Finite Group Databasebeta

← #29836867

Subgroups — #29836867

Order 15616.

580 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#21457506C211yesmaximal, characteristic, complemented
2#21448053C211yesmaximal, characteristic, complemented
3#21448021C211yesmaximal, characteristic, complemented
4#21448010C211yesmaximal, characteristic, complemented
5#21447973C211yesmaximal, characteristic, complemented
6#21447913C211yesmaximal, characteristic, complemented
7#21447903C211yesmaximal, characteristic, complemented
8#21447874C211yesmaximal, characteristic, complemented
9#21447740C211yesmaximal, characteristic, complemented
10#21447730C211yesmaximal, characteristic, complemented
11C4×#14519718C211yesmaximal, characteristic, complemented
12D4×#11758185C211yesmaximal, characteristic, complemented
13#21447524C211yesmaximal, characteristic, complemented
14C2×#16839562C211yesmaximal, characteristic, complemented
15C61×#3339C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C22×D488C2211yescharacteristic
18#16840408—21no—
19C2×#14519721C2211yescharacteristic, complemented
20C2×#14519718C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22C22×#11758185C2211yescharacteristic
23C22×#11758185C2211yescharacteristic, complemented
24#16840146C2211yescharacteristic
25#16840003C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839978—21no—
28#16839915—21no—
29#16839909—21no—
30C4×D488C2211yescharacteristic
31#16839589C2211yescharacteristic, complemented
32#16839587C2211yescharacteristic, complemented
33#16839587C2211yescharacteristic, complemented
34C4⋊#11758185C2211yescharacteristic, complemented
35#16839565C2211yescharacteristic, complemented
36#16839565C2211yescharacteristic, complemented
37#16839565C2211yescharacteristic, complemented
38#16839563C2211yescharacteristic, complemented
39#16839562C2211yescharacteristic
40#16839562C2211yescharacteristic
41#16839562C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic, complemented
47C4×#11758185C2211yescharacteristic, complemented
48C61×#553—21no—
49C61×#499C2211yescharacteristic, complemented
50C61×#482—21no—
51C61×#481—21no—
52C61×#478—21no—
53C61×#466C2211yescharacteristic
54C61×#466C2211yescharacteristic, complemented
55C4×D8×C61C2211yescharacteristic, complemented
56C8×D4×C61C2211yescharacteristic
57C61×#427C2211yescharacteristic, complemented
58C2×#107×C61C2211yescharacteristic
59C2×#11758222—21no—
60C22×D244—21no—
61#14519799—22no—
62#14519799—41no—
63C2×Dic244C2311yescharacteristic
64C2×#11758190—21no—
65C2×#11758190—21no—
66C2×D488—22no—
67C2×D488—21no—
68C2×D488—41no—
69C2×D488C2311yescharacteristic
70C2×D488C2311yescharacteristic
71#14519765—21no—
72#14519762—41no—
73#14519756—21no—
74#14519751—21no—
75#14519750—41no—
76#14519745—41no—
77C4×D244—21no—
78C22⋊C4×D61—41no—
79#14519721—41no—
80#14519718—22no—
81#14519718—41no—
82C2×#11758185—41no—
83C2×#11758185—41no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519702—21no—
90#14519699—21no—
91#14519699—21no—
92C2×D8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#126×C61—41no—
96#125×C61—21no—
97#123×C61—41no—
98#121×C61—21no—
99#121×C61—21no—
100#121×C61—41no—
101C4×D4×C61—21no—
102C4×D4×C61—41no—
103C4×D4×C61D411yescharacteristic
104#117×C61—21no—
105C2×C4⋊C4×C61—21no—
106#107×C61—21no—
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111#106×C61—21no—
112C4⋊C8×C61D411yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C2×D4×C61—21no—
121C2×D4×C61—41no—
122C2×D4×C61—41no—
123C2×D4×C61D811yescharacteristic
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130#11758222—42no—
131#11758222—81no—
132C2×D244—21no—
133C2×D244—21no—
134C2×D244—42no—
135C2×D244—41no—
136C2×D244—81no—
137C2×C4×D61—41no—
138C2×C4×D61—41no—
139C2×Dic122—21no—
140D8×C61—21no—
141D8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61C2411yescharacteristic
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61D811yescharacteristic
157C22⋊C4×C61—41no—
158C22⋊C4×C61—41no—
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C22⋊C4×C61D811yescharacteristic
162C22⋊C4×C61D811yescharacteristic
163C42×C61—41no—
164C42×C61C2×D411yescharacteristic
165C22⋊Dic61—41no—
166#11758198—41no—
167#11758198—41no—
168#11758198—41no—
169#11758198—41no—
170C4⋊Dic61—21no—
171#11758196—41no—
172Dic244—21no—
173Dic244—21no—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—42no—
178D488#4112yes—
179#11758190—42no—
180#11758190—81no—
181#11758185—21no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61C2×D811yescharacteristic
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—82no—
191C22×D61—82no—
192C22×D61—161no—
193D4×C61—22no—
194D4×C61—41no—
195D4×C61—41no—
196D4×C61—82no—
197D4×C61—161no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—161no—
206C2×C4×C61—161no—
207C2×C4×C61C2×D811yescharacteristic
208C2×C4×C61C2×D811yescharacteristic
209C2×C4×C61C2×D811yescharacteristic
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C22⋊D61—82no—
213C22⋊D61—161no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216D244—22no—
217D244—41no—
218D244—41no—
219D244—41no—
220D244—82no—
221C4×D61—82no—
222C4×D61—161no—
223Dic122—41no—
224Dic122—41no—
225C8×C61—21no—
226C8×C61—21no—
227C8×C61—21no—
228C8×C61C2×#4111yescharacteristic
229C8×C61H(5,𝔽2)11yescharacteristic
230#33864—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61#50812yes—
240C22×C61C22×D811yescharacteristic
241C2×D61—42no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—164no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—81no—
253C4×C61—81no—
254C4×C61—81no—
255C4×C61#54611yescharacteristic
256C4×C61#57711yescharacteristic
257Dic61—81no—
258Dic61—81no—
259#3339D6111yescharacteristic, complemented
260#3280—611no—
261#2242—611no—
262#2236—611no—
263#2234—611no—
264#2228—611no—
265#2217—611no—
266#2215—611no—
267#2210—611no—
268#2186—611no—
269#2184—611no—
270C4×D16—611no—
271D4×C16—611no—
272#2138—611no—
273C2×#357—611no—
274C2×C61—22no—
275C2×C61—41no—
276C2×C61—161no—
277C2×C61#329411yescharacteristic
278C2×C61C2×#50811yescharacteristic
279C2×C61#341511yescharacteristic
280D61—82no—
281D61—161no—
282C2×#135—611no—
283C22×D8—611no—
284#553—21no—
285#546—1221no—
286C2×SD32—611no—
287C2×D16—611no—
288C2×D16—611no—
289C22×C16—611no—
290C22×C16—611no—
291#499C2×D6111yescharacteristic, complemented
292#495—611no—
293#482—21no—
294#481—21no—
295#478—21no—
296#467—611no—
297#466—611no—
298#466C2×D6111yescharacteristic
299#466C2×D6111yescharacteristic, complemented
300#463—1221no—
301#450—1221no—
302#449—1221no—
303C4×D8—611no—
304C4×D8C2×D6111yescharacteristic, complemented
305C8×D4C2×D6111yescharacteristic
306#427C2×D6111yescharacteristic, complemented
307C2×#107C2×D6111yescharacteristic
308#367—611no—
309#366—611no—
310#366—611no—
311C4⋊C16—611no—
312#358—611no—
313#358—611no—
314#358—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322C22⋊C16—611no—
323C22⋊C16—611no—
324C4×C16—611no—
325C61#3386411yescharacteristic, complemented, Sylow
326C2×#41—1221no—
327C22×D4—1221no—
328#135—1222no—
329#135—2441no—
330C2×Q16—611no—
331C2×SD16—1221no—
332C2×SD16—1221no—
333C2×D8—611no—
334C2×D8—611no—
335C2×D8—1222no—
336C2×D8—1221no—
337C2×D8—2441no—
338C2×D8C22×D6111yescharacteristic
339C22×C8C22×D6111yescharacteristic
340C22×C8C22×D6111yescharacteristic
341#126—41no—
342#125—21no—
343#124—1221no—
344#123—41no—
345#123—2441no—
346C22⋊Q8—1221no—
347#121—21no—
348#121—21no—
349#121—41no—
350#121—1221no—
351#121—2441no—
352#120—2441no—
353C4×D4—21no—
354C4×D4—41no—
355C4×D4—1221no—
356C4×D4C22⋊D6111yescharacteristic
357#117—21no—
358C2×C4⋊C4—21no—
359C2×C22⋊C4—2441no—
360SD32—2441no—
361D16—1222no—
362D16—2441no—
363C2×C16—611no—
364C2×C16—611no—
365C2×C16—611no—
366C2×C16—611no—
367C2×C16—2441no—
368C2×C16—2441no—
369#107—21no—
370#107—611no—
371#107C22×D6111yescharacteristic
372#107C22×D6111yescharacteristic
373#107C22×D6111yescharacteristic
374#106—21no—
375#106—21no—
376C4⋊C8C22⋊D6111yescharacteristic
377#103—1221no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—1221no—
382#102—1221no—
383C22⋊C8C22⋊D6111yescharacteristic
384C22⋊C8C22⋊D6111yescharacteristic
385C4×C8C22×D6111yescharacteristic
386C24—2441no—
387#41—4881no—
388#41—2442no—
389C2×Q8—1221no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—1221no—
394C2×D4—1221no—
395C2×D4—4881no—
396C2×D4—2442no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4#1175819911yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4C2×C22⋊D6111yescharacteristic
406C22×C4C2×C22⋊D6111yescharacteristic
407Q16—1221no—
408Q16—1221no—
409SD16—4881no—
410SD16—2442no—
411D8—21no—
412D8—21no—
413D8—612no—
414D8—1221no—
415D8—1221no—
416D8—1221no—
417D8—2442no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×C22⋊D6111yescharacteristic
423C2×C8C2×C22⋊D6111yescharacteristic
424C2×C8C2×C22⋊D6111yescharacteristic
425C2×C8C23×D6111yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—1221no—
433C4⋊C4—2441no—
434C4⋊C4#1175819911yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C22⋊C4—2441no—
444C22⋊C4#1175819911yescharacteristic
445C22⋊C4#1175819911yescharacteristic
446C42—41no—
447C42C2×C22⋊D6111yescharacteristic
448C16—1221no—
449C16—1221no—
450C16—1221no—
451C16—1221no—
452C23—41no—
453C23—9761no—
454C23—4882no—
455C23—4882no—
456C23—2441no—
457C23—2441no—
458C23C2×#1175819911yescharacteristic
459C23C2×#1175819911yescharacteristic
460Q8—2441no—
461Q8—2441no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—161no—
467D4—1222no—
468D4—9761no—
469D4—4882no—
470D4—4882no—
471D4—2441no—
472D4—2441no—
473D4—2441no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—161no—
482C2×C4—161no—
483C2×C4—9761no—
484C2×C4—4882no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4C2×#1175819911yescharacteristic
488C2×C4C2×#1175819911yescharacteristic
489C2×C4C2×#1175819911yescharacteristic
490C2×C4C2×#1175819911yescharacteristic
491C2×C4C22×C22⋊D6111yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#41×D6111yescharacteristic
496C8#1451982311yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—9764no—
506C22—4881no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22—2442no—
512C22#1684019212yes—
513C22C22×#1175819911yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—4881no—
522C4—4881no—
523C4#1684040011yescharacteristic
524C4#1684057011yescharacteristic
525C2—22no—
526C2—41no—
527C2—161no—
528C2—9761no—
529C2—4882no—
530C2#2145762611yescharacteristic
531C2C2×#1684019211yescharacteristic
532C2#2145895811yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3339C2
socleC22×C61C22×D8
hypercenter#3339D61
hypocenterC61#33864
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #21457506C2semidirect
2. #21448053C2semidirect
3. #21448021C2semidirect
4. #21448010C2semidirect
5. #21447973C2semidirect
6. #21447913C2semidirect
7. #21447903C2semidirect
8. #21447874C2semidirect
9. #21447740C2semidirect
10. #21447730C2semidirect
11. C4×#14519718C2semidirect
12. D4×#11758185C2semidirect
13. #21447524C2semidirect
14. C2×#16839562C2semidirect
15. C61×#3339C2semidirect
19. C2×#14519721C22semidirect
23. C22×#11758185C22semidirect
31. #16839589C22semidirect
32. #16839587C22semidirect
33. #16839587C22semidirect
34. C4⋊#11758185C22semidirect
35. #16839565C22semidirect
36. #16839565C22semidirect
37. #16839565C22semidirect
38. #16839563C22semidirect
46. C22⋊#11758185C22semidirect
47. C4×#11758185C22semidirect
49. C61×#499C22semidirect
54. C61×#466C22semidirect
55. C4×D8×C61C22semidirect
57. C61×#427C22semidirect
259. #3339D61semidirect
291. #499C2×D61semidirect
299. #466C2×D61semidirect
304. C4×D8C2×D61semidirect
306. #427C2×D61semidirect
325. C61#33864semidirect

Maximal subgroups

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

subgroupindex
#214575062
#214480532
#214480212
#214480102
#214479732
#214479132
#214479032
#214478742
#214477402
#214477302
C4×#145197182
D4×#117581852
#214475242
C2×#168395622
C61×#33392
#3386461