Finite Group Databasebeta

← #29650241

Subgroups — #29650241

Order 15616.

604 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#21455839C211yesmaximal, characteristic
2#21454788C211yesmaximal, characteristic, complemented
3#21454780C211yesmaximal, characteristic, complemented
4#21444715C211yesmaximal, characteristic, complemented
5#21444708C211yesmaximal, characteristic, complemented
6#21444708C211yesmaximal, characteristic, complemented
7#21444703C211yesmaximal, characteristic, complemented
8#21444668C211yesmaximal, characteristic, complemented
9#21444661C211yesmaximal, characteristic, complemented
10#21444654C211yesmaximal, characteristic, complemented
11#21444647C211yesmaximal, characteristic, complemented
12#21444251C211yesmaximal, characteristic, complemented
13#21444225C211yesmaximal, characteristic, complemented
14#21444103C211yesmaximal, characteristic, complemented
15C61×#1572C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840104C411yescharacteristic
19#16840087C411yescharacteristic
20#16840070C411yescharacteristic
21#16840063C411yescharacteristic
22#16839985C411yescharacteristic
23#16839978C411yescharacteristic
24#16839926C411yescharacteristic
25#16839909C411yescharacteristic
26#16839889C2211yescharacteristic
27#16839889C2211yescharacteristic
28#16839889C2211yescharacteristic
29#16839886C2211yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758190C2211yescharacteristic
32C4×#11758190C2211yescharacteristic
33C4×D488C2211yescharacteristic
34#16839839C2211yescharacteristic
35#16839839C2211yescharacteristic
36#16839839C2211yescharacteristic
37#16839830—21no—
38#16839830—21no—
39#16839830—21no—
40#16839827C2211yescharacteristic
41#16839825—21no—
42#16839824—21no—
43#16839815C2211yescharacteristic
44#16839813—21no—
45#16839719—21no—
46C4×#11758189—21no—
47C2×C4×#92418C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839492C2211yescharacteristic
51#16839492C2211yescharacteristic
52#16839489C2211yescharacteristic
53#16839489C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418D411yescharacteristic
76C22×#92418D411yescharacteristic
77C2×C8×D61—21no—
78#14519771—21no—
79#14519769C2×C411yescharacteristic
80#14519765C2×C411yescharacteristic
81#14519760—21no—
82#14519756C2×C411yescharacteristic
83#14519751C2×C411yescharacteristic
84C4×Dic122C2×C411yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244C2×C411yescharacteristic
88C4×D244C2311yescharacteristic
89C4×D244C2311yescharacteristic
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93#14519736C2×C411yescharacteristic
94#14519734—21no—
95#14519734—21no—
96C42×D61—21no—
97#14519711C2×C411yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519709C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101C4⋊#92418—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519702C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114C22⋊#92418—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519687—21no—
120#14519687—21no—
121#14519687—21no—
122C4×#92418D411yescharacteristic
123C4×#92418D411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61C2×C411yescharacteristic
139C22⋊C8×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
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—41no—
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
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C22×C411yescharacteristic
167C42×C61C22×C411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61#4111yescharacteristic
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172C22⋊Dic61—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61C22×C411yescharacteristic
180C4⋊Dic61C22×C411yescharacteristic
181C4⋊Dic61C22×C411yescharacteristic
182C4⋊Dic61C22×C411yescharacteristic
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201Dic244—41no—
202D488—41no—
203#11758190—41no—
204#11758190—41no—
205#11758189—42no—
206#11758189—42no—
207#11758189—42no—
208C8×D61—42no—
209C23×C61C4×D411yescharacteristic
210C22×D61—21no—
211C22×D61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—41no—
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C23×C411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C22⋊D61—42no—
224C22⋊D61—42no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231D244—21no—
232D244—21no—
233D244—21no—
234D244—21no—
235C4×D61—42no—
236C4×D61—42no—
237C4×D61—41no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241Dic122—21no—
242Dic122—21no—
243Dic122—21no—
244Dic122—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253#92418—21no—
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418#13512yes—
258#92418#13512yes—
259#17932—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61C2×C4×D411yescharacteristic
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61#56811yescharacteristic
275C4×C61#56811yescharacteristic
276C4×C61C2×#13511yescharacteristic
277C4×C61C2×#13511yescharacteristic
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284#3102—611no—
285#2966—611no—
286#2965—611no—
287#1591—611no—
288#1590—611no—
289#1590—611no—
290#1589—611no—
291#1584—611no—
292#1583—611no—
293#1582—611no—
294#1581—611no—
295#1572D6111yescharacteristic, complemented
296#1488—611no—
297#1482—611no—
298#1450—611no—
299C2×C61—41no—
300C2×C61#293011yescharacteristic
301C2×C61C4×#13511yescharacteristic
302C2×C61#295511yescharacteristic
303D61—81no—
304D61—81no—
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—
316#446—611no—
317#446—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#436—611no—
325#436—611no—
326#435—1221no—
327#435—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4—1221no—
331#433—1221no—
332#432C2×D6111yescharacteristic
333#431—611no—
334#431—1221no—
335#431C2×D6111yescharacteristic
336#431C2×D6111yescharacteristic
337#405—1221no—
338C4×M16—1221no—
339C2×C4×C8—611no—
340#335C2×D6111yescharacteristic
341#335C2×D6111yescharacteristic
342#334C2×D6111yescharacteristic
343#334C2×D6111yescharacteristic
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354C82—611no—
355C82—611no—
356C61#1793211yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16—611no—
361C2×D8—611no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C22×C8—611no—
366C22×C8—611no—
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—611no—
379C4×D4—611no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4—1221no—
383#117—611no—
384#117—1221no—
385#117—1221no—
386C2×C42—1221no—
387C2×C42C22×D6111yescharacteristic
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C4×D6111yescharacteristic
398C4⋊C8C4×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
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#102—611no—
410#102—611no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8C4×D6111yescharacteristic
419C22⋊C8C4×D6111yescharacteristic
420#97—21no—
421#97—1221no—
422#97—1221no—
423#97—1221no—
424C4×C8—21no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434#41—2441no—
435#41—2441no—
436C2×Q8—611no—
437C2×Q8—611no—
438C2×D4—611no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4C2×C4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4#1175822611yescharacteristic
449Q16—2441no—
450SD16—2441no—
451SD16—2441no—
452D8—2441no—
453M16—2442no—
454M16—2442no—
455M16—2442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—1222no—
465C2×C8—1222no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—2442no—
469C2×C8C2×C4×D6111yescharacteristic
470C2×C8C2×C4×D6111yescharacteristic
471C2×C8C2×C4×D6111yescharacteristic
472C2×C8C2×C4×D6111yescharacteristic
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—1221no—
492C42—1221no—
493C42—1221no—
494C42—1221no—
495C42C2×C4×D6111yescharacteristic
496C42D4×D6111yescharacteristic
497C42#1175822611yescharacteristic
498C42C23×D6111yescharacteristic
499C23—1221no—
500C23—1221no—
501C23#1451973911yescharacteristic
502Q8—1221no—
503Q8—1221no—
504Q8—1221no—
505Q8—1221no—
506D4—1221no—
507D4—1221no—
508D4—1221no—
509D4—1221no—
510D4—2442no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—2442no—
524C2×C4—2442no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4#1451973911yescharacteristic
530C2×C4#1451973911yescharacteristic
531C2×C4#1451973911yescharacteristic
532C2×C4C22×C4×D6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4C2×#1175822611yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—612no—
544C8—612no—
545C8—1221no—
546C8—1221no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22C2×#1451973911yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—2441no—
564C4—2441no—
565C4—2441no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4#1684052711yescharacteristic
570C4#1684052711yescharacteristic
571C4#135×D6111yescharacteristic
572C4#135×D6111yescharacteristic
573C2—41no—
574C2—4881no—
575C2—4881no—
576C2#2145452111yescharacteristic
577C2#2145459011yescharacteristic
578C2#2145472111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1572C2
socleC22×C61C2×C4×D4
prime radical#16839909C4
cosocleC42×C61C24
hypercenter#1572D61
hypocenterC61#17932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #21454788C2semidirect
3. #21454780C2semidirect
4. #21444715C2semidirect
5. #21444708C2semidirect
6. #21444708C2semidirect
7. #21444703C2semidirect
8. #21444668C2semidirect
9. #21444661C2semidirect
10. #21444654C2semidirect
11. #21444647C2semidirect
12. #21444251C2semidirect
13. #21444225C2semidirect
14. #21444103C2semidirect
15. C61×#1572C2semidirect
295. #1572D61semidirect
356. C61#17932semidirect

Maximal subgroups

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

subgroupindex
#214558392
#214547882
#214547802
#214447152
#214447082
#214447032
#214446682
#214446612
#214446542
#214446472
#214442512
#214442252
#214441032
C61×#15722
#1793261