Finite Group Databasebeta

← #26187471

Subgroups — #26187471

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#20253468C211yesmaximal, characteristic
2#20252550C211yesmaximal, characteristic
3#20242283C211yesmaximal, characteristic, complemented
4#20242278C211yesmaximal, characteristic, complemented
5#20242266C211yesmaximal, characteristic, complemented
6#20242259C211yesmaximal, characteristic, complemented
7#20242257C211yesmaximal, characteristic, complemented
8#20242243C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625336C211yesmaximal, characteristic, complemented
11#20242174C211yesmaximal, characteristic, complemented
12#20241846C211yesmaximal, characteristic
13C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
14#20241672C211yesmaximal, characteristic, complemented
15C47×#2984C211yesmaximal, 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#15689191—21no—
33C8×D188C2211yescharacteristic
34(C22⋊D47)⋊C8—21no—
35#15689183—21no—
36#15689176C2211yescharacteristic
37#15689148—21no—
38C2×C4⋊(C47⋊C8)C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
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
54C8×C47⋊C8C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C2×C4×Q8×C47C2211yescharacteristic
57C47×#446—21no—
58C47×#446—21no—
59C47×#446C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C8×Q8×C47C2211yescharacteristic
63C47×#432—21no—
64C47×#432C2211yescharacteristic
65C47×#431—21no—
66C47×#431C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625324—21no—
72C22×C47⋊C8—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×Dic94C2311yescharacteristic
82C4×D188C2311yescharacteristic
83C4×C22⋊D47—21no—
84#13093981—21no—
85#13093957C2×C411yescharacteristic
86#13093957C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
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)C2×C411yescharacteristic
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106(C2×D47)⋊C8—21no—
107(C2×D47)⋊C8—21no—
108#13093934—21no—
109C4×C47⋊C8—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
137#97×C47—21no—
138#97×C47—21no—
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—22no—
146C2×Q8×C47—41no—
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—41no—
182#10625336—22no—
183#10625336—41no—
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—
195C2×C47⋊C8—24no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—81no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205#10625324—81no—
206C8×D47—81no—
207C23×C47C4×D411yescharacteristic
208C22×D47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—42no—
213Q8×C47#13112yes—
214C2×C4×C47—21no—
215C2×C4×C47—22no—
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—21no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C22⋊D47—42no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235D188—21no—
236D188—21no—
237C4×D47—41no—
238C4×D47—41no—
239Dic94—21no—
240Dic94—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—41no—
246C8×C47—41no—
247C47⋊C8—22no—
248C47⋊C8—22no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
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—22no—
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×C47#57711yescharacteristic
274C4×C47#57811yescharacteristic
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278#3108—471no—
279#2994—471no—
280#2984D4711yescharacteristic, complemented
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#1573—471no—
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×Q8C2×D4711yescharacteristic
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—21no—
309#446—21no—
310#446—471no—
311#446C2×D4711yescharacteristic
312#446C2×D4711yescharacteristic
313C8×Q8—471no—
314C8×Q8C2×D4711yescharacteristic
315C8×Q8C2×D4711yescharacteristic
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—21no—
326#432C2×D4711yescharacteristic
327#431—21no—
328#431—471no—
329#431C2×D4711yescharacteristic
330#424—941no—
331C2×C4⋊C8—471no—
332C2×C4×C8—471no—
333#335—471no—
334#335—471no—
335#334—471no—
336#334—471no—
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×Q8C4×D4711yescharacteristic
351C2×Q16—471no—
352C2×Q16—471no—
353C2×SD16—471no—
354C2×SD16—471no—
355C2×M16—941no—
356C22×C8—941no—
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—21no—
366C4×Q8—21no—
367C4×Q8—471no—
368C4×Q8C4×D4711yescharacteristic
369C4×Q8C4×D4711yescharacteristic
370C4×Q8C22×D4711yescharacteristic
371C4×Q8C22×D4711yescharacteristic
372C4×D4—471no—
373C4×D4—941no—
374#117—941no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C4×D4711yescharacteristic
377C2×C42—21no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—21no—
384C4⋊C8—21no—
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⋊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⋊C8C22⋊D4711yescharacteristic
412C22⋊C8C22⋊D4711yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—941no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—471no—
431C2×Q8C2×C4×D4711yescharacteristic
432C2×Q8C2×C4×D4711yescharacteristic
433C2×D4—471no—
434C2×D4—941no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—941no—
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4#1062535011yescharacteristic
440C22×C4C2×C22⋊D4711yescharacteristic
441Q16—942no—
442Q16—1881no—
443SD16—942no—
444SD16—1881no—
445M16—3761no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—471no—
449C2×C8—471no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—944no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—3761no—
458C2×C8—3761no—
459C2×C8C2×C22⋊D4711yescharacteristic
460C2×C8C2×C22⋊D4711yescharacteristic
461C2×C8C2×C22⋊D4711yescharacteristic
462C2×C8C2×C22⋊D4711yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—471no—
469C4⋊C4—471no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4C2×C4×D4711yescharacteristic
475C4⋊C4C2×C4×D4711yescharacteristic
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—941no—
486C42C2×C4×D4711yescharacteristic
487C42#1062535011yescharacteristic
488C42C2×C22⋊D4711yescharacteristic
489C42C23×D4711yescharacteristic
490C23—941no—
491C23C4×C22⋊D4711yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—941no—
497Q8—941no—
498Q8#1309403212yes—
499D4—941no—
500D4—941no—
501D4—1882no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—1881no—
517C2×C4—1881no—
518C2×C4C4×C22⋊D4711yescharacteristic
519C2×C4C4×C22⋊D4711yescharacteristic
520C2×C4C4×C22⋊D4711yescharacteristic
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C22×C22⋊D4711yescharacteristic
523C2×C4C2×#1062535011yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—942no—
531C8—942no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—1881no—
537C8—1881no—
538C22—21no—
539C22—21no—
540C22—1881no—
541C22—1881no—
542C22—1881no—
543C22#1568923812yes—
544C22C2×C4×C22⋊D4711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4C2×#1309403211yescharacteristic
557C4#1568988911yescharacteristic
558C4#1568993111yescharacteristic
559C4#1568993811yescharacteristic
560C2—22no—
561C2—3761no—
562C2#2025211311yescharacteristic
563C2#2025223111yescharacteristic
564C2C2×#1568923811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2984C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#2984D47
hypocenterC47#18017
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #20242283C2semidirect
4. #20242278C2semidirect
5. #20242266C2semidirect
6. #20242259C2semidirect
7. #20242257C2semidirect
8. #20242243C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625336C2semidirect
11. #20242174C2semidirect
13. C2×Q8⋊(C47⋊C8)C2semidirect
14. #20241672C2semidirect
15. C47×#2984C2semidirect
280. #2984D47semidirect
349. C47#18017semidirect

Maximal subgroups

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

subgroupindex
#202534682
#202525502
#202422832
#202422782
#202422662
#202422592
#202422572
#202422432
C8×#106253372
C8×#106253362
#202421742
#202418462
C2×Q8⋊(C47⋊C8)2
#202416722
C47×#29842
#1801747