Finite Group Databasebeta

← #26373132

Subgroups — #26373132

Order 12032.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20255075C211yesmaximal, characteristic, complemented
2#20245622C211yesmaximal, characteristic, complemented
3#20245590C211yesmaximal, characteristic, complemented
4#20245579C211yesmaximal, characteristic, complemented
5#20245542C211yesmaximal, characteristic, complemented
6#20245482C211yesmaximal, characteristic, complemented
7#20245472C211yesmaximal, characteristic, complemented
8#20245443C211yesmaximal, characteristic, complemented
9#20245309C211yesmaximal, characteristic, complemented
10#20245299C211yesmaximal, characteristic, complemented
11C4×#13093965C211yesmaximal, characteristic, complemented
12D4×C47⋊C16C211yesmaximal, characteristic, complemented
13#20245093C211yesmaximal, characteristic, complemented
14C2×#15688923C211yesmaximal, characteristic, complemented
15C47×#3339C211yesmaximal, characteristic, complemented
16C2×#13094046C2211yescharacteristic
17C22×D376C2211yescharacteristic
18#15689769—21no—
19C2×#13093968C2211yescharacteristic, complemented
20C2×#13093965C2211yescharacteristic
21C2×#13093965C2211yescharacteristic
22C22×C47⋊C16C2211yescharacteristic
23C22×C47⋊C16C2211yescharacteristic, complemented
24#15689507C2211yescharacteristic
25#15689364C2211yescharacteristic
26#15689359C2211yescharacteristic
27#15689339—21no—
28#15689276—21no—
29#15689270—21no—
30C4×D376C2211yescharacteristic
31#15688950C2211yescharacteristic, complemented
32#15688948C2211yescharacteristic, complemented
33#15688948C2211yescharacteristic, complemented
34C4⋊(C47⋊C16)C2211yescharacteristic, complemented
35#15688926C2211yescharacteristic, complemented
36#15688926C2211yescharacteristic, complemented
37#15688926C2211yescharacteristic, complemented
38#15688924C2211yescharacteristic, complemented
39#15688923C2211yescharacteristic
40#15688923C2211yescharacteristic
41#15688923C2211yescharacteristic
42#15688923C2211yescharacteristic
43#15688923C2211yescharacteristic
44#15688923C2211yescharacteristic
45C22⋊(C47⋊C16)C2211yescharacteristic
46C22⋊(C47⋊C16)C2211yescharacteristic, complemented
47C4×C47⋊C16C2211yescharacteristic, complemented
48C47×#553—21no—
49C47×#499C2211yescharacteristic, complemented
50C47×#482—21no—
51C47×#481—21no—
52C47×#478—21no—
53C47×#466C2211yescharacteristic
54C47×#466C2211yescharacteristic, complemented
55C4×D8×C47C2211yescharacteristic, complemented
56C8×D4×C47C2211yescharacteristic
57C47×#427C2211yescharacteristic, complemented
58C2×#107×C47C2211yescharacteristic
59C2×#10625350—21no—
60C22×D188—21no—
61#13094046—22no—
62#13094046—41no—
63C2×Dic188C2311yescharacteristic
64C2×#10625325—21no—
65C2×#10625325—21no—
66C2×D376—22no—
67C2×D376—21no—
68C2×D376—41no—
69C2×D376C2311yescharacteristic
70C2×D376C2311yescharacteristic
71#13094012—21no—
72#13094009—41no—
73#13094003—21no—
74#13093998—21no—
75#13093997—41no—
76#13093992—41no—
77C4×D188—21no—
78C22⋊C4×D47—41no—
79#13093968—41no—
80#13093965—22no—
81#13093965—41no—
82C2×C47⋊C16—41no—
83C2×C47⋊C16—41no—
84C2×C47⋊C16C2311yescharacteristic
85C2×C47⋊C16C2311yescharacteristic
86C2×C47⋊C16C2311yescharacteristic
87C2×C47⋊C16C2311yescharacteristic
88#13093958C2311yescharacteristic
89#13093949—21no—
90#13093946—21no—
91#13093946—21no—
92C2×D8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95#126×C47—41no—
96#125×C47—21no—
97#123×C47—41no—
98#121×C47—21no—
99#121×C47—21no—
100#121×C47—41no—
101C4×D4×C47—21no—
102C4×D4×C47—41no—
103C4×D4×C47D411yescharacteristic
104#117×C47—21no—
105C2×C4⋊C4×C47—21no—
106#107×C47—21no—
107#107×C47C2311yescharacteristic
108#107×C47C2311yescharacteristic
109#107×C47C2311yescharacteristic
110#106×C47—21no—
111#106×C47—21no—
112C4⋊C8×C47D411yescharacteristic
113#102×C47—21no—
114#102×C47—21no—
115#102×C47—21no—
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D411yescharacteristic
118C4×C8×C47C2311yescharacteristic
119C23×D47—41no—
120C2×D4×C47—21no—
121C2×D4×C47—41no—
122C2×D4×C47—41no—
123C2×D4×C47D811yescharacteristic
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C2×C22⋊D47—41no—
129C2×C22⋊D47—41no—
130#10625350—42no—
131#10625350—81no—
132C2×D188—21no—
133C2×D188—21no—
134C2×D188—42no—
135C2×D188—41no—
136C2×D188—81no—
137C2×C4×D47—41no—
138C2×C4×D47—41no—
139C2×Dic94—21no—
140D8×C47—21no—
141D8×C47—21no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47C2×D411yescharacteristic
147C2×C8×C47C2×D411yescharacteristic
148C2×C8×C47C2×D411yescharacteristic
149C2×C8×C47C2411yescharacteristic
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—41no—
154C4⋊C4×C47—41no—
155C4⋊C4×C47—41no—
156C4⋊C4×C47D811yescharacteristic
157C22⋊C4×C47—41no—
158C22⋊C4×C47—41no—
159C22⋊C4×C47—41no—
160C22⋊C4×C47—41no—
161C22⋊C4×C47D811yescharacteristic
162C22⋊C4×C47D811yescharacteristic
163C42×C47—41no—
164C42×C47C2×D411yescharacteristic
165C22⋊Dic47—41no—
166(C2×D47)⋊C4—41no—
167(C2×D47)⋊C4—41no—
168(C2×D47)⋊C4—41no—
169(C2×D47)⋊C4—41no—
170C4⋊Dic47—21no—
171Dic47⋊C4—41no—
172Dic188—21no—
173Dic188—21no—
174D376—21no—
175D376—21no—
176D376—21no—
177D376—42no—
178D376#4112yes—
179#10625325—42no—
180#10625325—81no—
181C47⋊C16—21no—
182C47⋊C16—21no—
183C47⋊C16—21no—
184C47⋊C16—21no—
185C23×C47—41no—
186C23×C47C2×D811yescharacteristic
187C23×C47C2×D811yescharacteristic
188C22×D47—41no—
189C22×D47—41no—
190C22×D47—82no—
191C22×D47—82no—
192C22×D47—161no—
193D4×C47—22no—
194D4×C47—41no—
195D4×C47—41no—
196D4×C47—82no—
197D4×C47—161no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—41no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—161no—
206C2×C4×C47—161no—
207C2×C4×C47C2×D811yescharacteristic
208C2×C4×C47C2×D811yescharacteristic
209C2×C4×C47C2×D811yescharacteristic
210C2×C4×C47C2×D811yescharacteristic
211C2×C4×C47C22×D411yescharacteristic
212C22⋊D47—82no—
213C22⋊D47—161no—
214C2×Dic47—41no—
215C2×Dic47—41no—
216D188—22no—
217D188—41no—
218D188—41no—
219D188—41no—
220D188—82no—
221C4×D47—82no—
222C4×D47—161no—
223Dic94—41no—
224Dic94—41no—
225C8×C47—21no—
226C8×C47—21no—
227C8×C47—21no—
228C8×C47C2×#4111yescharacteristic
229C8×C47H(5,𝔽2)11yescharacteristic
230#33864—471nomaximal, Sylow
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—81no—
237C22×C47—81no—
238C22×C47—81no—
239C22×C47#50812yes—
240C22×C47C22×D811yescharacteristic
241C2×D47—42no—
242C2×D47—81no—
243C2×D47—81no—
244C2×D47—81no—
245C2×D47—81no—
246C2×D47—81no—
247C2×D47—164no—
248C4×C47—21no—
249C4×C47—21no—
250C4×C47—21no—
251C4×C47—21no—
252C4×C47—81no—
253C4×C47—81no—
254C4×C47—81no—
255C4×C47#54611yescharacteristic
256C4×C47#57711yescharacteristic
257Dic47—81no—
258Dic47—81no—
259#3339D4711yescharacteristic, complemented
260#3280—471no—
261#2242—471no—
262#2236—471no—
263#2234—471no—
264#2228—471no—
265#2217—471no—
266#2215—471no—
267#2210—471no—
268#2186—471no—
269#2184—471no—
270C4×D16—471no—
271D4×C16—471no—
272#2138—471no—
273C2×#357—471no—
274C2×C47—22no—
275C2×C47—41no—
276C2×C47—161no—
277C2×C47#329411yescharacteristic
278C2×C47C2×#50811yescharacteristic
279C2×C47#341511yescharacteristic
280D47—82no—
281D47—161no—
282C2×#135—471no—
283C22×D8—471no—
284#553—21no—
285#546—941no—
286C2×SD32—471no—
287C2×D16—471no—
288C2×D16—471no—
289C22×C16—471no—
290C22×C16—471no—
291#499C2×D4711yescharacteristic, complemented
292#495—471no—
293#482—21no—
294#481—21no—
295#478—21no—
296#467—471no—
297#466—471no—
298#466C2×D4711yescharacteristic
299#466C2×D4711yescharacteristic, complemented
300#463—941no—
301#450—941no—
302#449—941no—
303C4×D8—471no—
304C4×D8C2×D4711yescharacteristic, complemented
305C8×D4C2×D4711yescharacteristic
306#427C2×D4711yescharacteristic, complemented
307C2×#107C2×D4711yescharacteristic
308#367—471no—
309#366—471no—
310#366—471no—
311C4⋊C16—471no—
312#358—471no—
313#358—471no—
314#358—471no—
315#357—471no—
316#357—471no—
317#357—471no—
318#357—471no—
319#357—471no—
320#357—471no—
321#357—471no—
322C22⋊C16—471no—
323C22⋊C16—471no—
324C4×C16—471no—
325C47#3386411yescharacteristic, complemented, Sylow
326C2×#41—941no—
327C22×D4—941no—
328#135—942no—
329#135—1881no—
330C2×Q16—471no—
331C2×SD16—941no—
332C2×SD16—941no—
333C2×D8—471no—
334C2×D8—471no—
335C2×D8—942no—
336C2×D8—941no—
337C2×D8—1881no—
338C2×D8C22×D4711yescharacteristic
339C22×C8C22×D4711yescharacteristic
340C22×C8C22×D4711yescharacteristic
341#126—41no—
342#125—21no—
343#124—941no—
344#123—41no—
345#123—1881no—
346C22⋊Q8—941no—
347#121—21no—
348#121—21no—
349#121—41no—
350#121—941no—
351#121—1881no—
352#120—1881no—
353C4×D4—21no—
354C4×D4—41no—
355C4×D4—941no—
356C4×D4C22⋊D4711yescharacteristic
357#117—21no—
358C2×C4⋊C4—21no—
359C2×C22⋊C4—1881no—
360SD32—1881no—
361D16—942no—
362D16—1881no—
363C2×C16—471no—
364C2×C16—471no—
365C2×C16—471no—
366C2×C16—471no—
367C2×C16—1881no—
368C2×C16—1881no—
369#107—21no—
370#107—471no—
371#107C22×D4711yescharacteristic
372#107C22×D4711yescharacteristic
373#107C22×D4711yescharacteristic
374#106—21no—
375#106—21no—
376C4⋊C8C22⋊D4711yescharacteristic
377#103—941no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—941no—
382#102—941no—
383C22⋊C8C22⋊D4711yescharacteristic
384C22⋊C8C22⋊D4711yescharacteristic
385C4×C8C22×D4711yescharacteristic
386C24—1881no—
387#41—3761no—
388#41—1882no—
389C2×Q8—941no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—941no—
394C2×D4—941no—
395C2×D4—3761no—
396C2×D4—1882no—
397C2×D4—1881no—
398C2×D4—1881no—
399C2×D4—1881no—
400C2×D4#1062533411yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—1881no—
404C22×C4—1881no—
405C22×C4C2×C22⋊D4711yescharacteristic
406C22×C4C2×C22⋊D4711yescharacteristic
407Q16—941no—
408Q16—941no—
409SD16—3761no—
410SD16—1882no—
411D8—21no—
412D8—21no—
413D8—472no—
414D8—941no—
415D8—941no—
416D8—941no—
417D8—1882no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×C22⋊D4711yescharacteristic
423C2×C8C2×C22⋊D4711yescharacteristic
424C2×C8C2×C22⋊D4711yescharacteristic
425C2×C8C23×D4711yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—941no—
433C4⋊C4—1881no—
434C4⋊C4#1062533411yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—1881no—
440C22⋊C4—1881no—
441C22⋊C4—1881no—
442C22⋊C4—1881no—
443C22⋊C4—1881no—
444C22⋊C4#1062533411yescharacteristic
445C22⋊C4#1062533411yescharacteristic
446C42—41no—
447C42C2×C22⋊D4711yescharacteristic
448C16—941no—
449C16—941no—
450C16—941no—
451C16—941no—
452C23—41no—
453C23—3762no—
454C23—3762no—
455C23—1881no—
456C23—1881no—
457C23—7521no—
458C23C2×#1062533411yescharacteristic
459C23C2×#1062533411yescharacteristic
460Q8—1881no—
461Q8—1881no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—161no—
467D4—942no—
468D4—3762no—
469D4—3762no—
470D4—1881no—
471D4—1881no—
472D4—1881no—
473D4—7521no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—161no—
482C2×C4—161no—
483C2×C4—3762no—
484C2×C4—1881no—
485C2×C4—1881no—
486C2×C4—7521no—
487C2×C4C2×#1062533411yescharacteristic
488C2×C4C2×#1062533411yescharacteristic
489C2×C4C2×#1062533411yescharacteristic
490C2×C4C2×#1062533411yescharacteristic
491C2×C4C22×C22⋊D4711yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#41×D4711yescharacteristic
496C8#1309407011yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—3761no—
506C22—3761no—
507C22—3761no—
508C22—3761no—
509C22—3761no—
510C22—1882no—
511C22—7524no—
512C22#1568955312yes—
513C22C22×#1062533411yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—3761no—
522C4—3761no—
523C4#1568976111yescharacteristic
524C4#1568993111yescharacteristic
525C2—22no—
526C2—41no—
527C2—161no—
528C2—3762no—
529C2—7521no—
530C2#2025519511yescharacteristic
531C2C2×#1568955311yescharacteristic
532C2#2025652711yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3339C2
socleC22×C47C22×D8
hypercenter#3339D47
hypocenterC47#33864
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #20255075C2semidirect
2. #20245622C2semidirect
3. #20245590C2semidirect
4. #20245579C2semidirect
5. #20245542C2semidirect
6. #20245482C2semidirect
7. #20245472C2semidirect
8. #20245443C2semidirect
9. #20245309C2semidirect
10. #20245299C2semidirect
11. C4×#13093965C2semidirect
12. D4×C47⋊C16C2semidirect
13. #20245093C2semidirect
14. C2×#15688923C2semidirect
15. C47×#3339C2semidirect
19. C2×#13093968C22semidirect
23. C22×C47⋊C16C22semidirect
31. #15688950C22semidirect
32. #15688948C22semidirect
33. #15688948C22semidirect
34. C4⋊(C47⋊C16)C22semidirect
35. #15688926C22semidirect
36. #15688926C22semidirect
37. #15688926C22semidirect
38. #15688924C22semidirect
46. C22⋊(C47⋊C16)C22semidirect
47. C4×C47⋊C16C22semidirect
49. C47×#499C22semidirect
54. C47×#466C22semidirect
55. C4×D8×C47C22semidirect
57. C47×#427C22semidirect
259. #3339D47semidirect
291. #499C2×D47semidirect
299. #466C2×D47semidirect
304. C4×D8C2×D47semidirect
306. #427C2×D47semidirect
325. C47#33864semidirect

Maximal subgroups

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

subgroupindex
#202550752
#202456222
#202455902
#202455792
#202455422
#202454822
#202454722
#202454432
#202453092
#202452992
C4×#130939652
D4×C47⋊C162
#202450932
C2×#156889232
C47×#33392
#3386447