Finite Group Databasebeta

← #29676735

Subgroups — #29676735

Order 15616.

556 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#21458850C211yesmaximal, characteristic
2#21458708C211yesmaximal, characteristic, complemented
3#21458600C211yesmaximal, characteristic
4#21445493C211yesmaximal, characteristic, complemented
5#21445403C211yesmaximal, characteristic, complemented
6#21445332C211yesmaximal, characteristic
7#21445311C211yesmaximal, characteristic, complemented
8#21445198C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic
10#21445060C211yesmaximal, characteristic, complemented
11#21445026C211yesmaximal, characteristic
12#21444976C211yesmaximal, characteristic, complemented
13#21444728C211yesmaximal, characteristic, complemented
14#21444660C211yesmaximal, characteristic
15C61×#3356C211yesmaximal, characteristic
16#16840491C2211yescharacteristic
17#16840491C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840163—21no—
21#16840157—21no—
22#16840141C2211yescharacteristic
23#16840132—21no—
24#16840114C2211yescharacteristic
25#16840112C2211yescharacteristic
26#16840071—21no—
27#16840071—21no—
28#16840066—21no—
29#16840054C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840047C2211yescharacteristic
32#16839981—21no—
33#16839972—21no—
34#16839969C2211yescharacteristic
35#16839967—21no—
36#16839967C2211yescharacteristic
37#16839967C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41#16839867—21no—
42#16839862—21no—
43Q16×Dic61—21no—
44C4×#11758200C2211yescharacteristic
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#485—21no—
60C61×#483—21no—
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C61×#470—21no—
64C4×Q16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#428—21no—
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200D411yescharacteristic
73#14519777—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519768—21no—
78#14519768—21no—
79#14519768—41no—
80#14519768—41no—
81Q8×Dic61—21no—
82Q8×Dic61—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86#14519711—21no—
87#14519711—21no—
88#14519710—21no—
89#14519710—41no—
90#14519708—21no—
91#14519708—21no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—41no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698D411yescharacteristic
110#14519688—21no—
111#14519688—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×Q16×C61D411yescharacteristic
116C2×M16×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#126×C61—41no—
120#125×C61—21no—
121#124×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131C2×C4⋊C4×C61—21no—
132#107×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C22⋊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
154Q16×C61—22no—
155M16×C61—42no—
156C2×C8×C61—21no—
157C2×C8×C61C2×D411yescharacteristic
158C2×C8×C61C2×D411yescharacteristic
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61C2×D411yescharacteristic
169C4⋊C4×C61C2×D411yescharacteristic
170C4⋊C4×C61C2×D411yescharacteristic
171C22⋊C4×C61—21no—
172C22⋊C4×C61—41no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—41no—
178C42×C61C2411yescharacteristic
179#11758202—42no—
180#11758202—81no—
181#11758202—81no—
182#11758200—41no—
183#11758200—42no—
184#11758200—81no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—41no—
190C4⋊Dic61—41no—
191C4⋊Dic61—41no—
192C4⋊Dic61—41no—
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C4×Dic61—41no—
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—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—81no—
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—41no—
241C8×C61#13712yes—
242#92418—21no—
243#92418—21no—
244#92418—41no—
245#92418—41no—
246#92418—41no—
247#92418—41no—
248#20279—611nomaximal, Sylow
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61D4211yescharacteristic
253C4×C61—21no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—81no—
260C4×C61—81no—
261C4×C61C2×#13711yescharacteristic
262C4×C61#57511yescharacteristic
263C4×C61#57711yescharacteristic
264C4×C61#57811yescharacteristic
265Dic61—41no—
266Dic61—41no—
267Dic61—81no—
268Dic61—81no—
269#3398—611no—
270#3383—611no—
271#3372—611no—
272#3356D6111yescharacteristic
273#1723—611no—
274#1704—611no—
275#1693—611no—
276#1690—611no—
277#1672—611no—
278#1650—611no—
279#1648—611no—
280#1643—611no—
281#1636—611no—
282#1593—611no—
283#1583—611no—
284C2×C61—81no—
285C2×C61#327111yescharacteristic
286C2×C61#327611yescharacteristic
287C2×C61#328911yescharacteristic
288#557—611no—
289#557—611no—
290#556C2×D6111yescharacteristic
291#554C2×D6111yescharacteristic
292#500—611no—
293#500—611no—
294#499—1221no—
295#498C2×D6111yescharacteristic
296#497—1221no—
297#494—611no—
298#491—1221no—
299#487—611no—
300#487—611no—
301#485—21no—
302#483—21no—
303#479—1221no—
304#479—1221no—
305#479—1221no—
306#477—611no—
307#477C2×D6111yescharacteristic
308#475—611no—
309#475—611no—
310#475C2×D6111yescharacteristic
311#470—21no—
312#464—1221no—
313#462—611no—
314#462—1221no—
315#461—611no—
316#461—611no—
317#461—1221no—
318#446—611no—
319#446—611no—
320C8×Q8—611no—
321#441—1221no—
322#440—1221no—
323C4×Q16—1221no—
324C4×Q16C2×D6111yescharacteristic
325C4×SD16—611no—
326#436C2×D6111yescharacteristic
327#428—21no—
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#2027911yescharacteristic, complemented, Sylow
340C2×Q16—1221no—
341C2×Q16—1221no—
342C2×Q16—1221no—
343C2×Q16C22⋊D6111yescharacteristic
344C2×SD16—611no—
345C2×SD16—1221no—
346C2×SD16—1221no—
347C2×M16—21no—
348C4⋊Q8—611no—
349C4⋊Q8—611no—
350C4⋊Q8—1221no—
351C4⋊Q8—1221no—
352C4⋊Q8C22×D6111yescharacteristic
353C4⋊Q8C22×D6111yescharacteristic
354#126—41no—
355#125—21no—
356#125—1221no—
357#125—1221no—
358#125—2441no—
359#125—2441no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8—611no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8C22×D6111yescharacteristic
371C4×Q8C22×D6111yescharacteristic
372C4×D4—21no—
373C4×D4C22×D6111yescharacteristic
374#117—21no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—1221no—
378#107—1221no—
379#107—1221no—
380#107—2441no—
381#107C22⋊D6111yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
385#106—611no—
386#106—1221no—
387#106—1221no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395#103—21no—
396#103—21no—
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—1221no—
406#103—2441no—
407#103C22⋊D6111yescharacteristic
408#103C22⋊D6111yescharacteristic
409#102—611no—
410C22⋊C8—21no—
411#97—1221no—
412#97—1221no—
413C4×C8—611no—
414C4×C8—611no—
415C4×C8—1221no—
416C4×C8C22×D6111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—611no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8C2×C22⋊D6111yescharacteristic
423C2×Q8C2×C22⋊D6111yescharacteristic
424C2×D4D4×D6111yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—22no—
428Q16—4881no—
429Q16—4881no—
430Q16—2442no—
431SD16—4881no—
432SD16—2441no—
433SD16—2442no—
434M16—42no—
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—611no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—2441no—
460C4⋊C4—2441no—
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—41no—
471C22⋊C4—41no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—1221no—
476C42—2441no—
477C42—2441no—
478C42C23×D6111yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—1221no—
488Q8—1221no—
489Q8—2441no—
490Q8—2441no—
491Q8—2441no—
492Q8—2441no—
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—41no—
514C8—1221no—
515C8—1221no—
516C8—2441no—
517C8—2441no—
518C8—2441no—
519C8—2441no—
520C8#1451980712yes—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D4×C22⋊D6111yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—4881no—
534C4—4881no—
535C4—2441no—
536C4—2441no—
537C4C2×#1451980711yescharacteristic
538C4#1684056111yescharacteristic
539C4#1684057111yescharacteristic
540C4#1684057711yescharacteristic
541C2—81no—
542C2#2145739811yescharacteristic
543C2#2145746111yescharacteristic
544C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3356C2
socleC22×C61D42
prime radicalC2×D4×C61C2×D4
hypercenter#3356D61
hypocenterC61#20279
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3356

Complements

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

NH ≅ G/Ntype
2. #21458708C2semidirect
4. #21445493C2semidirect
5. #21445403C2semidirect
7. #21445311C2semidirect
8. #21445198C2semidirect
10. #21445060C2semidirect
12. #21444976C2semidirect
13. #21444728C2semidirect
339. C61#20279semidirect

Maximal subgroups

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

subgroupindex
#214588502
#214587082
#214586002
#214454932
#214454032
#214453322
#214453112
#214451982
#214450752
#214450602
#214450262
#214449762
#214447282
#214446602
C61×#33562
#2027961