Finite Group Databasebeta

← #29670946

Subgroups — #29670946

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458684C211yesmaximal, characteristic, complemented
2#21458439C211yesmaximal, characteristic, complemented
3#21458176C211yesmaximal, characteristic, complemented
4#21445499C211yesmaximal, characteristic, complemented
5#21445316C211yesmaximal, characteristic, complemented
6#21445274C211yesmaximal, characteristic, complemented
7#21445218C211yesmaximal, characteristic, complemented
8#21445216C211yesmaximal, characteristic, complemented
9#21445024C211yesmaximal, characteristic, complemented
10#21444970C211yesmaximal, characteristic, complemented
11#21444964C211yesmaximal, characteristic, complemented
12#21444951C211yesmaximal, characteristic, complemented
13#21444649C211yesmaximal, characteristic, complemented
14#21444631C211yesmaximal, characteristic, complemented
15C61×#3303C211yesmaximal, characteristic
16#16840469C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840163—21no—
21#16840158C2211yescharacteristic
22#16840141C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840103—21no—
25#16840092—21no—
26#16840078—21no—
27#16840073—21no—
28#16840060—21no—
29#16840060—21no—
30#16840054C2211yescharacteristic
31#16840052C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840052C2211yescharacteristic
34#16840052C2211yescharacteristic
35#16840044C2211yescharacteristic
36#16840006—21no—
37#16839989—21no—
38C8×Dic122C2211yescharacteristic
39C4×#11758200C2211yescharacteristic
40D8×Dic61—21no—
41#16839840C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#16839805—21no—
44C2×#14519708—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839492C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#555C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#476C2211yescharacteristic
61C61×#465—21no—
62C61×#461C2211yescharacteristic
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C61×#416—21no—
67C2×#11758202—41no—
68C2×#11758200D411yescharacteristic
69C2×#11758194—21no—
70C22×#92418—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519768—21no—
74#14519768—21no—
75#14519756—21no—
76#14519756—21no—
77#14519754—41no—
78#14519754—41no—
79C4×Dic122C2311yescharacteristic
80D4×Dic61—21no—
81D4×Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84#14519711—21no—
85#14519711—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96#14519708D411yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—41no—
104#14519700D411yescharacteristic
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×SD16×C61—21no—
117C2×D8×C61D411yescharacteristic
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#124×C61—41no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
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×D4×C61—41no—
149C2×D4×C61—41no—
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—41no—
157C22×Dic61—41no—
158C22×Dic61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C2×D411yescharacteristic
162SD16×C61—81no—
163D8×C61—22no—
164C2×C8×C61—21no—
165C2×C8×C61—81no—
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—41no—
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C42×C61—41no—
183C42×C61C2411yescharacteristic
184C22⋊Dic61—41no—
185C22⋊Dic61—41no—
186#11758202—82no—
187#11758200—22no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—41no—
193C4⋊Dic61—41no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61—21no—
199#11758194—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—42no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213D4×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—82no—
219D4×C61—161no—
220D4×C61#13712yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—82no—
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—161no—
241C2×Dic61—161no—
242Dic122—21no—
243Dic122—21no—
244Dic122—81no—
245Dic122—81no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418#13512yes—
255#19861—611nomaximal, Sylow
256C22×C61—22no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61D4211yescharacteristic
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61C2×#13511yescharacteristic
273C4×C61C2×#13711yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57811yescharacteristic
276Dic61—41no—
277Dic61—41no—
278Dic61—81no—
279Dic61—81no—
280#3380—611no—
281#3357—611no—
282#3335—611no—
283#3303D6111yescharacteristic
284#1723—611no—
285#1691—611no—
286#1684—611no—
287#1675—611no—
288#1675—611no—
289#1643—611no—
290#1635—611no—
291#1634—611no—
292#1632—611no—
293#1581—611no—
294SD16⋊C8—611no—
295C2×C61—42no—
296C2×C61—81no—
297C2×C61—81no—
298C2×C61#326611yescharacteristic
299C2×C61#328311yescharacteristic
300C2×C61#328811yescharacteristic
301#555C2×D6111yescharacteristic
302#554—611no—
303#554—611no—
304#547C2×D6111yescharacteristic
305#500—611no—
306#500—611no—
307#499—1221no—
308#498—611no—
309#494—611no—
310#487—611no—
311#487C2×D6111yescharacteristic
312#485—21no—
313#485—1221no—
314#483—1221no—
315#481—1221no—
316#480—1221no—
317#478—1221no—
318#478—1221no—
319#477—611no—
320#476—611no—
321#476—611no—
322#476—611no—
323#476—611no—
324#476C2×D6111yescharacteristic
325#475—611no—
326#468—1221no—
327#465—21no—
328#465—1221no—
329#461C2×D6111yescharacteristic
330#449—21no—
331C8×Q8—611no—
332C4×SD16—611no—
333C4×D8—1221no—
334C4×D8C2×D6111yescharacteristic
335#436—611no—
336C8×D4—611no—
337C8×D4C2×D6111yescharacteristic
338#428—1221no—
339C2×#106—1221no—
340#416—21no—
341#335—611no—
342#335—611no—
343#333—611no—
344#333—611no—
345#333—611no—
346#332—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351#322—611no—
352C61#1986111yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×Q16—2441no—
355C2×SD16—21no—
356C2×SD16—611no—
357C2×D8C22⋊D6111yescharacteristic
358C2×M16—1221no—
359C22×C8—21no—
360C22×C8—1221no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#125—1221no—
366#125—1221no—
367#124—41no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—1221no—
371C22⋊Q8—1221no—
372C22⋊Q8—2441no—
373C22⋊Q8—2441no—
374#121—21no—
375#121—21no—
376#121—21no—
377C4×Q8—611no—
378C4×D4—1221no—
379C4×D4—1221no—
380C4×D4C22×D6111yescharacteristic
381C4×D4C22×D6111yescharacteristic
382C4×D4C22×D6111yescharacteristic
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107—1221no—
393#107C22⋊D6111yescharacteristic
394#106—21no—
395#106—611no—
396#106—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402#106—1221no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8C22×D6111yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—611no—
412#103—1221no—
413#103—1221no—
414#103—2441no—
415#102—21no—
416#102—611no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102C22⋊D6111yescharacteristic
422#102C22⋊D6111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—611no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4D4×D6111yescharacteristic
440C2×D4C2×C22⋊D6111yescharacteristic
441C2×D4C2×C22⋊D6111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—2441no—
447C22×C4—2441no—
448Q16—4882no—
449SD16—81no—
450SD16—1222no—
451D8—22no—
452M16—2442no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—2442no—
462C2×C8C2×C22⋊D6111yescharacteristic
463C2×C8C2×C22⋊D6111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—611no—
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
480C4⋊C4C2×C22⋊D6111yescharacteristic
481C4⋊C4C2×C22⋊D6111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C42—41no—
491C42—1221no—
492C42C23×D6111yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—1221no—
500Q8—1221no—
501Q8—4881no—
502Q8—4881no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—82no—
509D4—161no—
510D4#1451980712yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—9761no—
526C2×C4—9761no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4C2×D4×D6111yescharacteristic
530C2×C4C22×C22⋊D6111yescharacteristic
531C2×C4#1451982211yescharacteristic
532C8—21no—
533C8—21no—
534C8—41no—
535C8—612no—
536C8—1221no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22D4×C22⋊D6111yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—4881no—
558C4—4881no—
559C4—2441no—
560C4—2441no—
561C4#135×D6111yescharacteristic
562C4C2×#1451980711yescharacteristic
563C4#1684057311yescharacteristic
564C4#1684057611yescharacteristic
565C2—42no—
566C2—81no—
567C2—81no—
568C2#2145732511yescharacteristic
569C2#2145753511yescharacteristic
570C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3303C2
socleC22×C61D42
hypercenter#3303D61
hypocenterC61#19861
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #21458684C2semidirect
2. #21458439C2semidirect
3. #21458176C2semidirect
4. #21445499C2semidirect
5. #21445316C2semidirect
6. #21445274C2semidirect
7. #21445218C2semidirect
8. #21445216C2semidirect
9. #21445024C2semidirect
10. #21444970C2semidirect
11. #21444964C2semidirect
12. #21444951C2semidirect
13. #21444649C2semidirect
14. #21444631C2semidirect
352. C61#19861semidirect

Maximal subgroups

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

subgroupindex
#214586842
#214584392
#214581762
#214454992
#214453162
#214452742
#214452182
#214452162
#214450242
#214449702
#214449642
#214449512
#214446492
#214446312
C61×#33032
#1986161