Finite Group Databasebeta

← #29676705

Subgroups — #29676705

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#21458846C211yesmaximal, characteristic
2#21458559C211yesmaximal, characteristic
3#21458251C211yesmaximal, characteristic
4#21445493C211yesmaximal, characteristic, complemented
5#21445403C211yesmaximal, characteristic, complemented
6#21445337C211yesmaximal, characteristic, complemented
7#21445311C211yesmaximal, characteristic, complemented
8#21445191C211yesmaximal, characteristic
9#21445074C211yesmaximal, characteristic
10#21445061C211yesmaximal, characteristic, complemented
11#21445040C211yesmaximal, characteristic, complemented
12#21444990C211yesmaximal, characteristic
13#21444728C211yesmaximal, characteristic, complemented
14#21444653C211yesmaximal, characteristic
15C61×#3387C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840485C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840154—21no—
21#16840141C2211yescharacteristic
22#16840124—21no—
23#16840114C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840102—21no—
26#16840102—21no—
27#16840049C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840044—21no—
31#16840000—21no—
32#16839984—21no—
33#16839984—21no—
34#16839972C2211yescharacteristic
35#16839972C2211yescharacteristic
36#16839969—21no—
37#16839964C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839867—21no—
41#16839867—21no—
42C4×#11758201C2211yescharacteristic
43C8×D244C2211yescharacteristic
44#16839799—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#501—21no—
59C61×#498C2211yescharacteristic
60C61×#479—21no—
61C61×#477C2211yescharacteristic
62C61×#475—21no—
63C61×#475C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#441—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758201—21no—
72C2×#11758201D411yescharacteristic
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519772—41no—
77#14519772—41no—
78#14519765—21no—
79#14519765—21no—
80#14519753—21no—
81#14519753—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×D244C2311yescharacteristic
85#14519735—21no—
86#14519735—21no—
87#14519711—21no—
88#14519711—21no—
89#14519710—41no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708D411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—41no—
103#14519701D411yescharacteristic
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—41no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123#125×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131#107×C61—21no—
132#107×C61D411yescharacteristic
133#106×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×Q8×C61C2×D411yescharacteristic
150C2×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154Q16×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—21no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—41no—
177C42×C61—41no—
178C42×C61C2411yescharacteristic
179#11758202—42no—
180#11758202—42no—
181#11758202—81no—
182#11758202—81no—
183#11758201—41no—
184#11758201—81no—
185#11758198—21no—
186#11758198—41no—
187#11758198—41no—
188#11758198—41no—
189#11758198—41no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C8×D61—42no—
206C22×D61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—81no—
216Q8×C61—161no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231D244—21no—
232D244—21no—
233C4×D61—41no—
234C4×D61—41no—
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#20277—611nomaximal, Sylow
249C22×C61D4211yescharacteristic
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—41no—
253C4×C61—21no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—81no—
261C4×C61—81no—
262C4×C61C2×#13711yescharacteristic
263C4×C61#57511yescharacteristic
264C4×C61#57711yescharacteristic
265C4×C61#57811yescharacteristic
266Dic61—41no—
267Dic61—81no—
268Dic61—81no—
269#3398—611no—
270#3387D6111yescharacteristic, complemented
271#3369—611no—
272#3342—611no—
273#1723—611no—
274#1704—611no—
275#1694—611no—
276#1690—611no—
277#1671—611no—
278#1650—611no—
279#1648—611no—
280#1645—611no—
281#1638—611no—
282#1593—611no—
283#1582—611no—
284C2×C61#327111yescharacteristic
285C2×C61#327611yescharacteristic
286C2×C61#328911yescharacteristic
287D61—81no—
288Q82C2×D6111yescharacteristic
289#557C2×D6111yescharacteristic
290#556—611no—
291#556—611no—
292#501—21no—
293#500—611no—
294#500—611no—
295#498C2×D6111yescharacteristic
296#497—1221no—
297#494—611no—
298#489—1221no—
299#487—611no—
300#487—611no—
301#485—1221no—
302#485—1221no—
303#479—21no—
304#477C2×D6111yescharacteristic
305#476—611no—
306#475—21no—
307#475—611no—
308#475—611no—
309#475—1221no—
310#475C2×D6111yescharacteristic
311#467—1221no—
312#464—1221no—
313#464—1221no—
314#462—611no—
315#462—611no—
316#462—1221no—
317#461—611no—
318#446—611no—
319#446—611no—
320#446C2×D6111yescharacteristic
321#441—21no—
322#441—1221no—
323#441—1221no—
324C4×Q16C2×D6111yescharacteristic
325C4×SD16—611no—
326C8×D4—611no—
327#427—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#2027711yescharacteristic, complemented, Sylow
340C2×Q16—1221no—
341C2×Q16—1221no—
342C2×Q16—1221no—
343C2×Q16—1221no—
344C2×Q16C22⋊D6111yescharacteristic
345C2×SD16—611no—
346C2×SD16—1221no—
347C22×C8—1221no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—41no—
352C4⋊Q8—611no—
353C4⋊Q8—611no—
354C4⋊Q8C22×D6111yescharacteristic
355C4⋊Q8C22×D6111yescharacteristic
356#126—2441no—
357#126—2441no—
358#125—21no—
359#125—41no—
360#124—1221no—
361#124—1221no—
362C22⋊Q8—1221no—
363C22⋊Q8—1221no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8C22×D6111yescharacteristic
371C4×Q8C22×D6111yescharacteristic
372C4×Q8C22×D6111yescharacteristic
373C4×D4—611no—
374#117—1221no—
375#117—1221no—
376#107—21no—
377#107—1221no—
378#107—1221no—
379#107—2441no—
380#107C22⋊D6111yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—611no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
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—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—2441no—
406#103C22⋊D6111yescharacteristic
407#103C22⋊D6111yescharacteristic
408#102—611no—
409#102—1221no—
410C22⋊C8—1221no—
411#97—21no—
412#97—1221no—
413#97—1221no—
414C4×C8—611no—
415C4×C8—611no—
416C4×C8C22×D6111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8D4×D6111yescharacteristic
423C2×Q8C2×C22⋊D6111yescharacteristic
424C2×Q8C2×C22⋊D6111yescharacteristic
425C2×D4—611no—
426C22×C4—1221no—
427Q16—22no—
428Q16—4881no—
429Q16—4881no—
430Q16—2442no—
431Q16—2442no—
432SD16—4881no—
433SD16—2441no—
434C2×C8—21no—
435C2×C8—611no—
436C2×C8—611no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—2442no—
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—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—611no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—2441no—
462C4⋊C4—2441no—
463C4⋊C4D4×D6111yescharacteristic
464C4⋊C4C2×C22⋊D6111yescharacteristic
465C4⋊C4C2×C22⋊D6111yescharacteristic
466C22⋊C4—1221no—
467C22⋊C4—2441no—
468C22⋊C4—2441no—
469C22⋊C4—2441no—
470C22⋊C4—2441no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—41no—
476C42—2441no—
477C42—2441no—
478C42C23×D6111yescharacteristic
479C23—1221no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—161no—
490Q8—2441no—
491Q8—2441no—
492Q8—2441no—
493Q8—2441no—
494D4—1221no—
495D4—1221no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—1221no—
505C2×C4—2441no—
506C2×C4—2441no—
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#1451980812yes—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22D4×C22⋊D6111yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—4881no—
535C4—4881no—
536C4—2441no—
537C4C2×#1451980811yescharacteristic
538C4#1684056111yescharacteristic
539C4#1684057111yescharacteristic
540C4#1684057711yescharacteristic
541C2—4881no—
542C2#2145739811yescharacteristic
543C2#2145746511yescharacteristic
544C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3387C2
socleC22×C61D42
prime radicalC2×D244C2×D4
hypercenter#3387D61
hypocenterC61#20277
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3387

Complements

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

NH ≅ G/Ntype
4. #21445493C2semidirect
5. #21445403C2semidirect
6. #21445337C2semidirect
7. #21445311C2semidirect
10. #21445061C2semidirect
11. #21445040C2semidirect
13. #21444728C2semidirect
15. C61×#3387C2semidirect
270. #3387D61semidirect
339. C61#20277semidirect

Maximal subgroups

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

subgroupindex
#214588462
#214585592
#214582512
#214454932
#214454032
#214453372
#214453112
#214451912
#214450742
#214450612
#214450402
#214449902
#214447282
#214446532
C61×#33872
#2027761