Finite Group Databasebeta

← #29649608

Subgroups — #29649608

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454784C211yesmaximal, characteristic
2C8×Q8×D61C211yesmaximal, characteristic, complemented
3C4×#14519809C211yesmaximal, characteristic
4#21444696C211yesmaximal, characteristic, complemented
5#21444694C211yesmaximal, characteristic, complemented
6#21444693C211yesmaximal, characteristic, complemented
7#21444691C211yesmaximal, characteristic, complemented
8#21444667C211yesmaximal, characteristic, complemented
9#21444664C211yesmaximal, characteristic, complemented
10#21444662C211yesmaximal, characteristic, complemented
11#21444570C211yesmaximal, characteristic, complemented
12#21444212C211yesmaximal, characteristic, complemented
13#21444205C211yesmaximal, characteristic
14#21444105C211yesmaximal, characteristic, complemented
15C61×#1584C211yesmaximal, characteristic, complemented
16C2×#14519809C411yescharacteristic
17C4×#11758226C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16839893C2211yescharacteristic
20Q8×#92418C2211yescharacteristic
21C8×Dic122—21no—
22C8×Dic122C2211yescharacteristic
23#16839886—21no—
24#16839886C2211yescharacteristic
25#16839869C411yescharacteristic
26#16839866C411yescharacteristic
27#16839865C411yescharacteristic
28#16839861C411yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758190C2211yescharacteristic
31C4×#11758201C2211yescharacteristic
32#16839841C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839835—21no—
35#16839832—21no—
36#16839814—21no—
37#16839814C2211yescharacteristic
38#16839813C2211yescharacteristic
39#16839803C411yescharacteristic
40C4⋊C8×D61—21no—
41C4⋊C8×D61C2211yescharacteristic
42#16839769C411yescharacteristic
43#16839762C411yescharacteristic
44#16839714—21no—
45C4×#11758189C2211yescharacteristic
46C4×C8×D61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839513C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758226C2×C411yescharacteristic
68C2×Q8×D61C2×C411yescharacteristic
69#14519809—24no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758190C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189C2×C411yescharacteristic
76C2×#11758189C2×C411yescharacteristic
77C2×C8×D61—21no—
78C2×C8×D61D411yescharacteristic
79C2×C8×D61D411yescharacteristic
80Q8×Dic61C2×C411yescharacteristic
81Q8×Dic61C2×C411yescharacteristic
82C4×Dic122—21no—
83C4×Dic122C2311yescharacteristic
84#14519742—21no—
85#14519742C2×C411yescharacteristic
86C4×D244—21no—
87C4×D244C2311yescharacteristic
88#14519739—21no—
89#14519739C2×C411yescharacteristic
90#14519735—21no—
91#14519735C2×C411yescharacteristic
92C4⋊C4×D61—21no—
93C4⋊C4×D61C2×C411yescharacteristic
94C42×D61—21no—
95C42×D61—21no—
96C42×D61C2311yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519709C2×C411yescharacteristic
99#14519708C2×C411yescharacteristic
100C4⋊#92418—21no—
101C4⋊#92418—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519702C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519701C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519697C2×C411yescharacteristic
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519688—21no—
119#14519687C2×C411yescharacteristic
120#14519687C2×C411yescharacteristic
121C4×#92418—21no—
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×Q16×C61C2×C411yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147#11758226—22no—
148#11758226—22no—
149Q8×D61—22no—
150Q8×D61M1614yescomplemented
151C2×D244—21no—
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61C22×C411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61#4111yescharacteristic
161C2×Dic122—21no—
162C2×Dic122C22×C411yescharacteristic
163Q16×C61—22no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C42×C61—21no—
176C42×C61—21no—
177C42×C61C2411yescharacteristic
178#11758202—22no—
179#11758201—22no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205#11758190—22no—
206#11758189—22no—
207#11758189—22no—
208#11758189—42no—
209#11758189—42no—
210C8×D61—22no—
211C8×D61—41no—
212C8×D61—42no—
213C22×D61—21no—
214C22×D61C4×D411yescharacteristic
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61C2×M1612yes—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61C23×C411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C4×D411yescharacteristic
232D244—21no—
233D244—21no—
234D244—42no—
235C4×D61—24no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—42no—
244C4×D61C2×M1612yes—
245C4×D61#13112yes—
246Dic122—21no—
247Dic122—24no—
248Dic122C2×M1612yes—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61#13712yescomplemented
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#17870—611nomaximal, Sylow
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61#43512yes—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61C22×M1611yescharacteristic
277C4×C61C2×#13111yescharacteristic
278C4×C61C2×#13711yescharacteristic
279C4×C61#57511yescharacteristic
280Dic61—22no—
281Dic61—21no—
282Dic61—21no—
283Dic61—41no—
284Dic61—41no—
285Dic61#43512yes—
286#2965—611no—
287C2×C8×Q8—611no—
288C4×#137—611no—
289#1588—611no—
290#1588—611no—
291#1587—611no—
292#1587—611no—
293#1584—611no—
294#1584D6111yescharacteristic, complemented
295#1583—611no—
296#1583—611no—
297#1565—611no—
298#1479—611no—
299#1477—611no—
300#1451—611no—
301C2×C61C2×#43511yescharacteristic
302C2×C61C4×#13711yescharacteristic
303C2×C61#295511yescharacteristic
304D61—22no—
305D61—81no—
306C2×#137—611no—
307C4×#41—611no—
308C2×C4×Q8—611no—
309#446—611no—
310#446C2×D6111yescharacteristic
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—1221no—
315C8×Q8—1221no—
316C8×Q8C2×D6111yescharacteristic
317#441—611no—
318#441—611no—
319#440—611no—
320#440—611no—
321C4×Q16—611no—
322C4×Q16C2×D6111yescharacteristic
323C4×SD16—611no—
324C4×SD16—611no—
325#436—611no—
326#436—611no—
327#435—1221no—
328#435—1221no—
329#431—611no—
330#431—611no—
331#431—1221no—
332#428—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—1221no—
335#419—611no—
336#417—611no—
337C4×M16—611no—
338C4×M16—1221no—
339C2×C4×C8—611no—
340C2×C4×C8—1221no—
341#335—611no—
342#335C2×D6111yescharacteristic
343#334—611no—
344#334—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8C2×D6111yescharacteristic
350Q8⋊C8C2×D6111yescharacteristic
351D4⋊C8—611no—
352D4⋊C8—611no—
353#322—611no—
354#322—611no—
355#322—611no—
356#322C2×D6111yescharacteristic
357C61#1787011yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C22×Q8—611no—
360#137—1224no—
361C2×Q16—611no—
362C2×Q16C4×D6111yescharacteristic
363C2×SD16—611no—
364C2×SD16—611no—
365C2×M16—611no—
366C2×M16—611no—
367C2×M16—1221no—
368C2×M16—1221no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—1221no—
372C4×Q8—611no—
373C4×Q8—611no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—1221no—
377C4×Q8—1221no—
378C4×Q8C22×D6111yescharacteristic
379C4×Q8C22×D6111yescharacteristic
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384#117—611no—
385#117—1221no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1221no—
388C2×C42—611no—
389C2×C42—1221no—
390C2×C42—1221no—
391#107—611no—
392#107C4×D6111yescharacteristic
393#106—611no—
394#106—611no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8C22×D6111yescharacteristic
406C4⋊C8C22×D6111yescharacteristic
407#103—611no—
408#103—611no—
409#103—611no—
410#103—611no—
411#103C4×D6111yescharacteristic
412#103C4×D6111yescharacteristic
413#102—611no—
414#102—611no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419#97—21no—
420#97—611no—
421#97—611no—
422#97—1221no—
423C4×C8—21no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436#41—1222no—
437#41—1222no—
438C2×Q8—614no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1222no—
442C2×Q8C2×C4×D6111yescharacteristic
443C2×Q8C2×C4×D6111yescharacteristic
444C2×D4—611no—
445C2×D4—1221no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454Q16—22no—
455Q16—1222no—
456SD16—1222no—
457SD16—1222no—
458M16—1222no—
459M16—1222no—
460M16—2442no—
461M16—2442no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1222no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—2441no—
474C2×C8—2442no—
475C2×C8C2×C4×D6111yescharacteristic
476C2×C8C2×C4×D6111yescharacteristic
477C2×C8D4×D6111yescharacteristic
478C2×C8D4×D6111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—611no—
482C4⋊C4—611no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4C2×C4×D6111yescharacteristic
489C4⋊C4C2×C4×D6111yescharacteristic
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—21no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—1221no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C42C23×D6111yescharacteristic
504C23—611no—
505C23—1221no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—612no—
510Q8—1224no—
511Q8—1221no—
512Q8M16×D6112yes—
513D4—1221no—
514D4—1221no—
515D4—2442no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—611no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—1224no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4C22×C4×D6111yescharacteristic
538C2×C4C2×D4×D6111yescharacteristic
539C2×C4#41×D6111yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—1221no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C8#1451980912yescomplemented
554C22—612no—
555C22—1221no—
556C22—1221no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C4×D4×D6111yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—612no—
567C4—1221no—
568C4—1221no—
569C4—1222no—
570C4—2441no—
571C4—2441no—
572C4C2×M16×D6111yescharacteristic
573C4#131×D6111yescharacteristic
574C4C2×#1451980911yescharacteristic
575C4#1684055911yescharacteristic
576C2—1222no—
577C2—4881no—
578C2#435×D6111yescharacteristic
579C2C4×#1451980911yescharacteristic
580C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1584C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758226C2×C4
cosocleC42×C61C24
hypercenter#1584D61
hypocenterC61#17870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D61C2semidirect
4. #21444696C2semidirect
5. #21444694C2semidirect
6. #21444693C2semidirect
7. #21444691C2semidirect
8. #21444667C2semidirect
9. #21444664C2semidirect
10. #21444662C2semidirect
11. #21444570C2semidirect
12. #21444212C2semidirect
14. #21444105C2semidirect
15. C61×#1584C2semidirect
150. Q8×D61M16semidirect
255. C8×C61#137semidirect
294. #1584D61semidirect
357. C61#17870semidirect
553. C8#14519809semidirect

Maximal subgroups

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

subgroupindex
#214547842
C8×Q8×D612
C4×#145198092
#214446962
#214446942
#214446932
#214446912
#214446672
#214446642
#214446622
#214445702
#214442122
#214442052
#214441052
C61×#15842
#1787061