Finite Group Databasebeta

← #26187410

Subgroups — #26187410

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253464C211yesmaximal, characteristic
2#20252393C211yesmaximal, characteristic
3#20252339C211yesmaximal, characteristic, complemented
4#20242294C211yesmaximal, characteristic, complemented
5#20242281C211yesmaximal, characteristic, complemented
6#20242262C211yesmaximal, characteristic, complemented
7#20242242C211yesmaximal, characteristic, complemented
8#20242235C211yesmaximal, characteristic, complemented
9#20242234C211yesmaximal, characteristic, complemented
10#20242197C211yesmaximal, characteristic, complemented
11#20242192C211yesmaximal, characteristic, complemented
12#20242179C211yesmaximal, characteristic, complemented
13#20241784C211yesmaximal, characteristic, complemented
14#20241683C211yesmaximal, characteristic, complemented
15C47×#1495C211yesmaximal, characteristic
16C2×C4×Dic94C2211yescharacteristic
17#15689451C411yescharacteristic
18#15689434C411yescharacteristic
19#15689427C411yescharacteristic
20#15689427C411yescharacteristic
21#15689342C411yescharacteristic
22#15689342C411yescharacteristic
23#15689278C411yescharacteristic
24#15689261C411yescharacteristic
25#15689254C2211yescharacteristic
26#15689252—21no—
27#15689252—21no—
28#15689250C2211yescharacteristic
29#15689250C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31#15689247C2211yescharacteristic
32#15689247C2211yescharacteristic
33C4×#10625337C2211yescharacteristic
34C4×#10625337C2211yescharacteristic
35C4×#10625335C2211yescharacteristic
36C4×#10625335C2211yescharacteristic
37#15689201—21no—
38#15689201C2211yescharacteristic
39#15689195—21no—
40D4×C47⋊C8C2211yescharacteristic
41#15689184—21no—
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689146—21no—
45#15689079—21no—
46C4×#10625329C2211yescharacteristic
47M16×Dic47—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#529C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#423C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C2×#10625329—21no—
73C2×#10625329D411yescharacteristic
74C2×#10625329D411yescharacteristic
75C22×C47⋊C8—21no—
76C4×Dic94—21no—
77C4×Dic94—21no—
78C4×Dic94C2×C411yescharacteristic
79C4×Dic94C2×C411yescharacteristic
80C4×Dic94C2311yescharacteristic
81C4×Dic94C2311yescharacteristic
82C2×C4⋊Dic47C2×C411yescharacteristic
83C2×Dic47⋊C4—21no—
84C2×C4×Dic47—21no—
85#13093957C2×C411yescharacteristic
86#13093957C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
89C4⋊(C47⋊C8)—21no—
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2×C411yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94C4⋊(C47⋊C8)C2311yescharacteristic
95Dic47⋊C8—21no—
96Dic47⋊C8—21no—
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093947C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093947C2×C411yescharacteristic
105#13093945C2×C411yescharacteristic
106#13093945C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)C2×C411yescharacteristic
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112#13093935—21no—
113#13093935D411yescharacteristic
114#13093935D411yescharacteristic
115#13093934—21no—
116#13093934—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8C2311yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C2×M16×C47—21no—
126#126×C47—21no—
127#125×C47C2×C411yescharacteristic
128#124×C47C2×C411yescharacteristic
129#123×C47—21no—
130C22⋊Q8×C47C2×C411yescharacteristic
131#121×C47C2×C411yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47—21no—
134C4×D4×C47C2311yescharacteristic
135#117×C47—21no—
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47—21no—
138C4⋊C8×C47—21no—
139C4⋊C8×C47C2311yescharacteristic
140C4⋊C8×C47C2311yescharacteristic
141C22⋊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
151C22×Dic47—21no—
152C22×Dic47—21no—
153C2×Dic94—22no—
154C2×Dic94—21no—
155C2×Dic94—41no—
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158M16×C47—42no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47C22×C411yescharacteristic
168C4⋊C4×C47C22×C411yescharacteristic
169C22⋊C4×C47—21no—
170C22⋊C4×C47—21no—
171C22⋊C4×C47—21no—
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C42×C47—21no—
175C42×C47C22×C411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47#4111yescharacteristic
178C42×C47C2411yescharacteristic
179#10625337—22no—
180#10625337—41no—
181#10625335—22no—
182#10625335—41no—
183C4⋊Dic47—21no—
184C4⋊Dic47C22×C411yescharacteristic
185C4⋊Dic47C22×C411yescharacteristic
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194#10625329—22no—
195#10625329—41no—
196#10625329—42no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—42no—
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C23×C47—21no—
209C23×C47C4×D411yescharacteristic
210Q8×C47—21no—
211Q8×C47—21no—
212D4×C47—21no—
213D4×C47—21no—
214D4×C47—81no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—42no—
236C2×Dic47—81no—
237Dic94—21no—
238Dic94—21no—
239Dic94—21no—
240Dic94—42no—
241Dic94#13112yes—
242C8×C47—41no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8#13712yes—
256#18012—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47C2×C4×D411yescharacteristic
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47C2×#13111yescharacteristic
272C4×C47#56811yescharacteristic
273C4×C47C2×#13711yescharacteristic
274C4×C47#57511yescharacteristic
275Dic47—22no—
276Dic47—41no—
277Dic47—41no—
278Dic47—41no—
279#3108—471no—
280#2969—471no—
281Q8×M16—471no—
282#1593—471no—
283#1590—471no—
284#1587—471no—
285#1585—471no—
286#1584—471no—
287#1583—471no—
288SD16⋊C8—471no—
289C8×Q16—471no—
290#1574—471no—
291#1495D4711yescharacteristic
292#1479—471no—
293#1453—471no—
294C2×C47—41no—
295C2×C47—81no—
296C2×C47#293311yescharacteristic
297C2×C47C4×#13711yescharacteristic
298C2×C47#295711yescharacteristic
299#529C2×D4711yescharacteristic
300C2×C4×Q8—471no—
301#483—471no—
302#480—471no—
303#479—471no—
304#479—471no—
305#464—471no—
306#464—471no—
307#451—471no—
308#448—471no—
309#446—471no—
310#446—471no—
311#446—471no—
312#446—941no—
313#446—941no—
314C8×Q8—471no—
315C8×Q8—471no—
316C8×Q8—471no—
317C4×Q16—471no—
318C4×Q16—471no—
319C4×SD16—471no—
320C4×SD16—471no—
321#436—471no—
322#436—941no—
323#435—941no—
324C8×D4—471no—
325#433—941no—
326#431—471no—
327#431—471no—
328#431C2×D4711yescharacteristic
329#423—941no—
330#423C2×D4711yescharacteristic
331#405—941no—
332C4×M16—471no—
333C4×M16—941no—
334#335—471no—
335#335—471no—
336#334—471no—
337#334—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8C2×D4711yescharacteristic
343Q8⋊C8C2×D4711yescharacteristic
344D4⋊C8C2×D4711yescharacteristic
345D4⋊C8C2×D4711yescharacteristic
346#322—471no—
347#322—471no—
348#322—471no—
349C82—471no—
350C47#1801211yescharacteristic, complemented, Sylow
351C22×Q8—471no—
352C2×Q16—471no—
353C2×Q16—471no—
354C2×SD16—471no—
355C2×SD16—471no—
356C2×M16—21no—
357C2×M16—471no—
358C2×M16—471no—
359C2×M16—941no—
360C22×C8—941no—
361#126—21no—
362#125C4×D4711yescharacteristic
363#124C4×D4711yescharacteristic
364#123—21no—
365C22⋊Q8C4×D4711yescharacteristic
366#121C4×D4711yescharacteristic
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—471no—
370C4×Q8—471no—
371C4×Q8—941no—
372C4×Q8—941no—
373C4×Q8C22×D4711yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4711yescharacteristic
376#117—21no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—941no—
379C2×C42—941no—
380C2×C42C22×D4711yescharacteristic
381#107—471no—
382#107—471no—
383#106—471no—
384#106—471no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—471no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8—941no—
397C4⋊C8C22×D4711yescharacteristic
398C4⋊C8C22×D4711yescharacteristic
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#103—471no—
405#102—471no—
406#102—471no—
407C22⋊C8—21no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—941no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413#97—471no—
414#97—471no—
415#97—941no—
416#97—941no—
417#97—941no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8—941no—
426C4×C8C22×D4711yescharacteristic
427C4×C8C22×D4711yescharacteristic
428C2×Q8—471no—
429C2×Q8—471no—
430C2×Q8—942no—
431C2×Q8—941no—
432C2×Q8—1881no—
433C2×Q8C2×C4×D4711yescharacteristic
434C2×D4—21no—
435C2×D4C2×C4×D4711yescharacteristic
436C22×C4—21no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4D4×D4711yescharacteristic
441C22×C4#1062535211yescharacteristic
442Q16—942no—
443Q16—1881no—
444SD16—942no—
445SD16—1881no—
446M16—42no—
447M16—942no—
448M16—1882no—
449M16—1881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—1882no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—471no—
470C4⋊C4—471no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4C2×C4×D4711yescharacteristic
477C4⋊C4C2×C4×D4711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—941no—
485C42—941no—
486C42—941no—
487C42—941no—
488C42C2×C4×D4711yescharacteristic
489C42D4×D4711yescharacteristic
490C42#1062535211yescharacteristic
491C42C23×D4711yescharacteristic
492C23—21no—
493C23(C22⋊D47)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—472no—
497Q8—941no—
498Q8—941no—
499Q8—941no—
500Q8—1882no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—3761no—
519C2×C4—1882no—
520C2×C4(C22⋊D47)⋊C411yescharacteristic
521C2×C4(C22⋊D47)⋊C411yescharacteristic
522C2×C4(C22⋊D47)⋊C411yescharacteristic
523C2×C4C22×C4×D4711yescharacteristic
524C2×C4C2×D4×D4711yescharacteristic
525C2×C4C2×#1062535211yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—472no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—941no—
537C8—941no—
538C8—1881no—
539C8—1881no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×(C22⋊D47)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—942no—
555C4—1881no—
556C4—1881no—
557C4—1881no—
558C4#131×D4711yescharacteristic
559C4#1568988811yescharacteristic
560C4#137×D4711yescharacteristic
561C4#1568991911yescharacteristic
562C2—41no—
563C2—81no—
564C2#2025211811yescharacteristic
565C2#2025221211yescharacteristic
566C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1495C2
socleC22×C47C2×C4×D4
prime radical#121×C47C2×C4
cosocleC42×C47C24
hypercenter#1495D47
hypocenterC47#18012
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
3. #20252339C2semidirect
4. #20242294C2semidirect
5. #20242281C2semidirect
6. #20242262C2semidirect
7. #20242242C2semidirect
8. #20242235C2semidirect
9. #20242234C2semidirect
10. #20242197C2semidirect
11. #20242192C2semidirect
12. #20242179C2semidirect
13. #20241784C2semidirect
14. #20241683C2semidirect
350. C47#18012semidirect

Maximal subgroups

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

subgroupindex
#202534642
#202523932
#202523392
#202422942
#202422812
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C47×#14952
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