Finite Group Databasebeta

← #29650992

Subgroups — #29650992

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#21455833C211yesmaximal, characteristic
2#21454827C211yesmaximal, characteristic, complemented
3#21454820C211yesmaximal, characteristic, complemented
4#21444729C211yesmaximal, characteristic, complemented
5#21444718C211yesmaximal, characteristic, complemented
6#21444689C211yesmaximal, characteristic, complemented
7#21444684C211yesmaximal, characteristic, complemented
8#21444676C211yesmaximal, characteristic, complemented
9#21444676C211yesmaximal, characteristic, complemented
10#21444628C211yesmaximal, characteristic, complemented
11#21444596C211yesmaximal, characteristic, complemented
12#21444276C211yesmaximal, characteristic, complemented
13#21444198C211yesmaximal, characteristic, complemented
14#21444107C211yesmaximal, characteristic, complemented
15C61×#1580C211yesmaximal, characteristic, complemented
16#16840294C2211yescharacteristic
17C4×#11758224C2211yescharacteristic
18#16840105C411yescharacteristic
19#16840084C411yescharacteristic
20#16840068C411yescharacteristic
21#16840060C411yescharacteristic
22#16839983C411yescharacteristic
23#16839975C411yescharacteristic
24#16839925C411yescharacteristic
25#16839904C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839892C2211yescharacteristic
28#16839889C2211yescharacteristic
29#16839886C2211yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758200C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839837—21no—
35#16839833—21no—
36#16839833—21no—
37#16839830—21no—
38D4×#92418C2211yescharacteristic
39#16839820—21no—
40#16839818C2211yescharacteristic
41#16839816—21no—
42#16839814C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839717—21no—
45C4×#11758189C2211yescharacteristic
46C2×#14519687—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#16839484C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C8×D4×C61C2211yescharacteristic
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
71C2×#11758194—21no—
72C2×#11758189D411yescharacteristic
73C2×#11758189D411yescharacteristic
74C22×#92418—21no—
75C2×C8×D61—21no—
76#14519770—21no—
77#14519768C2×C411yescharacteristic
78#14519764C2×C411yescharacteristic
79#14519759—21no—
80#14519757C2×C411yescharacteristic
81#14519748C2×C411yescharacteristic
82C4×Dic122C2311yescharacteristic
83C4×Dic122C2311yescharacteristic
84#14519742C2×C411yescharacteristic
85D4×Dic61C2×C411yescharacteristic
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88#14519737—21no—
89#14519736—21no—
90#14519735C2×C411yescharacteristic
91#14519733—21no—
92C2×C4×Dic61—21no—
93C42×D61C2311yescharacteristic
94#14519711C2×C411yescharacteristic
95#14519708C2×C411yescharacteristic
96#14519708C2×C411yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
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#14519689C2×C411yescharacteristic
116#14519689C2×C411yescharacteristic
117#14519687—21no—
118#14519687—21no—
119#14519687—21no—
120#14519687—21no—
121#14519687D411yescharacteristic
122#14519687D411yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×D8×C61C2×C411yescharacteristic
130C22×C8×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—41no—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61#4111yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159D8×C61—22no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—42no—
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—41no—
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
197#11758194—42no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—42no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206Dic244—41no—
207#11758189—41no—
208#11758189—41no—
209C8×D61—42no—
210C23×C61—21no—
211C23×C61—21no—
212C22×D61C4×D411yescharacteristic
213D4×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61#13112yes—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61C23×C411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C22⋊D61—42no—
227C22⋊D61—81no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—42no—
233C2×Dic61—81no—
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—41no—
242Dic122—21no—
243Dic122—21no—
244Dic122—21no—
245Dic122—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253#92418—22no—
254#92418—21no—
255#92418—21no—
256#92418—21no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#18002—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61C2×C4×D411yescharacteristic
268C2×D61—21no—
269C2×D61—21no—
270C2×D61—21no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61C2×#13111yescharacteristic
275C4×C61#56811yescharacteristic
276C4×C61#57511yescharacteristic
277C4×C61#57511yescharacteristic
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
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#1580D6111yescharacteristic, complemented
295SD16⋊C8—611no—
296#1572—611no—
297#1494—611no—
298#1476—611no—
299#1451—611no—
300C2×C61—42no—
301C2×C61—81no—
302C2×C61#293311yescharacteristic
303C2×C61#294311yescharacteristic
304C2×C61#295611yescharacteristic
305D61—41no—
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×D8C2×D6111yescharacteristic
324#436—611no—
325#436—1221no—
326#435—1221no—
327#435—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4C2×D6111yescharacteristic
331C8×D4C2×D6111yescharacteristic
332#433—1221no—
333#432—611no—
334#432—1221no—
335#431—611no—
336#431—611no—
337#405—1221no—
338C4×M16—611no—
339C2×#97—1221no—
340C2×C4×C8—611no—
341#335—611no—
342#335—611no—
343#334—611no—
344#334C2×D6111yescharacteristic
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8C2×D6111yescharacteristic
352D4⋊C8C2×D6111yescharacteristic
353#322—611no—
354#322—611no—
355#322—611no—
356#322C2×D6111yescharacteristic
357C61#1800211yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8C4×D6111yescharacteristic
363C2×M16—611no—
364C2×M16—611no—
365C2×M16—1221no—
366C22×C8—21no—
367C22×C8—21no—
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—1221no—
381C4×D4—1221no—
382C4×D4—1221no—
383C4×D4C22×D6111yescharacteristic
384C4×D4C22×D6111yescharacteristic
385#117—611no—
386#117—1221no—
387#117—1221no—
388C2×C42—611no—
389C2×C42—1221no—
390#107—611no—
391#107C4×D6111yescharacteristic
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⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404#103—611no—
405#103—611no—
406#103—611no—
407#103—611no—
408#102—611no—
409#102—611no—
410#102C4×D6111yescharacteristic
411#102C4×D6111yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—611no—
415C22⋊C8—611no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—611no—
421#97—611no—
422#97—1221no—
423#97—1221no—
424#97—1221no—
425#97—1221no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—1222no—
436#41—2441no—
437C2×Q8—611no—
438C2×Q8—611no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4C2×C4×D6111yescharacteristic
442C2×D4C2×C4×D6111yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—1221no—
449C22×C4—1221no—
450Q16—2441no—
451SD16—1222no—
452SD16—2441no—
453D8—22no—
454M16—2441no—
455M16—2441no—
456M16—2442no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—42no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—2442no—
470C2×C8—2442no—
471C2×C8C2×C4×D6111yescharacteristic
472C2×C8C2×C4×D6111yescharacteristic
473C2×C8D4×D6111yescharacteristic
474C2×C8D4×D6111yescharacteristic
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
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—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42C23×D6111yescharacteristic
501C23—21no—
502C23—21no—
503C23—611no—
504Q8—1221no—
505Q8—1221no—
506Q8—1221no—
507Q8—1221no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—4881no—
512D4—2442no—
513D4#1451978312yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—4881no—
532C2×C4—2441no—
533C2×C4—2442no—
534C2×C4C22×C4×D6111yescharacteristic
535C2×C4C2×D4×D6111yescharacteristic
536C2×C4#41×D6111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—1222no—
545C8—1221no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—1221no—
558C22—1221no—
559C22—1221no—
560C22C4×D4×D6111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—1221no—
565C4—1221no—
566C4—1221no—
567C4—2441no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4C2×#1451978311yescharacteristic
572C4#1684052711yescharacteristic
573C4#1684055811yescharacteristic
574C4#1684055811yescharacteristic
575C2—42no—
576C2—81no—
577C2—2441no—
578C2#2145453911yescharacteristic
579C2#2145461611yescharacteristic
580C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1580C2
socleC22×C61C2×C4×D4
prime radical#16839904C4
cosocleC42×C61C24
hypercenter#1580D61
hypocenterC61#18002
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #21454827C2semidirect
3. #21454820C2semidirect
4. #21444729C2semidirect
5. #21444718C2semidirect
6. #21444689C2semidirect
7. #21444684C2semidirect
8. #21444676C2semidirect
9. #21444676C2semidirect
10. #21444628C2semidirect
11. #21444596C2semidirect
12. #21444276C2semidirect
13. #21444198C2semidirect
14. #21444107C2semidirect
15. C61×#1580C2semidirect
294. #1580D61semidirect
357. C61#18002semidirect

Maximal subgroups

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

subgroupindex
#214558332
#214548272
#214548202
#214447292
#214447182
#214446892
#214446842
#214446762
#214446282
#214445962
#214442762
#214441982
#214441072
C61×#15802
#1800261