Finite Group Databasebeta

← #29835289

Subgroups — #29835289

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456476C211yesmaximal, characteristic, complemented
2#21454719C211yesmaximal, characteristic
3#21448040C211yesmaximal, characteristic, complemented
4#21448037C211yesmaximal, characteristic, complemented
5#21447994C211yesmaximal, characteristic, complemented
6#21447993C211yesmaximal, characteristic, complemented
7#21447899C211yesmaximal, characteristic, complemented
8#21447898C211yesmaximal, characteristic, complemented
9#21447771C211yesmaximal, characteristic
10#21447768C211yesmaximal, characteristic
11#21447712C211yesmaximal, characteristic, complemented
12#21447710C211yesmaximal, characteristic, complemented
13#21447708C211yesmaximal, characteristic, complemented
14#21447633C211yesmaximal, characteristic, complemented
15C61×#2180C211yesmaximal, characteristic, complemented
16#16840559C2211yescharacteristic
17#131×D61—21no—
18#16840370—21no—
19#16840205C2211yescharacteristic
20#16840203C2211yescharacteristic
21#16840202C2211yescharacteristic
22#16840162C2211yescharacteristic, complemented
23#16840140C2211yescharacteristic, complemented
24#16840129—21no—
25#16840021C2211yescharacteristic
26#16840017C2211yescharacteristic
27#16840002—21no—
28#16839885C2211yescharacteristic
29#16839882—21no—
30#16839879C2211yescharacteristic
31#16839878C2211yescharacteristic
32#16839876—21no—
33#16839870C2211yescharacteristic, complemented
34C4×#11758202—21no—
35#16839809C2211yescharacteristic
36#16839777—21no—
37#16839719C2211yescharacteristic
38#16839586C2211yescharacteristic, complemented
39#16839585C2211yescharacteristic, complemented
40#16839584C2211yescharacteristic, complemented
41#16839582C2211yescharacteristic, complemented
42#16839582C2211yescharacteristic, complemented
43#16839579C2211yescharacteristic, complemented
44#16839578C2211yescharacteristic, complemented
45#16839577C2211yescharacteristic, complemented
46#16839573C2211yescharacteristic
47#16839572C2211yescharacteristic
48#16839571C2211yescharacteristic
49#16839543C2211yescharacteristic
50#16839543C2211yescharacteristic
51#16839540C2211yescharacteristic, complemented
52C61×#510C2211yescharacteristic
53C61×#444C2211yescharacteristic
54C61×#441C2211yescharacteristic, complemented
55C61×#365C2211yescharacteristic, complemented
56C61×#362C2211yescharacteristic, 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×Dic244C2311yescharacteristic
67C2×#11758202—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#14519775—21no—
79#14519772—41no—
80#14519771—41no—
81#14519769—41no—
82#14519768—21no—
83#14519767—41no—
84#14519757—21no—
85#14519753—21no—
86C4×Dic122—21no—
87#14519734D411yescharacteristic
88Dic488—21no—
89#14519723—21no—
90#14519723—21no—
91#14519722—21no—
92#14519721—21no—
93#14519720—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#14519702—21no—
104#14519701—21no—
105#14519700—21no—
106#14519687D411yescharacteristic
107C4×#92418D411yescharacteristic
108C8×Dic61C2311yescharacteristic
109#135×C61C2311yescharacteristic
110C2×Q16×C61C2311yescharacteristic
111#131×C61—21no—
112C4×Q8×C61—21no—
113Q32×C61—21no—
114SD32×C61—21no—
115M32×C61C2311yescharacteristic
116M32×C61C2311yescharacteristic
117#108×C61C2311yescharacteristic
118#106×C61C2311yescharacteristic
119#104×C61—21no—
120#103×C61—21no—
121#97×C61C2311yescharacteristic
122#41×C61—21no—
123C2×Q8×C61—21no—
124#11758226—21no—
125Q8×D61—21no—
126#11758224—21no—
127#11758224—41no—
128D4×D61—21no—
129D4×D61—41no—
130#11758222—21no—
131#11758222—41no—
132C2×C4×D61—41no—
133C2×C4×D61C2×D411yescharacteristic
134C2×Dic122—21no—
135Q16×C61—21no—
136Q16×C61—21no—
137Q16×C61#4111yescharacteristic
138SD16×C61—21no—
139D8×C61#4111yescharacteristic
140M16×C61—21no—
141M16×C61—41no—
142C2×C8×C61—41no—
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2411yescharacteristic
145C4⋊C4×C61—21no—
146C4⋊C4×C61—41no—
147C42×C61—41no—
148C42×C61C2×D411yescharacteristic
149#11758202—21no—
150#11758202—41no—
151#11758202—41no—
152#11758201—21no—
153#11758200—21no—
154#11758199—21no—
155#11758198—21no—
156#11758198—41no—
157#11758198—41no—
158C4⋊Dic61—21no—
159C4⋊Dic61—41no—
160C4⋊Dic61—41no—
161#11758196—21no—
162#11758196—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167C4×Dic61—41no—
168C4×Dic61C2×D411yescharacteristic
169#11758194—21no—
170#11758194—41no—
171C2×#92418—41no—
172C2×#92418C2×D411yescharacteristic
173C2×#92418C2×D411yescharacteristic
174Dic244—21no—
175Dic244—21no—
176Dic244#4111yescharacteristic
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—
193C22×D61—41no—
194C22×D61AGL(1,ℤ/8)11yescharacteristic
195Q8×C61—21no—
196Q8×C61—41no—
197Q8×C61—41no—
198D4×C61—21no—
199D4×C61—41no—
200C2×C4×C61—21no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61C22×D411yescharacteristic
205C22⋊D61—41no—
206C22⋊D61—41no—
207C22⋊D61—41no—
208C2×Dic61—21no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61AGL(1,ℤ/8)11yescharacteristic
213D244—21no—
214D244—41no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220Dic122—21no—
221Dic122—41no—
222Dic122—41no—
223Dic122—41no—
224C8×C61—21no—
225C8×C61—41no—
226C8×C61C2×#4111yescharacteristic
227C8×C61C2×#4111yescharacteristic
228#92418—21no—
229#92418—41no—
230#92418AGL(1,ℤ/8)11yescharacteristic
231#92418AGL(1,ℤ/8)11yescharacteristic
232#33693—611nomaximal, Sylow
233C22×C61—41no—
234C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
235C2×D61—21no—
236C2×D61—41no—
237C2×D61—41no—
238C2×D61—82no—
239C4×C61—41no—
240C4×C61—41no—
241C4×C61—81no—
242C4×C61—81no—
243C4×C61#52511yescharacteristic
244C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
245Dic61—21no—
246Dic61—41no—
247Dic61—41no—
248Dic61—81no—
249Dic61—81no—
250#3177—611no—
251#2955—611no—
252#2239—611no—
253#2239—611no—
254#2231—611no—
255#2231—611no—
256#2214—611no—
257#2214—611no—
258#2191—611no—
259#2191—611no—
260#2180—611no—
261#2180—611no—
262#2180—611no—
263#2180D6111yescharacteristic, complemented
264#2166—611no—
265C2×C61—21no—
266C2×C61—81no—
267C2×C61#310911yescharacteristic
268D61—41no—
269D61—81no—
270#575—611no—
271C2×#131—1221no—
272#541—1221no—
273#510—611no—
274#510—611no—
275#510—611no—
276#510C2×D6111yescharacteristic
277#499—611no—
278#494—611no—
279#491—1221no—
280#470—611no—
281#470—611no—
282#467—1221no—
283#444—611no—
284#444—1221no—
285#444C2×D6111yescharacteristic
286#443—611no—
287#443—611no—
288#443—1221no—
289#441—611no—
290#441C2×D6111yescharacteristic, complemented
291C4×Q16—1221no—
292#430—611no—
293#421—1221no—
294#405—611no—
295#365—611no—
296#365—611no—
297#365—611no—
298#365C2×D6111yescharacteristic, complemented
299#364—611no—
300#364—611no—
301#362—611no—
302#362—611no—
303#362—611no—
304#362C2×D6111yescharacteristic, complemented
305#360—611no—
306#360—611no—
307#360—611no—
308#360C2×D6111yescharacteristic
309#349—611no—
310#349—611no—
311#347—611no—
312#347C2×D6111yescharacteristic, complemented
313C61#3369311yescharacteristic, complemented, Sylow
314C2×#41—1221no—
315#137—1221no—
316#137—1221no—
317AGL(1,ℤ/8)—1221no—
318AGL(1,ℤ/8)—1221no—
319#135—611no—
320#135—1221no—
321#135C22×D6111yescharacteristic
322C2×Q16—611no—
323C2×Q16—1221no—
324C2×Q16C22×D6111yescharacteristic
325#131—21no—
326#131—1221no—
327#131—1221no—
328#131—1221no—
329#131—2441no—
330#131—2441no—
331C2×M16—611no—
332C2×M16—1221no—
333C2×M16—2441no—
334C22×C8—611no—
335C22×C8—2441no—
336C4⋊Q8—1221no—
337#126—2441no—
338#126—2441no—
339#125—1221no—
340#125—2441no—
341#125—2441no—
342C22⋊Q8—1221no—
343C22⋊Q8—1221no—
344C4×Q8—21no—
345C4×Q8—1221no—
346#117—611no—
347Q32—21no—
348Q32—1221no—
349Q32—1221no—
350Q32—1221no—
351SD32—21no—
352SD32—1221no—
353SD32—1221no—
354SD32—1221no—
355M32—611no—
356M32—611no—
357M32C22×D6111yescharacteristic
358M32C22×D6111yescharacteristic
359#108—611no—
360#108—1221no—
361#108C22×D6111yescharacteristic
362#107—1221no—
363#106—611no—
364#106C22×D6111yescharacteristic
365#104—21no—
366#104—1221no—
367#104—1221no—
368#104—1221no—
369#103—21no—
370#103—1221no—
371#103—1221no—
372#103—1221no—
373#97—611no—
374#97C22×D6111yescharacteristic
375C4×C8—611no—
376C4×C8—611no—
377#41—21no—
378#41—1221no—
379#41—1221no—
380#41—1221no—
381#41—2441no—
382#41—2441no—
383C2×Q8—21no—
384C2×Q8—1221no—
385C2×Q8—1221no—
386C2×D4—1221no—
387C2×D4—2441no—
388C22×C4—611no—
389C22×C4—2441no—
390Q16—21no—
391Q16—21no—
392Q16—611no—
393Q16—1221no—
394Q16—1221no—
395Q16—1221no—
396Q16—2441no—
397Q16—2441no—
398Q16#1175822211yescharacteristic
399SD16—21no—
400SD16—1221no—
401SD16—1221no—
402SD16—1221no—
403D8—611no—
404D8—1221no—
405D8#1175822211yescharacteristic
406M16—21no—
407M16—41no—
408M16—1221no—
409M16—1221no—
410M16—1221no—
411M16—2441no—
412M16—2441no—
413M16—2441no—
414M16—2441no—
415C2×C8—41no—
416C2×C8—611no—
417C2×C8—611no—
418C2×C8—1221no—
419C2×C8—1221no—
420C2×C8—2441no—
421C2×C8—2441no—
422C2×C8—2441no—
423C2×C8—2441no—
424C2×C8D4×D6111yescharacteristic
425C2×C8C23×D6111yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—1221no—
429C4⋊C4—1221no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C4⋊C4—2441no—
436C4⋊C4—2441no—
437C22⋊C4—1221no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C42—41no—
441C42—611no—
442C42—2441no—
443C42D4×D6111yescharacteristic
444C16—21no—
445C16—21no—
446C16—1221no—
447C16—1221no—
448C23—611no—
449C23—2441no—
450Q8—21no—
451Q8—41no—
452Q8—41no—
453Q8—1221no—
454Q8—2441no—
455Q8—2441no—
456Q8—2441no—
457D4—21no—
458D4—41no—
459D4—1221no—
460D4—2441no—
461D4—2441no—
462D4—2441no—
463D4—2441no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—611no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4C2×D4×D6111yescharacteristic
479C8—21no—
480C8—41no—
481C8—611no—
482C8—611no—
483C8—1221no—
484C8—2441no—
485C8#41×D6111yescharacteristic
486C8C2×#1175822211yescharacteristic
487C22—41no—
488C22—1221no—
489C22—4882no—
490C22—2441no—
491C22—2441no—
492C22AGL(1,ℤ/8)×D6111yescharacteristic
493C4—41no—
494C4—41no—
495C4—81no—
496C4—81no—
497C4—1221no—
498C4—4881no—
499C4—4881no—
500C4—2441no—
501C4—2441no—
502C4#1684027111yescharacteristic
503C4AGL(1,ℤ/8)×D6111yescharacteristic
504C2—21no—
505C2—81no—
506C2—4881no—
507C2—2441no—
508C2#2145590811yescharacteristic
subgroupG/H
centerC2#21455908
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2180C2
socleC2×C61#3109
prime radical#16840559C22
hypercenter#2180D61
hypocenterC61#33693
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

Complements

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

NH ≅ G/Ntype
1. #21456476C2semidirect
3. #21448040C2semidirect
4. #21448037C2semidirect
5. #21447994C2semidirect
6. #21447993C2semidirect
7. #21447899C2semidirect
8. #21447898C2semidirect
11. #21447712C2semidirect
12. #21447710C2semidirect
13. #21447708C2semidirect
14. #21447633C2semidirect
15. C61×#2180C2semidirect
22. #16840162C22semidirect
23. #16840140C22semidirect
33. #16839870C22semidirect
38. #16839586C22semidirect
39. #16839585C22semidirect
40. #16839584C22semidirect
41. #16839582C22semidirect
42. #16839582C22semidirect
43. #16839579C22semidirect
44. #16839578C22semidirect
45. #16839577C22semidirect
51. #16839540C22semidirect
54. C61×#441C22semidirect
55. C61×#365C22semidirect
56. C61×#362C22semidirect
58. C61×#347C22semidirect
263. #2180D61semidirect
290. #441C2×D61semidirect
298. #365C2×D61semidirect
304. #362C2×D61semidirect
312. #347C2×D61semidirect
313. C61#33693semidirect

Maximal subgroups

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

subgroupindex
#214564762
#214547192
#214480402
#214480372
#214479942
#214479932
#214478992
#214478982
#214477712
#214477682
#214477122
#214477102
#214477082
#214476332
C61×#21802
#3369361