Finite Group Databasebeta

← #30613652

Subgroups — #30613652

Order 15616.

600 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#21462655C211yesmaximal, characteristic, complemented
2#21462651C211yesmaximal, characteristic, complemented
3#21461457C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461429C211yesmaximal, characteristic, complemented
6#21461426C211yesmaximal, characteristic, complemented
7#21461425C211yesmaximal, characteristic, complemented
8#21461422C211yesmaximal, characteristic, complemented
9#21461406C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461367C211yesmaximal, characteristic, complemented
12#21461133C211yesmaximal, characteristic, complemented
13#21461131C211yesmaximal, characteristic, complemented
14C8×#11758213C211yesmaximal, characteristic, complemented
15#21456388C211yesmaximal, characteristic
16#16840813C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840811C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840796—21no—
22#16840796C2211yescharacteristic
23#16840795—21no—
24#16840792—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840787—21no—
29#16840786—21no—
30#16840781C2211yescharacteristic
31#16840781C2211yescharacteristic
32#16840781C2211yescharacteristic
33#16840727—21no—
34#16840726—21no—
35C4×#11758213C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840297C2211yescharacteristic
53#16840291C2211yescharacteristic
54#16840161C411yescharacteristic
55#16840144C411yescharacteristic
56#16840117C411yescharacteristic
57#16840002C411yescharacteristic
58#16839997C411yescharacteristic
59#16839994C411yescharacteristic
60#16839990C411yescharacteristic
61#16839854C2211yescharacteristic
62#16839853C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839842C2211yescharacteristic
65C4×C8×D61C2211yescharacteristic
66C61×#488C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213D411yescharacteristic
69C2×#11758213D411yescharacteristic
70C2×#11758217—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73#14519844—21no—
74#14519844—21no—
75C4⋊#92420—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832D411yescharacteristic
92#14519832D411yescharacteristic
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758202C2×C411yescharacteristic
102C2×#11758200C2×C411yescharacteristic
103C2×#11758201C2×C411yescharacteristic
104C2×#11758199C2×C411yescharacteristic
105C2×C8×D61C2×C411yescharacteristic
106C2×C8×D61C2×C411yescharacteristic
107#14519772—21no—
108#14519770—21no—
109#14519769C2×C411yescharacteristic
110#14519765C2×C411yescharacteristic
111#14519762—21no—
112#14519759—21no—
113#14519757C2×C411yescharacteristic
114#14519753C2×C411yescharacteristic
115#14519752C2×C411yescharacteristic
116#14519748C2×C411yescharacteristic
117Q8×Dic61C2311yescharacteristic
118#14519742C2311yescharacteristic
119D4×Dic61C2311yescharacteristic
120#14519739—21no—
121#14519739C2311yescharacteristic
122#14519737—21no—
123#14519735—21no—
124#14519733—21no—
125C42×D61C2311yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519708C2×C411yescharacteristic
129#14519708C2×C411yescharacteristic
130#14519702C2×C411yescharacteristic
131#14519702C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519699C2×C411yescharacteristic
134C4×#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#125×C61C2×C411yescharacteristic
138#124×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#103×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C4×C8×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C2×C22⋊D61—21no—
147C22×Dic61—21no—
148C2×D244—21no—
149C2×D244C22×C411yescharacteristic
150C2×C4×D61—21no—
151C2×C4×D61C22×C411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61#4111yescharacteristic
154C2×Dic122C22×C411yescharacteristic
155#11758217—42no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—42no—
163C2×#92420C2×D411yescharacteristic
164C2×#92420C2×D411yescharacteristic
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167#11758213—22no—
168#11758213—22no—
169#11758213—42no—
170D61⋊C8—42no—
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61C22×C411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C42×C61C22×C411yescharacteristic
180C22⋊Dic61—21no—
181C22⋊Dic61—21no—
182#11758202—22no—
183#11758201—41no—
184#11758200—41no—
185#11758199—22no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C8×D61—22no—
208C8×D61—41no—
209C23×C61—21no—
210C22×D61—21no—
211C22×D61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C22⋊D61—81no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C22×D411yescharacteristic
230C2×Dic61C2×#4111yescharacteristic
231D244—21no—
232D244—21no—
233D244—81no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241Dic122—21no—
242Dic122—21no—
243#92420—21no—
244#92420—21no—
245#92420—41no—
246#92420—41no—
247#92420—41no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420#13512yes—
252#92420#13512yes—
253C8×C61—21no—
254C8×C61—21no—
255#92418—21no—
256#92418#13112yes—
257#18069—611nomaximal, Sylow
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×C4×D411yescharacteristic
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61C2×#13111yescharacteristic
274C4×C61#56811yescharacteristic
275Dic61—21no—
276Dic61—21no—
277Dic61—41no—
278Dic61—41no—
279Dic61—41no—
280Dic61C2×#13511yescharacteristic
281Dic61C2×#13511yescharacteristic
282#3168—611no—
283#2969—611no—
284#2969—611no—
285#1591—611no—
286#1589—611no—
287#1583—611no—
288#1583—611no—
289#1582—611no—
290#1582—611no—
291C8×Q16—611no—
292C8×D8—611no—
293#1564—611no—
294#1482—611no—
295#1482—611no—
296C8×M16—611no—
297C2×C61—81no—
298C2×C61#293511yescharacteristic
299C2×C61C4×#13511yescharacteristic
300C2×C61#295711yescharacteristic
301D61—41no—
302D61—81no—
303#529—611no—
304#529—611no—
305#499—611no—
306#495—611no—
307#488—611no—
308#488#692311yescharacteristic
309#467—611no—
310#466—611no—
311#465—611no—
312#465—611no—
313#446—611no—
314#446—611no—
315C8×Q8—611no—
316C8×Q8—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320C4×D8—611no—
321#436—611no—
322#436—611no—
323#436—1221no—
324#436—1221no—
325#435—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
329#433—1221no—
330#433—1221no—
331#431—611no—
332#431—611no—
333#431—611no—
334#405—1221no—
335#405—1221no—
336C4×M16—611no—
337C2×C4×C8—611no—
338#335—611no—
339#335—611no—
340#334—611no—
341#334—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350#322—611no—
351#322—611no—
352C82—611no—
353C82—611no—
354C61#1806911yescharacteristic, complemented, Sylow
355C2×Q16—611no—
356C2×SD16—611no—
357C2×SD16—611no—
358C2×D8—611no—
359C2×M16—611no—
360C2×M16—611no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367#126—1221no—
368#126—1221no—
369#125—611no—
370#125C2×#692311yescharacteristic
371#124—611no—
372#124C2×#692311yescharacteristic
373#123—1221no—
374#123—1221no—
375C22⋊Q8—611no—
376C22⋊Q8—611no—
377#121—611no—
378#121—611no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×D4—611no—
382C4×D4—611no—
383C4×D4—1221no—
384C4×D4—1221no—
385#117—1221no—
386#117—1221no—
387C2×C42—611no—
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401#103—611no—
402#103—611no—
403#103C2×#692311yescharacteristic
404#103C2×#692311yescharacteristic
405#102—611no—
406#102—611no—
407#102C2×#692311yescharacteristic
408#102C2×#692311yescharacteristic
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—611no—
417#97—611no—
418#97—1221no—
419#97—1221no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8C2×#692311yescharacteristic
432C2×Q8—611no—
433C2×Q8C22×#692311yescharacteristic
434C2×D4—611no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4C22×#692311yescharacteristic
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1221no—
442C22×C4—1221no—
443Q16—1222no—
444SD16—2441no—
445SD16—2441no—
446D8—1222no—
447M16—1222no—
448M16—1222no—
449M16—2442no—
450M16—2442no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1222no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2441no—
465C2×C8—2442no—
466C2×C8—2442no—
467C2×C8C22×#692311yescharacteristic
468C2×C8C22×#692311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4C22×#692311yescharacteristic
480C4⋊C4C22×#692311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—1221no—
495C42—1221no—
496C42C22×#692311yescharacteristic
497C23—21no—
498C23—611no—
499C23—1221no—
500Q8—21no—
501Q8—21no—
502Q8—1221no—
503Q8—1221no—
504D4—21no—
505D4—21no—
506D4—1221no—
507D4—1221no—
508D4—4881no—
509D4—4881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4D4×#692311yescharacteristic
529C2×C4D4×#692311yescharacteristic
530C2×C4C23×#692311yescharacteristic
531C8—21no—
532C8—21no—
533C8—612no—
534C8—612no—
535C8—612no—
536C8—1221no—
537C8—1221no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—1221no—
549C22—1221no—
550C22—1221no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22C2×D4×#692311yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—611no—
561C4—611no—
562C4—1221no—
563C4—1221no—
564C4—2441no—
565C4—2441no—
566C4—2441no—
567C4D61⋊#13111yescharacteristic
568C4#1684084111yescharacteristic
569C2—81no—
570C2—4881no—
571C2—2441no—
572C2#2146256411yescharacteristic
573C2#135×#692311yescharacteristic
574C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#488C4
socleC22×C61C2×C4×D4
prime radical#16839997C4
cosocleC4×Dic61C24
hypercenter#488#6923
hypocenterC61#18069
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #21462655C2semidirect
2. #21462651C2semidirect
3. #21461457C2semidirect
4. #21461450C2semidirect
5. #21461429C2semidirect
6. #21461426C2semidirect
7. #21461425C2semidirect
8. #21461422C2semidirect
9. #21461406C2semidirect
10. #21461399C2semidirect
11. #21461367C2semidirect
12. #21461133C2semidirect
13. #21461131C2semidirect
14. C8×#11758213C2semidirect
354. C61#18069semidirect

Maximal subgroups

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

subgroupindex
#214626552
#214626512
#214614572
#214614502
#214614292
#214614262
#214614252
#214614222
#214614062
#214613992
#214613672
#214611332
#214611312
C8×#117582132
#214563882
#1806961