Finite Group Databasebeta

← #29665160

Subgroups — #29665160

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457181C211yesmaximal, characteristic
2#21456843C211yesmaximal, characteristic, complemented
3#21456213C211yesmaximal, characteristic, complemented
4#21445387C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic, complemented
6#21445373C211yesmaximal, characteristic, complemented
7#21445366C211yesmaximal, characteristic, complemented
8#21445263C211yesmaximal, characteristic, complemented
9#21445256C211yesmaximal, characteristic, complemented
10#21445249C211yesmaximal, characteristic, complemented
11#21445242C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444522C211yesmaximal, characteristic, complemented
14#21444490C211yesmaximal, characteristic, complemented
15C61×#2969C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840157—21no—
19#16840132—21no—
20#16840122—21no—
21#16840122—21no—
22#16840113C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840109C2211yescharacteristic
26#16840059—21no—
27#16840047C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16840013—21no—
30#16840010—21no—
31#16839974—21no—
32#16839972C2211yescharacteristic
33#16839972C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839957C2211yescharacteristic
38#16839917—21no—
39#16839900—21no—
40#16839819C2211yescharacteristic
41#16839786C2211yescharacteristic
42#16839764—21no—
43#16839764—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839507C2211yescharacteristic
51#16839507C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436—21no—
60C61×#436C2211yescharacteristic
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#405—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758222—21no—
68C22×Dic122—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758194—21no—
76#14519777—21no—
77#14519777—21no—
78#14519777—21no—
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519774C2311yescharacteristic
83#14519765—21no—
84#14519751—21no—
85#14519751—21no—
86C4×D244—21no—
87C4×D244—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90#14519710—21no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519702—21no—
98#14519702—21no—
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519699—21no—
107#14519699—21no—
108#14519699—21no—
109#14519699—21no—
110#14519698—21no—
111#14519697—21no—
112#14519697—21no—
113C22⋊#92418—21no—
114#14519688—21no—
115C2×M16×C61—21no—
116C2×M16×C61D411yescharacteristic
117C2×M16×C61D411yescharacteristic
118C22×C8×C61—21no—
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×C61D411yescharacteristic
139#97×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
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—
152C22×Dic61—41no—
153#11758222—42no—
154#11758222—42no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×C4×D61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—41no—
163C2×Dic122—81no—
164C2×Dic122—81no—
165M16×C61—41no—
166M16×C61—41no—
167M16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—42no—
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C42×C61—21no—
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61#4111yescharacteristic
190C42×C61C2411yescharacteristic
191#11758202—81no—
192#11758202—81no—
193#11758201—81no—
194#11758200—81no—
195#11758200—81no—
196#11758199—81no—
197#11758198—41no—
198#11758198—41no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—41no—
206C4⋊Dic61—41no—
207#11758194—81no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C23×C61—21no—
213C23×C61#12111yescharacteristic
214C22×D61—41no—
215Q8×C61—21no—
216Q8×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—81no—
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—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C22⋊D61—82no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—82no—
241D244—41no—
242D244—41no—
243D244—41no—
244D244—41no—
245D244—81no—
246C4×D61—82no—
247Dic122—41no—
248Dic122—41no—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122—82no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#19383—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61#57511yescharacteristic
283C4×C61#57511yescharacteristic
284C4×C61#57611yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289#3251—611no—
290#3218—611no—
291#3141—611no—
292#2969D6111yescharacteristic, complemented
293#1702—611no—
294#1701—611no—
295#1700—611no—
296#1699—611no—
297#1682—611no—
298#1681—611no—
299#1680—611no—
300#1679—611no—
301#1569—611no—
302#1553—611no—
303#1546—611no—
304C2×C61—41no—
305C2×C61—81no—
306C2×C61#304011yescharacteristic
307C2×C61#306211yescharacteristic
308C2×C61#306911yescharacteristic
309D61—161no—
310#532—611no—
311C2×C4⋊Q8—611no—
312#529C2×D6111yescharacteristic
313#497—1221no—
314#491—1221no—
315#489—1221no—
316#489—1221no—
317#487—611no—
318#487—611no—
319#486—611no—
320#486—611no—
321#478—1221no—
322#475—611no—
323#474—611no—
324#469—1221no—
325#468—1221no—
326#463—1221no—
327#462—611no—
328#462—611no—
329#461—611no—
330#461—611no—
331#460—611no—
332#459—611no—
333#451—1221no—
334#448—1221no—
335#446C2×D6111yescharacteristic
336C8×Q8C2×D6111yescharacteristic
337#436—21no—
338#436C2×D6111yescharacteristic
339#435—21no—
340C8×D4C2×D6111yescharacteristic
341#433—21no—
342#432—611no—
343#431C2×D6111yescharacteristic
344#423—611no—
345#417—1221no—
346#417—1221no—
347#405—21no—
348C4×M16C2×D6111yescharacteristic
349#335—611no—
350#335—611no—
351#334—611no—
352#334—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332—611no—
358#332—611no—
359#331—611no—
360#331—611no—
361C61#1938311yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C22×Q8—1221no—
364C2×Q16—1221no—
365C2×Q16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×D8—1221no—
370C2×M16—21no—
371C2×M16—1221no—
372C2×M16C22⋊D6111yescharacteristic
373C2×M16C22⋊D6111yescharacteristic
374C22×C8—21no—
375C4⋊Q8—611no—
376C4⋊Q8—611no—
377C4⋊Q8—611no—
378C4⋊Q8—1221no—
379C4⋊Q8—1221no—
380C4⋊Q8—1221no—
381#127—611no—
382#126—21no—
383#125D24411yescharacteristic
384#124—1221no—
385#124D24411yescharacteristic
386#123—21no—
387C22⋊Q8D24411yescharacteristic
388#121—1221no—
389#121—1221no—
390#121D24411yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—1221no—
394C4×D4—1221no—
395C4×D4C22×D6111yescharacteristic
396#117—21no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C42C22×D6111yescharacteristic
400#107—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⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—1221no—
431#97—21no—
432#97—1221no—
433#97C22⋊D6111yescharacteristic
434#97C22⋊D6111yescharacteristic
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C22×D6111yescharacteristic
438C4×C8C22×D6111yescharacteristic
439#41—2442no—
440#41—2442no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—4881no—
445C2×Q8—4881no—
446C2×Q8—2441no—
447C2×Q8C2×D24411yescharacteristic
448C2×D4—21no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—2441no—
453C2×D4C2×D24411yescharacteristic
454C22×C4—21no—
455C22×C4—2441no—
456C22×C4—2441no—
457C22×C4C2×D24411yescharacteristic
458C22×C4#1175822211yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460Q16—4881no—
461Q16—4881no—
462SD16—4881no—
463SD16—4881no—
464SD16—4881no—
465D8—4881no—
466M16—41no—
467M16—41no—
468M16—42no—
469M16—4881no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8C2×C22⋊D6111yescharacteristic
478C2×C8C2×C22⋊D6111yescharacteristic
479C2×C8C2×C22⋊D6111yescharacteristic
480C2×C8C2×C22⋊D6111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4C2×D24411yescharacteristic
494C4⋊C4C2×D24411yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C42—21no—
503C42C2×D24411yescharacteristic
504C42#1175822211yescharacteristic
505C42C2×C22⋊D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—2441no—
509C23#1451975111yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—4882no—
513Q8—2441no—
514Q8—2441no—
515Q8—2441no—
516Q8—2441no—
517Q8—2441no—
518Q8—2441no—
519D4—21no—
520D4—21no—
521D4—81no—
522D4—4881no—
523D4—4882no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—4882no—
539C2×C4—4882no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451975111yescharacteristic
544C2×C4#1451975111yescharacteristic
545C2×C4#1451975111yescharacteristic
546C2×C4C22×C22⋊D6111yescharacteristic
547C2×C4C22×D24411yescharacteristic
548C2×C4C2×#1175822211yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—4881no—
566C22—4881no—
567C22—4881no—
568C22C2×#1451975111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—4881no—
577C4—4881no—
578C4—4881no—
579C4#1684056011yescharacteristic
580C4#1684056011yescharacteristic
581C4#1684056711yescharacteristic
582C4#1684057411yescharacteristic
583C2—41no—
584C2—81no—
585C2—9761no—
586C2#2145531311yescharacteristic
587C2#2145549911yescharacteristic
588C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2969C2
socleC22×C61C2×#121
prime radical#21457181C2
hypercenter#2969D61
hypocenterC61#19383
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #21456843C2semidirect
3. #21456213C2semidirect
4. #21445387C2semidirect
5. #21445380C2semidirect
6. #21445373C2semidirect
7. #21445366C2semidirect
8. #21445263C2semidirect
9. #21445256C2semidirect
10. #21445249C2semidirect
11. #21445242C2semidirect
12. #21444586C2semidirect
13. #21444522C2semidirect
14. #21444490C2semidirect
15. C61×#2969C2semidirect
292. #2969D61semidirect
361. C61#19383semidirect

Maximal subgroups

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

subgroupindex
#214571812
#214568432
#214562132
#214453872
#214453802
#214453732
#214453662
#214452632
#214452562
#214452492
#214452422
#214445862
#214445222
#214444902
C61×#29692
#1938361