Finite Group Databasebeta

← #29663482

Subgroups — #29663482

Order 15616.

606 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#21457156C211yesmaximal, characteristic, complemented
2#21457145C211yesmaximal, characteristic
3#21456378C211yesmaximal, characteristic, complemented
4#21445325C211yesmaximal, characteristic, complemented
5#21445318C211yesmaximal, characteristic, complemented
6#21445291C211yesmaximal, characteristic, complemented
7#21445284C211yesmaximal, characteristic, complemented
8#21445277C211yesmaximal, characteristic, complemented
9#21445270C211yesmaximal, characteristic, complemented
10#21445263C211yesmaximal, characteristic, complemented
11#21445256C211yesmaximal, characteristic, complemented
12C2×#16839515C211yesmaximal, characteristic, complemented
13#21444520C211yesmaximal, characteristic, complemented
14#21444515C211yesmaximal, characteristic, complemented
15C61×#2966C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840312C2211yescharacteristic
18#16840160C2211yescharacteristic
19#16840135C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840109C2211yescharacteristic
22#16840066—21no—
23#16840059—21no—
24#16840057C2211yescharacteristic
25#16840052C2211yescharacteristic
26#16840047C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16840001—21no—
29#16839996—21no—
30#16839993—21no—
31#16839991—21no—
32#16839991—21no—
33#16839989—21no—
34#16839981—21no—
35#16839974—21no—
36#16839972C2211yescharacteristic
37#16839967C2211yescharacteristic
38#16839962C2211yescharacteristic
39#16839957C2211yescharacteristic
40C4×#11758190—21no—
41C4×#11758190—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839515C2211yescharacteristic
47#16839515C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436C2211yescharacteristic
60C61×#435—21no—
61C8×D4×C61—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#432C2211yescharacteristic
65C61×#405—21no—
66C2×C4×C8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758190—21no—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73C2×#11758199—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519774C2311yescharacteristic
80#14519769—21no—
81#14519765—21no—
82#14519756—21no—
83#14519756—21no—
84#14519751—21no—
85#14519751—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×D244—21no—
89C4×D244—21no—
90#14519736—21no—
91#14519710—21no—
92#14519710—21no—
93#14519709—21no—
94#14519709—21no—
95#14519708—21no—
96#14519708—21no—
97C4⋊#92418—21no—
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519702—21no—
104#14519702—21no—
105#14519701—21no—
106#14519701—21no—
107#14519700—21no—
108#14519700—21no—
109#14519699—21no—
110#14519699—21no—
111#14519698—21no—
112#14519698—21no—
113#14519697—21no—
114#14519697—21no—
115C2×M16×C61—21no—
116C22×C8×C61—21no—
117C22×C8×C61D411yescharacteristic
118C22×C8×C61D411yescharacteristic
119#126×C61—21no—
120#125×C61D411yescharacteristic
121#124×C61D411yescharacteristic
122#123×C61—21no—
123C22⋊Q8×C61D411yescharacteristic
124#121×C61D411yescharacteristic
125C4×Q8×C61C2311yescharacteristic
126C4×D4×C61—21no—
127C4×D4×C61C2311yescharacteristic
128#117×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×C61—21no—
139C4×C8×C61—21no—
140C4×C8×C61D411yescharacteristic
141C4×C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C2×D411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—41no—
152#11758222—82no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160M16×C61—42no—
161C2×C8×C61—22no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—41no—
165C2×C8×C61—42no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C42×C61—21no—
182C42×C61C2×D411yescharacteristic
183C42×C61C2×D411yescharacteristic
184C42×C61#4111yescharacteristic
185C42×C61C2411yescharacteristic
186C22⋊Dic61—41no—
187#11758202—81no—
188#11758201—81no—
189#11758200—81no—
190#11758199—81no—
191#11758198—41no—
192#11758198—41no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199#11758196—41no—
200#11758196—41no—
201C4×Dic61—41no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—81no—
207C2×#92418—81no—
208#11758190—42no—
209#11758190—42no—
210C23×C61—21no—
211C23×C61#12111yescharacteristic
212C22×D61—41no—
213Q8×C61—21no—
214Q8×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—42no—
218C2×C4×C61—22no—
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—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—82no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238D244—41no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—81no—
243C4×D61—82no—
244Dic122—41no—
245Dic122—41no—
246Dic122—41no—
247Dic122—41no—
248Dic122—81no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61#13512yes—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#19229—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61#47112yes—
266C22×C61C2×#12111yescharacteristic
267C2×D61—81no—
268C2×D61—81no—
269C2×D61—81no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61C2×#13511yescharacteristic
278C4×C61#57511yescharacteristic
279C4×C61#57611yescharacteristic
280C4×C61#57811yescharacteristic
281Dic61—81no—
282Dic61—81no—
283Dic61—81no—
284#3248—611no—
285#3247—611no—
286#3167—611no—
287#2966D6111yescharacteristic, complemented
288#1692—611no—
289#1691—611no—
290#1686—611no—
291#1685—611no—
292#1684—611no—
293#1683—611no—
294#1682—611no—
295#1681—611no—
296C2×#335—611no—
297#1552—611no—
298#1551—611no—
299C2×C61—22no—
300C2×C61—81no—
301C2×C61#303511yescharacteristic
302C2×C61#306111yescharacteristic
303C2×C61C2×#47111yescharacteristic
304D61—161no—
305#533—611no—
306#532—611no—
307#529C2×D6111yescharacteristic
308#498—611no—
309#492—611no—
310#487—611no—
311#486—611no—
312#479—1221no—
313#478—1221no—
314#477—611no—
315#476—611no—
316#475—611no—
317#474—611no—
318#467—1221no—
319#466—1221no—
320#465—1221no—
321#465—1221no—
322#465—1221no—
323#465—1221no—
324#464—1221no—
325#463—1221no—
326#462—611no—
327#461—611no—
328#460—611no—
329#459—611no—
330#446C2×D6111yescharacteristic
331C8×Q8C2×D6111yescharacteristic
332C4×SD16—1221no—
333C4×SD16—1221no—
334#436C2×D6111yescharacteristic
335#435—21no—
336C8×D4—21no—
337C8×D4C2×D6111yescharacteristic
338#433—21no—
339#432C2×D6111yescharacteristic
340C2×C4⋊C8—611no—
341C2×C4⋊C8—611no—
342#405—21no—
343C2×C4×C8C2×D6111yescharacteristic
344#335—611no—
345#335—611no—
346#335—611no—
347#335—611no—
348#333—611no—
349#333—611no—
350#332—611no—
351#332—611no—
352#332—611no—
353#332—611no—
354#331—611no—
355#331—611no—
356C61#1922911yescharacteristic, complemented, Sylow
357C2×#41—1221no—
358C2×Q16—1221no—
359C2×SD16—1221no—
360C2×SD16—1221no—
361C2×SD16—1221no—
362C2×SD16—1221no—
363C2×D8—1221no—
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8C22⋊D6111yescharacteristic
369C22×C8C22⋊D6111yescharacteristic
370C4⋊Q8—611no—
371C4⋊Q8—611no—
372C4⋊Q8—611no—
373#127—611no—
374#126—21no—
375#125—1221no—
376#125D24411yescharacteristic
377#124—1221no—
378#124D24411yescharacteristic
379#123—21no—
380C22⋊Q8—1221no—
381C22⋊Q8—1221no—
382C22⋊Q8D24411yescharacteristic
383#121—1221no—
384#121—1221no—
385#121D24411yescharacteristic
386C4×Q8—1221no—
387C4×Q8—1221no—
388C4×Q8C22×D6111yescharacteristic
389C4×D4—21no—
390C4×D4—1221no—
391C4×D4—1221no—
392C4×D4C22×D6111yescharacteristic
393#117—21no—
394#117—1221no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#107—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8C22⋊D6111yescharacteristic
431C4×C8C22⋊D6111yescharacteristic
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434#41—4882no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8C2×D24411yescharacteristic
439C2×D4—21no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—2441no—
444C2×D4C2×D24411yescharacteristic
445C22×C4—21no—
446C22×C4—2441no—
447C22×C4C2×D24411yescharacteristic
448C22×C4#1175822211yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450Q16—4881no—
451SD16—4881no—
452SD16—4881no—
453SD16—2442no—
454SD16—2442no—
455D8—4881no—
456M16—42no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—41no—
461C2×C8—42no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—4881no—
467C2×C8—4881no—
468C2×C8C2×C22⋊D6111yescharacteristic
469C2×C8C2×C22⋊D6111yescharacteristic
470C2×C8C2×C22⋊D6111yescharacteristic
471C2×C8C2×C22⋊D6111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—2441no—
483C4⋊C4—2441no—
484C4⋊C4C2×D24411yescharacteristic
485C4⋊C4C2×D24411yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—2441no—
492C22⋊C4—2441no—
493C22⋊C4—2441no—
494C42—21no—
495C42—2441no—
496C42C2×D24411yescharacteristic
497C42#1175822211yescharacteristic
498C42C2×C22⋊D6111yescharacteristic
499C42C23×D6111yescharacteristic
500C23—21no—
501C23—2441no—
502C23#1451975111yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—4881no—
506Q8—2441no—
507Q8—2441no—
508Q8—2441no—
509Q8—2441no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—4881no—
514D4—4882no—
515D4—2441no—
516D4—2441no—
517D4—2441no—
518D4—2441no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—4882no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4#1451975111yescharacteristic
534C2×C4#1451975111yescharacteristic
535C2×C4#1451975111yescharacteristic
536C2×C4C22×C22⋊D6111yescharacteristic
537C2×C4C22×D24411yescharacteristic
538C2×C4C2×#1175822211yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8#1451979712yes—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—4881no—
555C22—4881no—
556C22—4881no—
557C22#1684002512yes—
558C22C2×#1451975111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—4881no—
567C4—4881no—
568C4—4881no—
569C4C2×#1451979711yescharacteristic
570C4#1684056011yescharacteristic
571C4#1684056711yescharacteristic
572C4#1684057911yescharacteristic
573C2—22no—
574C2—81no—
575C2—9761no—
576C2#2145527411yescharacteristic
577C2#2145548911yescharacteristic
578C2C2×#1684002511yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2966C2
socleC22×C61C2×#121
prime radical#21457145C2
hypercenter#2966D61
hypocenterC61#19229
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #21457156C2semidirect
3. #21456378C2semidirect
4. #21445325C2semidirect
5. #21445318C2semidirect
6. #21445291C2semidirect
7. #21445284C2semidirect
8. #21445277C2semidirect
9. #21445270C2semidirect
10. #21445263C2semidirect
11. #21445256C2semidirect
12. C2×#16839515C2semidirect
13. #21444520C2semidirect
14. #21444515C2semidirect
15. C61×#2966C2semidirect
287. #2966D61semidirect
356. C61#19229semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214571452
#214563782
#214453252
#214453182
#214452912
#214452842
#214452772
#214452702
#214452632
#214452562
C2×#168395152
#214445202
#214445152
C61×#29662
#1922961