Finite Group Databasebeta

← #26188059

Subgroups — #26188059

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253952C211yesmaximal, characteristic
2#20252393C211yesmaximal, characteristic, complemented
3#20252386C211yesmaximal, characteristic, complemented
4#20242282C211yesmaximal, characteristic, complemented
5#20242270C211yesmaximal, characteristic, complemented
6#20242234C211yesmaximal, characteristic, complemented
7#20242228C211yesmaximal, characteristic, complemented
8#20242227C211yesmaximal, characteristic, complemented
9#20242221C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242180C211yesmaximal, characteristic, complemented
12#20242134C211yesmaximal, characteristic, complemented
13#20241797C211yesmaximal, characteristic, complemented
14#20241669C211yesmaximal, characteristic, complemented
15C47×#1482C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689522C411yescharacteristic
18#15689505C411yescharacteristic
19#15689480C411yescharacteristic
20#15689477C411yescharacteristic
21#15689362C411yescharacteristic
22#15689357C411yescharacteristic
23#15689354C411yescharacteristic
24#15689350C411yescharacteristic
25#15689254C2211yescharacteristic
26#15689250C2211yescharacteristic
27Q8×C47⋊C8C2211yescharacteristic
28#15689247C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625334C2211yescharacteristic
33#15689201—21no—
34#15689201C2211yescharacteristic
35#15689200C2211yescharacteristic
36#15689198—21no—
37#15689197—21no—
38#15689195—21no—
39D4×C47⋊C8C2211yescharacteristic
40#15689188C2211yescharacteristic
41#15689184—21no—
42#15689182—21no—
43#15689176C2211yescharacteristic
44#15689079—21no—
45#15689077—21no—
46C4×#10625329C2211yescharacteristic
47C2×C4×C47⋊C8C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#529C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329D411yescharacteristic
73C2×#10625329D411yescharacteristic
74C2×#10625324—21no—
75C22×C47⋊C8—21no—
76C22×C47⋊C8C2×C411yescharacteristic
77C22×C47⋊C8C2×C411yescharacteristic
78C2×C8×D47—21no—
79#13094018—21no—
80#13094016C2×C411yescharacteristic
81#13094012C2×C411yescharacteristic
82#13094007—21no—
83#13094003C2×C411yescharacteristic
84#13093998C2×C411yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×D188C2311yescharacteristic
87C4×C22⋊D47—21no—
88#13093981—21no—
89#13093957C2×C411yescharacteristic
90#13093957C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92#13093955C2×C411yescharacteristic
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)—21no—
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093947C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110(C2×D47)⋊C8—21no—
111(C2×D47)⋊C8—21no—
112#13093935—21no—
113#13093935D411yescharacteristic
114#13093935D411yescharacteristic
115#13093934—21no—
116C4×C47⋊C8—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8C2×C411yescharacteristic
119C4×C47⋊C8C2×C411yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125#126×C47—21no—
126#125×C47C2×C411yescharacteristic
127#124×C47C2×C411yescharacteristic
128#123×C47—21no—
129C22⋊Q8×C47C2×C411yescharacteristic
130#121×C47C2×C411yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132C4×D4×C47—21no—
133C4×D4×C47C2311yescharacteristic
134#117×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47—21no—
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C2×C22⋊D47—21no—
152C2×D188C22×C411yescharacteristic
153C2×C4×D47—21no—
154C2×Dic94C22×C411yescharacteristic
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47C22×C411yescharacteristic
164C4⋊C4×C47C22×C411yescharacteristic
165C22⋊C4×C47—21no—
166C22⋊C4×C47—21no—
167C22⋊C4×C47—21no—
168C22⋊C4×C47—21no—
169C22⋊C4×C47—21no—
170C42×C47—21no—
171C42×C47C22×C411yescharacteristic
172C42×C47C2×D411yescharacteristic
173C42×C47#4111yescharacteristic
174C42×C47C2411yescharacteristic
175C22⋊Dic47—21no—
176#10625337—22no—
177#10625336—41no—
178#10625335—41no—
179#10625334—22no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184C4⋊Dic47C22×C411yescharacteristic
185C4⋊Dic47C22×C411yescharacteristic
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191#10625329—22no—
192#10625329—22no—
193#10625329—42no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—41no—
198C2×C47⋊C8—42no—
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207#10625324—42no—
208C8×D47—42no—
209C23×C47—21no—
210C23×C47C4×D411yescharacteristic
211C22×D47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214D4×C47—21no—
215D4×C47—21no—
216D4×C47—81no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C23×C411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C22⋊D47—81no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237D188—21no—
238D188—21no—
239C4×D47—41no—
240C4×D47—41no—
241Dic94—21no—
242Dic94—21no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8#13112yes—
255C47⋊C8#13512yes—
256C47⋊C8#13512yes—
257#18069—471nomaximal, Sylow
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47C2×C4×D411yescharacteristic
265C2×D47—41no—
266C2×D47—41no—
267C2×D47—41no—
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47C2×#13111yescharacteristic
276C4×C47#56811yescharacteristic
277C4×C47C2×#13511yescharacteristic
278C4×C47C2×#13511yescharacteristic
279Dic47—41no—
280Dic47—41no—
281Dic47—41no—
282#3168—471no—
283#2969—471no—
284#2969—471no—
285#1591—471no—
286#1589—471no—
287#1583—471no—
288#1583—471no—
289#1582—471no—
290#1582—471no—
291C8×Q16—471no—
292C8×D8—471no—
293#1564—471no—
294#1482—471no—
295#1482D4711yescharacteristic, complemented
296C8×M16—471no—
297C2×C47—41no—
298C2×C47—81no—
299C2×C47#293511yescharacteristic
300C2×C47C4×#13511yescharacteristic
301C2×C47#295711yescharacteristic
302D47—81no—
303#529—471no—
304#529C2×D4711yescharacteristic
305#499—471no—
306#495—471no—
307#488—471no—
308#488—471no—
309#467—471no—
310#466—471no—
311#465—471no—
312#465—471no—
313#446—471no—
314#446—471no—
315C8×Q8—471no—
316C8×Q8—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16—471no—
320C4×D8—471no—
321#436—471no—
322#436—471no—
323#436—941no—
324#436—941no—
325#435—941no—
326#435—941no—
327C8×D4—471no—
328C8×D4—471no—
329#433—941no—
330#433—941no—
331#431—471no—
332#431C2×D4711yescharacteristic
333#431C2×D4711yescharacteristic
334#405—941no—
335#405—941no—
336C4×M16—471no—
337C2×C4×C8—471no—
338#335—471no—
339#335—471no—
340#334—471no—
341#334—471no—
342Q8⋊C8—471no—
343Q8⋊C8—471no—
344Q8⋊C8C2×D4711yescharacteristic
345Q8⋊C8C2×D4711yescharacteristic
346D4⋊C8—471no—
347D4⋊C8—471no—
348D4⋊C8C2×D4711yescharacteristic
349D4⋊C8C2×D4711yescharacteristic
350#322—471no—
351#322—471no—
352C82—471no—
353C82—471no—
354C47#1806911yescharacteristic, complemented, Sylow
355C2×Q16—471no—
356C2×SD16—471no—
357C2×SD16—471no—
358C2×D8—471no—
359C2×M16—471no—
360C2×M16—471no—
361C2×M16—941no—
362C2×M16—941no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—941no—
366C22×C8—941no—
367#126—21no—
368#126—941no—
369#125—471no—
370#125C4×D4711yescharacteristic
371#124—471no—
372#124C4×D4711yescharacteristic
373#123—21no—
374#123—941no—
375C22⋊Q8—471no—
376C22⋊Q8C4×D4711yescharacteristic
377#121—471no—
378#121C4×D4711yescharacteristic
379C4×Q8—471no—
380C4×Q8C22×D4711yescharacteristic
381C4×D4—21no—
382C4×D4—471no—
383C4×D4—941no—
384C4×D4C22×D4711yescharacteristic
385#117—21no—
386#117—941no—
387C2×C42C22×D4711yescharacteristic
388#107—471no—
389#107—471no—
390#106—471no—
391#106—471no—
392C4⋊C8—21no—
393C4⋊C8—471no—
394C4⋊C8—471no—
395C4⋊C8—941no—
396C4⋊C8—941no—
397C4⋊C8—941no—
398C4⋊C8—941no—
399C4⋊C8C22×D4711yescharacteristic
400C4⋊C8C22×D4711yescharacteristic
401#103—471no—
402#103—471no—
403#103—471no—
404#103—471no—
405#102—471no—
406#102—471no—
407#102—471no—
408#102—471no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413C22⋊C8—941no—
414C22⋊C8—941no—
415C22⋊C8—941no—
416#97—471no—
417#97—471no—
418#97—941no—
419#97—941no—
420C4×C8—21no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—941no—
428C4×C8—941no—
429C4×C8—941no—
430C4×C8C22×D4711yescharacteristic
431C4×C8C22×D4711yescharacteristic
432C2×Q8—471no—
433C2×Q8C2×C4×D4711yescharacteristic
434C2×D4—21no—
435C2×D4—471no—
436C2×D4—941no—
437C2×D4C2×C4×D4711yescharacteristic
438C22×C4—21no—
439C22×C4—941no—
440C22×C4C2×C4×D4711yescharacteristic
441C22×C4D4×D4711yescharacteristic
442C22×C4#1062535211yescharacteristic
443Q16—942no—
444SD16—1881no—
445SD16—1881no—
446D8—942no—
447M16—942no—
448M16—942no—
449M16—1882no—
450M16—1882no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—942no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—1882no—
467C2×C8—1882no—
468C2×C8—1881no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—471no—
474C4⋊C4—471no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4C2×C4×D4711yescharacteristic
480C4⋊C4C2×C4×D4711yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—941no—
487C22⋊C4—941no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C42—21no—
492C42—941no—
493C42C2×C4×D4711yescharacteristic
494C42D4×D4711yescharacteristic
495C42#1062535211yescharacteristic
496C42C23×D4711yescharacteristic
497C23—21no—
498C23—941no—
499C23(C22⋊D47)⋊C411yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—941no—
503Q8—941no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—941no—
508D4—941no—
509D4—3761no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—941no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—1881no—
524C2×C4—1881no—
525C2×C4(C22⋊D47)⋊C411yescharacteristic
526C2×C4(C22⋊D47)⋊C411yescharacteristic
527C2×C4(C22⋊D47)⋊C411yescharacteristic
528C2×C4C22×C4×D4711yescharacteristic
529C2×C4C2×D4×D4711yescharacteristic
530C2×C4C2×#1062535211yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—472no—
536C8—472no—
537C8—472no—
538C8—941no—
539C8—941no—
540C8—941no—
541C8—941no—
542C8—941no—
543C8—1881no—
544C8—1881no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—1881no—
552C22—1881no—
553C22—1881no—
554C22C2×(C22⋊D47)⋊C411yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—1881no—
563C4—1881no—
564C4—1881no—
565C4#131×D4711yescharacteristic
566C4#1568988811yescharacteristic
567C4#135×D4711yescharacteristic
568C4#135×D4711yescharacteristic
569C2—41no—
570C2—81no—
571C2—3761no—
572C2#2025212811yescharacteristic
573C2#2025215611yescharacteristic
574C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1482C2
socleC22×C47C2×C4×D4
prime radical#15689357C4
cosocleC42×C47C24
hypercenter#1482D47
hypocenterC47#18069
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #20252393C2semidirect
3. #20252386C2semidirect
4. #20242282C2semidirect
5. #20242270C2semidirect
6. #20242234C2semidirect
7. #20242228C2semidirect
8. #20242227C2semidirect
9. #20242221C2semidirect
10. #20242192C2semidirect
11. #20242180C2semidirect
12. #20242134C2semidirect
13. #20241797C2semidirect
14. #20241669C2semidirect
15. C47×#1482C2semidirect
295. #1482D47semidirect
354. C47#18069semidirect

Maximal subgroups

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

subgroupindex
#202539522
#202523932
#202523862
#202422822
#202422702
#202422342
#202422282
#202422272
#202422212
#202421922
#202421802
#202421342
#202417972
#202416692
C47×#14822
#1806947