Finite Group Databasebeta

← #26187469

Subgroups — #26187469

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253470C211yesmaximal, characteristic
2#20252544C211yesmaximal, characteristic
3#20252478C211yesmaximal, characteristic, complemented
4#20242284C211yesmaximal, characteristic, complemented
5#20242277C211yesmaximal, characteristic, complemented
6#20242265C211yesmaximal, characteristic, complemented
7#20242258C211yesmaximal, characteristic, complemented
8#20242258C211yesmaximal, characteristic, complemented
9#20242244C211yesmaximal, characteristic, complemented
10#20242194C211yesmaximal, characteristic, complemented
11#20242187C211yesmaximal, characteristic, complemented
12#20241846C211yesmaximal, characteristic
13C2×#15688853C211yesmaximal, characteristic, complemented
14#20241672C211yesmaximal, characteristic, complemented
15C47×#1573C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689454C411yescharacteristic
19#15689437C411yescharacteristic
20#15689431C411yescharacteristic
21#15689431C411yescharacteristic
22#15689346C411yescharacteristic
23#15689346C411yescharacteristic
24#15689281C411yescharacteristic
25#15689264C411yescharacteristic
26#15689251—21no—
27#15689251—21no—
28#15689250C2211yescharacteristic
29#15689250C2211yescharacteristic
30#15689250C2211yescharacteristic
31#15689247C2211yescharacteristic
32#15689247C2211yescharacteristic
33#15689247C2211yescharacteristic
34C4×Dic188C2211yescharacteristic
35C4×Dic188C2211yescharacteristic
36C4×#10625325C2211yescharacteristic
37C4×#10625325C2211yescharacteristic
38#15689200C2211yescharacteristic
39#15689194—21no—
40#15689188C2211yescharacteristic
41C8×C22⋊D47—21no—
42#15689183—21no—
43#15689177—21no—
44#15689176C2211yescharacteristic
45#15689173—21no—
46#15689148—21no—
47C2×C4×C47⋊C8C2211yescharacteristic
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50#15688853C2211yescharacteristic
51#15688853C2211yescharacteristic
52#15688853C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688850C2211yescharacteristic
55#15688850C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#432C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625324—21no—
73C22×C47⋊C8—21no—
74C2×C8×D47—21no—
75#13094018—21no—
76#13094016C2×C411yescharacteristic
77#13094012C2×C411yescharacteristic
78#13094007—21no—
79#13094003C2×C411yescharacteristic
80#13093998C2×C411yescharacteristic
81C4×Dic94—21no—
82C4×Dic94—21no—
83C4×Dic94C2×C411yescharacteristic
84C4×Dic94C2×C411yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×Dic94C2311yescharacteristic
87C4×Dic94C2311yescharacteristic
88C4×D188C2311yescharacteristic
89C4×C22⋊D47—21no—
90#13093981—21no—
91C2×C4⋊Dic47C2×C411yescharacteristic
92C2×Dic47⋊C4—21no—
93C2×C4×Dic47—21no—
94#13093958C2×C411yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093956C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98C4⋊(C47⋊C8)D411yescharacteristic
99C4⋊(C47⋊C8)D411yescharacteristic
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106#13093949C2×C411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093949C2×C411yescharacteristic
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115C22⋊(C47⋊C8)D411yescharacteristic
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118#13093934—21no—
119#13093934—21no—
120#13093934—21no—
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C22×C8×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C4⋊C8×C47—21no—
132C4⋊C8×C47C2×C411yescharacteristic
133C4⋊C8×C47C2×C411yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C2×D188C22×C411yescharacteristic
151C2×C4×D47—21no—
152C2×Dic94—22no—
153C2×Dic94—21no—
154C2×Dic94—41no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—81no—
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C22×C411yescharacteristic
167C42×C47C22×C411yescharacteristic
168C42×C47C2×D411yescharacteristic
169C42×C47#4111yescharacteristic
170C42×C47C2411yescharacteristic
171C22⋊Dic47—21no—
172(C2×D47)⋊C4—21no—
173(C2×D47)⋊C4—21no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47C22×C411yescharacteristic
178C4⋊Dic47C22×C411yescharacteristic
179C4⋊Dic47C22×C411yescharacteristic
180C4⋊Dic47C22×C411yescharacteristic
181Dic47⋊C4—21no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C2×C47⋊C8—24no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8C2×D411yescharacteristic
198C2×C47⋊C8C2×D411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201Dic188—22no—
202Dic188—41no—
203#10625325—22no—
204#10625325—41no—
205#10625324—81no—
206C8×D47—81no—
207C23×C47C4×D411yescharacteristic
208C22×D47—21no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C23×C411yescharacteristic
218C2×C4×C47C22×D411yescharacteristic
219C2×C4×C47C2×#4111yescharacteristic
220C22⋊D47—42no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230D188—21no—
231D188—21no—
232C4×D47—41no—
233C4×D47—41no—
234Dic94—21no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—42no—
240Dic94#13112yes—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C47⋊C8—22no—
250C47⋊C8—22no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255#18017—471nomaximal, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47#44312yes—
259C22×C47C2×C4×D411yescharacteristic
260C2×D47—41no—
261C2×D47—41no—
262C2×D47—41no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47C2×#13111yescharacteristic
268C4×C47#56811yescharacteristic
269C4×C47#57711yescharacteristic
270C4×C47#57811yescharacteristic
271Dic47—22no—
272Dic47—41no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278#3108—471no—
279#2994—471no—
280#2984—471no—
281#1591—471no—
282#1590—471no—
283#1588—471no—
284#1587—471no—
285#1587—471no—
286#1585—471no—
287C8×Q16—471no—
288C8×SD16—471no—
289#1573D4711yescharacteristic, complemented
290#1494—471no—
291C2×Q8⋊C8—471no—
292#1450—471no—
293C2×C47—22no—
294C2×C47#293311yescharacteristic
295C2×C47#294711yescharacteristic
296C2×C47C2×#44311yescharacteristic
297D47—81no—
298#529—471no—
299C2×C4×Q8—471no—
300#483—471no—
301#480—471no—
302#479—471no—
303#479—471no—
304#464—471no—
305#464—471no—
306#451—471no—
307#448—471no—
308#446—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8—471no—
316C4×Q16—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16—471no—
320#436—471no—
321#435—941no—
322C8×D4—471no—
323C8×D4—941no—
324#433—941no—
325#432—941no—
326#432C2×D4711yescharacteristic
327#431—471no—
328#431—941no—
329#431C2×D4711yescharacteristic
330#424—941no—
331C2×C4⋊C8C2×D4711yescharacteristic
332C2×C4×C8—471no—
333#335C2×D4711yescharacteristic
334#335C2×D4711yescharacteristic
335#334C2×D4711yescharacteristic
336#334C2×D4711yescharacteristic
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8—471no—
343D4⋊C8—471no—
344D4⋊C8—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C82—471no—
349C47#1801711yescharacteristic, complemented, Sylow
350C22×Q8—471no—
351C2×Q16—471no—
352C2×Q16—471no—
353C2×SD16—471no—
354C2×SD16—471no—
355C2×M16—941no—
356C22×C8—21no—
357C22×C8—941no—
358C22×C8—941no—
359#126—941no—
360#125—471no—
361#124—471no—
362#123—941no—
363C22⋊Q8—471no—
364#121—471no—
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—471no—
370C4×Q8—941no—
371C4×Q8—941no—
372C4×D4—471no—
373C4×D4—941no—
374#117—941no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—941no—
377C2×C42—941no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—21no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—941no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8C4×D4711yescharacteristic
393C4⋊C8C4×D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396C4⋊C8C22×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#102—471no—
405#102—471no—
406C22⋊C8—21no—
407C22⋊C8—471no—
408C22⋊C8—471no—
409C22⋊C8—941no—
410C22⋊C8—941no—
411C22⋊C8C4×D4711yescharacteristic
412C22⋊C8C4×D4711yescharacteristic
413#97—21no—
414#97—941no—
415#97—941no—
416#97—941no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427C2×Q8—471no—
428C2×Q8—471no—
429C2×Q8—471no—
430C2×Q8—942no—
431C2×Q8—941no—
432C2×Q8—1881no—
433C2×D4—471no—
434C2×D4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4D4×D4711yescharacteristic
440C22×C4#1062535411yescharacteristic
441Q16—942no—
442Q16—1881no—
443SD16—942no—
444SD16—1881no—
445M16—3761no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—944no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—3761no—
459C2×C8C2×C4×D4711yescharacteristic
460C2×C8C2×C4×D4711yescharacteristic
461C2×C8C2×C4×D4711yescharacteristic
462C2×C8C2×C4×D4711yescharacteristic
463C4⋊C4—471no—
464C4⋊C4—471no—
465C4⋊C4—471no—
466C4⋊C4—471no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42—941no—
485C42—941no—
486C42C2×C4×D4711yescharacteristic
487C42D4×D4711yescharacteristic
488C42#1062535411yescharacteristic
489C42C23×D4711yescharacteristic
490C23—941no—
491C23#1309398611yescharacteristic
492Q8—472no—
493Q8—941no—
494Q8—941no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—1882no—
499D4—941no—
500D4—941no—
501D4—1882no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—1882no—
515C2×C4—1882no—
516C2×C4—1881no—
517C2×C4—1881no—
518C2×C4#1309398611yescharacteristic
519C2×C4#1309398611yescharacteristic
520C2×C4#1309398611yescharacteristic
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4C2×#1062535411yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—942no—
533C8—942no—
534C8—941no—
535C8—941no—
536C8—941no—
537C8—941no—
538C22—21no—
539C22—21no—
540C22—1881no—
541C22—1881no—
542C22—1881no—
543C22#1568923912yes—
544C22C2×#1309398611yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—942no—
550C4—1881no—
551C4—1881no—
552C4—1881no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4#131×D4711yescharacteristic
557C4#1568988811yescharacteristic
558C4#1568993311yescharacteristic
559C4#1568993911yescharacteristic
560C2—22no—
561C2—3761no—
562C2#2025211211yescharacteristic
563C2#2025222911yescharacteristic
564C2C2×#1568923911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1573C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#1573D47
hypocenterC47#18017
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #20252478C2semidirect
4. #20242284C2semidirect
5. #20242277C2semidirect
6. #20242265C2semidirect
7. #20242258C2semidirect
8. #20242258C2semidirect
9. #20242244C2semidirect
10. #20242194C2semidirect
11. #20242187C2semidirect
13. C2×#15688853C2semidirect
14. #20241672C2semidirect
15. C47×#1573C2semidirect
289. #1573D47semidirect
349. C47#18017semidirect

Maximal subgroups

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

subgroupindex
#202534702
#202525442
#202524782
#202422842
#202422772
#202422652
#202422582
#202422442
#202421942
#202421872
#202418462
C2×#156888532
#202416722
C47×#15732
#1801747