Finite Group Databasebeta

← #29665523

Subgroups — #29665523

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456974C211yesmaximal, characteristic, complemented
2#21455982C211yesmaximal, characteristic
3#21455884C211yesmaximal, characteristic
4#21454928C211yesmaximal, characteristic
5#21445276C211yesmaximal, characteristic, complemented
6#21445269C211yesmaximal, characteristic, complemented
7#21445248C211yesmaximal, characteristic, complemented
8#21445241C211yesmaximal, characteristic, complemented
9#21445212C211yesmaximal, characteristic, complemented
10#21445207C211yesmaximal, characteristic, complemented
11#21445200C211yesmaximal, characteristic, complemented
12#21445193C211yesmaximal, characteristic, complemented
13#21444600C211yesmaximal, characteristic, complemented
14#21444477C211yesmaximal, characteristic, complemented
15C61×#1552C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840104—21no—
23#16840100—21no—
24#16840100—21no—
25#16840100—21no—
26#16840069—21no—
27#16840069—21no—
28#16840058C2211yescharacteristic
29#16840053C2211yescharacteristic
30#16840044C2211yescharacteristic
31#16840039C2211yescharacteristic
32#16839973C2211yescharacteristic
33#16839969C2211yescharacteristic
34#16839968C2211yescharacteristic
35#16839964C2211yescharacteristic
36#16839926—21no—
37#16839922—21no—
38#16839886C2211yescharacteristic
39#16839886C2211yescharacteristic
40#16839870—21no—
41#16839864—21no—
42C4×#11758202—21no—
43C4×#11758201—21no—
44#16839827C2211yescharacteristic
45#16839827C2211yescharacteristic
46C8×C22⋊D61—21no—
47C8×C22⋊D61—21no—
48#16839815C2211yescharacteristic
49#16839815C2211yescharacteristic
50#16839814—21no—
51C4⋊C8×D61—21no—
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×Dic244—21no—
69C2×#11758202—21no—
70C2×#11758190—21no—
71C2×#11758201—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519769—21no—
77#14519756—21no—
78#14519756—21no—
79C4×Dic122—21no—
80C4×Dic122—21no—
81C4×Dic122D411yescharacteristic
82C4×Dic122C2311yescharacteristic
83C4×D244D411yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87#14519736—21no—
88#14519736D411yescharacteristic
89#14519734—21no—
90C42×D61—21no—
91#14519711—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—21no—
95#14519709—21no—
96#14519708—21no—
97#14519708—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100C4⋊#92418D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519702—21no—
106#14519702—21no—
107#14519702—21no—
108#14519701—21no—
109#14519701—21no—
110#14519701—21no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519700—21no—
115#14519699—21no—
116#14519697—21no—
117C22⋊#92418—21no—
118C22⋊#92418D411yescharacteristic
119C22⋊#92418D411yescharacteristic
120#14519689—21no—
121#14519689—21no—
122C4×#92418—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2311yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130#125×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C4×Q8×C61—21no—
134C4×Q8×C61—21no—
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143#97×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C2×C22⋊D61—21no—
150#11758222—22no—
151#11758222—22no—
152C2×D244C2×D411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122C2×D411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—81no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C22⋊C4×C61—41no—
171C42×C61—41no—
172C42×C61C2×D411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61#4111yescharacteristic
175C42×C61C2411yescharacteristic
176C22⋊Dic61—21no—
177C22⋊Dic61—41no—
178#11758202—42no—
179#11758201—42no—
180#11758198—21no—
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61C2×D411yescharacteristic
187C4⋊Dic61C2×D411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—41no—
191#11758196—41no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—41no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202Dic244—42no—
203#11758190—42no—
204C8×D61—81no—
205C8×D61—81no—
206C23×C61#12111yescharacteristic
207C22×D61—21no—
208Q8×C61—41no—
209Q8×C61—41no—
210Q8×C61—41no—
211Q8×C61—41no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C22⋊D61—24no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231D244—21no—
232D244#13512yes—
233C4×D61—24no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61—81no—
237Dic122—21no—
238Dic122—41no—
239Dic122—41no—
240Dic122—81no—
241Dic122#13512yes—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#19418—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61C2×#12111yescharacteristic
257C2×D61—22no—
258C2×D61—41no—
259C2×D61—41no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61C2×#13511yescharacteristic
267C4×C61C2×#13511yescharacteristic
268C4×C61#57711yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—22no—
271Dic61—41no—
272Dic61—41no—
273Dic61—81no—
274Dic61—81no—
275#3231—611no—
276#3116—611no—
277#3107—611no—
278#2988—611no—
279#1684—611no—
280#1683—611no—
281#1680—611no—
282#1679—611no—
283#1674—611no—
284#1673—611no—
285#1672—611no—
286#1671—611no—
287#1572—611no—
288#1552D6111yescharacteristic, complemented
289#1542—611no—
290C2×C61—41no—
291C2×C61#304611yescharacteristic
292C2×C61#305011yescharacteristic
293C2×C61#306911yescharacteristic
294D61—42no—
295#533—611no—
296#533C2×D6111yescharacteristic
297C4×#41—611no—
298#500—611no—
299#498—611no—
300#487—611no—
301#487—611no—
302#485—1221no—
303#485—1221no—
304#485—1221no—
305#485—1221no—
306#479—1221no—
307#479—1221no—
308#477—611no—
309#476—611no—
310#475—611no—
311#474—611no—
312#462—611no—
313#462—611no—
314#461—611no—
315#461—611no—
316#452—1221no—
317#452—1221no—
318C8×Q8—611no—
319C8×Q8—611no—
320#441—1221no—
321#440—1221no—
322C4×Q16—1221no—
323C4×SD16—1221no—
324C8×D4—611no—
325C8×D4—611no—
326C8×D4—1221no—
327C8×D4—1221no—
328#432C2×D6111yescharacteristic
329#431—611no—
330#431—611no—
331#431—1221no—
332C2×C4⋊C8—1221no—
333C2×C4⋊C8C2×D6111yescharacteristic
334#335—611no—
335#335—611no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#332—611no—
342#332C2×D6111yescharacteristic
343#332C2×D6111yescharacteristic
344#332C2×D6111yescharacteristic
345#332C2×D6111yescharacteristic
346C61#1941811yescharacteristic, complemented, Sylow
347C2×#41—611no—
348C2×Q16—1221no—
349C2×Q16—1221no—
350C2×SD16—1221no—
351C2×SD16—1221no—
352C22×C8—21no—
353C22×C8—1221no—
354C22×C8—1221no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8C22×D6111yescharacteristic
358C4⋊Q8C22×D6111yescharacteristic
359#125—21no—
360#125—1221no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—1221no—
364C22⋊Q8—1221no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×D4—611no—
372C4×D4—611no—
373C4×D4—1221no—
374C4×D4—1221no—
375#117—21no—
376#117—611no—
377#117—1221no—
378#117—1221no—
379C2×C42—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388#106—1221no—
389C4⋊C8—21no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—21no—
413C22⋊C8—611no—
414C22⋊C8—611no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418#97—21no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424#41—1222no—
425#41—1222no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×D4—611no—
432C2×D4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4#1175822211yescharacteristic
437C22×C4D4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439Q16—2442no—
440Q16—2442no—
441SD16—2442no—
442SD16—2442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—4881no—
455C2×C8—4881no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C22⋊C4—41no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—2441no—
477C42—41no—
478C42—1221no—
479C42—1221no—
480C42—1221no—
481C42—2441no—
482C42#1175822211yescharacteristic
483C42D4×D6111yescharacteristic
484C42D4×D6111yescharacteristic
485C42C23×D6111yescharacteristic
486C23—1221no—
487C23#1451975011yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—612no—
493Q8—1221no—
494Q8—4881no—
495Q8—2441no—
496Q8—2441no—
497D4—612no—
498D4—1224no—
499D4—1221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—1224no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—4881no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451975011yescharacteristic
517C2×C4#1451975011yescharacteristic
518C2×C4#1451975011yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—1221no—
530C8—2441no—
531C8—2441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—1222no—
536C22—2441no—
537C22—2441no—
538C22C2×#1451975011yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—1222no—
546C4—4881no—
547C4—4881no—
548C4—2441no—
549C4—2441no—
550C4#135×D6111yescharacteristic
551C4#135×D6111yescharacteristic
552C4#1684057211yescharacteristic
553C4#1684057811yescharacteristic
554C2—41no—
555C2—2442no—
556C2#2145536811yescharacteristic
557C2#2145539911yescharacteristic
558C2#2145555511yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1552C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#1552D61
hypocenterC61#19418
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
1. #21456974C2semidirect
5. #21445276C2semidirect
6. #21445269C2semidirect
7. #21445248C2semidirect
8. #21445241C2semidirect
9. #21445212C2semidirect
10. #21445207C2semidirect
11. #21445200C2semidirect
12. #21445193C2semidirect
13. #21444600C2semidirect
14. #21444477C2semidirect
15. C61×#1552C2semidirect
288. #1552D61semidirect
346. C61#19418semidirect

Maximal subgroups

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

subgroupindex
#214569742
#214559822
#214558842
#214549282
#214452762
#214452692
#214452482
#214452412
#214452122
#214452072
#214452002
#214451932
#214446002
#214444772
C61×#15522
#1941861