Finite Group Databasebeta

← #29650960

Subgroups — #29650960

Order 15616.

616 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#21455837C211yesmaximal, characteristic
2#21454823C211yesmaximal, characteristic, complemented
3#21444707C211yesmaximal, characteristic, complemented
4#21444702C211yesmaximal, characteristic, complemented
5#21444669C211yesmaximal, characteristic, complemented
6#21444662C211yesmaximal, characteristic, complemented
7#21444660C211yesmaximal, characteristic, complemented
8#21444646C211yesmaximal, characteristic, complemented
9C8×#11758202C211yesmaximal, characteristic, complemented
10C8×#11758201C211yesmaximal, characteristic, complemented
11#21444600C211yesmaximal, characteristic, complemented
12#21444277C211yesmaximal, characteristic, complemented
13#21444201C211yesmaximal, characteristic, complemented
14M16×#92418C211yesmaximal, characteristic, complemented
15C61×#2971C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840103C411yescharacteristic
18#16840086C411yescharacteristic
19#16840069C411yescharacteristic
20#16840062C411yescharacteristic
21#16839984C411yescharacteristic
22#16839977C411yescharacteristic
23#16839924C411yescharacteristic
24#16839907C411yescharacteristic
25#16839892C2211yescharacteristic
26C8×Dic122C2211yescharacteristic
27C4×#11758202C2211yescharacteristic
28C4×#11758201C2211yescharacteristic
29C4×#11758200C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839838—21no—
33#16839831—21no—
34C8×D244C2211yescharacteristic
35#16839824—21no—
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839719—21no—
39C2×C4×#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46#16839492C2211yescharacteristic
47#16839492C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839483C2211yescharacteristic
53#16839483C2211yescharacteristic
54C8×#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436—21no—
60C61×#436—21no—
61C61×#436C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#432—21no—
64C61×#432C2211yescharacteristic
65C4×M16×C61—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758189—21no—
72C22×#92418—21no—
73C2×C8×D61—21no—
74#14519771—21no—
75#14519769C2×C411yescharacteristic
76#14519765C2×C411yescharacteristic
77#14519760—21no—
78#14519756C2×C411yescharacteristic
79#14519751C2×C411yescharacteristic
80C4×Dic122C2311yescharacteristic
81C4×D244C2311yescharacteristic
82C4×C22⋊D61—21no—
83#14519734—21no—
84#14519710C2×C411yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88C4⋊#92418C2×C411yescharacteristic
89C4⋊#92418C2×C411yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92#14519706—21no—
93#14519706—21no—
94#14519701C2×C411yescharacteristic
95#14519701C2×C411yescharacteristic
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519698C2×C411yescharacteristic
99#14519698C2×C411yescharacteristic
100#14519697C2×C411yescharacteristic
101#14519697C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418C2×C411yescharacteristic
104C22⋊#92418C2×C411yescharacteristic
105#14519689—21no—
106#14519689—21no—
107#14519687—21no—
108C4×#92418—21no—
109C4×#92418—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61C2×C411yescharacteristic
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61D411yescharacteristic
119C2×M16×C61D411yescharacteristic
120C4×Q8×C61C2×C411yescharacteristic
121C4×Q8×C61C2311yescharacteristic
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61C2×C411yescharacteristic
125C4×D4×C61C2311yescharacteristic
126#117×C61—21no—
127#117×C61C2×C411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137#97×C61—21no—
138#97×C61D411yescharacteristic
139#97×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—41no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×Dic122C22×C411yescharacteristic
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—42no—
162M16×C61—42no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61C22×C411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183C22⋊Dic61—21no—
184#11758202—22no—
185#11758201—22no—
186#11758200—41no—
187#11758199—41no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—42no—
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208#11758189—42no—
209C8×D61—42no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213Q8×C61—21no—
214Q8×C61#13112yes—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—42no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—81no—
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C23×C411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C22⋊D61—81no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240D244—21no—
241D244—21no—
242C4×D61—41no—
243C4×D61—41no—
244Dic122—21no—
245Dic122—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61#13512yes—
251C8×C61#13512yes—
252#92418—22no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#92418—21no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#17999—611nomaximal, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61C2×C4×D411yescharacteristic
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—22no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61C2×#13111yescharacteristic
279C4×C61#56811yescharacteristic
280C4×C61C2×#13511yescharacteristic
281C4×C61C2×#13511yescharacteristic
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285#3102—611no—
286#2971D6111yescharacteristic, complemented
287#2969—611no—
288#1590—611no—
289#1589—611no—
290#1584—611no—
291#1583—611no—
292#1583—611no—
293#1581—611no—
294C8×Q16—611no—
295C8×SD16—611no—
296#1572—611no—
297#1494—611no—
298#1476—611no—
299C8×M16—611no—
300C2×C61—41no—
301C2×C61—81no—
302C2×C61#293311yescharacteristic
303C2×C61C4×#13511yescharacteristic
304C2×C61#295611yescharacteristic
305D61—81no—
306#529—611no—
307C4×#41C2×D6111yescharacteristic
308#485—611no—
309#482—611no—
310#479—611no—
311#478—611no—
312#464—611no—
313#463—611no—
314#452—611no—
315#449—611no—
316#446—611no—
317C8×Q8—611no—
318C8×Q8C2×D6111yescharacteristic
319C8×Q8C2×D6111yescharacteristic
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×D8—611no—
324#436—21no—
325#436—21no—
326#436—611no—
327#436—1221no—
328#436C2×D6111yescharacteristic
329#436C2×D6111yescharacteristic
330#435—1221no—
331C8×D4—611no—
332#433—1221no—
333#432—21no—
334#432C2×D6111yescharacteristic
335#431—611no—
336#431—611no—
337#405—1221no—
338C4×M16—21no—
339C4×M16C2×D6111yescharacteristic
340C2×C4×C8—611no—
341#335—611no—
342#335—611no—
343#334—611no—
344#334—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353#322—611no—
354#322—611no—
355C82—611no—
356C82—611no—
357C61#1799911yescharacteristic, complemented, Sylow
358C2×#41C4×D6111yescharacteristic
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8—611no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—1221no—
366C2×M16C22⋊D6111yescharacteristic
367C2×M16C22⋊D6111yescharacteristic
368C22×C8—1221no—
369C22×C8—1221no—
370#126—1221no—
371#125—611no—
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375#121—611no—
376C4×Q8—611no—
377C4×Q8C4×D6111yescharacteristic
378C4×Q8C22×D6111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4C4×D6111yescharacteristic
384C4×D4C22×D6111yescharacteristic
385#117—21no—
386#117—1221no—
387#117C4×D6111yescharacteristic
388C2×C42—21no—
389C2×C42C22×D6111yescharacteristic
390#107—611no—
391#107—611no—
392#106—611no—
393#106—611no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404#103—611no—
405#103—611no—
406#103—611no—
407#103—611no—
408#102—611no—
409#102—611no—
410#102—611no—
411#102—611no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—21no—
421#97—1221no—
422#97C22⋊D6111yescharacteristic
423#97C22⋊D6111yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—22no—
436#41—41no—
437C2×Q8—611no—
438C2×Q8C2×C4×D6111yescharacteristic
439C2×D4—21no—
440C2×D4—611no—
441C2×D4—1221no—
442C2×D4C2×C4×D6111yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—1221no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4#1175822211yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450Q16—1222no—
451SD16—1222no—
452SD16—2441no—
453D8—2441no—
454M16—22no—
455M16—22no—
456M16—42no—
457M16—42no—
458M16—2442no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—2442no—
470C2×C8—2442no—
471C2×C8C2×C22⋊D6111yescharacteristic
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—611no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4C2×C4×D6111yescharacteristic
484C4⋊C4C2×C4×D6111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—1221no—
497C42C2×C4×D6111yescharacteristic
498C42#1175822211yescharacteristic
499C42C2×C22⋊D6111yescharacteristic
500C42C23×D6111yescharacteristic
501C23—21no—
502C23—1221no—
503C23C4×C22⋊D6111yescharacteristic
504Q8—21no—
505Q8—1221no—
506Q8—1221no—
507Q8#1451978512yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—1221no—
512D4—1221no—
513D4—4881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4C4×C22⋊D6111yescharacteristic
532C2×C4C4×C22⋊D6111yescharacteristic
533C2×C4C4×C22⋊D6111yescharacteristic
534C2×C4C22×C4×D6111yescharacteristic
535C2×C4C22×C22⋊D6111yescharacteristic
536C2×C4C2×#1175822211yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—1222no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8#1451979712yes—
550C8#1451979712yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C2×C4×C22⋊D6111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—22no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4C2×#1451978511yescharacteristic
572C4#1684052811yescharacteristic
573C4C2×#1451979711yescharacteristic
574C4C2×#1451979711yescharacteristic
575C2—41no—
576C2—81no—
577C2—4881no—
578C2#2145454411yescharacteristic
579C2C4×#1451979711yescharacteristic
580C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2971C2
socleC22×C61C2×C4×D4
prime radical#16839907C4
cosocleC42×C61C24
hypercenter#2971D61
hypocenterC61#17999
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #21454823C2semidirect
3. #21444707C2semidirect
4. #21444702C2semidirect
5. #21444669C2semidirect
6. #21444662C2semidirect
7. #21444660C2semidirect
8. #21444646C2semidirect
9. C8×#11758202C2semidirect
10. C8×#11758201C2semidirect
11. #21444600C2semidirect
12. #21444277C2semidirect
13. #21444201C2semidirect
14. M16×#92418C2semidirect
15. C61×#2971C2semidirect
286. #2971D61semidirect
357. C61#17999semidirect

Maximal subgroups

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

subgroupindex
#214558372
#214548232
#214447072
#214447022
#214446692
#214446622
#214446602
#214446462
C8×#117582022
C8×#117582012
#214446002
#214442772
#214442012
M16×#924182
C61×#29712
#1799961