Finite Group Databasebeta

← #29835281

Subgroups — #29835281

Order 15616.

536 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#21456467C211yesmaximal, characteristic, complemented
2#21454719C211yesmaximal, characteristic, complemented
3#21448035C211yesmaximal, characteristic, complemented
4#21448032C211yesmaximal, characteristic, complemented
5#21447994C211yesmaximal, characteristic, complemented
6#21447993C211yesmaximal, characteristic, complemented
7#21447894C211yesmaximal, characteristic, complemented
8#21447893C211yesmaximal, characteristic, complemented
9#21447766C211yesmaximal, characteristic, complemented
10#21447763C211yesmaximal, characteristic, complemented
11#21447719C211yesmaximal, characteristic, complemented
12#21447717C211yesmaximal, characteristic, complemented
13#21447715C211yesmaximal, characteristic, complemented
14#21447633C211yesmaximal, characteristic, complemented
15C61×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16#16840559C2211yescharacteristic
17#131×D61—21no—
18#16840363—21no—
19#16840200C2211yescharacteristic
20#16840198C2211yescharacteristic
21#16840197C2211yescharacteristic
22#16840162C2211yescharacteristic, complemented
23#16840137C2211yescharacteristic, complemented
24#16840125—21no—
25#16840016C2211yescharacteristic
26#16840012C2211yescharacteristic
27#16839997—21no—
28#16839885C2211yescharacteristic
29#16839882—21no—
30#16839879C2211yescharacteristic
31#16839878C2211yescharacteristic
32#16839876—21no—
33#16839875C2211yescharacteristic, complemented
34C4×#11758199—21no—
35#16839809C2211yescharacteristic
36#16839777—21no—
37#16839719C2211yescharacteristic
38#16839586C2211yescharacteristic, complemented
39#16839585C2211yescharacteristic, complemented
40#16839584C2211yescharacteristic, complemented
41#16839582C2211yescharacteristic, complemented
42#16839582C2211yescharacteristic, complemented
43#16839576C2211yescharacteristic, complemented
44#16839575C2211yescharacteristic, complemented
45#16839574C2211yescharacteristic, complemented
46#16839573C2211yescharacteristic
47#16839572C2211yescharacteristic
48#16839571C2211yescharacteristic
49#16839543C2211yescharacteristic
50#16839543C2211yescharacteristic
51#16839540C2211yescharacteristic, complemented
52C61×#509C2211yescharacteristic
53C61×#444C2211yescharacteristic
54C61×#442C2211yescharacteristic, complemented
55C61×#365C2211yescharacteristic, complemented
56C61×#361C2211yescharacteristic, complemented
57C61×#360C2211yescharacteristic
58C61×#347C2211yescharacteristic, complemented
59#41×D61—21no—
60#14519809—21no—
61#14519806—21no—
62#14519804—21no—
63#14519801—21no—
64#14519799C2311yescharacteristic
65#14519797—21no—
66C2×D488C2311yescharacteristic
67C2×#11758199—21no—
68#14519785—21no—
69#14519785—41no—
70#14519784—21no—
71#14519783—21no—
72#14519783—41no—
73C2×#11758189C2311yescharacteristic
74M16×D61—21no—
75M16×D61—41no—
76C2×C8×D61—41no—
77C2×C8×D61D411yescharacteristic
78#14519773—21no—
79#14519768—21no—
80#14519760—41no—
81#14519759—41no—
82#14519752—21no—
83#14519751—41no—
84#14519750—41no—
85#14519748—21no—
86C4×D244—21no—
87#14519734D411yescharacteristic
88#14519722—21no—
89#14519721—21no—
90#14519720—21no—
91D976—21no—
92#14519718—21no—
93#14519718—21no—
94#14519717C2311yescharacteristic
95#14519717C2311yescharacteristic
96#14519713C2311yescharacteristic
97#14519712—21no—
98#14519710—21no—
99#14519709C2311yescharacteristic
100#14519705—21no—
101#14519704—21no—
102#14519703—21no—
103#14519699—21no—
104#14519698—21no—
105#14519697—21no—
106#14519687D411yescharacteristic
107C4×#92418D411yescharacteristic
108C8×Dic61C2311yescharacteristic
109#135×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111#131×C61—21no—
112C4×D4×C61—21no—
113SD32×C61—21no—
114D16×C61—21no—
115M32×C61C2311yescharacteristic
116M32×C61C2311yescharacteristic
117#108×C61C2311yescharacteristic
118#106×C61C2311yescharacteristic
119#104×C61—21no—
120#102×C61—21no—
121#97×C61C2311yescharacteristic
122#41×C61—21no—
123C2×D4×C61—21no—
124C22×C4×C61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128#11758226—21no—
129Q8×D61—21no—
130#11758224—21no—
131#11758224—41no—
132D4×D61—21no—
133D4×D61—41no—
134#11758222—21no—
135#11758222—41no—
136C2×D244—21no—
137C2×D244—41no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61C2×D411yescharacteristic
141Q16×C61#4111yescharacteristic
142SD16×C61—21no—
143D8×C61—21no—
144D8×C61—21no—
145D8×C61#4111yescharacteristic
146M16×C61—21no—
147M16×C61—41no—
148C2×C8×C61—41no—
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2411yescharacteristic
151C4⋊C4×C61—21no—
152C22⋊C4×C61—41no—
153C42×C61C2×D411yescharacteristic
154C22⋊Dic61—41no—
155#11758202—21no—
156#11758201—21no—
157#11758200—21no—
158#11758199—21no—
159#11758199—41no—
160#11758199—41no—
161#11758198—21no—
162#11758198—41no—
163#11758198—41no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166#11758196—21no—
167#11758196—41no—
168C4×Dic61C2×D411yescharacteristic
169#11758194—21no—
170#11758194—41no—
171C2×#92418—41no—
172C2×#92418C2×D411yescharacteristic
173C2×#92418C2×D411yescharacteristic
174Dic244#4111yescharacteristic
175D488—21no—
176D488—21no—
177D488#4111yescharacteristic
178#11758190—21no—
179#11758189—21no—
180#11758189—21no—
181#11758189—41no—
182#11758189—41no—
183#11758189—41no—
184C8×D61—21no—
185C8×D61—21no—
186C8×D61—41no—
187C8×D61—41no—
188C8×D61—41no—
189C16×C61—21no—
190C16×C61—21no—
191#11758185—21no—
192#11758185—21no—
193C23×C61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61AGL(1,ℤ/8)11yescharacteristic
197Q8×C61—21no—
198D4×C61—21no—
199D4×C61—41no—
200D4×C61—41no—
201D4×C61—41no—
202C2×C4×C61—21no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—161no—
206C2×C4×C61C22×D411yescharacteristic
207C22⋊D61—41no—
208C22⋊D61—41no—
209C22⋊D61—41no—
210C22⋊D61—161no—
211C22⋊D61—161no—
212C22⋊D61—161no—
213C2×Dic61—21no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61AGL(1,ℤ/8)11yescharacteristic
217D244—21no—
218D244—41no—
219D244—41no—
220D244—41no—
221D244—161no—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227C4×D61—161no—
228Dic122—21no—
229Dic122—41no—
230C8×C61—21no—
231C8×C61—41no—
232C8×C61C2×#4111yescharacteristic
233C8×C61C2×#4111yescharacteristic
234#92418—21no—
235#92418—41no—
236#92418AGL(1,ℤ/8)11yescharacteristic
237#92418AGL(1,ℤ/8)11yescharacteristic
238#33692—611nomaximal, Sylow
239C22×C61—41no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61—81no—
243C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
244C2×D61—21no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—82no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C4×C61—41no—
252C4×C61—41no—
253C4×C61—81no—
254C4×C61#52511yescharacteristic
255C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
256Dic61—21no—
257Dic61—41no—
258Dic61—41no—
259Dic61—81no—
260#3176—611no—
261#2955—611no—
262#2238—611no—
263#2238—611no—
264#2231—611no—
265#2231—611no—
266#2213—611no—
267#2213—611no—
268#2190—611no—
269#2190—611no—
270AGL(1,ℤ/16)—611no—
271AGL(1,ℤ/16)—611no—
272AGL(1,ℤ/16)—611no—
273AGL(1,ℤ/16)D6111yescharacteristic, complemented
274#2166—611no—
275C2×C61—21no—
276C2×C61—81no—
277C2×C61—161no—
278C2×C61#310911yescharacteristic
279D61—41no—
280D61—81no—
281D61—161no—
282#575—611no—
283C2×#131—1221no—
284#540—1221no—
285#509—611no—
286#509—611no—
287#509—611no—
288#509C2×D6111yescharacteristic
289#499—611no—
290#493—611no—
291#490—1221no—
292#469—611no—
293#469—611no—
294#466—1221no—
295#444—611no—
296#444—1221no—
297#444C2×D6111yescharacteristic
298#443—611no—
299#443—611no—
300#443—1221no—
301#442—611no—
302#442C2×D6111yescharacteristic, complemented
303C4×D8—1221no—
304#430—611no—
305#421—1221no—
306#405—611no—
307#365—611no—
308#365—611no—
309#365—611no—
310#365C2×D6111yescharacteristic, complemented
311#364—611no—
312#364—611no—
313#361—611no—
314#361—611no—
315#361—611no—
316#361C2×D6111yescharacteristic, complemented
317#360—611no—
318#360—611no—
319#360—611no—
320#360C2×D6111yescharacteristic
321#349—611no—
322#349—611no—
323#347—611no—
324#347C2×D6111yescharacteristic, complemented
325C61#3369211yescharacteristic, complemented, Sylow
326C2×#41—1221no—
327#137—1221no—
328#137—1221no—
329AGL(1,ℤ/8)—1221no—
330AGL(1,ℤ/8)—1221no—
331#135—611no—
332#135—1221no—
333#135C22×D6111yescharacteristic
334C2×D8—611no—
335C2×D8—1221no—
336C2×D8C22×D6111yescharacteristic
337#131—21no—
338#131—1221no—
339#131—1221no—
340#131—1221no—
341#131—2441no—
342#131—2441no—
343C2×M16—611no—
344C2×M16—1221no—
345C2×M16—2441no—
346C22×C8—611no—
347C22×C8—2441no—
348#127—1221no—
349#125—1221no—
350#123—2441no—
351#123—2441no—
352#121—1221no—
353#121—1221no—
354#121—2441no—
355#121—2441no—
356C4×D4—21no—
357C4×D4—1221no—
358#117—611no—
359SD32—21no—
360SD32—1221no—
361SD32—1221no—
362SD32—1221no—
363D16—21no—
364D16—1221no—
365D16—1221no—
366D16—1221no—
367M32—611no—
368M32—611no—
369M32C22×D6111yescharacteristic
370M32C22×D6111yescharacteristic
371#108—611no—
372#108—1221no—
373#108C22×D6111yescharacteristic
374#107—1221no—
375#106—611no—
376#106C22×D6111yescharacteristic
377#104—21no—
378#104—1221no—
379#104—1221no—
380#104—1221no—
381#102—21no—
382#102—1221no—
383#102—1221no—
384#102—1221no—
385#97—611no—
386#97C22×D6111yescharacteristic
387C4×C8—611no—
388C4×C8—611no—
389#41—21no—
390#41—1221no—
391#41—1221no—
392#41—1221no—
393#41—2441no—
394#41—2441no—
395C2×Q8—1221no—
396C2×D4—21no—
397C2×D4—1221no—
398C2×D4—1221no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C2×D4—2441no—
404C22×C4—41no—
405C22×C4—611no—
406C22×C4—2441no—
407C22×C4—2441no—
408Q16—611no—
409Q16—1221no—
410Q16#1175822211yescharacteristic
411SD16—21no—
412SD16—1221no—
413SD16—1221no—
414SD16—1221no—
415D8—21no—
416D8—21no—
417D8—611no—
418D8—1221no—
419D8—1221no—
420D8—1221no—
421D8—2441no—
422D8—2441no—
423D8#1175822211yescharacteristic
424M16—21no—
425M16—41no—
426M16—1221no—
427M16—1221no—
428M16—1221no—
429M16—2441no—
430M16—2441no—
431M16—2441no—
432M16—2441no—
433C2×C8—41no—
434C2×C8—611no—
435C2×C8—611no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—2441no—
439C2×C8—2441no—
440C2×C8—2441no—
441C2×C8—2441no—
442C2×C8D4×D6111yescharacteristic
443C2×C8C23×D6111yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—1221no—
446C4⋊C4—1221no—
447C4⋊C4—2441no—
448C4⋊C4—2441no—
449C22⋊C4—41no—
450C22⋊C4—1221no—
451C22⋊C4—2441no—
452C22⋊C4—2441no—
453C22⋊C4—2441no—
454C42—611no—
455C42D4×D6111yescharacteristic
456C16—21no—
457C16—21no—
458C16—1221no—
459C16—1221no—
460C23—41no—
461C23—611no—
462C23—2441no—
463C23—2441no—
464Q8—21no—
465Q8—1221no—
466Q8—2441no—
467D4—21no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—1221no—
472D4—9761no—
473D4—9761no—
474D4—9761no—
475D4—9761no—
476D4—2441no—
477D4—2441no—
478D4—2441no—
479D4—2441no—
480D4—2441no—
481D4—2441no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—161no—
486C2×C4—611no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—9761no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4C2×D4×D6111yescharacteristic
497C8—21no—
498C8—41no—
499C8—611no—
500C8—611no—
501C8—1221no—
502C8—2441no—
503C8#41×D6111yescharacteristic
504C8C2×#1175822211yescharacteristic
505C22—41no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—1221no—
510C22—4881no—
511C22—4881no—
512C22—4882no—
513C22—4881no—
514C22—2441no—
515C22—2441no—
516C22AGL(1,ℤ/8)×D6111yescharacteristic
517C4—41no—
518C4—41no—
519C4—81no—
520C4—1221no—
521C4—4881no—
522C4—2441no—
523C4—2441no—
524C4#1684027111yescharacteristic
525C4AGL(1,ℤ/8)×D6111yescharacteristic
526C2—21no—
527C2—81no—
528C2—161no—
529C2—9761no—
530C2—4881no—
531C2—2441no—
532C2#2145590811yescharacteristic
subgroupG/H
centerC2#21455908
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×AGL(1,ℤ/16)C2
socleC2×C61#3109
hypercenterAGL(1,ℤ/16)D61
hypocenterC61#33692
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

NH ≅ G/Ntype
1. #21456467C2semidirect
2. #21454719C2semidirect
3. #21448035C2semidirect
4. #21448032C2semidirect
5. #21447994C2semidirect
6. #21447993C2semidirect
7. #21447894C2semidirect
8. #21447893C2semidirect
9. #21447766C2semidirect
10. #21447763C2semidirect
11. #21447719C2semidirect
12. #21447717C2semidirect
13. #21447715C2semidirect
14. #21447633C2semidirect
15. C61×AGL(1,ℤ/16)C2semidirect
22. #16840162C22semidirect
23. #16840137C22semidirect
33. #16839875C22semidirect
38. #16839586C22semidirect
39. #16839585C22semidirect
40. #16839584C22semidirect
41. #16839582C22semidirect
42. #16839582C22semidirect
43. #16839576C22semidirect
44. #16839575C22semidirect
45. #16839574C22semidirect
51. #16839540C22semidirect
54. C61×#442C22semidirect
55. C61×#365C22semidirect
56. C61×#361C22semidirect
58. C61×#347C22semidirect
273. AGL(1,ℤ/16)D61semidirect
302. #442C2×D61semidirect
310. #365C2×D61semidirect
316. #361C2×D61semidirect
324. #347C2×D61semidirect
325. C61#33692semidirect

Maximal subgroups

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

subgroupindex
#214564672
#214547192
#214480352
#214480322
#214479942
#214479932
#214478942
#214478932
#214477662
#214477632
#214477192
#214477172
#214477152
#214476332
C61×AGL(1,ℤ/16)2
#3369261