Finite Group Databasebeta

← #30614538

Subgroups — #30614538

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840805C212yesmaximal
2#21462391C211yesmaximal, characteristic, complemented
3#21462390C211yesmaximal, characteristic, complemented
4C4×#14519847C211yesmaximal, characteristic, complemented
5#21461622C212yesmaximal, complemented
6#21461600C212yesmaximal, complemented
7#21461598C212yesmaximal, complemented
8#21461583C211yesmaximal, characteristic, complemented
9#21461582C211yesmaximal, characteristic, complemented
10#21461475C211yesmaximal, characteristic, complemented
11C4×#14519798C211yesmaximal, characteristic
12C2×#14519865C2212yes—
13C2×#14519864C2212yes—
14#16840805C4116yescomplemented
15C2×#14519847C2212yes—
16C2×#14519842C2212yes—
17C2×#14519841C2212yes—
18#16840727—22no—
19#16840727C2212yes—
20#16840727C2212yes—
21#16840726—22no—
22C4×#11758213—21no—
23C4×#11758213C2211yescharacteristic
24C4×#11758213C2211yescharacteristic
25C4×#11758217—21no—
26#16840721—21no—
27#16840721C2211yescharacteristic
28C2×#14519832—21no—
29C2×#14519831C2212yes—
30C2×C8×#6923C2212yes—
31#16840698C2211yescharacteristic
32#16840638C2212yes—
33#16840632C2212yes—
34#16840632C2212yes—
35C2×#14519798C2211yescharacteristic
36C4×#11758226C2211yescharacteristic
37C4×#11758224C2211yescharacteristic
38C4×#11758202C411yescharacteristic, complemented
39#16839854C411yescharacteristic, complemented
40C4×#11758190C411yescharacteristic, complemented
41SD16×Dic61C411yescharacteristic, complemented
42#16839849C411yescharacteristic, complemented
43C4×#11758199C411yescharacteristic, complemented
44#16839842C411yescharacteristic, complemented
45#16839797C2211yescharacteristic
46#16839757C2211yescharacteristic
47#16839755C2211yescharacteristic
48C4×C8×D61C2211yescharacteristic
49C4×SD16×C61C411yescharacteristic, complemented
50#14519865—24no—
51#14519865C2×C418yescomplemented
52#14519864—24no—
53#14519864C2×C418yescomplemented
54C2×#11758213—22no—
55C2×#11758213C2312yes—
56C2×#11758213C2312yes—
57C2×#11758217—22no—
58C2×D61⋊C8—22no—
59C2×D61⋊C8C2312yes—
60C22×#92420—22no—
61C2×C4×#6923C2312yes—
62#14519847C2×C418yescomplemented
63#14519842C2×C418yescomplemented
64#14519841C2×C418yescomplemented
65#14519832—22no—
66#14519832—22no—
67#14519832—21no—
68#14519832—21no—
69#14519832D411yescharacteristic
70#14519832D411yescharacteristic
71#14519832D412yes—
72#14519831—24no—
73C4×#92420—22no—
74C4×#92420—22no—
75C4×#92420—21no—
76C4×#92420—21no—
77C8×#6923C2×C418yescomplemented
78(C2×#6923)⋊C4—21no—
79(C2×#6923)⋊C4—21no—
80C2×#11758226C2311yescharacteristic
81C2×#11758224C2311yescharacteristic
82#14519798C2×C418yes—
83C2×#11758202C2×C411yescharacteristic
84C2×#11758190C2×C411yescharacteristic
85C2×#11758199C2×C411yescharacteristic
86C2×C8×D61C2311yescharacteristic
87C2×C8×D61C2311yescharacteristic
88Q8×Dic61C2×C411yescharacteristic
89C4×Dic122C2×C411yescharacteristic
90#14519742C2×C411yescharacteristic
91C4×D244—21no—
92C4×D244C2×C411yescharacteristic
93D4×Dic61C2×C411yescharacteristic
94#14519739—21no—
95#14519739C2×C411yescharacteristic
96C4×C22⋊D61—21no—
97#14519737—21no—
98#14519735—21no—
99#14519735C2311yescharacteristic
100#14519735C2311yescharacteristic
101#14519733—21no—
102C2×C4×Dic61—21no—
103C42×D61—21no—
104C42×D61C2311yescharacteristic
105#14519710C2×C411yescharacteristic
106#14519710C2×C411yescharacteristic
107#14519709C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113#14519697C2×C411yescharacteristic
114C4×#92418C2×C411yescharacteristic
115C8×Dic61C2×C411yescharacteristic
116C8×Dic61C2×C411yescharacteristic
117C2×SD16×C61C2×C411yescharacteristic
118C4×Q8×C61C2×C411yescharacteristic
119C4×D4×C61C2×C411yescharacteristic
120#106×C61C2×C411yescharacteristic
121#103×C61C2×C411yescharacteristic
122#102×C61C2×C411yescharacteristic
123C4×C8×C61C2×C411yescharacteristic
124C22×#6923—22no—
125C2×Q8×C61C22×C411yescharacteristic
126C2×D4×C61C22×C411yescharacteristic
127C22×C4×C61—21no—
128C2×C22⋊D61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131#11758226—22no—
132#11758226C22×C414yes—
133#11758224—22no—
134#11758224C22×C414yes—
135C2×D244—21no—
136C2×D244C22×C411yescharacteristic
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61#4111yescharacteristic
141C2×C4×D61#4111yescharacteristic
142C2×C4×D61C2411yescharacteristic
143C2×Dic122C22×C411yescharacteristic
144#11758217—28no—
145C2×#92420—22no—
146C2×#92420—22no—
147C2×#92420—28no—
148C2×#92420C2×D412yes—
149C2×#92420C2×D412yes—
150C4×#6923—22no—
151C4×#6923C22×C414yes—
152#11758213—22no—
153#11758213—22no—
154#11758213—28no—
155#11758213C22×C414yes—
156#11758213C22×C414yes—
157D61⋊C8—28no—
158D61⋊C8C22×C414yes—
159D61⋊C8#4114yes—
160SD16×C61C4214yes—
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61C22×C411yescharacteristic
165C4⋊C4×C61C22×C411yescharacteristic
166C22⋊C4×C61—21no—
167C42×C61—21no—
168C42×C61C22×C411yescharacteristic
169C22⋊Dic61—21no—
170#11758202C4214yes—
171#11758199C4214yes—
172#11758198—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61C22×C411yescharacteristic
178C4⋊Dic61C22×C411yescharacteristic
179#11758196—21no—
180#11758196—21no—
181C4×Dic61—21no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61C22×C411yescharacteristic
187C4×Dic61C2×D411yescharacteristic
188C4×Dic61C2×D411yescharacteristic
189C2×#92418C22×C411yescharacteristic
190C2×#92418C22×C411yescharacteristic
191#11758190C4214yes—
192C8×D61—22no—
193C8×D61C22×C414yes—
194C23×C61—21no—
195C22×D61—21no—
196C22×D61C2×#4111yescharacteristic
197C2×#6923—24no—
198C2×#6923—42no—
199C2×#6923—42no—
200Q8×C61—21no—
201Q8×C61C2×C4212yes—
202D4×C61—21no—
203D4×C61C2×C4212yes—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—81no—
208C2×C4×C61C4×D411yescharacteristic
209C2×C4×C61C4×D411yescharacteristic
210C2×C4×C61C23×C411yescharacteristic
211C22⋊D61—24no—
212C2×Dic61—21no—
213C2×Dic61—24no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—81no—
217C2×Dic61C4×D411yescharacteristic
218C2×Dic61C4×D411yescharacteristic
219C2×Dic61C22×D411yescharacteristic
220D244—24no—
221D244—21no—
222D244C2×C4212yes—
223C4×D61—24no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—81no—
227C4×D61—81no—
228C4×D61C23×C412yes—
229C4×D61C2×#4112yes—
230Dic122—21no—
231Dic122C2×C4212yes—
232#92420—24no—
233#92420—24no—
234#92420C4×D414yes—
235#92420C4×D414yes—
236C8×C61—21no—
237C8×C61C2×C4212yes—
238#92418—21no—
239#92418C2×C4212yes—
240#20514—611nomaximal, Sylow
241C22×C61—22no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61C2×C4×D411yescharacteristic
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—22no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61C4×#4112yes—
251#6923—44no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—22no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61C22×C4211yescharacteristic
258C4×C61C4×#4111yescharacteristic
259Dic61—21no—
260Dic61—21no—
261Dic61—22no—
262Dic61—41no—
263Dic61—41no—
264Dic61C2×C4×D412yes—
265C2×#443—612no—
266C4×#135—611no—
267#2875—611no—
268#2875—611no—
269C4×#108—611no—
270#1772—612no—
271#1765—612no—
272#1765—612no—
273#1759—611no—
274#1759—611no—
275#1726—611no—
276C2×C61—42no—
277C2×C61C42×D411yescharacteristic
278C2×C61#295711yescharacteristic
279C2×C61#295711yescharacteristic
280D61—22no—
281D61—42no—
282C2×#135—611no—
283C2×#131—612no—
284C2×#131—612no—
285C4×#41—611no—
286C4×#41—611no—
287#443—6116no—
288C4×Q16—611no—
289C4×Q16—611no—
290C4×SD16—611no—
291C4×SD16—611no—
292C4×SD16—611no—
293C4×SD16#692311yescharacteristic, complemented
294C4×D8—611no—
295C4×D8—611no—
296C2×#108—612no—
297#427—611no—
298C2×#104—612no—
299C2×#104—612no—
300#416—611no—
301#416—611no—
302#405—612no—
303#405—612no—
304#405—1222no—
305#405—1222no—
306C4×M16—611no—
307C4×M16—611no—
308C4×M16—1221no—
309C4×M16—1221no—
310C2×#97—611no—
311C2×#97—612no—
312C2×#97—1221no—
313C2×#97—1221no—
314C2×C4×C8—612no—
315C2×C4×C8—611no—
316#376—611no—
317#341—612no—
318#339—612no—
319#339—612no—
320C61#2051411yescharacteristic, complemented, Sylow
321C2×#41—611no—
322C2×#41—611no—
323#135—618no—
324C2×Q16—611no—
325C2×SD16—611no—
326C2×SD16C2×#692311yescharacteristic
327C2×D8—611no—
328#131—618no—
329#131—618no—
330#131—1224no—
331#131—1224no—
332C2×M16—612no—
333C2×M16—612no—
334C2×M16—1222no—
335C2×M16—1222no—
336C22×C8—612no—
337C22×C8—611no—
338C22×C8—611no—
339C22×C8—1222no—
340C22×C8—1222no—
341C4×Q8—611no—
342C4×Q8—611no—
343C4×Q8—611no—
344C4×Q8C2×#692311yescharacteristic
345C4×D4—611no—
346C4×D4—611no—
347C4×D4—611no—
348C4×D4—1221no—
349C4×D4—1221no—
350C4×D4—1221no—
351C4×D4—1221no—
352C4×D4C2×#692311yescharacteristic
353#117—611no—
354#117—611no—
355#117—1221no—
356#117—1221no—
357C2×C42—611no—
358C2×C42—612no—
359C2×C42—1221no—
360C2×C42—1221no—
361#108—618no—
362#107—611no—
363#107—611no—
364#106—611no—
365#106C2×#692311yescharacteristic
366#104—618no—
367#104—618no—
368#103—611no—
369#103—611no—
370#103—611no—
371#103C2×#692311yescharacteristic
372#102—611no—
373#102—611no—
374#102—611no—
375#102C2×#692311yescharacteristic
376#97—611no—
377#97—611no—
378#97—612no—
379#97—1221no—
380#97—1221no—
381#97—1224no—
382#97—1222no—
383#97—1222no—
384C4×C8—618no—
385C4×C8—611no—
386C4×C8—611no—
387C4×C8—611no—
388C4×C8—1221no—
389C4×C8—1221no—
390C4×C8—1222no—
391C4×C8—1222no—
392C4×C8C2×#692311yescharacteristic
393#95—1221no—
394#95—1221no—
395#41—614no—
396#41—614no—
397#41—1222no—
398#41—1222no—
399C2×Q8—611no—
400C2×Q8C22×#692311yescharacteristic
401C2×D4—611no—
402C2×D4—1221no—
403C2×D4—1221no—
404C2×D4C22×#692311yescharacteristic
405C22×C4—21no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1221no—
412C22×C4—1221no—
413C22×C4—1222no—
414C22×C4—1221no—
415Q16—614no—
416SD16—614no—
417SD16C4×#692314yes—
418D8—614no—
419M16—614no—
420M16—614no—
421M16—1228no—
422M16—1228no—
423M16—1222no—
424M16—1222no—
425C2×C8—614no—
426C2×C8—612no—
427C2×C8—612no—
428C2×C8—614no—
429C2×C8—611no—
430C2×C8—614no—
431C2×C8—611no—
432C2×C8—1222no—
433C2×C8—1228no—
434C2×C8—1228no—
435C2×C8—1222no—
436C2×C8—1222no—
437C2×C8C22×#692311yescharacteristic
438C2×C8C22×#692311yescharacteristic
439C4⋊C4—21no—
440C4⋊C4—611no—
441C4⋊C4—611no—
442C4⋊C4—1221no—
443C4⋊C4—1221no—
444C4⋊C4—1221no—
445C4⋊C4C22×#692311yescharacteristic
446C4⋊C4C22×#692311yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—1221no—
449C22⋊C4—1221no—
450C22⋊C4—1221no—
451C22⋊C4—1221no—
452C22⋊C4—1221no—
453C42—21no—
454C42—611no—
455C42—611no—
456C42—611no—
457C42—614no—
458C42—1221no—
459C42—1221no—
460C42—1221no—
461C42—1221no—
462C42—1222no—
463C42—1221no—
464C42C22×#692311yescharacteristic
465C23—21no—
466C23—611no—
467C23—1221no—
468Q8—21no—
469Q8—612no—
470Q8—1221no—
471Q8C2×C4×#692312yes—
472D4—21no—
473D4—612no—
474D4—1224no—
475D4—1224no—
476D4—1221no—
477D4C2×C4×#692312yes—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—81no—
482C2×C4—611no—
483C2×C4—612no—
484C2×C4—612no—
485C2×C4—611no—
486C2×C4—611no—
487C2×C4—1224no—
488C2×C4—1224no—
489C2×C4—1221no—
490C2×C4—1224no—
491C2×C4—1221no—
492C2×C4—1221no—
493C2×C4—4881no—
494C2×C4—4881no—
495C2×C4—4881no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4D4×#692311yescharacteristic
501C2×C4D4×#692311yescharacteristic
502C2×C4C23×#692311yescharacteristic
503C8—21no—
504C8—614no—
505C8—614no—
506C8—612no—
507C8—1224no—
508C8—1224no—
509C8—1221no—
510C8C2×C4×#692312yes—
511C22—22no—
512C22—41no—
513C22—41no—
514C22—612no—
515C22—1221no—
516C22—1221no—
517C22—1222no—
518C22—2441no—
519C22—2441no—
520C22C2×D4×#692311yescharacteristic
521C4—21no—
522C4—21no—
523C4—22no—
524C4—41no—
525C4—41no—
526C4—612no—
527C4—1221no—
528C4—1221no—
529C4—1222no—
530C4—2444no—
531C4—2441no—
532C4—2441no—
533C4C22×C4×#692311yescharacteristic
534C4#41×#692311yescharacteristic
535C2—42no—
536C2—1222no—
537C2—2442no—
538C2C4×D4×#692311yescharacteristic
539C2#2146259711yescharacteristic
540C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC4×SD16×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519798C22
cosocleC2×C4×D61C24
hypercenterC4×SD16#6923
hypocenterC61#20514
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #21462391C2semidirect
3. #21462390C2semidirect
4. C4×#14519847C2semidirect
5. #21461622C2semidirect
6. #21461600C2semidirect
7. #21461598C2semidirect
8. #21461583C2semidirect
9. #21461582C2semidirect
10. #21461475C2semidirect
14. #16840805C4semidirect
38. C4×#11758202C4semidirect
39. #16839854C4semidirect
40. C4×#11758190C4semidirect
41. SD16×Dic61C4semidirect
42. #16839849C4semidirect
43. C4×#11758199C4semidirect
44. #16839842C4semidirect
49. C4×SD16×C61C4semidirect
51. #14519865C2×C4semidirect
53. #14519864C2×C4semidirect
62. #14519847C2×C4semidirect
63. #14519842C2×C4semidirect
64. #14519841C2×C4semidirect
77. C8×#6923C2×C4semidirect
293. C4×SD16#6923semidirect
320. C61#20514semidirect

Maximal subgroups

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

subgroupindex
C2×#168408052
#214623912
#214623902
C4×#145198472
#214616222
#214616002
#214615982
#214615832
#214615822
#214614752
C4×#145197982
#2051461