Finite Group Databasebeta

← #29669705

Subgroups — #29669705

Order 15616.

606 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#21458464C211yesmaximal, characteristic, complemented
2#21458162C211yesmaximal, characteristic
3#21458137C211yesmaximal, characteristic, complemented
4#21445466C211yesmaximal, characteristic, complemented
5#21445363C211yesmaximal, characteristic, complemented
6#21445270C211yesmaximal, characteristic, complemented
7#21445268C211yesmaximal, characteristic, complemented
8#21445211C211yesmaximal, characteristic, complemented
9#21445102C211yesmaximal, characteristic, complemented
10#21445089C211yesmaximal, characteristic, complemented
11#21445031C211yesmaximal, characteristic, complemented
12#21444970C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3302C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840416C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840116—21no—
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840094—21no—
25#16840075—21no—
26#16840073—21no—
27#16840069—21no—
28#16840052C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840042C2211yescharacteristic
31#16840039C2211yescharacteristic
32#16840019—21no—
33#16839996—21no—
34#16839974—21no—
35#16839972C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839921—21no—
38Q8×#92418C2211yescharacteristic
39C4×#11758201—21no—
40C4×#11758199C2211yescharacteristic
41#16839841C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43C2×#14519710—21no—
44#16839760—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#474C2211yescharacteristic
61C61×#467—21no—
62C61×#462C2211yescharacteristic
63C61×#452—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C61×#416—21no—
67C2×#11758224—21no—
68C2×#11758202—21no—
69C2×#11758201—21no—
70C2×#11758199D411yescharacteristic
71C2×#11758189—21no—
72C22×#92418—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—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91#14519708—21no—
92#14519708—41no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519700—21no—
103#14519700—41no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698D411yescharacteristic
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×Q16×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#126×C61—41no—
122#124×C61—21no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132C2×C4⋊C4×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×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—41no—
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—41no—
155C2×C22⋊D61—41no—
156C22×Dic61—41no—
157#11758224—42no—
158#11758224—81no—
159C2×D244C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—41no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164Q16×C61—81no—
165SD16×C61—22no—
166C2×C8×C61—21no—
167C2×C8×C61—81no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
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—81no—
189#11758201—42no—
190#11758199—41no—
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—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—42no—
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—41no—
218Q8×C61—41no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—82no—
223D4×C61#13512yes—
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—21no—
255#92418—21no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#19778—611nomaximal, Sylow
261C22×C61—22no—
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×#13511yescharacteristic
279C4×C61#57511yescharacteristic
280C4×C61#57611yescharacteristic
281C4×C61#57811yescharacteristic
282Dic61—41no—
283Dic61—81no—
284Dic61—81no—
285#3360—611no—
286#3334—611no—
287#3331—611no—
288#3302D6111yescharacteristic, complemented
289#1718—611no—
290#1699—611no—
291#1683—611no—
292#1683—611no—
293#1674—611no—
294#1654—611no—
295#1652—611no—
296#1644—611no—
297#1635—611no—
298#1581—611no—
299SD16⋊C8—611no—
300C2×C61—42no—
301C2×C61—81no—
302C2×C61#326911yescharacteristic
303C2×C61#328011yescharacteristic
304C2×C61#328911yescharacteristic
305D61—81no—
306#556C2×D6111yescharacteristic
307#554—611no—
308#547—611no—
309#547C2×D6111yescharacteristic
310#500—611no—
311#498—611no—
312#488—1221no—
313#487—611no—
314#487—611no—
315#487—611no—
316#487C2×D6111yescharacteristic
317#485—21no—
318#483—1221no—
319#480—1221no—
320#480—1221no—
321#479—1221no—
322#476—611no—
323#476—611no—
324#474—611no—
325#474—611no—
326#474C2×D6111yescharacteristic
327#470—1221no—
328#467—21no—
329#466—1221no—
330#463—1221no—
331#462—611no—
332#462C2×D6111yescharacteristic
333#461—611no—
334#452—21no—
335#452—1221no—
336C8×Q8—611no—
337C4×SD16—1221no—
338C4×SD16C2×D6111yescharacteristic
339C4×D8—611no—
340#436—611no—
341C8×D4—611no—
342C8×D4C2×D6111yescharacteristic
343C2×#107—1221no—
344#417—1221no—
345#416—21no—
346#335—611no—
347#335—611no—
348#333—611no—
349#332—611no—
350#332—611no—
351#332—611no—
352Q8⋊C8—611no—
353D4⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356#322—611no—
357C61#1977811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41—1221no—
360C2×Q16—21no—
361C2×Q16—1221no—
362C2×SD16—1221no—
363C2×SD16C22⋊D6111yescharacteristic
364C2×D8—611no—
365C2×M16—1221no—
366C22×C8—21no—
367C22×C8—1221no—
368C4⋊Q8—611no—
369C4⋊Q8—611no—
370C4⋊Q8C22×D6111yescharacteristic
371C4⋊Q8C22×D6111yescharacteristic
372#126—41no—
373#125—1221no—
374#124—21no—
375#123—41no—
376#123—2441no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—1221no—
380C22⋊Q8—1221no—
381C22⋊Q8—2441no—
382#121—21no—
383#121—1221no—
384C4×Q8—21no—
385C4×Q8C22×D6111yescharacteristic
386C4×D4—611no—
387C4×D4—1221no—
388C4×D4C22×D6111yescharacteristic
389C4×D4C22×D6111yescharacteristic
390#117—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394#107—21no—
395#107—611no—
396#107—1221no—
397#107—1221no—
398#107—1221no—
399#107—1221no—
400#106—1221no—
401#106—1221no—
402#106—2441no—
403#106C22⋊D6111yescharacteristic
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8C22×D6111yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—2441no—
419#103C22⋊D6111yescharacteristic
420#102—21no—
421#102—611no—
422#102—611no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102C22⋊D6111yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—1221no—
434C4×C8C22×D6111yescharacteristic
435#41—42no—
436#41—81no—
437#41—4881no—
438#41—2442no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8C2×C22⋊D6111yescharacteristic
444C2×D4—41no—
445C2×D4—611no—
446C2×D4—2441no—
447C2×D4D4×D6111yescharacteristic
448C2×D4C2×C22⋊D6111yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—1221no—
453C22×C4—2441no—
454C22×C4—2441no—
455Q16—81no—
456Q16—4881no—
457SD16—22no—
458SD16—2442no—
459D8—2441no—
460M16—4881no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—2442no—
470C2×C8C2×C22⋊D6111yescharacteristic
471C2×C8C2×C22⋊D6111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
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—41no—
509Q8—41no—
510Q8—4881no—
511Q8—2441no—
512Q8—2441no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—82no—
517D4—1221no—
518D4—1221no—
519D4—4882no—
520D4#1451979712yes—
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—1221no—
546C8—1221no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—22no—
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—
571C4C2×#1451979711yescharacteristic
572C4#1684055911yescharacteristic
573C4#1684056511yescharacteristic
574C4#1684057611yescharacteristic
575C2—42no—
576C2—81no—
577C2—4881no—
578C2#2145737411yescharacteristic
579C2#2145750011yescharacteristic
580C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3302C2
socleC22×C61D42
prime radical#21458162C2
hypercenter#3302D61
hypocenterC61#19778
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3302

Complements

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

NH ≅ G/Ntype
1. #21458464C2semidirect
3. #21458137C2semidirect
4. #21445466C2semidirect
5. #21445363C2semidirect
6. #21445270C2semidirect
7. #21445268C2semidirect
8. #21445211C2semidirect
9. #21445102C2semidirect
10. #21445089C2semidirect
11. #21445031C2semidirect
12. #21444970C2semidirect
13. #21444648C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3302C2semidirect
288. #3302D61semidirect
357. C61#19778semidirect

Maximal subgroups

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

subgroupindex
#214584642
#214581622
#214581372
#214454662
#214453632
#214452702
#214452682
#214452112
#214451022
#214450892
#214450312
#214449702
#214446482
SD16⋊#924182
C61×#33022
#1977861