Finite Group Databasebeta

← #29663293

Subgroups — #29663293

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456962C211yesmaximal, characteristic
2#21456766C211yesmaximal, characteristic
3#487×D61C211yesmaximal, characteristic
4#21454748C211yesmaximal, characteristic
5#21445376C211yesmaximal, characteristic, complemented
6#21445375C211yesmaximal, characteristic, complemented
7#21445372C211yesmaximal, characteristic, complemented
8#21445371C211yesmaximal, characteristic, complemented
9#21445250C211yesmaximal, characteristic, complemented
10#21445249C211yesmaximal, characteristic, complemented
11#21445246C211yesmaximal, characteristic, complemented
12#21444564C211yesmaximal, characteristic
13#21444502C211yesmaximal, characteristic
14#21444489C211yesmaximal, characteristic
15C61×#1680C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19#16840159—21no—
20#16840140—21no—
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840111—21no—
25#16840111—21no—
26#16840111—21no—
27#16840111—21no—
28#16840094—21no—
29#16840091—21no—
30#16840048C2211yescharacteristic
31#16840047C2211yescharacteristic
32#16840044C2211yescharacteristic
33#16839973C2211yescharacteristic
34#16839972C2211yescharacteristic
35#16839969C2211yescharacteristic
36#16839919—21no—
37#16839916—21no—
38#16839893C2211yescharacteristic
39#16839891—21no—
40#16839889C2211yescharacteristic
41C8×Dic122—21no—
42C8×Dic122C2211yescharacteristic
43#16839814C2211yescharacteristic
44#16839814C2211yescharacteristic
45#16839787—21no—
46#16839784C2211yescharacteristic
47#103×D61—21no—
48#103×D61—21no—
49#16839716—21no—
50C4×C8×D61C2211yescharacteristic
51#16839514C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839513C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839508C2211yescharacteristic
57#16839508C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#475C2211yescharacteristic
62C61×#462C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Dic244—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758189—21no—
73C2×C8×D61D411yescharacteristic
74C2×C8×D61D411yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519776—21no—
80#14519776—21no—
81#14519776D411yescharacteristic
82#14519775—21no—
83#14519775—21no—
84#14519775D411yescharacteristic
85#14519767—21no—
86#14519757D411yescharacteristic
87#14519755—21no—
88#14519753D411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91#14519734—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C42×D61C2311yescharacteristic
97#14519709—21no—
98#14519708—21no—
99#14519708—21no—
100C4⋊#92418—21no—
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519702—21no—
109#14519702—21no—
110#14519702—21no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519701—21no—
115#14519700—21no—
116#14519700—21no—
117#14519700—21no—
118#14519700—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688—21no—
122#14519687—21no—
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×Q16×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147Q8×D61—42no—
148Q8×D61—42no—
149Q8×D61—81no—
150Q8×D61—81no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61#4111yescharacteristic
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—41no—
160C2×Dic122—41no—
161C2×Dic122C2×D411yescharacteristic
162Q16×C61—81no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C2×D411yescharacteristic
174C42×C61—21no—
175C42×C61C2411yescharacteristic
176#11758202—81no—
177#11758202—81no—
178#11758198—21no—
179#11758198—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C2×D411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—41no—
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195C4×Dic61—21no—
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61#4111yescharacteristic
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204Dic244—81no—
205#11758189—42no—
206C8×D61—22no—
207C8×D61—22no—
208C22×D61#12111yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61#12111yescharacteristic
227C2×Dic61#12111yescharacteristic
228C2×Dic61#12111yescharacteristic
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—22no—
232C4×D61—82no—
233C4×D61—82no—
234C4×D61#13512yes—
235C4×D61#13712yes—
236Dic122—21no—
237Dic122—21no—
238Dic122—42no—
239Dic122—41no—
240Dic122—41no—
241Dic122—41no—
242Dic122—41no—
243Dic122—82no—
244Dic122—82no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#19213—611nomaximal, Sylow
256C22×C61C2×#12111yescharacteristic
257C2×D61—21no—
258C2×D61—21no—
259C2×D61#46412yes—
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—81no—
264C4×C61—81no—
265C4×C61C2×#13511yescharacteristic
266C4×C61C2×#13711yescharacteristic
267C4×C61#57711yescharacteristic
268C4×C61#57711yescharacteristic
269Dic61—21no—
270Dic61—41no—
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274Dic61#46412yes—
275Dic61#47312yes—
276#3229—611no—
277#3209—611no—
278C2×#487—611no—
279#2960—611no—
280#1700—611no—
281#1700—611no—
282#1700—611no—
283#1700—611no—
284#1680—611no—
285#1680—611no—
286#1680—611no—
287#1680D6111yescharacteristic, complemented
288#1564—611no—
289#1549—611no—
290#1546—611no—
291C2×C61C2×#46411yescharacteristic
292C2×C61#305711yescharacteristic
293C2×C61C2×#47311yescharacteristic
294D61—22no—
295#533—611no—
296C2×C4⋊Q8—611no—
297C2×C4⋊Q8—611no—
298#498—1221no—
299#494—1221no—
300#487—611no—
301#487—611no—
302#487—611no—
303#487—1221no—
304#487—1221no—
305#487—1221no—
306#487—1221no—
307#487C2×D6111yescharacteristic
308#483—1221no—
309#483—1221no—
310#475—611no—
311#475—611no—
312#475—611no—
313#475C2×D6111yescharacteristic
314#462—611no—
315#462—611no—
316#462—611no—
317#462C2×D6111yescharacteristic
318#451—1221no—
319#451—1221no—
320#446—611no—
321#446—611no—
322#446—1221no—
323C8×Q8—611no—
324C8×Q8—1221no—
325C8×Q8C2×D6111yescharacteristic
326#431—611no—
327#431—611no—
328#424—1221no—
329#423—611no—
330C2×#103—1221no—
331C2×#103—1221no—
332#405—1221no—
333C2×C4×C8—611no—
334#335—611no—
335#335—611no—
336#334—611no—
337#334C2×D6111yescharacteristic
338#332—611no—
339#332—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332C2×D6111yescharacteristic
345#332C2×D6111yescharacteristic
346C61#1921311yescharacteristic, complemented, Sylow
347C22×Q8—1221no—
348C22×Q8—1221no—
349C2×Q16—21no—
350C2×Q16—1221no—
351C2×Q16—1221no—
352C2×Q16—1221no—
353C2×M16—1221no—
354C22×C8—611no—
355C22×C8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359C4⋊Q8—611no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362C4⋊Q8—1221no—
363C4⋊Q8—1221no—
364C4⋊Q8—1221no—
365C4⋊Q8—1221no—
366C4⋊Q8C22×D6111yescharacteristic
367C4⋊Q8C22×D6111yescharacteristic
368#125—1221no—
369C22⋊Q8—611no—
370C22⋊Q8—611no—
371C22⋊Q8—1221no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×Q8C22×D6111yescharacteristic
375#117—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C42—611no—
381#106—21no—
382#106—1221no—
383#106—1221no—
384#106—1221no—
385C4⋊C8—21no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—21no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—611no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×Q8—4881no—
431C2×Q8—4881no—
432C2×Q8—2441no—
433C2×Q8—2441no—
434C2×Q8—2442no—
435C2×Q8—2442no—
436C2×Q8D4×D6111yescharacteristic
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—2441no—
441C22×C4—2441no—
442Q16—81no—
443Q16—4881no—
444Q16—4881no—
445Q16—4881no—
446M16—2442no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1222no—
453C2×C8—1222no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8D4×D6111yescharacteristic
458C2×C8D4×D6111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—611no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—2441no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4D4×D6111yescharacteristic
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C42—21no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—1221no—
487C42C23×D6111yescharacteristic
488C23—611no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—1221no—
496Q8—1221no—
497Q8—4882no—
498Q8—4882no—
499Q8—2442no—
500Q8—2441no—
501Q8—2441no—
502Q8—2441no—
503Q8—2441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—612no—
511C2×C4—612no—
512C2×C4—611no—
513C2×C4—1222no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—4882no—
519C2×C4—4882no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C2×C4#41×D6111yescharacteristic
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—1221no—
531C8—1221no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C22—612no—
536C22—1221no—
537C22—1221no—
538C22#121×D6111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—612no—
545C4—612no—
546C4—1221no—
547C4—4881no—
548C4—4881no—
549C4—2441no—
550C4—2441no—
551C4#135×D6111yescharacteristic
552C4#137×D6111yescharacteristic
553C4#1684056811yescharacteristic
554C4#1684056911yescharacteristic
555C2—1222no—
556C2#464×D6111yescharacteristic
557C2#2145545311yescharacteristic
558C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1680C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1680D61
hypocenterC61#19213
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1680

Complements

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

NH ≅ G/Ntype
5. #21445376C2semidirect
6. #21445375C2semidirect
7. #21445372C2semidirect
8. #21445371C2semidirect
9. #21445250C2semidirect
10. #21445249C2semidirect
11. #21445246C2semidirect
15. C61×#1680C2semidirect
287. #1680D61semidirect
346. C61#19213semidirect

Maximal subgroups

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

subgroupindex
#214569622
#214567662
#487×D612
#214547482
#214453762
#214453752
#214453722
#214453712
#214452502
#214452492
#214452462
#214445642
#214445022
#214444892
C61×#16802
#1921361