Finite Group Databasebeta

← #26202224

Subgroups — #26202224

Order 12032.

744 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254303C211yesmaximal, characteristic, complemented
2C2×#15689318C211yesmaximal, characteristic, complemented
3#20252423C211yesmaximal, characteristic, complemented
4#20242923C212yesmaximal, complemented
5#20242865C212yesmaximal, complemented
6#20242799C212yesmaximal, complemented
7#20242741C212yesmaximal, complemented
8#20242174C211yesmaximal, characteristic, complemented
9#20242101C211yesmaximal, characteristic, complemented
10#20242083C211yesmaximal, characteristic, complemented
11C47×#3109C211yesmaximal, characteristic, complemented
12C22×#10625334—21no—
13C2×#13094021C2211yescharacteristic
14#15689499C2212yescomplemented
15#15689471C2212yescomplemented
16#15689318—22no—
17#15689318—21no—
18#15689318—21no—
19#15689318C2212yes—
20#15689318C2212yes—
21#15689256—21no—
22#15689256—21no—
23#15689201C2212yescomplemented
24#15689195—22no—
25D4×C47⋊C8C2212yescomplemented
26#15689180C2211yescharacteristic
27#15689176C2211yescharacteristic
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×#13093944—21no—
30#15689087—21no—
31C2×C22⋊(C47⋊C8)—21no—
32#15688875C2212yescomplemented
33#15688873C2212yescomplemented
34#15688872C2212yescomplemented
35#15688867C2212yescomplemented
36#15688866C2212yescomplemented
37#15688866C2212yescomplemented
38C47×#532C2211yescharacteristic
39C2×C4×D4×C47C2211yescharacteristic
40C47×#481—21no—
41C47×#476C2211yescharacteristic, complemented
42C47×#476C2211yescharacteristic, complemented
43C47×#459C2211yescharacteristic, complemented
44C47×#459C2211yescharacteristic, complemented
45C47×#447—21no—
46C47×#442—21no—
47C47×#442—21no—
48C47×#432C2211yescharacteristic
49C22×D188—21no—
50C22×D188—21no—
51C22×D188—21no—
52C2×#10625334—22no—
53C2×#10625334—22no—
54C2×#10625334—22no—
55C2×#10625334—22no—
56C2×#10625334—44no—
57C2×#10625329—22no—
58C22×C47⋊C8—21no—
59C22×C47⋊C8—22no—
60#13094021—21no—
61#13094021—21no—
62#13094021—21no—
63#13094021C2312yes—
64C4⋊(C47⋊C8)—21no—
65C4⋊(C47⋊C8)D412yes—
66C4⋊(C47⋊C8)C2312yes—
67C4⋊(C47⋊C8)C2312yes—
68#13093944—22no—
69#13093944—22no—
70#13093944—22no—
71#13093944—22no—
72C22⋊(C47⋊C8)—21no—
73C22⋊(C47⋊C8)—22no—
74C22⋊(C47⋊C8)—22no—
75C22⋊(C47⋊C8)D411yescharacteristic
76C22⋊(C47⋊C8)D411yescharacteristic
77#13093935—21no—
78C4×C47⋊C8C2312yes—
79C2×#41×C47—21no—
80C22×D4×C47D411yescharacteristic
81C23×C4×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47—21no—
84C4⋊Q8×C47C2311yescharacteristic
85#127×C47C2311yescharacteristic
86#124×C47—21no—
87#121×C47—21no—
88#121×C47—21no—
89C4×D4×C47—21no—
90C4×D4×C47—21no—
91C4×D4×C47—21no—
92C4×D4×C47—21no—
93C4×D4×C47D411yescharacteristic
94C4×D4×C47D411yescharacteristic
95C4×D4×C47C2311yescharacteristic
96C4×D4×C47C2311yescharacteristic
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C22⋊C4×C47—21no—
99C2×C42×C47C2311yescharacteristic
100#106×C47—21no—
101#106×C47—21no—
102C4⋊C8×C47C2311yescharacteristic
103C4⋊C8×C47C2311yescharacteristic
104#102×C47—21no—
105#102×C47—21no—
106#102×C47—21no—
107#102×C47—21no—
108C22⋊C8×C47—21no—
109#97×C47—21no—
110C24×C47—21no—
111C23×D47—41no—
112#41×C47—82no—
113C2×Q8×C47—21no—
114C2×D4×C47—22no—
115C2×D4×C47—21no—
116C2×D4×C47—21no—
117C2×D4×C47—21no—
118C2×D4×C47—21no—
119C2×D4×C47—41no—
120C2×D4×C47—41no—
121C2×D4×C47C2×D411yescharacteristic
122C2×D4×C47C2×D411yescharacteristic
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—41no—
129C22×C4×C47—82no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C2×D188—22no—
134C2×D188—22no—
135C2×D188—22no—
136C2×D188—42no—
137C2×D188—42no—
138C2×D188—41no—
139C2×D188—41no—
140C2×D188—41no—
141C2×D188—82no—
142C2×D188—82no—
143D8×C47—42no—
144D8×C47—42no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47C2×D411yescharacteristic
151C4⋊C4×C47C2×D411yescharacteristic
152C22⋊C4×C47—21no—
153C22⋊C4×C47—21no—
154C22⋊C4×C47—21no—
155C22⋊C4×C47—21no—
156C22⋊C4×C47—41no—
157C22⋊C4×C47—41no—
158C42×C47C2×D411yescharacteristic
159C42×C47C2×D411yescharacteristic
160C42×C47#4111yescharacteristic
161C42×C47C2411yescharacteristic
162#10625334—44no—
163#10625334—44no—
164#10625334—82no—
165#10625334—82no—
166#10625329—82no—
167C2×C47⋊C8—22no—
168C2×C47⋊C8—22no—
169C2×C47⋊C8—42no—
170C2×C47⋊C8—82no—
171C2×C47⋊C8C2×D412yes—
172C2×C47⋊C8C2×D412yes—
173C23×C47—21no—
174C23×C47—21no—
175C23×C47—42no—
176C23×C47—42no—
177C23×C47—41no—
178C23×C47—81no—
179C23×C47#12111yescharacteristic
180C22×D47—42no—
181C22×D47—82no—
182C22×D47—82no—
183C22×D47—82no—
184Q8×C47—81no—
185D4×C47—21no—
186D4×C47—21no—
187D4×C47—21no—
188D4×C47—42no—
189D4×C47—41no—
190D4×C47—41no—
191D4×C47—42no—
192D4×C47—81no—
193D4×C47—82no—
194D4×C47AGL(1,ℤ/8)12yes—
195C2×C4×C47—22no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—22no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—41no—
204C2×C4×C47—81no—
205C2×C4×C47—81no—
206C2×C4×C47—82no—
207C2×C4×C47—81no—
208C2×C4×C47#12111yescharacteristic
209C2×C4×C47#12111yescharacteristic
210C2×C4×C47#12111yescharacteristic
211C2×C4×C47C22×D411yescharacteristic
212C2×C4×C47C22×D411yescharacteristic
213C2×C4×C47C2×#4111yescharacteristic
214D188—42no—
215D188—42no—
216D188—42no—
217D188—42no—
218D188—82no—
219D188—82no—
220D188—82no—
221D188—82no—
222C8×C47—41no—
223C8×C47—41no—
224C47⋊C8—22no—
225C47⋊C8—22no—
226C47⋊C8—42no—
227C47⋊C8—42no—
228#19458—471nomaximal, Sylow
229C22×C47—21no—
230C22×C47—21no—
231C22×C47—22no—
232C22×C47—41no—
233C22×C47—41no—
234C22×C47—41no—
235C22×C47—41no—
236C22×C47—41no—
237C22×C47—84no—
238C22×C47—81no—
239C22×C47—81no—
240C22×C47—81no—
241C22×C47#47212yes—
242C22×C47C2×#12111yescharacteristic
243C2×D47—82no—
244C2×D47—82no—
245C2×D47—82no—
246C2×D47—164no—
247C4×C47—21no—
248C4×C47—21no—
249C4×C47—21no—
250C4×C47—21no—
251C4×C47—41no—
252C4×C47—41no—
253C4×C47—81no—
254C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
255C4×C47#57511yescharacteristic
256C4×C47#57612yes—
257#3205—471no—
258#3109D4711yescharacteristic, complemented
259C2×#459—471no—
260#2974—471no—
261#1697—472no—
262#1687—472no—
263#1677—472no—
264#1667—472no—
265#1573—471no—
266#1555—471no—
267#1551—471no—
268C2×C47—22no—
269C2×C47—42no—
270C2×C47—81no—
271C2×C47—161no—
272C2×C47#304111yescharacteristic
273C2×C47#305511yescharacteristic
274C2×C47C2×#47211yescharacteristic
275D47—162no—
276C22×D8—941no—
277#532C2×D4711yescharacteristic
278C2×#127—471no—
279C2×C4×D4C2×D4711yescharacteristic
280#493—472no—
281#486—472no—
282#481—21no—
283#476C2×D4711yescharacteristic, complemented
284#476C2×D4711yescharacteristic, complemented
285#459—472no—
286#459—472no—
287#459—942no—
288#459—941no—
289#459—941no—
290#459C2×D4711yescharacteristic, complemented
291#459C2×D4711yescharacteristic, complemented
292#447—21no—
293#447—941no—
294#447—941no—
295#442—21no—
296#442—21no—
297#436—472no—
298#435—942no—
299C8×D4—472no—
300#432—471no—
301#432C2×D4711yescharacteristic
302#431—471no—
303C2×C4⋊C8—471no—
304C2×#102—941no—
305#407—941no—
306C2×C22⋊C8—941no—
307#335—472no—
308#334—472no—
309#333—472no—
310#331—472no—
311#331—472no—
312#331—472no—
313C47#1945811yescharacteristic, complemented, Sylow
314C2×#41—21no—
315C22×D4—941no—
316C22×D4—941no—
317C22×D4—941no—
318C22×D4C22⋊D4711yescharacteristic
319C23×C4—21no—
320C2×D8—21no—
321C2×D8—21no—
322C2×D8—942no—
323C2×D8—942no—
324C2×D8—942no—
325C2×D8—942no—
326C2×D8—1884no—
327C2×M16—942no—
328C22×C8—942no—
329C22×C8—941no—
330C4⋊Q8C22×D4711yescharacteristic
331#127—472no—
332#127—941no—
333#127—941no—
334#127—941no—
335#127C22×D4711yescharacteristic
336#124—21no—
337#121—21no—
338#121—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4C22⋊D4711yescharacteristic
344C4×D4C22⋊D4711yescharacteristic
345C4×D4C22×D4711yescharacteristic
346C4×D4C22×D4711yescharacteristic
347C2×C4⋊C4C22⋊D4711yescharacteristic
348C2×C22⋊C4—21no—
349C2×C42C22×D4711yescharacteristic
350#106—21no—
351#106—21no—
352C4⋊C8—472no—
353C4⋊C8—472no—
354C4⋊C8—472no—
355C4⋊C8—941no—
356C4⋊C8C22×D4711yescharacteristic
357C4⋊C8C22×D4711yescharacteristic
358#102—21no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—942no—
363#102—942no—
364#102—942no—
365#102—942no—
366C22⋊C8—21no—
367C22⋊C8—471no—
368C22⋊C8—471no—
369C22⋊C8—942no—
370C22⋊C8—942no—
371C22⋊C8—941no—
372#97—21no—
373#97—941no—
374C4×C8—472no—
375C24—21no—
376C24—1881no—
377#41—82no—
378C2×Q8—21no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—942no—
387C2×D4—942no—
388C2×D4—942no—
389C2×D4—3762no—
390C2×D4—3762no—
391C2×D4—1882no—
392C2×D4—1882no—
393C2×D4—1881no—
394C2×D4—1881no—
395C2×D4—1881no—
396C2×D4C2×C22⋊D4711yescharacteristic
397C2×D4C2×C22⋊D4711yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—41no—
404C22×C4—82no—
405C22×C4D4×D4711yescharacteristic
406C22×C4#1062535211yescharacteristic
407C22×C4C2×C22⋊D4711yescharacteristic
408D8—42no—
409D8—42no—
410D8—3762no—
411D8—3762no—
412D8—1884no—
413D8—1884no—
414M16—3762no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—472no—
418C2×C8—472no—
419C2×C8—942no—
420C2×C8—942no—
421C2×C8—3762no—
422C2×C8—1882no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4C2×C22⋊D4711yescharacteristic
427C4⋊C4C2×C22⋊D4711yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C42D4×D4711yescharacteristic
435C42#1062535211yescharacteristic
436C42C2×C22⋊D4711yescharacteristic
437C42C23×D4711yescharacteristic
438C23—21no—
439C23—21no—
440C23—42no—
441C23—42no—
442C23—41no—
443C23—81no—
444C23—3762no—
445C23—3762no—
446C23—3762no—
447C23—1882no—
448C23#1309399611yescharacteristic
449Q8—81no—
450D4—21no—
451D4—21no—
452D4—21no—
453D4—42no—
454D4—41no—
455D4—41no—
456D4—42no—
457D4—81no—
458D4—82no—
459D4—3762no—
460D4—3762no—
461D4—3762no—
462D4—3762no—
463D4—1882no—
464D4—1882no—
465D4—1882no—
466D4—1882no—
467D4#1309404912yes—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—82no—
480C2×C4—81no—
481C2×C4#1309399611yescharacteristic
482C2×C4#1309399611yescharacteristic
483C2×C4#1309399611yescharacteristic
484C2×C4C2×D4×D4711yescharacteristic
485C2×C4C22×C22⋊D4711yescharacteristic
486C2×C4C2×#1062535211yescharacteristic
487C8—41no—
488C8—41no—
489C8—942no—
490C8—942no—
491C8—1882no—
492C8—1882no—
493C22—21no—
494C22—21no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—84no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—3762no—
506C22—3762no—
507C22—3762no—
508C22—7524no—
509C22#1568939112yes—
510C22C2×#1309399611yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—41no—
516C4—41no—
517C4—81no—
518C4C2×#1309404911yescharacteristic
519C4#1568992111yescharacteristic
520C4#1568992712yes—
521C2—22no—
522C2—42no—
523C2—81no—
524C2—161no—
525C2—7522no—
526C2#2025289311yescharacteristic
527C2#2025300911yescharacteristic
528C2C2×#1568939111yescharacteristic
subgroupG/H
centerC22C2×#13093996
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#3109C2
socleC22×C47C2×#121
hypercenter#3109D47
hypocenterC47#19458
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #20254303C2semidirect
2. C2×#15689318C2semidirect
3. #20252423C2semidirect
4. #20242923C2semidirect
5. #20242865C2semidirect
6. #20242799C2semidirect
7. #20242741C2semidirect
8. #20242174C2semidirect
9. #20242101C2semidirect
10. #20242083C2semidirect
11. C47×#3109C2semidirect
14. #15689499C22semidirect
15. #15689471C22semidirect
23. #15689201C22semidirect
25. D4×C47⋊C8C22semidirect
32. #15688875C22semidirect
33. #15688873C22semidirect
34. #15688872C22semidirect
35. #15688867C22semidirect
36. #15688866C22semidirect
37. #15688866C22semidirect
41. C47×#476C22semidirect
42. C47×#476C22semidirect
43. C47×#459C22semidirect
44. C47×#459C22semidirect
258. #3109D47semidirect
283. #476C2×D47semidirect
284. #476C2×D47semidirect
290. #459C2×D47semidirect
291. #459C2×D47semidirect
313. C47#19458semidirect

Maximal subgroups

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

subgroupindex
#202543032
C2×#156893182
#202524232
#202429232
#202428652
#202427992
#202427412
#202421742
#202421012
#202420832
C47×#31092
#1945847