Finite Group Databasebeta

← #29670035

Subgroups — #29670035

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458557C211yesmaximal, characteristic, complemented
2#21458486C211yesmaximal, characteristic, complemented
3#21458232C211yesmaximal, characteristic, complemented
4#21445480C211yesmaximal, characteristic, complemented
5#21445356C211yesmaximal, characteristic, complemented
6#21445270C211yesmaximal, characteristic, complemented
7#21445226C211yesmaximal, characteristic, complemented
8#21445203C211yesmaximal, characteristic, complemented
9#21445012C211yesmaximal, characteristic, complemented
10#21444964C211yesmaximal, characteristic, complemented
11#21444958C211yesmaximal, characteristic, complemented
12#21444927C211yesmaximal, characteristic, complemented
13#21444655C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3305C211yesmaximal, characteristic
16Q8×Dic122C2211yescharacteristic
17#16840482C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840141C2211yescharacteristic
20#16840120—21no—
21#16840113C2211yescharacteristic
22#16840108—21no—
23#16840108C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840103—21no—
26#16840083—21no—
27#16840054C2211yescharacteristic
28#16840052—21no—
29#16840052C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840046—21no—
32#16840042C2211yescharacteristic
33#16839989—21no—
34#16839982—21no—
35#16839972C2211yescharacteristic
36#16839959—21no—
37#16839959C2211yescharacteristic
38#16839892C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839866—21no—
41C4×#11758200—21no—
42C4×#11758200C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44#16839798—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#555C2211yescharacteristic
57C61×#550C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#482—21no—
60C61×#477C2211yescharacteristic
61C61×#466—21no—
62C61×#459C2211yescharacteristic
63C61×#449—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C61×#416—21no—
67C2×#11758202—21no—
68C2×#11758202—41no—
69C2×#11758200—21no—
70C2×#11758200D411yescharacteristic
71C22×#92418—21no—
72#14519777—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519776—21no—
76#14519776—41no—
77#14519770—41no—
78#14519764—21no—
79#14519756—21no—
80Q8×Dic61—21no—
81C4×Dic122—21no—
82C4×Dic122C2311yescharacteristic
83#14519742—21no—
84#14519736—21no—
85#14519710—21no—
86#14519710—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700D411yescharacteristic
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—41no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111#14519687—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×SD16×C61D411yescharacteristic
117C2×D8×C61—21no—
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61—21no—
121#127×C61C2311yescharacteristic
122#124×C61—41no—
123#121×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—41no—
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×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
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×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162C2×Dic122C2×D411yescharacteristic
163SD16×C61—22no—
164D8×C61—81no—
165C2×C8×C61—21no—
166C2×C8×C61—81no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C42×C61—21no—
181C42×C61—41no—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185#11758202—42no—
186#11758202—82no—
187#11758200—41no—
188#11758200—42no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—41no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61—21no—
199C4×Dic61—41no—
200C4×Dic61—41no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—42no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—41no—
211Q8×C61—21no—
212Q8×C61—81no—
213Q8×C61#13512yes—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—82no—
223D4×C61—81no—
224D4×C61—161no—
225D4×C61—161no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—82no—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243Dic122—21no—
244Dic122—21no—
245Dic122—41no—
246Dic122—41no—
247Dic122—81no—
248Dic122—161no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#19800—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61D4211yescharacteristic
269C4×C61—22no—
270C4×C61—21no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—81no—
275C4×C61C2×#13511yescharacteristic
276C4×C61#57511yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57811yescharacteristic
279Dic61—41no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283#3369—611no—
284#3362—611no—
285#3340—611no—
286#3305D6111yescharacteristic
287#1720—611no—
288#1698—611no—
289#1683—611no—
290#1677—611no—
291#1672—611no—
292#1641—611no—
293#1634—611no—
294#1633—611no—
295#1628—611no—
296#1582—611no—
297SD16⋊C8—611no—
298C2×C61—81no—
299C2×C61—81no—
300C2×C61—161no—
301C2×C61#326911yescharacteristic
302C2×C61#328211yescharacteristic
303C2×C61#328811yescharacteristic
304Q82—611no—
305#556—611no—
306#555C2×D6111yescharacteristic
307#550C2×D6111yescharacteristic
308#498—611no—
309#494—611no—
310#489—1221no—
311#487—611no—
312#486—611no—
313#486—611no—
314#486—1221no—
315#486C2×D6111yescharacteristic
316#485—1221no—
317#482—21no—
318#482—1221no—
319#477—611no—
320#477C2×D6111yescharacteristic
321#476—611no—
322#476—611no—
323#476—1221no—
324#475—1221no—
325#474—611no—
326#466—21no—
327#465—1221no—
328#464—1221no—
329#462—611no—
330#460—611no—
331#460—1221no—
332#459C2×D6111yescharacteristic
333#449—21no—
334#446—611no—
335C8×Q8—611no—
336#441—1221no—
337C4×SD16—611no—
338C4×SD16—1221no—
339C4×SD16C2×D6111yescharacteristic
340C8×D4—611no—
341C8×D4C2×D6111yescharacteristic
342#427—1221no—
343#416—21no—
344#335—611no—
345#334—611no—
346#333—611no—
347#333—611no—
348#332—611no—
349#331—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352D4⋊C8—611no—
353D4⋊C8—611no—
354#322—611no—
355C61#1980011yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×Q16—1221no—
358C2×Q16—2441no—
359C2×SD16—611no—
360C2×SD16—1221no—
361C2×SD16C22⋊D6111yescharacteristic
362C2×D8—21no—
363C22×C8—21no—
364C22×C8—1221no—
365C4⋊Q8—611no—
366C4⋊Q8—611no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369C4⋊Q8—2441no—
370C4⋊Q8C22×D6111yescharacteristic
371#127—21no—
372#127C22×D6111yescharacteristic
373#126—2441no—
374#124—41no—
375#124—1221no—
376C22⋊Q8—1221no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—41no—
381C4×Q8—611no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8—1221no—
385C4×Q8C22×D6111yescharacteristic
386C4×D4—21no—
387C4×D4C22×D6111yescharacteristic
388C4×D4C22×D6111yescharacteristic
389#117—21no—
390#117—21no—
391#117—1221no—
392#107—21no—
393#107—1221no—
394#107—1221no—
395#106—611no—
396#106—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
400#106C22⋊D6111yescharacteristic
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8C22×D6111yescharacteristic
407#103—21no—
408#103—611no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103C22⋊D6111yescharacteristic
414#102—21no—
415#102—21no—
416#102—21no—
417#102—611no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—2441no—
425#102C22⋊D6111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—1221no—
428#97—1221no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—611no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—2441no—
440C2×Q8C2×C22⋊D6111yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4D4×D6111yescharacteristic
448C2×D4C2×C22⋊D6111yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452Q16—4882no—
453Q16—2442no—
454SD16—22no—
455SD16—2441no—
456SD16—2442no—
457D8—81no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—2442no—
467C2×C8C2×C22⋊D6111yescharacteristic
468C2×C8C2×C22⋊D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—611no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C4⋊C4D4×D6111yescharacteristic
482C4⋊C4C2×C22⋊D6111yescharacteristic
483C4⋊C4C2×C22⋊D6111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—2441no—
490C22⋊C4—2441no—
491C42—21no—
492C42—41no—
493C42—1221no—
494C42—2441no—
495C42—2441no—
496C42C23×D6111yescharacteristic
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—81no—
502Q8—1221no—
503Q8—1221no—
504Q8—9761no—
505Q8—4881no—
506Q8—2441no—
507Q8—2441no—
508Q8#1451979712yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—82no—
518D4—81no—
519D4—161no—
520D4—161no—
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—82no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4C2×D4×D6111yescharacteristic
536C2×C4C22×C22⋊D6111yescharacteristic
537C2×C4#1451982211yescharacteristic
538C8—21no—
539C8—21no—
540C8—41no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D4×C22⋊D6111yescharacteristic
557C4—22no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—4881no—
564C4—4881no—
565C4—2441no—
566C4—2441no—
567C4C2×#1451979711yescharacteristic
568C4#1684055911yescharacteristic
569C4#1684057311yescharacteristic
570C4#1684057611yescharacteristic
571C2—81no—
572C2—81no—
573C2—161no—
574C2#2145737411yescharacteristic
575C2#2145752211yescharacteristic
576C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3305C2
socleC22×C61D42
hypercenter#3305D61
hypocenterC61#19800
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3305

Complements

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

NH ≅ G/Ntype
1. #21458557C2semidirect
2. #21458486C2semidirect
3. #21458232C2semidirect
4. #21445480C2semidirect
5. #21445356C2semidirect
6. #21445270C2semidirect
7. #21445226C2semidirect
8. #21445203C2semidirect
9. #21445012C2semidirect
10. #21444964C2semidirect
11. #21444958C2semidirect
12. #21444927C2semidirect
13. #21444655C2semidirect
14. SD16⋊#92418C2semidirect
355. C61#19800semidirect

Maximal subgroups

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

subgroupindex
#214585572
#214584862
#214582322
#214454802
#214453562
#214452702
#214452262
#214452032
#214450122
#214449642
#214449582
#214449272
#214446552
SD16⋊#924182
C61×#33052
#1980061