Finite Group Databasebeta

← #29670149

Subgroups — #29670149

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#21458692C211yesmaximal, characteristic, complemented
2#21458461C211yesmaximal, characteristic, complemented
3#21458176C211yesmaximal, characteristic
4#21445450C211yesmaximal, characteristic, complemented
5#21445318C211yesmaximal, characteristic, complemented
6#21445244C211yesmaximal, characteristic, complemented
7#21445199C211yesmaximal, characteristic, complemented
8#21445186C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic
10#21445094C211yesmaximal, characteristic, complemented
11#21445024C211yesmaximal, characteristic, complemented
12#21444984C211yesmaximal, characteristic, complemented
13#21444660C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3276C211yesmaximal, characteristic
16#16840491C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840162—21no—
19#16840160C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840158C2211yescharacteristic
22#16840114—21no—
23#16840114C2211yescharacteristic
24#16840114C2211yescharacteristic
25#16840092—21no—
26#16840078—21no—
27#16840067—21no—
28#16840064—21no—
29#16840057C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840044—21no—
32#16840044C2211yescharacteristic
33#16840044C2211yescharacteristic
34#16840042C2211yescharacteristic
35#16839989—21no—
36#16839967—21no—
37#16839967C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40SD16×Dic61—21no—
41C4×#11758200—21no—
42C4×#11758200C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519708—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C2×#137×C61—21no—
57D4×Q8×C61C2211yescharacteristic
58C61×#547C2211yescharacteristic
59C61×#494C2211yescharacteristic
60C61×#470—21no—
61C61×#462C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#452—21no—
64C61×#451—21no—
65C4×SD16×C61C2211yescharacteristic
66C61×#436C2211yescharacteristic
67C2×#11758200—21no—
68C2×#11758200D411yescharacteristic
69C22×#92418—21no—
70#14519777—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519768—21no—
74#14519768—21no—
75#14519768—41no—
76#14519756—21no—
77#14519754—41no—
78Q8×Dic61—21no—
79C4×Dic122—21no—
80C4×Dic122C2311yescharacteristic
81D4×Dic61—21no—
82C2×C4⋊Dic61—21no—
83#14519710—21no—
84#14519710—21no—
85#14519709—21no—
86#14519709—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—41no—
93#14519708D411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519701—21no—
100#14519700—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—41no—
106#14519700D411yescharacteristic
107#14519698—21no—
108#14519698—21no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C22×Q8×C61—21no—
117#137×C61—44no—
118C2×Q16×C61—21no—
119C2×Q16×C61—21no—
120C2×Q16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61D411yescharacteristic
123C2×M16×C61—21no—
124C4⋊Q8×C61—21no—
125C4⋊Q8×C61C2311yescharacteristic
126C4⋊Q8×C61C2311yescharacteristic
127#123×C61—41no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—41no—
131#121×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136C2×C4⋊C4×C61—21no—
137#106×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#103×C61D411yescharacteristic
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×C61—41no—
150C2×Q8×C61—42no—
151C2×Q8×C61—81no—
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×Dic61—41no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122C2×D411yescharacteristic
164Q16×C61—42no—
165Q16×C61—42no—
166Q16×C61—81no—
167SD16×C61—42no—
168SD16×C61SD1614yescomplemented
169M16×C61—42no—
170C2×C8×C61—21no—
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—41no—
186C22⋊C4×C61—41no—
187C42×C61—21no—
188C42×C61C2411yescharacteristic
189C22⋊Dic61—41no—
190#11758200—41no—
191#11758200—42no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—41no—
197C4⋊Dic61—41no—
198C4⋊Dic61—41no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—21no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—21no—
204C4×Dic61—41no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—42no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C23×C61—21no—
213C23×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—82no—
220Q8×C61C2×SD1612yes—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—82no—
225D4×C61C2×SD1612yes—
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—41no—
236C2×C4×C61—82no—
237C2×C4×C61—82no—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—161no—
246Dic122—21no—
247Dic122—21no—
248Dic122—41no—
249Dic122—41no—
250Dic122—81no—
251C8×C61—21no—
252C8×C61—41no—
253C8×C61C2×SD1612yes—
254#92418—21no—
255#92418—21no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
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—22no—
269C4×C61—21no—
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—41no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283#3381—611no—
284#3359—611no—
285#3335—611no—
286#3276D6111yescharacteristic
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—21no—
304#557—611no—
305#554—611no—
306D4×Q8C2×D6111yescharacteristic
307#547C2×D6111yescharacteristic
308#499—1221no—
309#498—611no—
310#498—611no—
311#498—611no—
312#494C2×D6111yescharacteristic
313#487—611no—
314#487—611no—
315#487—1221no—
316#483—1221no—
317#481—1221no—
318#479—1221no—
319#478—1221no—
320#477—611no—
321#476—611no—
322#475—611no—
323#475—611no—
324#475—1221no—
325#474—611no—
326#470—21no—
327#465—1221no—
328#462C2×D6111yescharacteristic
329#461—611no—
330#461—1221no—
331#461C2×D6111yescharacteristic
332#452—21no—
333#451—21no—
334C8×Q8—611no—
335C8×Q8—611no—
336C4×SD16—611no—
337C4×SD16—1221no—
338C4×SD16—1221no—
339C4×SD16C2×D6111yescharacteristic
340#436C2×D6111yescharacteristic
341C8×D4—611no—
342C2×#106—1221no—
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—21no—
357#137—44no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—611no—
363C2×SD16—1221no—
364C2×SD16C22⋊D6111yescharacteristic
365C2×M16—21no—
366C22×C8—1221no—
367C4⋊Q8—21no—
368C4⋊Q8—611no—
369C4⋊Q8—611no—
370C4⋊Q8—1221no—
371C4⋊Q8C22×D6111yescharacteristic
372C4⋊Q8C22×D6111yescharacteristic
373#125—1221no—
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—1221no—
393#107—1221no—
394#107—1221no—
395#106—611no—
396#106—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
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—21no—
413#103—611no—
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—611no—
423#102—1221no—
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—41no—
438C2×Q8—42no—
439C2×Q8—81no—
440C2×Q8—611no—
441C2×Q8—1221no—
442C2×Q8—1221no—
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—42no—
453Q16—42no—
454Q16—81no—
455SD16—42no—
456SD16—2441no—
457SD16—2442no—
458SD16#1175820014yescomplemented
459M16—42no—
460C2×C8—21no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—2442no—
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—611no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—2441no—
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—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—82no—
508Q8—1221no—
509Q8—1221no—
510Q8—4881no—
511Q8—2441no—
512Q8—2441no—
513Q8C2×#1175820012yes—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4C2×#1175820012yes—
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—82no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—9761no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C22×C22⋊D6111yescharacteristic
538C2×C4#1451982211yescharacteristic
539C8—21no—
540C8—41no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8C2×#1175820012yes—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22D4×C22⋊D6111yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—4881no—
563C4—4881no—
564C4—2441no—
565C4—2441no—
566C4C22×#1175820011yescharacteristic
567C4#1684056111yescharacteristic
568C4#1684057311yescharacteristic
569C4#1684057811yescharacteristic
570C2—42no—
571C2—81no—
572C2#2145736811yescharacteristic
573C2D4×#1175820011yescharacteristic
574C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3276C2
socleC22×C61D42
prime radicalC61×#547C22
hypercenter#3276D61
hypocenterC61#19808
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3276

Complements

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

NH ≅ G/Ntype
1. #21458692C2semidirect
2. #21458461C2semidirect
4. #21445450C2semidirect
5. #21445318C2semidirect
6. #21445244C2semidirect
7. #21445199C2semidirect
8. #21445186C2semidirect
10. #21445094C2semidirect
11. #21445024C2semidirect
12. #21444984C2semidirect
13. #21444660C2semidirect
14. SD16⋊#92418C2semidirect
168. SD16×C61SD16semidirect
354. C61#19808semidirect
458. SD16#11758200semidirect

Maximal subgroups

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

subgroupindex
#214586922
#214584612
#214581762
#214454502
#214453182
#214452442
#214451992
#214451862
#214451032
#214450942
#214450242
#214449842
#214446602
SD16⋊#924182
C61×#32762
#1980861