Finite Group Databasebeta

← #29651001

Subgroups — #29651001

Order 15616.

610 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#21455839C211yesmaximal, characteristic
2#21454834C211yesmaximal, characteristic, complemented
3#21454823C211yesmaximal, characteristic, complemented
4#21444729C211yesmaximal, characteristic, complemented
5#21444723C211yesmaximal, characteristic, complemented
6#21444692C211yesmaximal, characteristic, complemented
7#21444685C211yesmaximal, characteristic, complemented
8#21444678C211yesmaximal, characteristic, complemented
9#21444678C211yesmaximal, characteristic, complemented
10#21444644C211yesmaximal, characteristic, complemented
11#21444633C211yesmaximal, characteristic, complemented
12#21444599C211yesmaximal, characteristic, complemented
13#21444280C211yesmaximal, characteristic, complemented
14#21444202C211yesmaximal, characteristic, complemented
15C61×#1451C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840104C411yescharacteristic
19#16840087C411yescharacteristic
20#16840070C411yescharacteristic
21#16840063C411yescharacteristic
22#16839985C411yescharacteristic
23#16839978C411yescharacteristic
24#16839926C411yescharacteristic
25#16839909C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839892C2211yescharacteristic
28#16839892C2211yescharacteristic
29C8×Dic122C2211yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758190C2211yescharacteristic
32C4×#11758190C2211yescharacteristic
33C4×D488C2211yescharacteristic
34#16839841C2211yescharacteristic
35#16839838—21no—
36#16839831—21no—
37#16839831—21no—
38#16839831—21no—
39C8×D244C2211yescharacteristic
40C8×D244C2211yescharacteristic
41C8×D244C2211yescharacteristic
42#16839824—21no—
43#16839819C2211yescharacteristic
44#16839817—21no—
45#16839815C2211yescharacteristic
46#16839719—21no—
47#97×D61—21no—
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839491C2211yescharacteristic
57#16839491C2211yescharacteristic
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C4×M16×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×#322C2211yescharacteristic
64C61×#322C2211yescharacteristic
65C61×#322C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76#14519771—21no—
77#14519769C2×C411yescharacteristic
78#14519765C2×C411yescharacteristic
79#14519760—21no—
80#14519756C2×C411yescharacteristic
81#14519751C2×C411yescharacteristic
82C4×Dic122C2×C411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×Dic122C2311yescharacteristic
85C4×D244C2×C411yescharacteristic
86C4×D244C2311yescharacteristic
87C4×D244C2311yescharacteristic
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91#14519736C2×C411yescharacteristic
92#14519734—21no—
93#14519734—21no—
94C42×D61—21no—
95#14519711C2×C411yescharacteristic
96#14519711C2×C411yescharacteristic
97#14519709C2×C411yescharacteristic
98#14519709C2×C411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114#14519699C2×C411yescharacteristic
115C22⋊#92418—21no—
116C22⋊#92418—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688—21no—
122#14519687—21no—
123#14519687—21no—
124#14519687—21no—
125C4×#92418—21no—
126C8×Dic61—21no—
127C2×M16×C61D411yescharacteristic
128C2×M16×C61D411yescharacteristic
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132C4⋊C8×C61C2×C411yescharacteristic
133C22⋊C8×C61C2×C411yescharacteristic
134C22⋊C8×C61C2×C411yescharacteristic
135#97×C61D411yescharacteristic
136#97×C61D411yescharacteristic
137C4×C8×C61—21no—
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C2×C22⋊D61—21no—
149#11758222—22no—
150#11758222—41no—
151C2×D244C22×C411yescharacteristic
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×Dic122C22×C411yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159M16×C61—41no—
160M16×C61—41no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—42no—
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C42×C61C22×C411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61#4111yescharacteristic
175C42×C61C2411yescharacteristic
176C22⋊Dic61—21no—
177C22⋊Dic61—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202Dic244—41no—
203D488—22no—
204#11758190—22no—
205#11758190—41no—
206#11758189—42no—
207C8×D61—42no—
208C8×D61—42no—
209C8×D61—42no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212C22×D61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—41no—
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C22⋊D61—42no—
225C22⋊D61—81no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232D244—21no—
233D244—21no—
234D244—21no—
235D244#13112yes—
236C4×D61—42no—
237C4×D61—41no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—81no—
242Dic122—21no—
243Dic122—21no—
244Dic122—21no—
245Dic122—21no—
246C8×C61—22no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#18002—611nomaximal, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—22no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61C2×#13111yescharacteristic
276C4×C61#56811yescharacteristic
277C4×C61#57511yescharacteristic
278C4×C61#57511yescharacteristic
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285#3102—611no—
286#2970—611no—
287#2969—611no—
288#1593—611no—
289#1592—611no—
290#1587—611no—
291#1586—611no—
292#1585—611no—
293#1585—611no—
294#1580—611no—
295SD16⋊C8—611no—
296#1572—611no—
297#1494—611no—
298#1476—611no—
299#1451D6111yescharacteristic, complemented
300C2×C61—41no—
301C2×C61#293311yescharacteristic
302C2×C61#294311yescharacteristic
303C2×C61#295611yescharacteristic
304D61—42no—
305D61—81no—
306#529—611no—
307C4×#41—611no—
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—
317#446—611no—
318#446—611no—
319C8×Q8—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×D8—611no—
324#436—611no—
325#436—1221no—
326#435—1221no—
327#435—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4—611no—
331C8×D4—611no—
332#433—1221no—
333#432—611no—
334#432—1221no—
335#431—611no—
336#431C2×D6111yescharacteristic
337#405—1221no—
338C4×M16C2×D6111yescharacteristic
339C2×#97—1221no—
340C2×C4×C8C2×D6111yescharacteristic
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#322C2×D6111yescharacteristic
354#322C2×D6111yescharacteristic
355#322C2×D6111yescharacteristic
356#322C2×D6111yescharacteristic
357C61#1800211yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8—611no—
363C2×M16—1221no—
364C2×M16D24411yescharacteristic
365C2×M16D24411yescharacteristic
366C22×C8—21no—
367C22×C8—1221no—
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×Q8—611no—
378C4×Q8—611no—
379C4×D4—611no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4—1221no—
385#117—611no—
386#117—1221no—
387#117—1221no—
388C2×C42—1221no—
389C2×C42C22×D6111yescharacteristic
390#107—611no—
391#107—611no—
392#106—611no—
393#106—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C4×D6111yescharacteristic
403C4⋊C8C4×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—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8C4×D6111yescharacteristic
419C22⋊C8C4×D6111yescharacteristic
420#97—1221no—
421#97—1221no—
422#97—1221no—
423#97—1221no—
424#97D24411yescharacteristic
425#97D24411yescharacteristic
426C4×C8—21no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—1222no—
436#41—2441no—
437C2×Q8—611no—
438C2×Q8—611no—
439C2×D4—611no—
440C2×D4—611no—
441C2×D4—1221no—
442C2×D4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×D24411yescharacteristic
449C22×C4#1175822211yescharacteristic
450Q16—2441no—
451SD16—1222no—
452SD16—2441no—
453D8—1222no—
454M16—41no—
455M16—41no—
456M16—2442no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2442no—
465C2×C8—2442no—
466C2×C8—2442no—
467C2×C8C2×C4×D6111yescharacteristic
468C2×C8C2×C4×D6111yescharacteristic
469C2×C8C2×C4×D6111yescharacteristic
470C2×C8C2×C4×D6111yescharacteristic
471C2×C8C2×D24411yescharacteristic
472C2×C8C2×D24411yescharacteristic
473C2×C8C2×D24411yescharacteristic
474C2×C8C2×D24411yescharacteristic
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—611no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42C2×C4×D6111yescharacteristic
498C42C2×D24411yescharacteristic
499C42#1175822211yescharacteristic
500C42C23×D6111yescharacteristic
501C23—1221no—
502C23—1221no—
503C23C4×D24411yescharacteristic
504Q8—1221no—
505Q8—1221no—
506Q8—1221no—
507Q8—1221no—
508D4—612no—
509D4—1221no—
510D4—1221no—
511D4—1221no—
512D4—4881no—
513D4—2442no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—4881no—
526C2×C4—2442no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4C4×D24411yescharacteristic
532C2×C4C4×D24411yescharacteristic
533C2×C4C4×D24411yescharacteristic
534C2×C4C22×C4×D6111yescharacteristic
535C2×C4C22×D24411yescharacteristic
536C2×C4C2×#1175822211yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—1222no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C2×C4×D24411yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—2441no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4#131×D6111yescharacteristic
572C4#1684052711yescharacteristic
573C4#1684056211yescharacteristic
574C4#1684056211yescharacteristic
575C2—41no—
576C2—4881no—
577C2—2442no—
578C2#2145454711yescharacteristic
579C2#2145462111yescharacteristic
580C2#2145473011yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1451C2
socleC22×C61C2×C4×D4
prime radical#16839909C4
cosocleC42×C61C24
hypercenter#1451D61
hypocenterC61#18002
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #21454834C2semidirect
3. #21454823C2semidirect
4. #21444729C2semidirect
5. #21444723C2semidirect
6. #21444692C2semidirect
7. #21444685C2semidirect
8. #21444678C2semidirect
9. #21444678C2semidirect
10. #21444644C2semidirect
11. #21444633C2semidirect
12. #21444599C2semidirect
13. #21444280C2semidirect
14. #21444202C2semidirect
15. C61×#1451C2semidirect
299. #1451D61semidirect
357. C61#18002semidirect

Maximal subgroups

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

subgroupindex
#214558392
#214548342
#214548232
#214447292
#214447232
#214446922
#214446852
#214446782
#214446442
#214446332
#214445992
#214442802
#214442022
C61×#14512
#1800261