Finite Group Databasebeta

← #29834761

Subgroups — #29834761

Order 15616.

514 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456348C211yesmaximal, characteristic, complemented
2#21454731C211yesmaximal, characteristic
3#21447994C211yesmaximal, characteristic, complemented
4#21447993C211yesmaximal, characteristic, complemented
5#21447992C211yesmaximal, characteristic, complemented
6#21447991C211yesmaximal, characteristic, complemented
7#21447990C211yesmaximal, characteristic, complemented
8#21447989C211yesmaximal, characteristic, complemented
9#21447988C211yesmaximal, characteristic, complemented
10#21447590C211yesmaximal, characteristic, complemented
11#365×D61C211yesmaximal, characteristic, complemented
12#21447583C211yesmaximal, characteristic, complemented
13#21447553C211yesmaximal, characteristic
14#360×D61C211yesmaximal, characteristic
15C61×#2231C211yesmaximal, characteristic, complemented
16#135×D61C2211yescharacteristic
17#16840527—21no—
18#16840392—21no—
19M32×D61C2211yescharacteristic
20M32×D61C2211yescharacteristic
21#16840172—21no—
22#16840170—21no—
23#16840162C2211yescharacteristic, complemented
24#16840160C2211yescharacteristic, complemented
25#16840159C2211yescharacteristic, complemented
26#16839882—21no—
27#16839881—21no—
28#16839880C2211yescharacteristic
29#16839879C2211yescharacteristic
30#16839878C2211yescharacteristic
31#108×D61C2211yescharacteristic
32#16839803—21no—
33#16839797C2211yescharacteristic
34#106×D61C2211yescharacteristic
35#16839777—21no—
36#16839716C2211yescharacteristic
37#16839586C2211yescharacteristic, complemented
38#16839586C2211yescharacteristic, complemented
39#16839585C2211yescharacteristic, complemented
40#16839585C2211yescharacteristic, complemented
41#16839584C2211yescharacteristic, complemented
42#16839584C2211yescharacteristic, complemented
43#16839583C2211yescharacteristic, complemented
44#16839582C2211yescharacteristic, complemented
45#16839582C2211yescharacteristic, complemented
46#16839573C2211yescharacteristic
47#16839573C2211yescharacteristic
48#16839572C2211yescharacteristic
49#16839572C2211yescharacteristic
50#16839571C2211yescharacteristic
51#16839571C2211yescharacteristic
52C61×#499C2211yescharacteristic, complemented
53C61×#443C2211yescharacteristic
54C61×#365C2211yescharacteristic, complemented
55C61×#365C2211yescharacteristic, complemented
56C61×#364C2211yescharacteristic, complemented
57C61×#360C2211yescharacteristic
58C61×#360C2211yescharacteristic
59#41×D61—21no—
60#14519800Q811yescharacteristic, complemented
61#14519799C2311yescharacteristic
62#14519798—21no—
63#14519797—21no—
64#14519796Q811yescharacteristic, complemented
65Q16×D61Q811yescharacteristic, complemented
66SD16×D61—21no—
67D8×D61Q811yescharacteristic, complemented
68#14519785—21no—
69#14519785—41no—
70#14519784—21no—
71#14519783—21no—
72#14519783—41no—
73C2×#11758189—41no—
74C2×#11758189D411yescharacteristic
75M16×D61—21no—
76M16×D61—41no—
77C2×C8×D61C2311yescharacteristic
78#14519777—21no—
79#14519776—21no—
80#14519776—41no—
81#14519768—21no—
82#14519767—41no—
83#14519757—41no—
84#14519755—41no—
85#14519735—21no—
86#14519734D411yescharacteristic
87C4⋊C4×D61—21no—
88#14519717C2311yescharacteristic
89#14519717C2311yescharacteristic
90#14519716—21no—
91#14519716—21no—
92C16×D61—21no—
93C16×D61—21no—
94#14519713C2311yescharacteristic
95#14519712—21no—
96#14519710—21no—
97#14519710—21no—
98#14519709—21no—
99#14519709C2311yescharacteristic
100#14519709C2311yescharacteristic
101#14519708—21no—
102#14519708—21no—
103#14519705—21no—
104#14519704—21no—
105#14519703—21no—
106#14519688D411yescharacteristic
107#14519687D411yescharacteristic
108C8×Dic61C2311yescharacteristic
109#135×C61C2311yescharacteristic
110#131×C61—21no—
111#125×C61—21no—
112M32×C61C2311yescharacteristic
113M32×C61C2311yescharacteristic
114#108×C61C2311yescharacteristic
115#107×C61—21no—
116#106×C61C2311yescharacteristic
117#106×C61C2311yescharacteristic
118#104×C61—21no—
119C4×C8×C61C2311yescharacteristic
120#41×C61—21no—
121#11758226—21no—
122Q8×D61—21no—
123#11758224—21no—
124#11758224—41no—
125D4×D61—21no—
126D4×D61—41no—
127#11758222—21no—
128#11758222—41no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61C2×D411yescharacteristic
132C2×Dic122—41no—
133C2×Dic122—41no—
134Q16×C61C2×Q811yescharacteristic
135SD16×C61—21no—
136D8×C61C2×Q811yescharacteristic
137M16×C61—21no—
138M16×C61—41no—
139C2×C8×C61—41no—
140C2×C8×C61C2×D411yescharacteristic
141C2×C8×C61C2411yescharacteristic
142C4⋊C4×C61—21no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C42×C61C2×D411yescharacteristic
147#11758202—21no—
148#11758201—21no—
149#11758200—21no—
150#11758199—21no—
151#11758198—21no—
152#11758198—41no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—41no—
156C4⋊Dic61—41no—
157#11758196—21no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162C4×Dic61C2×D411yescharacteristic
163#11758194—21no—
164#11758194—41no—
165C2×#92418—41no—
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244C2×Q811yescharacteristic
169D488C2×Q811yescharacteristic
170#11758190—21no—
171#11758189—41no—
172#11758189—41no—
173#11758189—41no—
174#11758189SD1611yescharacteristic
175#11758189SD1611yescharacteristic
176#11758189SD1611yescharacteristic
177#11758189SD1611yescharacteristic
178C8×D61—41no—
179C8×D61—41no—
180C8×D61—41no—
181C8×D61C2×Q811yescharacteristic
182C8×D61C2×Q811yescharacteristic
183C8×D61#4111yescharacteristic
184C8×D61#4111yescharacteristic
185C16×C61—21no—
186C16×C61—21no—
187#11758185—21no—
188#11758185—21no—
189C22×D61—41no—
190C22×D61AGL(1,ℤ/8)11yescharacteristic
191Q8×C61—21no—
192D4×C61—21no—
193D4×C61—41no—
194C2×C4×C61—21no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61C22×D411yescharacteristic
199C22⋊D61—41no—
200C22⋊D61—41no—
201C22⋊D61—41no—
202C2×Dic61—21no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61AGL(1,ℤ/8)11yescharacteristic
207D244—21no—
208D244—41no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—161no—
213C4×D61C22⋊Q811yescharacteristic
214C4×D61C22⋊Q811yescharacteristic
215C4×D61C2×SD1611yescharacteristic
216C4×D61C2×SD1611yescharacteristic
217Dic122—21no—
218Dic122—41no—
219Dic122—161no—
220Dic122—161no—
221C8×C61—41no—
222C8×C61C2×SD1611yescharacteristic
223C8×C61C2×SD1611yescharacteristic
224C8×C61C22×Q811yescharacteristic
225C8×C61C2×#4111yescharacteristic
226#92418—41no—
227#92418C22⋊Q811yescharacteristic
228#92418C22⋊Q811yescharacteristic
229#92418C2×SD1611yescharacteristic
230#92418C2×SD1611yescharacteristic
231#33638—611nomaximal, Sylow
232C22×C61—41no—
233C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
234C2×D61—41no—
235C2×D61—41no—
236C2×D61—161no—
237C2×D61#47611yescharacteristic
238C2×D61#47611yescharacteristic
239C4×C61—41no—
240C4×C61—41no—
241C4×C61—81no—
242C4×C61—81no—
243C4×C61C2×C22⋊Q811yescharacteristic
244C4×C61C22×SD1611yescharacteristic
245Dic61—41no—
246Dic61—41no—
247Dic61—81no—
248Dic61—81no—
249Dic61#47611yescharacteristic
250Dic61#47611yescharacteristic
251#3163—611no—
252#2957—611no—
253#2231—611no—
254#2231—611no—
255#2231—611no—
256#2231D6111yescharacteristic, complemented
257#2230—611no—
258#2230—611no—
259#2230—611no—
260#2230—611no—
261#2155—611no—
262C2×#365—611no—
263#2153—611no—
264#2145—611no—
265C2×#360—611no—
266C2×C61—21no—
267C2×C61—81no—
268C2×C61C2×#47611yescharacteristic
269D61—21no—
270D61—21no—
271D61—81no—
272C2×#135—611no—
273#568—1221no—
274#544—1221no—
275C2×M32—611no—
276C2×M32—611no—
277#501—1221no—
278#501—1221no—
279#499—611no—
280#499C2×D6111yescharacteristic, complemented
281#498—611no—
282#498—611no—
283#444—1221no—
284#444—1221no—
285#443—611no—
286#443—611no—
287#443—611no—
288#443C2×D6111yescharacteristic
289C2×#108—611no—
290#428—1221no—
291#427—611no—
292C2×#106—611no—
293#421—1221no—
294#405—611no—
295#365—611no—
296#365—611no—
297#365—611no—
298#365—611no—
299#365—611no—
300#365—611no—
301#365C2×D6111yescharacteristic, complemented
302#365C2×D6111yescharacteristic, complemented
303#364—611no—
304#364—611no—
305#364—611no—
306#364C2×D6111yescharacteristic, complemented
307#360—611no—
308#360—611no—
309#360—611no—
310#360—611no—
311#360—611no—
312#360—611no—
313#360C2×D6111yescharacteristic
314#360C2×D6111yescharacteristic
315C61#3363811yescharacteristic, complemented, Sylow
316C2×#41—1221no—
317#135—611no—
318#135—611no—
319#135—611no—
320#135—1221no—
321#135—1221no—
322#135C22×D6111yescharacteristic
323C2×Q16—611no—
324C2×SD16—1221no—
325C2×D8—611no—
326#131—21no—
327#131—1221no—
328#131—1221no—
329#131—1221no—
330#131—2441no—
331#131—2441no—
332C2×M16—611no—
333C2×M16—1221no—
334C2×M16—2441no—
335C2×M16—2441no—
336C22×C8—611no—
337C4⋊Q8—1221no—
338C4⋊Q8—1221no—
339C4⋊Q8—2441no—
340#125—21no—
341#125—1221no—
342#125—2441no—
343C22⋊Q8—2441no—
344C22⋊Q8—2441no—
345#117—611no—
346#117—1221no—
347C2×C4⋊C4—1221no—
348M32—611no—
349M32—611no—
350M32—1221no—
351M32—1221no—
352M32C22×D6111yescharacteristic
353M32C22×D6111yescharacteristic
354C2×C16—1221no—
355C2×C16—1221no—
356#108—611no—
357#108—1221no—
358#108C22×D6111yescharacteristic
359#107—21no—
360#107—1221no—
361#107—1221no—
362#106—611no—
363#106—611no—
364#106—1221no—
365#106—1221no—
366#106—1221no—
367#106C22×D6111yescharacteristic
368#106C22×D6111yescharacteristic
369#104—21no—
370#104—1221no—
371#104—1221no—
372#104—1221no—
373#97—611no—
374#97—611no—
375C4×C8—611no—
376C4×C8C22×D6111yescharacteristic
377#41—21no—
378#41—1221no—
379#41—1221no—
380#41—1221no—
381#41—2441no—
382#41—2441no—
383C2×Q8—1221no—
384C2×Q8—2441no—
385C2×Q8—2441no—
386C2×D4—1221no—
387C2×D4—2441no—
388C22×C4—611no—
389C22×C4—2441no—
390C22×C4—2441no—
391Q16—611no—
392Q16—1221no—
393Q16Q8×D6111yescharacteristic
394SD16—21no—
395SD16—1221no—
396SD16—1221no—
397SD16—1221no—
398D8—611no—
399D8—1221no—
400D8Q8×D6111yescharacteristic
401M16—21no—
402M16—41no—
403M16—611no—
404M16—611no—
405M16—611no—
406M16—611no—
407M16—1221no—
408M16—2441no—
409M16—2441no—
410M16—2441no—
411M16—2441no—
412C2×C8—41no—
413C2×C8—611no—
414C2×C8—611no—
415C2×C8—611no—
416C2×C8—611no—
417C2×C8—611no—
418C2×C8—611no—
419C2×C8—2441no—
420C2×C8—2441no—
421C2×C8—2441no—
422C2×C8—2441no—
423C2×C8D4×D6111yescharacteristic
424C2×C8C23×D6111yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—1221no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C4⋊C4—2441no—
436C4⋊C4—2441no—
437C22⋊C4—1221no—
438C22⋊C4—2441no—
439C42—611no—
440C42—2441no—
441C42D4×D6111yescharacteristic
442C16—21no—
443C16—21no—
444C16—1221no—
445C16—1221no—
446C23—611no—
447C23—2441no—
448Q8—21no—
449Q8—1221no—
450Q8—9761no—
451Q8—9761no—
452Q8—2441no—
453D4—21no—
454D4—41no—
455D4—1221no—
456D4—2441no—
457D4—2441no—
458D4—2441no—
459D4—2441no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—611no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—1221no—
470C2×C4—9761no—
471C2×C4—2441no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4C2×D4×D6111yescharacteristic
478C8—41no—
479C8—611no—
480C8—611no—
481C8—611no—
482C8—611no—
483C8—2441no—
484C8SD16×D6111yescharacteristic
485C8SD16×D6111yescharacteristic
486C8C2×Q8×D6111yescharacteristic
487C8#41×D6111yescharacteristic
488C22—41no—
489C22—611no—
490C22—611no—
491C22—9761no—
492C22—2441no—
493C22—2441no—
494C22AGL(1,ℤ/8)×D6111yescharacteristic
495C4—41no—
496C4—41no—
497C4—81no—
498C4—81no—
499C4—611no—
500C4—611no—
501C4—4881no—
502C4—4881no—
503C4—2441no—
504C4—2441no—
505C4C22⋊Q8×D6111yescharacteristic
506C4C2×SD16×D6111yescharacteristic
507C2—21no—
508C2—81no—
509C2—1221no—
510C2—1221no—
511C2—4881no—
512C2#476×D6111yescharacteristic
subgroupG/H
centerC2#476×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2231C2
socleC2×C61C2×#476
prime radical#135×D61C22
hypercenter#2231D61
hypocenterC61#33638
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2231

Complements

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

NH ≅ G/Ntype
1. #21456348C2semidirect
3. #21447994C2semidirect
4. #21447993C2semidirect
5. #21447992C2semidirect
6. #21447991C2semidirect
7. #21447990C2semidirect
8. #21447989C2semidirect
9. #21447988C2semidirect
10. #21447590C2semidirect
11. #365×D61C2semidirect
12. #21447583C2semidirect
15. C61×#2231C2semidirect
23. #16840162C22semidirect
24. #16840160C22semidirect
25. #16840159C22semidirect
37. #16839586C22semidirect
38. #16839586C22semidirect
39. #16839585C22semidirect
40. #16839585C22semidirect
41. #16839584C22semidirect
42. #16839584C22semidirect
43. #16839583C22semidirect
44. #16839582C22semidirect
45. #16839582C22semidirect
52. C61×#499C22semidirect
54. C61×#365C22semidirect
55. C61×#365C22semidirect
56. C61×#364C22semidirect
60. #14519800Q8semidirect
64. #14519796Q8semidirect
65. Q16×D61Q8semidirect
67. D8×D61Q8semidirect
256. #2231D61semidirect
280. #499C2×D61semidirect
301. #365C2×D61semidirect
302. #365C2×D61semidirect
306. #364C2×D61semidirect
315. C61#33638semidirect

Maximal subgroups

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

subgroupindex
#214563482
#214547312
#214479942
#214479932
#214479922
#214479912
#214479902
#214479892
#214479882
#214475902
#365×D612
#214475832
#214475532
#360×D612
C61×#22312
#3363861