharacteristic
341#431C2×D4711yescharacteristic
342#408—21no—
343#408—21no—
344#335—471no—
345#335—471no—
346#334—471no—
347#334—471no—
348Q8⋊C8—471no—
349Q8⋊C8—471no—
350Q8⋊C8—471no—
351Q8⋊C8—471no—
352D4⋊C8—471no—
353D4⋊C8—471no—
354D4⋊C8—471no—
355D4⋊C8—471no—
356#322—471no—
357#322—471no—
358#322—471no—
359C82—471no—
360C47#1803011yescharacteristic, complemented, Sylow
361C2×#41—21no—
362C22×Q8—471no—
363C2×SD16—471no—
364C2×SD16—471no—
365C2×SD16—471no—
366C2×SD16—471no—
367C2×M16—21no—
368C2×M16—21no—
369C22×C8—21no—
370C22×C8—21no—
371C4⋊Q8C4×D4711yescharacteristic
372#127C4×D4711yescharacteristic
373#124—21no—
374#121—21no—
375#121C4×D4711yescharacteristic
376#121C4×D4711yescharacteristic
377C4×Q8—471no—
378C4×Q8—471no—
379C4×Q8—471no—
380C4×Q8—471no—
381C4×Q8—941no—
382C4×Q8—941no—
383C4×D4—21no—
384C4×D4C22×D4711yescharacteristic
385C4×D4C22×D4711yescharacteristic
386C2×C4⋊C4—471no—
387C2×C4⋊C4—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390#106—471no—
391#106—471no—
392#106—471no—
393#106—471no—
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⋊C8—941no—
403C4⋊C8C22⋊D4711yescharacteristic
404C4⋊C8C22⋊D4711yescharacteristic
405C4⋊C8C22×D4711yescharacteristic
406C4⋊C8C22×D4711yescharacteristic
407#103—471no—
408#103—471no—
409#103—471no—
410#103—471no—
411#102—471no—
412#102—471no—
413#102—471no—
414#102—471no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—471no—
421C22⋊C8—471no—
422C22⋊C8—941no—
423C22⋊C8—941no—
424C22⋊C8C22⋊D4711yescharacteristic
425C22⋊C8C22⋊D4711yescharacteristic
426#97—941no—
427#97—941no—
428#97—941no—
429C4×C8—21no—
430C4×C8—471no—
431C4×C8—471no—
432C4×C8—471no—
433C4×C8—471no—
434C4×C8—941no—
435C4×C8—941no—
436C4×C8C22×D4711yescharacteristic
437C4×C8C22×D4711yescharacteristic
438#41—81no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—471no—
442C2×Q8—471no—
443C2×Q8—942no—
444C2×Q8—941no—
445C2×Q8—1881no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D4711yescharacteristic
451C2×D4C2×C4×D4711yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4C2×C4×D4711yescharacteristic
457C22×C4#1062535011yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459SD16—942no—
460SD16—942no—
461SD16—1881no—
462SD16—1881no—
463M16—81no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—81no—
469C2×C8—471no—
470C2×C8—471no—
471C2×C8—471no—
472C2×C8—471no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8C2×C22⋊D4711yescharacteristic
478C2×C8C2×C22⋊D4711yescharacteristic
479C2×C8C2×C22⋊D4711yescharacteristic
480C2×C8C2×C22⋊D4711yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—471no—
483C4⋊C4—471no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4C2×C4×D4711yescharacteristic
490C4⋊C4C2×C4×D4711yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C42—941no—
496C42—941no—
497C42—941no—
498C42—941no—
499C42C2×C4×D4711yescharacteristic
500C42#1062535011yescharacteristic
501C42C2×C22⋊D4711yescharacteristic
502C42C23×D4711yescharacteristic
503C23—21no—
504C23—21no—
505C23C4×C22⋊D4711yescharacteristic
506Q8—81no—
507Q8—472no—
508Q8—941no—
509Q8—941no—
510Q8—941no—
511Q8—1882no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4C4×C22⋊D4711yescharacteristic
538C2×C4C4×C22⋊D4711yescharacteristic
539C2×C4C4×C22⋊D4711yescharacteristic
540C2×C4C22×C4×D4711yescharacteristic
541C2×C4C22×C22⋊D4711yescharacteristic
542C2×C4C2×#1062535011yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—941no—
550C8—941no—
551C8—941no—
552C8—941no—
553C8—1881no—
554C8—1881no—
555C8—1881no—
556C8—1881no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×C4×C22⋊D4711yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—942no—
574C4—1881no—
575C4—1881no—
576C4—1881no—
577C4#131×D4711yescharacteristic
578C4#1568988811yescharacteristic
579C4#1568993411yescharacteristic
580C4#1568993411yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#2025211011yescharacteristic
585C2#2025224511yescharacteristic
586C2#2025228911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2979C2
socleC22×C47C2×C4×D4
prime radicalC47×#532C22
cosocleC42×C47C24
hypercenter#2979D47
hypocenterC47#18030
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #20252475C2semidirect
3. #20242290C2semidirect
4. #20242276C2semidirect
5. #20242264C2semidirect
6. #20242245C2semidirect
7. #20242229C2semidirect
8. #20242224C2semidirect
9. #20242200C2semidirect
10. C8×#10625335C2semidirect
11. #20242166C2semidirect
13. #20241782C2semidirect
14. #20241688C2semidirect
360. C47#18030semidirect

Maximal subgroups

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

subgroupindex
#202534152
#202524752
#202422902
#202422762
#202422642
#202422452
#202422292
#202422242
#202422002
C8×#106253352
#202421662
#202418572
#202417822
#202416882
C47×#29792
#1803047