Finite Group Databasebeta

← #26186353

Subgroups — #26186353

Order 12032.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253468C211yesmaximal, characteristic
2#20252539C211yesmaximal, characteristic
3#20242266C211yesmaximal, characteristic, complemented
4#20242259C211yesmaximal, characteristic, complemented
5#20242238C211yesmaximal, characteristic, complemented
6#20242231C211yesmaximal, characteristic, complemented
7#20242205C211yesmaximal, characteristic, complemented
8#20242198C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625336C211yesmaximal, characteristic, complemented
11#20242176C211yesmaximal, characteristic, complemented
12#20241817C211yesmaximal, characteristic, complemented
13#20241794C211yesmaximal, characteristic
14#20241688C211yesmaximal, characteristic, complemented
15C47×#2982C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689453C411yescharacteristic
18#15689436C411yescharacteristic
19#15689430C411yescharacteristic
20#15689430C411yescharacteristic
21#15689345C411yescharacteristic
22#15689345C411yescharacteristic
23#15689279C411yescharacteristic
24#15689262C411yescharacteristic
25#15689253C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625337C2211yescharacteristic
28C4×#10625337C2211yescharacteristic
29C4×#10625336C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31#15689202C2211yescharacteristic
32#15689198—21no—
33#15689197—21no—
34C8×D188C2211yescharacteristic
35#15689183—21no—
36#15689176C2211yescharacteristic
37#15689176C2211yescharacteristic
38#15689148—21no—
39#15689147C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46Q8⋊(C47⋊C8)C2211yescharacteristic
47Q8⋊(C47⋊C8)C2211yescharacteristic
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54#15688844C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C2×C4×Q8×C47C2211yescharacteristic
57C8×Q8×C47—21no—
58C8×Q8×C47—21no—
59C8×Q8×C47C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C8×Q8×C47C2211yescharacteristic
63C47×#431—21no—
64C47×#431—21no—
65C47×#431C2211yescharacteristic
66C47×#431C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625324—21no—
73C2×C8×D47—21no—
74#13094018—21no—
75#13094016C2×C411yescharacteristic
76#13094012C2×C411yescharacteristic
77#13094007—21no—
78#13094003C2×C411yescharacteristic
79#13093998C2×C411yescharacteristic
80C4×Dic94C2311yescharacteristic
81C4×D188C2311yescharacteristic
82C4×C22⋊D47—21no—
83#13093981—21no—
84#13093957C2×C411yescharacteristic
85#13093957C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)—21no—
90C4⋊(C47⋊C8)C2×C411yescharacteristic
91C4⋊(C47⋊C8)C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2311yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94Dic47⋊C8—21no—
95Dic47⋊C8—21no—
96#13093948C2×C411yescharacteristic
97#13093948C2×C411yescharacteristic
98#13093948C2×C411yescharacteristic
99#13093948C2×C411yescharacteristic
100#13093947C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093944C2×C411yescharacteristic
103#13093944C2×C411yescharacteristic
104C22⋊(C47⋊C8)—21no—
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106C22⋊(C47⋊C8)C2×C411yescharacteristic
107(C2×D47)⋊C8—21no—
108(C2×D47)⋊C8—21no—
109#13093934—21no—
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
114C8×Dic47—21no—
115C22×Q8×C47C2×C411yescharacteristic
116C4×Q8×C47—21no—
117C4×Q8×C47—21no—
118C4×Q8×C47C2×C411yescharacteristic
119C4×Q8×C47C2×C411yescharacteristic
120C4×Q8×C47C2311yescharacteristic
121C4×Q8×C47C2311yescharacteristic
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47C2×C411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126C4⋊C8×C47—21no—
127C4⋊C8×C47—21no—
128C4⋊C8×C47—21no—
129C4⋊C8×C47—21no—
130C4⋊C8×C47D411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47D411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137C4×C8×C47—21no—
138C4×C8×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—21no—
147C2×Q8×C47C22×C411yescharacteristic
148C2×Q8×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C2×C22⋊D47—21no—
155C2×D188C22×C411yescharacteristic
156C2×C4×D47—21no—
157C2×Dic94C22×C411yescharacteristic
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47C2×D411yescharacteristic
161C2×C8×C47C2×D411yescharacteristic
162C2×C8×C47C2×D411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47C22×C411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47#4111yescharacteristic
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180#10625337—22no—
181#10625337—22no—
182#10625336—22no—
183#10625336—22no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194C4×Dic47—21no—
195#10625329—81no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204#10625324—81no—
205C8×D47—81no—
206C23×C47C4×D411yescharacteristic
207C22×D47—21no—
208Q8×C47—24no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47#13112yes—
212Q8×C47#13112yes—
213C2×C4×C47—24no—
214C2×C4×C47—21no—
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—81no—
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C22⋊D47—81no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234D188—21no—
235D188—21no—
236C4×D47—41no—
237C4×D47—41no—
238Dic94—21no—
239Dic94—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—41no—
245C8×C47—41no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254#17919—471nomaximal, Sylow
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—21no—
258C22×C47C2×C4×D411yescharacteristic
259C2×D47—41no—
260C2×D47—41no—
261C2×D47—41no—
262C4×C47—22no—
263C4×C47—22no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47C2×#13111yescharacteristic
271C4×C47C2×#13111yescharacteristic
272C4×C47#57711yescharacteristic
273C4×C47#57811yescharacteristic
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277#3108—471no—
278#2993—471no—
279#2982D4711yescharacteristic, complemented
280#1588—471no—
281#1587—471no—
282#1584—471no—
283#1583—471no—
284#1579—471no—
285SD16⋊C8—471no—
286C8×Q16—471no—
287C8×SD16—471no—
288#1574—471no—
289#1487—471no—
290#1482—471no—
291#1454—471no—
292C2×C47—41no—
293C2×C47#292911yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47#295711yescharacteristic
296D47—81no—
297#529—471no—
298C2×C4×Q8C2×D4711yescharacteristic
299#483—471no—
300#480—471no—
301#479—471no—
302#479—471no—
303#464—471no—
304#464—471no—
305#451—471no—
306#448—471no—
307#446—471no—
308C8×Q8—21no—
309C8×Q8—21no—
310C8×Q8—471no—
311C8×Q8C2×D4711yescharacteristic
312C8×Q8C2×D4711yescharacteristic
313C8×Q8C2×D4711yescharacteristic
314C8×Q8C2×D4711yescharacteristic
315C4×Q16—471no—
316C4×Q16—471no—
317C4×SD16—471no—
318C4×SD16—471no—
319#436—471no—
320#436—941no—
321#435—941no—
322C8×D4—471no—
323#433—941no—
324#431—21no—
325#431—21no—
326#431—471no—
327#431—471no—
328#431C2×D4711yescharacteristic
329#431C2×D4711yescharacteristic
330#424—941no—
331#423—471no—
332#335—471no—
333#335—471no—
334#334—471no—
335#334—471no—
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342D4⋊C8—471no—
343D4⋊C8—471no—
344#322—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C47#1791911yescharacteristic, complemented, Sylow
349C22×Q8C4×D4711yescharacteristic
350C2×Q16—471no—
351C2×Q16—471no—
352C2×SD16—471no—
353C2×SD16—471no—
354C2×M16—941no—
355C2×M16—941no—
356C22×C8—941no—
357#126—941no—
358#125—471no—
359#124—471no—
360#123—941no—
361C22⋊Q8—471no—
362#121—471no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—471no—
366C4×Q8C4×D4711yescharacteristic
367C4×Q8C4×D4711yescharacteristic
368C4×Q8C22×D4711yescharacteristic
369C4×Q8C22×D4711yescharacteristic
370C4×D4—471no—
371C4×D4—941no—
372#117—941no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C4×D4711yescharacteristic
375C2×C42—21no—
376C2×C42C22×D4711yescharacteristic
377#107—471no—
378#107—471no—
379#106—471no—
380#106—471no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8C22⋊D4711yescharacteristic
394C4⋊C8C22⋊D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396C4⋊C8C22×D4711yescharacteristic
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#102—471no—
404#102—471no—
405C22⋊C8—21no—
406C22⋊C8—471no—
407C22⋊C8—471no—
408C22⋊C8—941no—
409C22⋊C8—941no—
410C22⋊C8—941no—
411C22⋊C8C22⋊D4711yescharacteristic
412C22⋊C8C22⋊D4711yescharacteristic
413#97—941no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—941no—
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—471no—
430C2×Q8C2×C4×D4711yescharacteristic
431C2×Q8C2×C4×D4711yescharacteristic
432C2×D4—471no—
433C2×D4—941no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—941no—
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4#1062535011yescharacteristic
439C22×C4C2×C22⋊D4711yescharacteristic
440Q16—942no—
441Q16—942no—
442SD16—942no—
443SD16—942no—
444M16—3761no—
445M16—3761no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—471no—
449C2×C8—471no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—3761no—
457C2×C8C2×C22⋊D4711yescharacteristic
458C2×C8C2×C22⋊D4711yescharacteristic
459C2×C8C2×C22⋊D4711yescharacteristic
460C2×C8C2×C22⋊D4711yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—471no—
467C4⋊C4—471no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4C2×C4×D4711yescharacteristic
473C4⋊C4C2×C4×D4711yescharacteristic
474C22⋊C4—941no—
475C22⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42#1062535011yescharacteristic
486C42C2×C22⋊D4711yescharacteristic
487C42C23×D4711yescharacteristic
488C23—941no—
489C23C4×C22⋊D4711yescharacteristic
490Q8—24no—
491Q8—21no—
492Q8—21no—
493Q8—941no—
494Q8—941no—
495Q8#1309403012yes—
496Q8#1309403012yes—
497D4—941no—
498D4—941no—
499D4—3761no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—81no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—1881no—
515C2×C4—1881no—
516C2×C4C4×C22⋊D4711yescharacteristic
517C2×C4C4×C22⋊D4711yescharacteristic
518C2×C4C4×C22⋊D4711yescharacteristic
519C2×C4C22×C4×D4711yescharacteristic
520C2×C4C22×C22⋊D4711yescharacteristic
521C2×C4C2×#1062535011yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—941no—
529C8—941no—
530C8—941no—
531C8—941no—
532C8—1881no—
533C8—1881no—
534C8—1881no—
535C8—1881no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1881no—
540C22—1881no—
541C22—1881no—
542C22C2×C4×C22⋊D4711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—1881no—
552C4—1881no—
553C4—1881no—
554C4C2×#1309403011yescharacteristic
555C4C2×#1309403011yescharacteristic
556C4#1568993111yescharacteristic
557C4#1568993811yescharacteristic
558C2—41no—
559C2—3761no—
560C2#2025208211yescharacteristic
561C2#2025223111yescharacteristic
562C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2982C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#2982D47
hypocenterC47#17919
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. #20242266C2semidirect
4. #20242259C2semidirect
5. #20242238C2semidirect
6. #20242231C2semidirect
7. #20242205C2semidirect
8. #20242198C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625336C2semidirect
11. #20242176C2semidirect
12. #20241817C2semidirect
14. #20241688C2semidirect
15. C47×#2982C2semidirect
279. #2982D47semidirect
348. C47#17919semidirect

Maximal subgroups

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

subgroupindex
#202534682
#202525392
#202422662
#202422592
#202422382
#202422312
#202422052
#202421982
C8×#106253372
C8×#106253362
#202421762
#202418172
#202417942
#202416882
C47×#29822
#1791947