Finite Group Databasebeta

← #29649965

Subgroups — #29649965

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455833C211yesmaximal, characteristic
2#21454797C211yesmaximal, characteristic, complemented
3C8×#11758224C211yesmaximal, characteristic, complemented
4#21444695C211yesmaximal, characteristic, complemented
5#21444692C211yesmaximal, characteristic, complemented
6#21444676C211yesmaximal, characteristic, complemented
7#21444643C211yesmaximal, characteristic, complemented
8#21444637C211yesmaximal, characteristic, complemented
9#21444628C211yesmaximal, characteristic, complemented
10#21444628C211yesmaximal, characteristic, complemented
11#21444596C211yesmaximal, characteristic, complemented
12#21444250C211yesmaximal, characteristic, complemented
13#21444224C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1586C211yesmaximal, characteristic, complemented
16#16840294C2211yescharacteristic
17C4×#11758224C2211yescharacteristic
18#16840105C411yescharacteristic
19#16840084C411yescharacteristic
20#16840068C411yescharacteristic
21#16840060C411yescharacteristic
22#16839983C411yescharacteristic
23#16839975C411yescharacteristic
24#16839925C411yescharacteristic
25#16839904C411yescharacteristic
26#16839892C2211yescharacteristic
27C8×Dic122C2211yescharacteristic
28#16839886C2211yescharacteristic
29#16839886C2211yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758200C2211yescharacteristic
33#16839831—21no—
34D4×#92418C2211yescharacteristic
35D4×#92418C2211yescharacteristic
36C8×C22⋊D61—21no—
37#16839825—21no—
38#16839825—21no—
39#16839820—21no—
40#16839818C2211yescharacteristic
41#16839814C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839812—21no—
45#16839720—21no—
46C2×C8×Dic61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839492C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758224C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C22×#92418—21no—
72C22×#92418—21no—
73C2×C8×D61D411yescharacteristic
74C2×C8×D61D411yescharacteristic
75#14519770—21no—
76#14519768C2×C411yescharacteristic
77#14519764C2×C411yescharacteristic
78#14519759—21no—
79#14519757C2×C411yescharacteristic
80#14519748C2×C411yescharacteristic
81C4×Dic122C2311yescharacteristic
82C4×Dic122C2311yescharacteristic
83#14519742C2×C411yescharacteristic
84D4×Dic61C2×C411yescharacteristic
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87#14519737—21no—
88#14519736—21no—
89#14519735C2×C411yescharacteristic
90#14519733—21no—
91C2×C4×Dic61—21no—
92C42×D61C2311yescharacteristic
93#14519711C2×C411yescharacteristic
94#14519708C2×C411yescharacteristic
95#14519708C2×C411yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519706—21no—
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706C2×C411yescharacteristic
104#14519706C2×C411yescharacteristic
105#14519702C2×C411yescharacteristic
106#14519702C2×C411yescharacteristic
107#14519700C2×C411yescharacteristic
108#14519700C2×C411yescharacteristic
109#14519698C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689C2×C411yescharacteristic
117#14519689C2×C411yescharacteristic
118#14519687—21no—
119#14519687—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×D8×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131C22×C8×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#107×C61C2×C411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#102×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×D4×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152#11758224—22no—
153#11758224—22no—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61#4111yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159D8×C61—22no—
160M16×C61—42no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—42no—
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61C22×C411yescharacteristic
170C4⋊C4×C61C22×C411yescharacteristic
171C22⋊C4×C61—21no—
172C22⋊C4×C61—21no—
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175C22⋊Dic61—21no—
176C22⋊Dic61—21no—
177C22⋊Dic61—21no—
178#11758200—22no—
179#11758200—22no—
180#11758198—21no—
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—42no—
201C2×#92418—42no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206Dic244—22no—
207C8×D61—41no—
208C8×D61—41no—
209C23×C61—21no—
210C23×C61—21no—
211C22×D61C4×D411yescharacteristic
212D4×C61—21no—
213D4×C61—21no—
214D4×C61—21no—
215D4×C61#13112yes—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C22⋊D61—24no—
226C22⋊D61—42no—
227C2×Dic61—24no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—42no—
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—41no—
241Dic122—21no—
242Dic122—21no—
243Dic122—21no—
244Dic122#13112yes—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#17909—611nomaximal, Sylow
260C22×C61—22no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—21no—
270C4×C61—21no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61C2×#13111yescharacteristic
274C4×C61C2×#13111yescharacteristic
275C4×C61#57511yescharacteristic
276C4×C61#57511yescharacteristic
277Dic61—22no—
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284#3102—611no—
285#2966—611no—
286C8×#41—611no—
287#1588—611no—
288#1587—611no—
289#1586D6111yescharacteristic, complemented
290#1585—611no—
291#1580—611no—
292#1579—611no—
293SD16⋊C8—611no—
294SD16⋊C8—611no—
295#1572—611no—
296#1488—611no—
297#1482—611no—
298#1452—611no—
299C2×C61—42no—
300C2×C61—81no—
301C2×C61#292911yescharacteristic
302C2×C61#294311yescharacteristic
303C2×C61#295511yescharacteristic
304D61—41no—
305#529—611no—
306C4×#41—611no—
307#485—611no—
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463—611no—
313#452—611no—
314#449—611no—
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8C2×D6111yescharacteristic
323#436C2×D6111yescharacteristic
324#435—1221no—
325C8×D4—611no—
326C8×D4—611no—
327C8×D4—1221no—
328C8×D4—1221no—
329C8×D4—1221no—
330C8×D4C2×D6111yescharacteristic
331#433—1221no—
332#432—611no—
333#431—611no—
334#431—611no—
335#431—611no—
336#431—1221no—
337#405—1221no—
338C2×C4×C8—611no—
339C2×C4×C8—1221no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334C2×D6111yescharacteristic
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8C2×D6111yescharacteristic
351D4⋊C8C2×D6111yescharacteristic
352#322—611no—
353#322—611no—
354#322—611no—
355#322C2×D6111yescharacteristic
356C61#1790911yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16—611no—
361C2×D8C4×D6111yescharacteristic
362C2×M16—21no—
363C22×C8—21no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—1221no—
367C22×C8—1221no—
368#126—1221no—
369#125—611no—
370#124—611no—
371#123—1221no—
372C22⋊Q8—611no—
373#121—611no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—1221no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4C22×D6111yescharacteristic
382C4×D4C22×D6111yescharacteristic
383#117—611no—
384#117—1221no—
385#117—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388#107—611no—
389#107C4×D6111yescharacteristic
390#106—611no—
391#106—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403#103—611no—
404#103—611no—
405#103—611no—
406#103—611no—
407#102—611no—
408#102—611no—
409#102C4×D6111yescharacteristic
410#102C4×D6111yescharacteristic
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—611no—
414C22⋊C8—611no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—1221no—
421#97—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8C22×D6111yescharacteristic
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434#41—1222no—
435#41—1222no—
436C2×Q8—611no—
437C2×Q8—611no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4C2×C4×D6111yescharacteristic
441C2×D4C2×C4×D6111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—1221no—
448C22×C4—1221no—
449Q16—1222no—
450SD16—1222no—
451SD16—1222no—
452D8—22no—
453M16—42no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—42no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—2441no—
466C2×C8—2441no—
467C2×C8—2442no—
468C2×C8—2442no—
469C2×C8C2×C4×D6111yescharacteristic
470C2×C8C2×C4×D6111yescharacteristic
471C2×C8D4×D6111yescharacteristic
472C2×C8D4×D6111yescharacteristic
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C2×C4×D6111yescharacteristic
482C4⋊C4C2×C4×D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42C23×D6111yescharacteristic
499C23—21no—
500C23—21no—
501C23—611no—
502Q8—612no—
503Q8—1221no—
504Q8—1221no—
505Q8—1221no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—1224no—
510D4—2442no—
511D4#1451978512yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—1224no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—2441no—
531C2×C4—2442no—
532C2×C4C22×C4×D6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4#41×D6111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C22—22no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—1221no—
556C22—1221no—
557C22—1221no—
558C22C4×D4×D6111yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—1221no—
563C4—1221no—
564C4—1221no—
565C4—1222no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4#131×D6111yescharacteristic
570C4C2×#1451978511yescharacteristic
571C4#1684055811yescharacteristic
572C4#1684055811yescharacteristic
573C2—42no—
574C2—81no—
575C2—2441no—
576C2#2145451011yescharacteristic
577C2#2145461611yescharacteristic
578C2#2145471711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1586C2
socleC22×C61C2×C4×D4
prime radical#16839904C4
cosocleC42×C61C24
hypercenter#1586D61
hypocenterC61#17909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #21454797C2semidirect
3. C8×#11758224C2semidirect
4. #21444695C2semidirect
5. #21444692C2semidirect
6. #21444676C2semidirect
7. #21444643C2semidirect
8. #21444637C2semidirect
9. #21444628C2semidirect
10. #21444628C2semidirect
11. #21444596C2semidirect
12. #21444250C2semidirect
13. #21444224C2semidirect
14. #21444110C2semidirect
15. C61×#1586C2semidirect
289. #1586D61semidirect
356. C61#17909semidirect

Maximal subgroups

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

subgroupindex
#214558332
#214547972
C8×#117582242
#214446952
#214446922
#214446762
#214446432
#214446372
#214446282
#214445962
#214442502
#214442242
#214441102
C61×#15862
#1790961