Finite Group Databasebeta

← #29671251

Subgroups — #29671251

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458822C211yesmaximal, characteristic, complemented
2#21458502C211yesmaximal, characteristic
3#21458434C211yesmaximal, characteristic
4#21445451C211yesmaximal, characteristic, complemented
5#21445306C211yesmaximal, characteristic
6#21445249C211yesmaximal, characteristic, complemented
7#21445203C211yesmaximal, characteristic, complemented
8#21445198C211yesmaximal, characteristic, complemented
9#21445096C211yesmaximal, characteristic, complemented
10#21445088C211yesmaximal, characteristic
11#21445033C211yesmaximal, characteristic
12#21444976C211yesmaximal, characteristic, complemented
13#21444663C211yesmaximal, characteristic
14#21444636C211yesmaximal, characteristic, complemented
15C61×#3381C211yesmaximal, characteristic
16#16840491C2211yescharacteristic
17#16840482C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840141—21no—
21#16840141C2211yescharacteristic
22#16840115—21no—
23#16840113C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840100—21no—
26#16840092—21no—
27#16840072—21no—
28#16840054C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840042C2211yescharacteristic
31#16840018—21no—
32#16839982—21no—
33#16839972—21no—
34#16839972C2211yescharacteristic
35#16839972C2211yescharacteristic
36#16839969—21no—
37#16839969C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40C4×#11758202—21no—
41C4×#11758202C2211yescharacteristic
42#16839854—21no—
43#16839840C2211yescharacteristic
44#16839802—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#557C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#499—21no—
59C61×#498C2211yescharacteristic
60C61×#479—21no—
61C61×#478—21no—
62C61×#477C2211yescharacteristic
63C61×#474C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×SD16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758202D411yescharacteristic
73C2×#11758194—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519770—41no—
78#14519768—21no—
79#14519768—41no—
80#14519764—21no—
81#14519756—21no—
82Q8×Dic61—21no—
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85#14519742—21no—
86#14519736—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—41no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—41no—
104#14519701D411yescharacteristic
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×SD16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#125×C61—21no—
120#125×C61—21no—
121#125×C61—41no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#106×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—41no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122C2×D411yescharacteristic
154SD16×C61—22no—
155C2×C8×C61—21no—
156C2×C8×C61C2×D411yescharacteristic
157C2×C8×C61C2×D411yescharacteristic
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61C2×D411yescharacteristic
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—41no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—41no—
177C42×C61C2411yescharacteristic
178C22⋊Dic61—41no—
179C22⋊Dic61—41no—
180#11758202—22no—
181#11758202—42no—
182#11758202—42no—
183#11758202—81no—
184#11758202—81no—
185#11758202—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—41no—
191C4⋊Dic61—41no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199#11758194—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213Q8×C61#13712yes—
214D4×C61—21no—
215D4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—161no—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61H(5,𝔽2)11yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233Dic122—21no—
234Dic122—21no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—41no—
242#92418—21no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#92418—41no—
247#92418#13512yes—
248#19881—611nomaximal, Sylow
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61D4211yescharacteristic
253C4×C61—22no—
254C4×C61—21no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—81no—
260C4×C61—81no—
261C4×C61C2×#13511yescharacteristic
262C4×C61C2×#13711yescharacteristic
263C4×C61#57711yescharacteristic
264C4×C61#57811yescharacteristic
265Dic61—41no—
266Dic61—41no—
267Dic61—81no—
268Dic61—81no—
269#3395—611no—
270#3381D6111yescharacteristic
271#3364—611no—
272#3356—611no—
273#1716—611no—
274#1689—611no—
275#1680—611no—
276#1672—611no—
277#1672—611no—
278#1653—611no—
279#1652—611no—
280#1644—611no—
281#1636—611no—
282#1583—611no—
283#1579—611no—
284C2×C61—81no—
285C2×C61#327011yescharacteristic
286C2×C61#328411yescharacteristic
287C2×C61#328911yescharacteristic
288#557—611no—
289#557C2×D6111yescharacteristic
290#556—611no—
291#554C2×D6111yescharacteristic
292#499—21no—
293#498—611no—
294#498—611no—
295#498C2×D6111yescharacteristic
296#494—611no—
297#494—1221no—
298#488—1221no—
299#487—611no—
300#487—611no—
301#485—1221no—
302#483—1221no—
303#479—21no—
304#479—1221no—
305#478—21no—
306#477—611no—
307#477C2×D6111yescharacteristic
308#475—611no—
309#474—611no—
310#474C2×D6111yescharacteristic
311#470—1221no—
312#464—1221no—
313#462—611no—
314#462—611no—
315#462—611no—
316#462—1221no—
317#462—1221no—
318C8×Q8—611no—
319C8×Q8—611no—
320C8×Q8C2×D6111yescharacteristic
321C4×Q16—611no—
322C4×Q16—1221no—
323C4×Q16—1221no—
324C4×SD16—21no—
325C4×SD16C2×D6111yescharacteristic
326#436—611no—
327#428—1221no—
328#334—611no—
329#334—611no—
330#333—611no—
331#332—611no—
332#332—611no—
333#332—611no—
334Q8⋊C8—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337D4⋊C8—611no—
338#322—611no—
339C61#1988111yescharacteristic, complemented, Sylow
340C2×Q16—611no—
341C2×Q16—1221no—
342C2×Q16—1221no—
343C2×Q16—1221no—
344C2×Q16—1221no—
345C2×Q16—1221no—
346C2×SD16C22⋊D6111yescharacteristic
347C2×M16—1221no—
348C4⋊Q8—21no—
349C4⋊Q8—611no—
350C4⋊Q8—611no—
351C4⋊Q8—1221no—
352C4⋊Q8C22×D6111yescharacteristic
353C4⋊Q8C22×D6111yescharacteristic
354#126—2441no—
355#125—21no—
356#125—21no—
357#125—41no—
358#125—1221no—
359#125—2441no—
360#124—1221no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363C22⋊Q8—1221no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—611no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8C22×D6111yescharacteristic
371C4×Q8C22×D6111yescharacteristic
372C4×D4—21no—
373C4×D4C22×D6111yescharacteristic
374#117—1221no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—611no—
379#107—1221no—
380#107—1221no—
381#106—21no—
382#106—21no—
383#106—1221no—
384#106—1221no—
385#106—1221no—
386#106—2441no—
387#106C22⋊D6111yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395#103—21no—
396#103—611no—
397#103—611no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—2441no—
406#103C22⋊D6111yescharacteristic
407#102—21no—
408#102—1221no—
409#102C22⋊D6111yescharacteristic
410C22⋊C8—1221no—
411C4×C8—21no—
412C4×C8—611no—
413C4×C8—611no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8C22×D6111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—611no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8D4×D6111yescharacteristic
423C2×Q8C2×C22⋊D6111yescharacteristic
424C2×D4C2×C22⋊D6111yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—1222no—
428Q16—4881no—
429Q16—4881no—
430Q16—4881no—
431Q16—2442no—
432Q16—2442no—
433SD16—22no—
434M16—2442no—
435C2×C8—21no—
436C2×C8—611no—
437C2×C8—611no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8C2×C22⋊D6111yescharacteristic
443C2×C8C2×C22⋊D6111yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—611no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—2441no—
462C4⋊C4—2441no—
463C4⋊C4—2441no—
464C4⋊C4—2441no—
465C4⋊C4D4×D6111yescharacteristic
466C4⋊C4C2×C22⋊D6111yescharacteristic
467C4⋊C4C2×C22⋊D6111yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—2441no—
471C22⋊C4—2441no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—1221no—
476C42—2441no—
477C42—2441no—
478C42C23×D6111yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—1221no—
487Q8—1221no—
488Q8—2441no—
489Q8—2441no—
490Q8—2441no—
491Q8—2441no—
492Q8#1451980812yes—
493D4—21no—
494D4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—161no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4C2×D4×D6111yescharacteristic
510C2×C4C22×C22⋊D6111yescharacteristic
511C2×C4#1451982211yescharacteristic
512C8—21no—
513C8—21no—
514C8—41no—
515C8—612no—
516C8—1221no—
517C8—2441no—
518C8—2441no—
519C8—2441no—
520C8—2441no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D4×C22⋊D6111yescharacteristic
525C4—21no—
526C4—22no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—4881no—
534C4—4881no—
535C4—2441no—
536C4—2441no—
537C4#135×D6111yescharacteristic
538C4C2×#1451980811yescharacteristic
539C4#1684056911yescharacteristic
540C4#1684057711yescharacteristic
541C2—81no—
542C2#2145739011yescharacteristic
543C2#2145754311yescharacteristic
544C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3381C2
socleC22×C61D42
prime radicalC2×D4×C61C2×D4
hypercenter#3381D61
hypocenterC61#19881
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #21458822C2semidirect
4. #21445451C2semidirect
6. #21445249C2semidirect
7. #21445203C2semidirect
8. #21445198C2semidirect
9. #21445096C2semidirect
12. #21444976C2semidirect
14. #21444636C2semidirect
339. C61#19881semidirect

Maximal subgroups

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

subgroupindex
#214588222
#214585022
#214584342
#214454512
#214453062
#214452492
#214452032
#214451982
#214450962
#214450882
#214450332
#214449762
#214446632
#214446362
C61×#33812
#1988161