Finite Group Databasebeta

← #29676490

Subgroups — #29676490

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458846C211yesmaximal, characteristic, complemented
2#21458405C211yesmaximal, characteristic
3#21458129C211yesmaximal, characteristic
4#21445493C211yesmaximal, characteristic, complemented
5#21445403C211yesmaximal, characteristic, complemented
6#21445315C211yesmaximal, characteristic, complemented
7#21445306C211yesmaximal, characteristic, complemented
8#21445213C211yesmaximal, characteristic, complemented
9#21445061C211yesmaximal, characteristic, complemented
10#21445053C211yesmaximal, characteristic
11#21445033C211yesmaximal, characteristic, complemented
12#21444990C211yesmaximal, characteristic, complemented
13#21444722C211yesmaximal, characteristic, complemented
14#21444662C211yesmaximal, characteristic, complemented
15C61×#3381C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840417C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840154—21no—
21#16840141C2211yescharacteristic
22#16840114C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840096—21no—
25#16840092—21no—
26#16840084—21no—
27#16840049C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840018—21no—
31#16840005—21no—
32#16839984—21no—
33#16839972C2211yescharacteristic
34#16839972C2211yescharacteristic
35#16839969—21no—
36#16839964C2211yescharacteristic
37#16839922—21no—
38#16839893C2211yescharacteristic
39#16839867—21no—
40C4×#11758201C2211yescharacteristic
41#16839841C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839801—21no—
44#16839761—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#557C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#499—21no—
59C61×#498C2211yescharacteristic
60C61×#479—21no—
61C61×#478—21no—
62C61×#477C2211yescharacteristic
63C61×#474C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×SD16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758201—21no—
73C2×#11758201D411yescharacteristic
74C2×#11758194—21no—
75C2×#11758189—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519772—41no—
79#14519765—21no—
80#14519759—41no—
81#14519756—21no—
82#14519753—21no—
83#14519748—21no—
84C4×Dic122—21no—
85C4×D244C2311yescharacteristic
86#14519735—21no—
87C4⋊C4×D61—21no—
88#14519711—21no—
89#14519711—21no—
90#14519710—21no—
91#14519710—41no—
92#14519708—21no—
93#14519708—21no—
94#14519708D411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519701—21no—
101#14519701—41no—
102#14519701D411yescharacteristic
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519698—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×SD16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#125×C61—21no—
120#125×C61—21no—
121#125×C61—41no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#106×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—41no—
151C2×C22⋊D61—41no—
152#11758222—42no—
153#11758222—81no—
154C2×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159SD16×C61—22no—
160C2×C8×C61—21no—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—41no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—41no—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184#11758202—42no—
185#11758202—81no—
186#11758202—81no—
187#11758202—81no—
188#11758201—41no—
189#11758201—81no—
190#11758198—21no—
191#11758198—41no—
192#11758198—41no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—41no—
201#11758194—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758189—42no—
209C23×C61—21no—
210C22×D61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—81no—
218D4×C61—21no—
219D4×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—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—161no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C22⋊D61—82no—
234C2×Dic61—21no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237D244—21no—
238D244—21no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—82no—
242Dic122—41no—
243Dic122—41no—
244Dic122—41no—
245Dic122—41no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61#13712yes—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#20263—611nomaximal, Sylow
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61D4211yescharacteristic
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C4×C61—21no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—81no—
270C4×C61—81no—
271C4×C61C2×#13711yescharacteristic
272C4×C61#57511yescharacteristic
273C4×C61#57611yescharacteristic
274C4×C61#57811yescharacteristic
275Dic61—41no—
276Dic61—81no—
277Dic61—81no—
278#3398—611no—
279#3381D6111yescharacteristic, complemented
280#3353—611no—
281#3331—611no—
282#1723—611no—
283#1704—611no—
284#1691—611no—
285#1689—611no—
286#1674—611no—
287#1648—611no—
288#1647—611no—
289#1644—611no—
290#1638—611no—
291#1592—611no—
292#1583—611no—
293C2×C61—81no—
294C2×C61#326811yescharacteristic
295C2×C61#327611yescharacteristic
296C2×C61#328911yescharacteristic
297D61—81no—
298#557C2×D6111yescharacteristic
299#556—611no—
300#554C2×D6111yescharacteristic
301#547—611no—
302#500—611no—
303#500—611no—
304#499—21no—
305#498C2×D6111yescharacteristic
306#497—1221no—
307#494—611no—
308#487—611no—
309#487—611no—
310#484—1221no—
311#483—1221no—
312#482—1221no—
313#479—21no—
314#478—21no—
315#477C2×D6111yescharacteristic
316#476—611no—
317#475—611no—
318#474—611no—
319#474C2×D6111yescharacteristic
320#470—1221no—
321#468—1221no—
322#464—1221no—
323#462—611no—
324#462—611no—
325#462—1221no—
326#461—611no—
327#452—1221no—
328#446—611no—
329C8×Q8C2×D6111yescharacteristic
330#441—1221no—
331C4×SD16—21no—
332C4×SD16—611no—
333C4×SD16C2×D6111yescharacteristic
334#436—611no—
335#436—611no—
336#428—1221no—
337#417—1221no—
338#335—611no—
339#334—611no—
340#333—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348#322—611no—
349C61#2026311yescharacteristic, complemented, Sylow
350C2×#41—1221no—
351C2×Q16—1221no—
352C2×Q16—1221no—
353C2×Q16—1221no—
354C2×Q16—1221no—
355C2×SD16—611no—
356C2×SD16—1221no—
357C2×SD16C22⋊D6111yescharacteristic
358C2×M16—1221no—
359C2×M16—1221no—
360C4⋊Q8—21no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#126—2441no—
366#125—21no—
367#125—21no—
368#125—41no—
369#124—1221no—
370#123—2441no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—1221no—
374C22⋊Q8—1221no—
375#121—1221no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—1221no—
379C4×Q8C22×D6111yescharacteristic
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4—611no—
383C4×D4C22×D6111yescharacteristic
384#117—1221no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—1221no—
387#107—21no—
388#107—21no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107—2441no—
393#106—21no—
394#106—21no—
395#106—611no—
396#106—1221no—
397#106—1221no—
398#106C22⋊D6111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8C22×D6111yescharacteristic
405#103—21no—
406#103—611no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—2441no—
414#103C22⋊D6111yescharacteristic
415#102—21no—
416#102—611no—
417#102—1221no—
418#102—1221no—
419#102C22⋊D6111yescharacteristic
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422#97—1221no—
423C4×C8—21no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8C22×D6111yescharacteristic
427#41—4881no—
428#41—2442no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8D4×D6111yescharacteristic
434C2×Q8C2×C22⋊D6111yescharacteristic
435C2×D4—611no—
436C2×D4—2441no—
437C2×D4C2×C22⋊D6111yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4—1221no—
441C22×C4—2441no—
442Q16—4881no—
443Q16—4881no—
444Q16—4881no—
445Q16—2442no—
446SD16—22no—
447SD16—4881no—
448SD16—2441no—
449M16—4881no—
450M16—2442no—
451C2×C8—21no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8C2×C22⋊D6111yescharacteristic
459C2×C8C2×C22⋊D6111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—611no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C4⋊C4D4×D6111yescharacteristic
479C4⋊C4C2×C22⋊D6111yescharacteristic
480C4⋊C4C2×C22⋊D6111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—1221no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C22⋊C4—2441no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—2441no—
491C42C23×D6111yescharacteristic
492C23—21no—
493C23—1221no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—2441no—
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505D4—21no—
506D4—21no—
507D4—1221no—
508D4—1221no—
509D4—4882no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—1221no—
521C2×C4—4882no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4C22×C22⋊D6111yescharacteristic
528C2×C4#1451982211yescharacteristic
529C8—21no—
530C8—41no—
531C8—1221no—
532C8—1221no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8#1451980812yes—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22D4×C22⋊D6111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—4881no—
554C4—4881no—
555C4—2441no—
556C4C2×#1451980811yescharacteristic
557C4#1684055911yescharacteristic
558C4#1684056411yescharacteristic
559C4#1684057711yescharacteristic
560C2—81no—
561C2—4881no—
562C2#2145735911yescharacteristic
563C2#2145746511yescharacteristic
564C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3381C2
socleC22×C61D42
prime radical#16840417C22
hypercenter#3381D61
hypocenterC61#20263
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #21458846C2semidirect
4. #21445493C2semidirect
5. #21445403C2semidirect
6. #21445315C2semidirect
7. #21445306C2semidirect
8. #21445213C2semidirect
9. #21445061C2semidirect
11. #21445033C2semidirect
12. #21444990C2semidirect
13. #21444722C2semidirect
14. #21444662C2semidirect
15. C61×#3381C2semidirect
279. #3381D61semidirect
349. C61#20263semidirect

Maximal subgroups

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

subgroupindex
#214588462
#214584052
#214581292
#214454932
#214454032
#214453152
#214453062
#214452132
#214450612
#214450532
#214450332
#214449902
#214447222
#214446622
C61×#33812
#2026361