Finite Group Databasebeta

← #29667610

Subgroups — #29667610

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457145C211yesmaximal, characteristic
2#21456949C211yesmaximal, characteristic, complemented
3#21456843C211yesmaximal, characteristic, complemented
4#21445387C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic, complemented
6#21445325C211yesmaximal, characteristic, complemented
7#21445318C211yesmaximal, characteristic, complemented
8#21445263C211yesmaximal, characteristic, complemented
9#21445256C211yesmaximal, characteristic, complemented
10#21445201C211yesmaximal, characteristic, complemented
11#21445194C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444512C211yesmaximal, characteristic, complemented
14C2×#16839507C211yesmaximal, characteristic, complemented
15C61×#2994C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840160C2211yescharacteristic
19#16840160C2211yescharacteristic
20#16840157—21no—
21#16840132—21no—
22#16840109C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840081—21no—
25#16840081—21no—
26#16840059—21no—
27#16840057C2211yescharacteristic
28#16840053—21no—
29#16840053—21no—
30#16840052C2211yescharacteristic
31#16839996—21no—
32#16839993—21no—
33#16839974—21no—
34#16839972C2211yescharacteristic
35#16839972C2211yescharacteristic
36#16839967C2211yescharacteristic
37#16839967C2211yescharacteristic
38#16839962C2211yescharacteristic
39#16839957C2211yescharacteristic
40#16839917—21no—
41#16839900—21no—
42#16839819C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839507C2211yescharacteristic
51#16839507C2211yescharacteristic
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×#431C2211yescharacteristic
65C61×#424—21no—
66C2×C4⋊C8×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—
75C22×#92418—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#14519709—21no—
92#14519709—21no—
93#14519709—21no—
94#14519709—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
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—
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61D411yescharacteristic
120#124×C61D411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61D411yescharacteristic
123#121×C61D411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61C2311yescharacteristic
127#117×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140#97×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—82no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×C4×D61—41no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162C2×Dic122—81no—
163C2×Dic122—81no—
164M16×C61—81no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—81no—
168C2×C8×C61—81no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C42×C61—21no—
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61#4111yescharacteristic
188C42×C61C2411yescharacteristic
189#11758202—81no—
190#11758202—81no—
191#11758201—81no—
192#11758200—81no—
193#11758200—81no—
194#11758199—81no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—41no—
204C4⋊Dic61—41no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—81no—
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—
238C2×Dic61—82no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—81no—
244C4×D61—82no—
245Dic122—41no—
246Dic122—41no—
247Dic122—41no—
248Dic122—41no—
249Dic122—82no—
250Dic122—81no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#19589—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61#47112yes—
268C22×C61C2×#12111yescharacteristic
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61#57611yescharacteristic
280C4×C61#57711yescharacteristic
281C4×C61#57711yescharacteristic
282C4×C61#57811yescharacteristic
283Dic61—81no—
284Dic61—81no—
285Dic61—81no—
286#3247—611no—
287#3227—611no—
288#3218—611no—
289#2994D6111yescharacteristic, complemented
290#1702—611no—
291#1701—611no—
292#1692—611no—
293#1691—611no—
294#1682—611no—
295#1681—611no—
296#1672—611no—
297#1671—611no—
298#1573—611no—
299#1551—611no—
300C2×#332—611no—
301C2×C61—22no—
302C2×C61—81no—
303C2×C61#304611yescharacteristic
304C2×C61#306211yescharacteristic
305C2×C61C2×#47111yescharacteristic
306D61—161no—
307#532—611no—
308C2×C4⋊Q8—611no—
309#529C2×D6111yescharacteristic
310#498—611no—
311#498—611no—
312#497—1221no—
313#491—1221no—
314#486—611no—
315#486—611no—
316#481—1221no—
317#481—1221no—
318#478—1221no—
319#477—611no—
320#476—611no—
321#476—1221no—
322#476—1221no—
323#466—1221no—
324#465—1221no—
325#463—1221no—
326#462—611no—
327#462—611no—
328#461—611no—
329#461—611no—
330#460—611no—
331#459—611no—
332#451—1221no—
333#448—1221no—
334#446C2×D6111yescharacteristic
335C8×Q8C2×D6111yescharacteristic
336#436C2×D6111yescharacteristic
337#435—21no—
338C8×D4—21no—
339C8×D4C2×D6111yescharacteristic
340#433—21no—
341#432—611no—
342#431C2×D6111yescharacteristic
343#424—21no—
344C2×C4⋊C8—611no—
345C2×C4⋊C8C2×D6111yescharacteristic
346#335—611no—
347#335—611no—
348#334—611no—
349#334—611no—
350#333—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#331—611no—
357#331—611no—
358C61#1958911yescharacteristic, complemented, Sylow
359C2×#41—1221no—
360C22×Q8—1221no—
361C2×Q16—1221no—
362C2×Q16—1221no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×D8—1221no—
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—1221no—
371C4⋊Q8—611no—
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8—1221no—
377#127—611no—
378#126—21no—
379#125D24411yescharacteristic
380#124—1221no—
381#124D24411yescharacteristic
382#123—21no—
383C22⋊Q8D24411yescharacteristic
384#121—1221no—
385#121—1221no—
386#121D24411yescharacteristic
387C4×Q8C22×D6111yescharacteristic
388C4×D4—21no—
389C4×D4—1221no—
390C4×D4—1221no—
391C4×D4C22×D6111yescharacteristic
392#117—21no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8C22⋊D6111yescharacteristic
411C4⋊C8C22⋊D6111yescharacteristic
412C4⋊C8C22×D6111yescharacteristic
413C4⋊C8C22×D6111yescharacteristic
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—1221no—
429C22⋊C8C22⋊D6111yescharacteristic
430C22⋊C8C22⋊D6111yescharacteristic
431#97—21no—
432#97—1221no—
433C4×C8—21no—
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436#41—4882no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—4881no—
441C2×Q8—4881no—
442C2×Q8—2441no—
443C2×Q8C2×D24411yescharacteristic
444C2×D4—21no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—2441no—
449C2×D4C2×D24411yescharacteristic
450C22×C4—21no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4C2×D24411yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456Q16—4881no—
457Q16—4881no—
458SD16—4881no—
459SD16—4881no—
460SD16—4881no—
461D8—4881no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—81no—
466C2×C8—81no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—4881no—
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C2×C8C2×C22⋊D6111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—2441no—
487C4⋊C4—2441no—
488C4⋊C4C2×D24411yescharacteristic
489C4⋊C4C2×D24411yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—2441no—
496C22⋊C4—2441no—
497C42—21no—
498C42C2×D24411yescharacteristic
499C42#1175822211yescharacteristic
500C42C2×C22⋊D6111yescharacteristic
501C42C23×D6111yescharacteristic
502C23—21no—
503C23—2441no—
504C23#1451975111yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—4881no—
508Q8—4882no—
509Q8—2441no—
510Q8—2441no—
511Q8—2441no—
512Q8—2441no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—4881no—
517D4—4882no—
518D4—2441no—
519D4—2441no—
520D4—2441no—
521D4—2441no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—4882no—
533C2×C4—4882no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4#1451975111yescharacteristic
538C2×C4#1451975111yescharacteristic
539C2×C4#1451975111yescharacteristic
540C2×C4C22×C22⋊D6111yescharacteristic
541C2×C4C22×D24411yescharacteristic
542C2×C4C2×#1175822211yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—4881no—
559C22—4881no—
560C22—4881no—
561C22#1684002512yes—
562C22C2×#1451975111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—4881no—
571C4—4881no—
572C4—4881no—
573C4#1684056711yescharacteristic
574C4#1684057311yescharacteristic
575C4#1684057411yescharacteristic
576C4#1684057711yescharacteristic
577C2—22no—
578C2—81no—
579C2—9761no—
580C2#2145536911yescharacteristic
581C2#2145549911yescharacteristic
582C2C2×#1684002511yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2994C2
socleC22×C61C2×#121
prime radical#21457145C2
hypercenter#2994D61
hypocenterC61#19589
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #21456949C2semidirect
3. #21456843C2semidirect
4. #21445387C2semidirect
5. #21445380C2semidirect
6. #21445325C2semidirect
7. #21445318C2semidirect
8. #21445263C2semidirect
9. #21445256C2semidirect
10. #21445201C2semidirect
11. #21445194C2semidirect
12. #21444604C2semidirect
13. #21444512C2semidirect
14. C2×#16839507C2semidirect
15. C61×#2994C2semidirect
289. #2994D61semidirect
358. C61#19589semidirect

Maximal subgroups

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

subgroupindex
#214571452
#214569492
#214568432
#214453872
#214453802
#214453252
#214453182
#214452632
#214452562
#214452012
#214451942
#214446042
#214445122
C2×#168395072
C61×#29942
#1958961