Finite Group Databasebeta

← #29670151

Subgroups — #29670151

Order 15616.

624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458694C211yesmaximal, characteristic, complemented
2#21458459C211yesmaximal, characteristic, complemented
3#21457461C211yesmaximal, characteristic
4#21445451C211yesmaximal, characteristic, complemented
5#21445320C211yesmaximal, characteristic, complemented
6#21445242C211yesmaximal, characteristic, complemented
7#21445198C211yesmaximal, characteristic, complemented
8#21445187C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic
10#21445095C211yesmaximal, characteristic, complemented
11#21445026C211yesmaximal, characteristic, complemented
12#21444983C211yesmaximal, characteristic, complemented
13#21444663C211yesmaximal, characteristic, complemented
14#21444631C211yesmaximal, characteristic, complemented
15C61×#3335C211yesmaximal, characteristic
16C2×#14519807—21no—
17#16840490C2211yescharacteristic
18D4×Dic122C2211yescharacteristic
19#16840161—21no—
20#16840158C2211yescharacteristic
21#16840158C2211yescharacteristic
22#16840141C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840111—21no—
26#16840066—21no—
27#16840062—21no—
28#16840054C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840046—21no—
31#16840042C2211yescharacteristic
32#16840018—21no—
33#16839969C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839965—21no—
37#16839924—21no—
38#16839917—21no—
39Q8×#92418C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41#16839853—21no—
42C4×#11758200—21no—
43C4×#11758200C2211yescharacteristic
44#16839840C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#483—21no—
60C61×#481—21no—
61C61×#476C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C61×#465—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#106×C61—21no—
67C22×Dic122—21no—
68#14519807—44no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200D411yescharacteristic
75C2×#11758194—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519776—21no—
79#14519775—21no—
80#14519769—21no—
81#14519767—41no—
82#14519756—21no—
83#14519754—41no—
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87D4×Dic61—21no—
88#14519710—21no—
89#14519710—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—41no—
94#14519708D411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519702—21no—
101#14519702—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701—41no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110#14519698D411yescharacteristic
111C22⋊#92418—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C8×Dic61—21no—
116C2×#41×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126#121×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133#106×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137#106×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
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—
156C22×C4×C61—41no—
157C22×Dic61—41no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—42no—
161C2×Dic122—41no—
162C2×Dic122—81no—
163C2×Dic122C2×D411yescharacteristic
164SD16×C61—41no—
165C2×C8×C61—21no—
166C2×C8×C61—42no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
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—
184C42×C61—21no—
185C42×C61C2411yescharacteristic
186C22⋊Dic61—41no—
187#11758202—42no—
188#11758202—42no—
189#11758202—81no—
190#11758200—42no—
191#11758200—42no—
192#11758200SD1614yescomplemented
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—41no—
200#11758196—41no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—21no—
204C4×Dic61—41no—
205#11758194—42no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C23×C61—21no—
213C23×C61—21no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—81no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—82no—
223D4×C61C2×SD1612yes—
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×C61—161no—
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—
243C2×Dic61—82no—
244Dic122—21no—
245Dic122—41no—
246Dic122—41no—
247Dic122—41no—
248Dic122—41no—
249Dic122—82no—
250Dic122C2×SD1612yes—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—41no—
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418C2×SD1612yes—
260#19808—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61D4211yescharacteristic
268C4×C61—21no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61C22×SD1611yescharacteristic
276C4×C61#57511yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57811yescharacteristic
279Dic61—22no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283#3381—611no—
284#3359—611no—
285#3335D6111yescharacteristic
286#3276—611no—
287#1716—611no—
288#1691—611no—
289#1679—611no—
290#1672—611no—
291#1670—611no—
292#1654—611no—
293#1653—611no—
294#1643—611no—
295#1637—611no—
296#1583—611no—
297SD16⋊C8—611no—
298C2×C61—42no—
299C2×C61—81no—
300C2×C61#326911yescharacteristic
301C2×C61D4×SD1611yescharacteristic
302C2×C61#328911yescharacteristic
303C2×#137—1221no—
304#557—611no—
305#554C2×D6111yescharacteristic
306D4×Q8—611no—
307#547C2×D6111yescharacteristic
308#499—1221no—
309#498—611no—
310#498—611no—
311#498C2×D6111yescharacteristic
312#494—611no—
313#487—611no—
314#487—611no—
315#487—1221no—
316#483—21no—
317#481—21no—
318#479—1221no—
319#478—1221no—
320#477—611no—
321#476C2×D6111yescharacteristic
322#475—611no—
323#475—1221no—
324#475C2×D6111yescharacteristic
325#474—611no—
326#470—1221no—
327#465—21no—
328#462—611no—
329#461—611no—
330#461—611no—
331#461—1221no—
332#452—1221no—
333#451—1221no—
334C8×Q8—611no—
335C8×Q8—611no—
336C4×SD16—611no—
337C4×SD16—1221no—
338C4×SD16—1221no—
339C4×SD16C2×D6111yescharacteristic
340#436—611no—
341C8×D4C2×D6111yescharacteristic
342C2×#106—21no—
343#335—611no—
344#334—611no—
345#333—611no—
346#332—611no—
347#332—611no—
348#332—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353#322—611no—
354C61#1980811yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C22×Q8—1221no—
357#137—2444no—
358C2×Q16—1221no—
359C2×Q16—1221no—
360C2×Q16—1221no—
361C2×SD16—611no—
362C2×SD16—1221no—
363C2×SD16—1221no—
364C2×SD16C22⋊D6111yescharacteristic
365C2×M16—1221no—
366C22×C8—21no—
367C4⋊Q8—611no—
368C4⋊Q8—611no—
369C4⋊Q8—1221no—
370C4⋊Q8—1221no—
371C4⋊Q8C22×D6111yescharacteristic
372C4⋊Q8C22×D6111yescharacteristic
373#125—21no—
374#125—1221no—
375#125—2441no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—1221no—
381C22⋊Q8—2441no—
382#121—21no—
383C4×Q8—611no—
384C4×Q8—1221no—
385C4×Q8—1221no—
386C4×Q8C22×D6111yescharacteristic
387C4×D4—21no—
388C4×D4—1221no—
389C4×D4C22×D6111yescharacteristic
390C4×D4C22×D6111yescharacteristic
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393#107—1221no—
394#107—1221no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—611no—
400#106—1221no—
401#106—1221no—
402#106—1221no—
403#106—2441no—
404#106C22⋊D6111yescharacteristic
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411#103—21no—
412#103—611no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—2441no—
421#103C22⋊D6111yescharacteristic
422#102—21no—
423#102—611no—
424#102—1221no—
425#102C22⋊D6111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—611no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—4881no—
441C2×Q8—2441no—
442C2×Q8—2442no—
443C2×Q8C2×C22⋊D6111yescharacteristic
444C2×D4—41no—
445C2×D4D4×D6111yescharacteristic
446C2×D4C2×C22⋊D6111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—2441no—
452Q16—4881no—
453Q16—2442no—
454Q16—2442no—
455SD16—41no—
456SD16—614no—
457SD16—2442no—
458SD16—2442no—
459M16—2442no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8C2×C22⋊D6111yescharacteristic
469C2×C8C2×C22⋊D6111yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—2441no—
485C4⋊C4—2441no—
486C4⋊C4—2441no—
487C4⋊C4—2441no—
488C4⋊C4D4×D6111yescharacteristic
489C4⋊C4C2×C22⋊D6111yescharacteristic
490C4⋊C4C2×C22⋊D6111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—2441no—
496C42—21no—
497C42—1221no—
498C42—2441no—
499C42C23×D6111yescharacteristic
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—612no—
508Q8—1221no—
509Q8—4882no—
510Q8—2441no—
511Q8—2441no—
512Q8—2441no—
513Q8—2441no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4SD16×D6112yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—161no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—4882no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C22×C22⋊D6111yescharacteristic
538C2×C4#1451982211yescharacteristic
539C8—21no—
540C8—21no—
541C8—41no—
542C8—612no—
543C8—1221no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22D4×C22⋊D6111yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—1222no—
563C4—4881no—
564C4—4881no—
565C4—2441no—
566C4C2×SD16×D6111yescharacteristic
567C4#1684056011yescharacteristic
568C4#1684056811yescharacteristic
569C4#1684057711yescharacteristic
570C2—42no—
571C2—81no—
572C2#2145737011yescharacteristic
573C2SD16×C22⋊D6111yescharacteristic
574C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3335C2
socleC22×C61D42
prime radicalC61×#547C22
hypercenter#3335D61
hypocenterC61#19808
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3335

Complements

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

NH ≅ G/Ntype
1. #21458694C2semidirect
2. #21458459C2semidirect
4. #21445451C2semidirect
5. #21445320C2semidirect
6. #21445242C2semidirect
7. #21445198C2semidirect
8. #21445187C2semidirect
10. #21445095C2semidirect
11. #21445026C2semidirect
12. #21444983C2semidirect
13. #21444663C2semidirect
14. #21444631C2semidirect
192. #11758200SD16semidirect
354. C61#19808semidirect

Maximal subgroups

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

subgroupindex
#214586942
#214584592
#214574612
#214454512
#214453202
#214452422
#214451982
#214451872
#214451032
#214450952
#214450262
#214449832
#214446632
#214446312
C61×#33352
#1980861