Finite Group Databasebeta

← #29677087

Subgroups — #29677087

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458714C211yesmaximal, characteristic, complemented
2#21458408C211yesmaximal, characteristic
3#21458137C211yesmaximal, characteristic, complemented
4#21445415C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445391C211yesmaximal, characteristic, complemented
7#21445327C211yesmaximal, characteristic, complemented
8#21445316C211yesmaximal, characteristic, complemented
9#21445068C211yesmaximal, characteristic, complemented
10#21445052C211yesmaximal, characteristic, complemented
11#21444964C211yesmaximal, characteristic, complemented
12#21444952C211yesmaximal, characteristic, complemented
13#21444710C211yesmaximal, characteristic, complemented
14#21444702C211yesmaximal, characteristic, complemented
15C61×#3329C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840416C2211yescharacteristic
18#16840168—21no—
19#16840165C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840158C2211yescharacteristic
22#16840141C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840094—21no—
25#16840086—21no—
26#16840078—21no—
27#16840062—21no—
28#16840052C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840049—21no—
31#16840049C2211yescharacteristic
32#16840042C2211yescharacteristic
33#16840039C2211yescharacteristic
34#16840019—21no—
35#16840013—21no—
36#16839972C2211yescharacteristic
37#16839921—21no—
38#16839893C2211yescharacteristic
39#16839872—21no—
40C4×#11758199C2211yescharacteristic
41#16839841C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839805—21no—
44#16839760—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#555C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#477C2211yescharacteristic
61C61×#468—21no—
62C61×#461C2211yescharacteristic
63C61×#448—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#419—21no—
67C2×#11758224—21no—
68C2×#11758202—21no—
69C2×#11758202—41no—
70C2×#11758199D411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519769—21no—
76#14519761—41no—
77#14519757—21no—
78#14519755—41no—
79#14519753—21no—
80#14519751—21no—
81C4×D244—21no—
82C4×D244C2311yescharacteristic
83C2×C4⋊Dic61—21no—
84C4⋊C4×D61—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—41no—
88#14519710D411yescharacteristic
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519702—21no—
101#14519702—21no—
102#14519700—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#124×C61—41no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125#121×C61—21no—
126#121×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#117×C61—21no—
133#107×C61—21no—
134#106×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—41no—
156C2×C22⋊D61—41no—
157C22×Dic61—41no—
158#11758224—42no—
159#11758224—81no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—41no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165SD16×C61—41no—
166SD16×C61—81no—
167M16×C61—81no—
168C2×C8×C61—21no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C42×C61—21no—
186C42×C61—41no—
187C42×C61C2411yescharacteristic
188#11758202—82no—
189#11758202—81no—
190#11758199—22no—
191#11758198—21no—
192#11758198—41no—
193#11758198—41no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—41no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—41no—
201#11758196—41no—
202#11758194—42no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758189—81no—
210C23×C61—21no—
211C23×C61—21no—
212C22×D61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—81no—
218Q8×C61—82no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—161no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—82no—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61H(5,𝔽2)11yescharacteristic
238C22⋊D61—82no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—82no—
243D244—21no—
244D244—21no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—161no—
248Dic122—41no—
249Dic122—41no—
250Dic122—81no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—41no—
254#92418—22no—
255#92418—21no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418#13712yes—
260#20305—611nomaximal, Sylow
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61D4211yescharacteristic
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61C2×#13711yescharacteristic
279C4×C61#57511yescharacteristic
280C4×C61#57611yescharacteristic
281C4×C61#57811yescharacteristic
282Dic61—41no—
283Dic61—81no—
284Dic61—81no—
285#3384—611no—
286#3354—611no—
287#3331—611no—
288#3329D6111yescharacteristic, complemented
289#1707—611no—
290#1703—611no—
291#1703—611no—
292#1692—611no—
293#1691—611no—
294#1649—611no—
295#1647—611no—
296#1634—611no—
297#1632—611no—
298#1590—611no—
299#1589—611no—
300C2×C61—81no—
301C2×C61—81no—
302C2×C61#327311yescharacteristic
303C2×C61#327611yescharacteristic
304C2×C61#329111yescharacteristic
305D61—81no—
306#555C2×D6111yescharacteristic
307#554—611no—
308D4×Q8C2×D6111yescharacteristic
309#547—611no—
310#501—1221no—
311#500—611no—
312#498—611no—
313#498—611no—
314#494—611no—
315#487—611no—
316#487C2×D6111yescharacteristic
317#485—21no—
318#483—1221no—
319#482—1221no—
320#481—1221no—
321#478—1221no—
322#477C2×D6111yescharacteristic
323#476—611no—
324#476—611no—
325#476—611no—
326#476—1221no—
327#474—611no—
328#474—611no—
329#470—1221no—
330#469—1221no—
331#468—21no—
332#462—611no—
333#461C2×D6111yescharacteristic
334#452—1221no—
335#448—21no—
336#446—611no—
337#442—1221no—
338C4×SD16C2×D6111yescharacteristic
339C4×D8—611no—
340#436—611no—
341#436—611no—
342#436C2×D6111yescharacteristic
343#428—1221no—
344#419—21no—
345#417—1221no—
346#335—611no—
347#334—611no—
348#333—611no—
349#333—611no—
350#332—611no—
351#332—611no—
352Q8⋊C8—611no—
353D4⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356C82—611no—
357C61#2030511yescharacteristic, complemented, Sylow
358C2×#41—1221no—
359C22×Q8—21no—
360C2×Q16—1221no—
361C2×Q16—2441no—
362C2×SD16—21no—
363C2×SD16C22⋊D6111yescharacteristic
364C2×D8—611no—
365C2×M16—21no—
366C2×M16—1221no—
367C2×M16—1221no—
368C4⋊Q8—21no—
369C4⋊Q8—611no—
370C4⋊Q8—611no—
371C4⋊Q8C22×D6111yescharacteristic
372C4⋊Q8C22×D6111yescharacteristic
373#125—1221no—
374#124—41no—
375#123—2441no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380C22⋊Q8—2441no—
381#121—21no—
382#121—21no—
383#121—1221no—
384C4×Q8C22×D6111yescharacteristic
385C4×D4—21no—
386C4×D4—611no—
387C4×D4—1221no—
388C4×D4C22×D6111yescharacteristic
389C4×D4C22×D6111yescharacteristic
390#117—21no—
391#117—21no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394#107—21no—
395#107—611no—
396#107—1221no—
397#107—1221no—
398#107—2441no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402#106—1221no—
403#106—1221no—
404#106—1221no—
405#106—1221no—
406#106C22⋊D6111yescharacteristic
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103C22⋊D6111yescharacteristic
420#102—611no—
421#102—611no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102C22⋊D6111yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—1221no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8C22×D6111yescharacteristic
435#41—4881no—
436#41—2442no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8C2×C22⋊D6111yescharacteristic
445C2×D4—41no—
446C2×D4—611no—
447C2×D4—2441no—
448C2×D4D4×D6111yescharacteristic
449C2×D4C2×C22⋊D6111yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—1221no—
454C22×C4—2441no—
455C22×C4—2441no—
456Q16—4882no—
457Q16—4881no—
458SD16—41no—
459SD16—81no—
460D8—1222no—
461M16—81no—
462M16—4881no—
463M16—2442no—
464C2×C8—21no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8C2×C22⋊D6111yescharacteristic
472C2×C8C2×C22⋊D6111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—611no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—2441no—
485C4⋊C4—2441no—
486C4⋊C4—2441no—
487C4⋊C4D4×D6111yescharacteristic
488C4⋊C4C2×C22⋊D6111yescharacteristic
489C4⋊C4C2×C22⋊D6111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—1221no—
496C22⋊C4—2441no—
497C22⋊C4—2441no—
498C42—21no—
499C42—41no—
500C42C23×D6111yescharacteristic
501C23—21no—
502C23—21no—
503C23—1221no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—82no—
510Q8—4881no—
511Q8—2441no—
512Q8—2441no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—161no—
518D4—1221no—
519D4—1221no—
520D4—4882no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—1221no—
533C2×C4—9761no—
534C2×C4—4882no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4C2×D4×D6111yescharacteristic
540C2×C4C22×C22⋊D6111yescharacteristic
541C2×C4#1451982211yescharacteristic
542C8—21no—
543C8—21no—
544C8—41no—
545C8—612no—
546C8—1222no—
547C8—1221no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22D4×C22⋊D6111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—4881no—
569C4—4881no—
570C4—2441no—
571C4#137×D6111yescharacteristic
572C4#1684056011yescharacteristic
573C4#1684056511yescharacteristic
574C4#1684057811yescharacteristic
575C2—81no—
576C2—81no—
577C2—4881no—
578C2#2145742611yescharacteristic
579C2#2145745911yescharacteristic
580C2#2145761011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3329C2
socleC22×C61D42
prime radical#21458408C2
hypercenter#3329D61
hypocenterC61#20305
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3329

Complements

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

NH ≅ G/Ntype
1. #21458714C2semidirect
3. #21458137C2semidirect
4. #21445415C2semidirect
5. #21445394C2semidirect
6. #21445391C2semidirect
7. #21445327C2semidirect
8. #21445316C2semidirect
9. #21445068C2semidirect
10. #21445052C2semidirect
11. #21444964C2semidirect
12. #21444952C2semidirect
13. #21444710C2semidirect
14. #21444702C2semidirect
15. C61×#3329C2semidirect
288. #3329D61semidirect
357. C61#20305semidirect

Maximal subgroups

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

subgroupindex
#214587142
#214584082
#214581372
#214454152
#214453942
#214453912
#214453272
#214453162
#214450682
#214450522
#214449642
#214449522
#214447102
#214447022
C61×#33292
#2030561