Finite Group Databasebeta

← #29650195

Subgroups — #29650195

Order 15616.

620 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#21455835C211yesmaximal, characteristic
2#21454963C211yesmaximal, characteristic, complemented
3#21454929C211yesmaximal, characteristic, complemented
4#21444690C211yesmaximal, characteristic, complemented
5#21444681C211yesmaximal, characteristic, complemented
6#21444657C211yesmaximal, characteristic, complemented
7#21444640C211yesmaximal, characteristic, complemented
8#21444635C211yesmaximal, characteristic, complemented
9SD16×#92418C211yesmaximal, characteristic, complemented
10#21444618C211yesmaximal, characteristic, complemented
11#21444588C211yesmaximal, characteristic, complemented
12#21444257C211yesmaximal, characteristic, complemented
13#21444229C211yesmaximal, characteristic, complemented
14#21444115C211yesmaximal, characteristic, complemented
15C61×#1583C211yesmaximal, characteristic, complemented
16#16840294C2211yescharacteristic
17C4×#11758226C2211yescharacteristic
18#16840106C411yescharacteristic
19#16840085C411yescharacteristic
20#16840067C411yescharacteristic
21#16840061C411yescharacteristic
22#16839982C411yescharacteristic
23#16839976C411yescharacteristic
24#16839927C411yescharacteristic
25#16839906C411yescharacteristic
26#16839892C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28#16839886C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758190C2211yescharacteristic
31C4×#11758199C2211yescharacteristic
32#16839838—21no—
33#16839830—21no—
34C8×D244—21no—
35C8×D244C2211yescharacteristic
36D4×#92418C2211yescharacteristic
37#16839827—21no—
38#16839827C2211yescharacteristic
39#16839820—21no—
40#16839813—21no—
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839790—21no—
44#16839784C2211yescharacteristic
45C4⋊C8×D61—21no—
46C4⋊C8×D61C2211yescharacteristic
47C4×#11758189C2211yescharacteristic
48#16839513C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758226C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758189—21no—
72C2×#11758189—21no—
73C22×#92418—21no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77#14519770—21no—
78#14519768C2×C411yescharacteristic
79#14519764C2×C411yescharacteristic
80#14519759—21no—
81#14519757C2×C411yescharacteristic
82#14519748C2×C411yescharacteristic
83Q8×Dic61C2×C411yescharacteristic
84C4×Dic122C2311yescharacteristic
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87#14519739—21no—
88#14519739C2×C411yescharacteristic
89C4×C22⋊D61—21no—
90#14519736—21no—
91#14519735—21no—
92#14519735C2×C411yescharacteristic
93C42×D61—21no—
94C42×D61C2311yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519709C2×C411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706C2×C411yescharacteristic
106#14519706C2×C411yescharacteristic
107#14519706D411yescharacteristic
108#14519706D411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519701C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519697C2×C411yescharacteristic
115C22⋊#92418—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689C2×C411yescharacteristic
119#14519689C2×C411yescharacteristic
120#14519689D411yescharacteristic
121#14519689D411yescharacteristic
122#14519687—21no—
123#14519687—21no—
124C4×#92418—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C2×C22⋊D61—21no—
148#11758226—22no—
149#11758226—22no—
150C2×D244—21no—
151C2×D244C22×C411yescharacteristic
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159SD16×C61—22no—
160M16×C61—81no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61C22×C411yescharacteristic
170C4⋊C4×C61C22×C411yescharacteristic
171C22⋊C4×C61—21no—
172C42×C61—21no—
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175C22⋊Dic61—21no—
176C22⋊Dic61—21no—
177#11758202—22no—
178#11758199—22no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61C22×C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61C22×C411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204#11758190—22no—
205#11758189—42no—
206#11758189—81no—
207C8×D61—81no—
208C8×D61—81no—
209C8×D61—81no—
210C23×C61—21no—
211C22×D61—21no—
212C22×D61C4×D411yescharacteristic
213Q8×C61—21no—
214Q8×C61#13112yes—
215D4×C61—21no—
216D4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C22⋊D61—81no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C4×D411yescharacteristic
232D244—24no—
233D244—21no—
234D244#13112yes—
235C4×D61—24no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—81no—
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#17927—611nomaximal, Sylow
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—21no—
266C2×D61—22no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61C2×#13111yescharacteristic
276C4×C61C2×#13111yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57711yescharacteristic
279Dic61—21no—
280Dic61—21no—
281Dic61—21no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285#3102—611no—
286#2993—611no—
287#2988—611no—
288#1587—611no—
289#1586—611no—
290#1583D6111yescharacteristic, complemented
291#1582—611no—
292#1580—611no—
293#1579—611no—
294C8×SD16—611no—
295C8×SD16—611no—
296#1570—611no—
297#1489—611no—
298#1483—611no—
299#1453—611no—
300C2×C61—81no—
301C2×C61#292911yescharacteristic
302C2×C61#295211yescharacteristic
303C2×C61#295611yescharacteristic
304D61—41no—
305D61—42no—
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—
317C8×Q8—611no—
318C8×Q8—611no—
319C8×Q8C2×D6111yescharacteristic
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16C2×D6111yescharacteristic
323C4×D8—611no—
324#436—1221no—
325#436C2×D6111yescharacteristic
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
329C8×D4—611no—
330C8×D4—1221no—
331C8×D4—1221no—
332#433—1221no—
333#431—611no—
334#431—611no—
335#431—1221no—
336#424—1221no—
337#423—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—1221no—
340C4×M16—611no—
341#334—611no—
342#334—611no—
343#334—611no—
344#334C2×D6111yescharacteristic
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8C2×D6111yescharacteristic
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8C2×D6111yescharacteristic
353#322—611no—
354#322—611no—
355#322C2×D6111yescharacteristic
356C82—611no—
357C61#1792711yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16C4×D6111yescharacteristic
362C2×D8—611no—
363C2×M16—21no—
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—1221no—
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×Q8C22×D6111yescharacteristic
379C4×D4—611no—
380C4×D4—611no—
381C4×D4—1221no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C22×D6111yescharacteristic
385#117—611no—
386#117—1221no—
387#117—1221no—
388C2×C42—611no—
389C2×C42—1221no—
390#107—611no—
391#107—611no—
392#106—611no—
393#106C4×D6111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8C22×D6111yescharacteristic
407C4⋊C8C22×D6111yescharacteristic
408#103—611no—
409#103—611no—
410#103—611no—
411#103C4×D6111yescharacteristic
412#102—611no—
413#102—611no—
414#102—611no—
415#102C4×D6111yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—611no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424#97—1221no—
425#97—1221no—
426C4×C8—21no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—1222no—
436#41—1222no—
437C2×Q8—611no—
438C2×Q8C2×C4×D6111yescharacteristic
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4C2×C4×D6111yescharacteristic
443C22×C4—21no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450Q16—1222no—
451SD16—22no—
452SD16—1222no—
453D8—1222no—
454M16—81no—
455M16—4881no—
456M16—2442no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—4881no—
468C2×C8—4881no—
469C2×C8—4881no—
470C2×C8—4881no—
471C2×C8C2×C4×D6111yescharacteristic
472C2×C8C2×C4×D6111yescharacteristic
473C2×C8D4×D6111yescharacteristic
474C2×C8D4×D6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—611no—
477C4⋊C4—611no—
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—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42C23×D6111yescharacteristic
501C23—21no—
502C23—611no—
503C23—1221no—
504Q8—21no—
505Q8—1221no—
506Q8—1221no—
507Q8#1451978512yes—
508D4—21no—
509D4—21no—
510D4—612no—
511D4—1224no—
512D4—1221no—
513D4—4881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—1224no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—4881no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
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—41no—
552C22—41no—
553C22—41no—
554C22—1221no—
555C22—1221no—
556C22—1222no—
557C22—1221no—
558C22—2441no—
559C22—2441no—
560C22C4×D4×D6111yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—1221no—
566C4—1221no—
567C4—1221no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4#131×D6111yescharacteristic
572C4C2×#1451978511yescharacteristic
573C4#1684056811yescharacteristic
574C4#1684056911yescharacteristic
575C2—81no—
576C2—2441no—
577C2—2442no—
578C2#2145451011yescharacteristic
579C2#2145469711yescharacteristic
580C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1583C2
socleC22×C61C2×C4×D4
prime radical#16839906C4
cosocleC42×C61C24
hypercenter#1583D61
hypocenterC61#17927
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #21454963C2semidirect
3. #21454929C2semidirect
4. #21444690C2semidirect
5. #21444681C2semidirect
6. #21444657C2semidirect
7. #21444640C2semidirect
8. #21444635C2semidirect
9. SD16×#92418C2semidirect
10. #21444618C2semidirect
11. #21444588C2semidirect
12. #21444257C2semidirect
13. #21444229C2semidirect
14. #21444115C2semidirect
15. C61×#1583C2semidirect
290. #1583D61semidirect
357. C61#17927semidirect

Maximal subgroups

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

subgroupindex
#214558352
#214549632
#214549292
#214446902
#214446812
#214446572
#214446402
#214446352
SD16×#924182
#214446182
#214445882
#214442572
#214442292
#214441152
C61×#15832
#1792761