Finite Group Databasebeta

← #29833795

Subgroups — #29833795

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519799C211yesmaximal, characteristic, complemented
2C2×#16840194C212yesmaximal, complemented
3#21455400C211yesmaximal, characteristic, complemented
4#21447761C212yesmaximal, complemented
5#21447755C211yesmaximal, characteristic, complemented
6#21447750C211yesmaximal, characteristic, complemented
7#21447744C212yesmaximal, complemented
8#21447738C211yesmaximal, characteristic, complemented
9#21447733C211yesmaximal, characteristic, complemented
10#21447527C212yesmaximal, complemented
11C2×C61×C22⋊C16C211yesmaximal, characteristic, complemented
12C22×#11758222—21no—
13C2×#14519799—28no—
14C2×#14519799—21no—
15C2×#14519799—21no—
16C2×#14519799C2212yes—
17C2×#14519799C2212yes—
18C2×#14519799C2211yescharacteristic, complemented
19C22×Dic244C2211yescharacteristic
20C22×#11758190—21no—
21C22×D488C2211yescharacteristic
22#16840273—21no—
23#16840194—28no—
24C2×Dic488C2212yescomplemented
25C2×#14519722C2212yescomplemented
26C2×#14519722C2212yescomplemented
27C2×D976C2212yescomplemented
28#16840003C2211yescharacteristic
29#16840003C2211yescharacteristic, complemented
30#16839998C2211yescharacteristic
31#16839998C2211yescharacteristic, complemented
32#16839991—21no—
33#16839991—21no—
34#16839800C2211yescharacteristic, complemented
35#16839759—21no—
36#16839567C2212yescomplemented
37#16839567C2212yescomplemented
38#16839564C2212yescomplemented
39#16839564C2212yescomplemented
40C23×C8×C61C2211yescharacteristic
41C22×C16×C61C2212yescomplemented
42C61×C22⋊C16C2211yescharacteristic
43C61×C22⋊C16C2211yescharacteristic
44C61×C22⋊C16C2212yescomplemented
45C2×#11758222—28no—
46C2×#11758222—22no—
47C2×#11758222—22no—
48C2×#11758222—21no—
49C2×#11758222—44no—
50C2×#11758222—41no—
51C2×#11758222—41no—
52C22×Dic122—21no—
53C22×D244—21no—
54C22×C22⋊D61—41no—
55C22×C4×D61—41no—
56#14519799—28no—
57#14519799—28no—
58#14519799—24no—
59#14519799—24no—
60#14519799—24no—
61#14519799—24no—
62#14519799D418yescomplemented
63C2×Dic244—21no—
64C2×Dic244—24no—
65C2×Dic244C2311yescharacteristic
66C2×Dic244C2312yes—
67C2×#11758190—28no—
68C2×#11758190—22no—
69C2×#11758190—22no—
70C2×#11758190—21no—
71C2×D488—21no—
72C2×D488—24no—
73C2×D488C2311yescharacteristic
74C2×D488C2312yes—
75#14519760—41no—
76#14519756—21no—
77#14519756—21no—
78#14519751—21no—
79#14519751—21no—
80#14519746—41no—
81C4×C22⋊D61—41no—
82C4×C22⋊D61—41no—
83#14519736—21no—
84Dic488—24no—
85#14519722—24no—
86#14519722—24no—
87D976—24no—
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519709—21no—
91#14519702—21no—
92#14519702—21no—
93#14519699—21no—
94#14519699—21no—
95C23×C4×C61D411yescharacteristic
96C22×C8×C61—24no—
97C22×C8×C61D411yescharacteristic
98C22×C8×C61D411yescharacteristic
99C22×C8×C61D411yescharacteristic
100C22×C8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103C2×C16×C61—24no—
104C2×C16×C61C2312yes—
105C2×C16×C61C2312yes—
106C24×C61D811yescharacteristic
107C23×D61—41no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61D811yescharacteristic
111C22×C4×C61D811yescharacteristic
112C22×C4×C61D811yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C2×C22⋊D61—48no—
117C2×C22⋊D61—42no—
118C2×C22⋊D61—42no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C22×Dic61—41no—
123#11758222—28no—
124#11758222—28no—
125#11758222—48no—
126#11758222—48no—
127#11758222—44no—
128#11758222—44no—
129#11758222—42no—
130#11758222—42no—
131C2×D244—24no—
132C2×D244—22no—
133C2×D244—21no—
134C2×D244—42no—
135C2×D244—41no—
136C2×C4×D61—48no—
137C2×C4×D61—42no—
138C2×C4×D61—42no—
139C2×C4×D61—41no—
140C2×Dic122—24no—
141C2×Dic122—22no—
142C2×Dic122—21no—
143C2×Dic122—42no—
144C2×Dic122—41no—
145C2×C8×C61—22no—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C2×C8×C61C2×D411yescharacteristic
151C2×C8×C61C2×D411yescharacteristic
152C2×C8×C61C2×D411yescharacteristic
153C2×C8×C61C2×D414yes—
154C2×C8×C61C2411yescharacteristic
155C22⋊Dic61—41no—
156C22⋊Dic61—41no—
157C22⋊Dic61—41no—
158#11758198—41no—
159#11758198—41no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162#11758196—41no—
163#11758196—41no—
164C4×Dic61—41no—
165Dic244—24no—
166Dic244—22no—
167Dic244—22no—
168Dic244C2×D414yes—
169D488—24no—
170D488—22no—
171D488—22no—
172D488C2×D414yes—
173#11758190—28no—
174#11758190—28no—
175#11758190—42no—
176C16×C61—22no—
177C16×C61—22no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61—41no—
181C23×C61C2×D811yescharacteristic
182C23×C61C2×D811yescharacteristic
183C23×C61C2×D811yescharacteristic
184C22×D61—44no—
185C22×D61—42no—
186C22×D61—41no—
187C22×D61—82no—
188C22×D61—82no—
189C2×C4×C61—22no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61#12012yes—
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61AGL(1,ℤ/8)12yes—
201C2×C4×C61C22×D411yescharacteristic
202C22⋊D61—48no—
203C22⋊D61—48no—
204C22⋊D61—82no—
205C22⋊D61—82no—
206C22⋊D61—82no—
207C2×Dic61—44no—
208C2×Dic61—42no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212D244—24no—
213D244—44no—
214D244—41no—
215D244—42no—
216D244—41no—
217C4×D61—48no—
218C4×D61—48no—
219C4×D61—82no—
220Dic122—24no—
221Dic122—44no—
222Dic122—42no—
223Dic122—41no—
224Dic122—41no—
225C8×C61—21no—
226C8×C61—21no—
227C8×C61#12012yes—
228C8×C61C22×D412yes—
229#33516—611nomaximal, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—44no—
238C22×C61#44712yes—
239C22×C61#50812yescomplemented
240C22×C61C22×D811yescharacteristic
241C2×D61—44no—
242C2×D61—88no—
243C2×D61—82no—
244C2×D61—82no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—81no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61#44712yes—
251C4×C61C2×#12011yescharacteristic
252C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
253Dic61—44no—
254Dic61—81no—
255Dic61—81no—
256Dic61—81no—
257C22×#135—611no—
258C2×#508—612no—
259#3050—611no—
260#2189—612no—
261#2188—611no—
262#2187—611no—
263#2186—612no—
264#2185—611no—
265#2184—611no—
266#2138—612no—
267C2×C22⋊C16D6111yescharacteristic, complemented
268C2×C61—22no—
269C2×C61—22no—
270C2×C61—41no—
271C2×C61C2×#44711yescharacteristic
272C2×C61C2×#50811yescharacteristic
273C2×C61#341411yescharacteristic
274D61—84no—
275D61—161no—
276C22×#41—1221no—
277C2×#135—612no—
278C2×#135—611no—
279C2×#135—612no—
280C2×#135—1228no—
281C2×#135—1221no—
282C2×#135—1221no—
283C22×Q16—611no—
284C22×SD16—1221no—
285C22×D8—611no—
286C23×C8C2×D6111yescharacteristic
287#525—1221no—
288#508—1228no—
289C2×Q32—612no—
290C2×SD32—612no—
291C2×SD32—612no—
292C2×D16—612no—
293C22×C16C2×D6112yescomplemented
294#467—611no—
295#467—611no—
296#466—611no—
297#466—611no—
298#465—1221no—
299#465—1221no—
300#427—611no—
301#416—1221no—
302#358—612no—
303#358—612no—
304#357—612no—
305#357—612no—
306C22⋊C16C2×D6111yescharacteristic
307C22⋊C16C2×D6111yescharacteristic
308C22⋊C16C2×D6112yescomplemented
309C61#3351611yescharacteristic, complemented, Sylow
310C2×#41—1228no—
311C2×#41—1222no—
312C2×#41—1222no—
313C2×#41—1221no—
314C2×#41—2444no—
315C2×#41—2441no—
316C2×#41—2441no—
317C22×Q8—1221no—
318C22×D4—1221no—
319C22×D4—2441no—
320C23×C4—2441no—
321C23×C4D24411yescharacteristic
322#135—618no—
323#135—1224no—
324#135—1224no—
325#135—1228no—
326#135—1228no—
327#135—1224no—
328#135—1224no—
329C2×Q16—612no—
330C2×Q16—611no—
331C2×Q16—1224no—
332C2×Q16—1221no—
333C2×SD16—1228no—
334C2×SD16—1222no—
335C2×SD16—1222no—
336C2×SD16—1221no—
337C2×D8—612no—
338C2×D8—611no—
339C2×D8—1224no—
340C2×D8—1221no—
341C22×C8—24no—
342C22×C8D24411yescharacteristic
343C22×C8D24411yescharacteristic
344C22×C8D24411yescharacteristic
345C22×C8C22×D6111yescharacteristic
346C22×C8C22×D6111yescharacteristic
347C22×C8C22×D6111yescharacteristic
348#123—2441no—
349C22⋊Q8—1221no—
350C22⋊Q8—1221no—
351#121—1221no—
352#121—1221no—
353#120—2441no—
354C4×D4—2441no—
355C4×D4—2441no—
356#117—1221no—
357Q32—1224no—
358SD32—1224no—
359SD32—1224no—
360D16—1224no—
361C2×C16—24no—
362C2×C16C22×D6112yes—
363C2×C16C22×D6112yes—
364#107—611no—
365#107—611no—
366#106—1221no—
367#103—1221no—
368#103—1221no—
369#102—1221no—
370#102—1221no—
371C24—2441no—
372C24D48811yescharacteristic
373#41—1228no—
374#41—1228no—
375#41—2448no—
376#41—2444no—
377#41—2448no—
378#41—2442no—
379#41—2442no—
380#41—2444no—
381C2×Q8—1224no—
382C2×Q8—1222no—
383C2×Q8—1221no—
384C2×Q8—2442no—
385C2×Q8—2441no—
386C2×D4—1224no—
387C2×D4—1222no—
388C2×D4—1221no—
389C2×D4—2442no—
390C2×D4—2441no—
391C2×D4—2441no—
392C2×D4—2441no—
393C2×D4—2448no—
394C2×D4—2442no—
395C2×D4—2442no—
396C2×D4—2441no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—2448no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4D48811yescharacteristic
405C22×C4D48811yescharacteristic
406C22×C4D48811yescharacteristic
407C22×C4C2×D24411yescharacteristic
408C22×C4C2×D24411yescharacteristic
409C22×C4C2×D24411yescharacteristic
410Q16—614no—
411Q16—1224no—
412Q16—1222no—
413Q16—1222no—
414SD16—1228no—
415SD16—1228no—
416SD16—2442no—
417D8—614no—
418D8—1224no—
419D8—1222no—
420D8—1222no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8C2×D24411yescharacteristic
427C2×C8C2×D24411yescharacteristic
428C2×C8C2×D24411yescharacteristic
429C2×C8D4×D6114yes—
430C2×C8C23×D6111yescharacteristic
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C42—2441no—
441C16—22no—
442C16—22no—
443C23—22no—
444C23—22no—
445C23—41no—
446C23—4882no—
447C23—4882no—
448C23—2444no—
449C23—2441no—
450C23—2442no—
451C23C2×D48811yescharacteristic
452C23C2×D48811yescharacteristic
453C23C2×D48811yescharacteristic
454Q8—1224no—
455Q8—2444no—
456Q8—2441no—
457Q8—2441no—
458Q8—2442no—
459D4—1224no—
460D4—4882no—
461D4—4882no—
462D4—4882no—
463D4—2444no—
464D4—2448no—
465D4—2448no—
466D4—2441no—
467D4—2441no—
468D4—2442no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—4882no—
477C2×C4—2448no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2444no—
482C2×C4—2442no—
483C2×C4—2448no—
484C2×C4#1451974712yes—
485C2×C4C2×D48811yescharacteristic
486C2×C4C2×D48811yescharacteristic
487C2×C4C2×D48811yescharacteristic
488C2×C4#1451980512yes—
489C2×C4C22×D24411yescharacteristic
490C8—21no—
491C8—21no—
492C8#1451974712yes—
493C8C2×D4×D6112yes—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—44no—
502C22—4888no—
503C22—4881no—
504C22—4881no—
505C22—4881no—
506C22—4882no—
507C22—4882no—
508C22—2444no—
509C22#1683989812yes—
510C22#1684019412yescomplemented
511C22C22×D48811yescharacteristic
512C4—21no—
513C4—21no—
514C4—4881no—
515C4—4881no—
516C4—4881no—
517C4—2444no—
518C4#1683989812yes—
519C4C2×#1451974711yescharacteristic
520C4C2×#1451980511yescharacteristic
521C2—22no—
522C2—22no—
523C2—41no—
524C2—9761no—
525C2—4884no—
526C2C2×#1683989811yescharacteristic
527C2C2×#1684019411yescharacteristic
528C2#2145895511yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×C22⋊C16C2
socleC22×C61C22×D8
hypercenterC2×C22⋊C16D61
hypocenterC61#33516
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C22×#14519799C2semidirect
2. C2×#16840194C2semidirect
3. #21455400C2semidirect
4. #21447761C2semidirect
5. #21447755C2semidirect
6. #21447750C2semidirect
7. #21447744C2semidirect
8. #21447738C2semidirect
9. #21447733C2semidirect
10. #21447527C2semidirect
11. C2×C61×C22⋊C16C2semidirect
18. C2×#14519799C22semidirect
24. C2×Dic488C22semidirect
25. C2×#14519722C22semidirect
26. C2×#14519722C22semidirect
27. C2×D976C22semidirect
29. #16840003C22semidirect
31. #16839998C22semidirect
34. #16839800C22semidirect
36. #16839567C22semidirect
37. #16839567C22semidirect
38. #16839564C22semidirect
39. #16839564C22semidirect
41. C22×C16×C61C22semidirect
44. C61×C22⋊C16C22semidirect
62. #14519799D4semidirect
239. C22×C61#508semidirect
267. C2×C22⋊C16D61semidirect
293. C22×C16C2×D61semidirect
308. C22⋊C16C2×D61semidirect
309. C61#33516semidirect
510. C22#16840194semidirect

Maximal subgroups

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

subgroupindex
C22×#145197992
C2×#168401942
#214554002
#214477612
#214477552
#214477502
#214477442
#214477382
#214477332
#214475272
C2×C61×C22⋊C162
#3351661