Finite Group Databasebeta

← #30613624

Subgroups — #30613624

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462679C211yesmaximal, characteristic, complemented
2#21462677C211yesmaximal, characteristic, complemented
3#21461467C212yesmaximal, complemented
4#21461420C212yesmaximal, complemented
5#21461419C212yesmaximal, complemented
6#21461416C212yesmaximal, complemented
7#21461382C211yesmaximal, characteristic, complemented
8#21461159C211yesmaximal, characteristic, complemented
9#21461159C211yesmaximal, characteristic, complemented
10#21461029C211yesmaximal, characteristic, complemented
11C4×D8×D61C211yesmaximal, characteristic
12#16840797C2212yescomplemented
13#16840796C2212yescomplemented
14#16840794—22no—
15#16840791—22no—
16#16840790C2212yescomplemented
17D4×#92420C2212yescomplemented
18#16840784C2211yescharacteristic
19#16840784C2211yescharacteristic
20#16840781C2211yescharacteristic
21#16840734—21no—
22#16840733—21no—
23C2×#14519834—21no—
24D61⋊(C22⋊C8)—21no—
25C4×#11758213C2211yescharacteristic
26#16840626C2212yescomplemented
27#16840624C2212yescomplemented
28#16840610C2212yescomplemented
29#16840610C2212yescomplemented
30D4⋊#92420C2212yescomplemented
31D4⋊#92420C2212yescomplemented
32#92420⋊C8C2212yescomplemented
33#16840603C2212yescomplemented
34C2×D8×D61C411yescharacteristic
35C4×D4×D61C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37C4×D488C411yescharacteristic
38D8×Dic61C2211yescharacteristic
39#16839844C2211yescharacteristic
40C4×#11758199C411yescharacteristic
41C4×#11758199C411yescharacteristic
42#16839842C2211yescharacteristic
43#16839842C2211yescharacteristic
44#107×D61C411yescharacteristic
45#102×D61C411yescharacteristic
46#102×D61C411yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×D8×C61C411yescharacteristic
49C2×#11758213—21no—
50C2×#11758213—22no—
51C2×#11758217—22no—
52C2×D61⋊C8—22no—
53C22×#92420—22no—
54C4⋊#92420D412yes—
55C4⋊#92420C2312yes—
56C4⋊#92420C2312yes—
57#14519834—21no—
58#14519834—21no—
59#14519834—22no—
60#14519834—22no—
61#14519834D411yescharacteristic
62#14519834D411yescharacteristic
63C22⋊#92420—22no—
64C22⋊#92420—22no—
65#14519832—21no—
66#14519832—21no—
67#14519832—21no—
68C4×#92420C2312yes—
69C4×#92420C2312yes—
70C2×D4×D61C2×C411yescharacteristic
71C2×D4×D61C2×C411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×D488C2×C411yescharacteristic
75C2×#11758199C2×C411yescharacteristic
76C2×#11758199C2×C411yescharacteristic
77D8×D61—24no—
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61C2×C411yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244C2×C411yescharacteristic
82D4×Dic61C2311yescharacteristic
83D4×Dic61C2311yescharacteristic
84#14519739C2311yescharacteristic
85#14519739C2311yescharacteristic
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88#14519737—21no—
89#14519737—21no—
90C4⋊C4×D61C2×C411yescharacteristic
91C4⋊C4×D61C2×C411yescharacteristic
92C22⋊C4×D61—21no—
93C22⋊C4×D61—21no—
94C42×D61C2311yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519699C2×C411yescharacteristic
99#14519699C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102#14519697C2×C411yescharacteristic
103#14519697C2×C411yescharacteristic
104C4×#92418C2×C411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C8×Dic61C2311yescharacteristic
107C2×D8×C61C2×C411yescharacteristic
108C4×D4×C61C2×C411yescharacteristic
109C4×D4×C61C2×C411yescharacteristic
110#107×C61C2×C411yescharacteristic
111#102×C61C2×C411yescharacteristic
112#102×C61C2×C411yescharacteristic
113C4×C8×C61C2×C411yescharacteristic
114C23×D61—21no—
115C23×D61—21no—
116C2×D4×C61C22×C411yescharacteristic
117C2×D4×C61C22×C411yescharacteristic
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C2×C22⋊D61—21no—
121C2×C22⋊D61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124D4×D61—22no—
125D4×D61—22no—
126D4×D61—41no—
127D4×D61—41no—
128C2×D244C22×C411yescharacteristic
129C2×D244C22×C411yescharacteristic
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—82no—
137C2×C4×D61—82no—
138C2×C4×D61C22×C411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×C4×D61#4111yescharacteristic
141#11758217—82no—
142C2×#92420—22no—
143C2×#92420—22no—
144C2×#92420—22no—
145C2×#92420—82no—
146C2×#92420C2×D412yes—
147C2×#92420C2×D412yes—
148#11758213—42no—
149#11758213—82no—
150D61⋊C8—82no—
151D8×C61—22no—
152C2×C8×C61C22×C411yescharacteristic
153C2×C8×C61C22×C411yescharacteristic
154C4⋊C4×C61C22×C411yescharacteristic
155C4⋊C4×C61C22×C411yescharacteristic
156C22⋊C4×C61—21no—
157C22⋊C4×C61—21no—
158C42×C61C22×C411yescharacteristic
159C22⋊Dic61—21no—
160C22⋊Dic61—21no—
161#11758199—22no—
162#11758199M1614yescomplemented
163#11758198—21no—
164#11758198—21no—
165#11758198—21no—
166#11758198—21no—
167C4⋊Dic61C22×C411yescharacteristic
168C4⋊Dic61C22×C411yescharacteristic
169#11758196—21no—
170#11758196—21no—
171C4×Dic61C2×D411yescharacteristic
172C4×Dic61#4111yescharacteristic
173C4×Dic61C2411yescharacteristic
174C2×#92418C22×C411yescharacteristic
175C2×#92418C22×C411yescharacteristic
176D488—22no—
177C8×D61—22no—
178C8×D61—41no—
179C23×C61—21no—
180C23×C61—21no—
181C22×D61—21no—
182C22×D61—21no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—42no—
187C22×D61—81no—
188C22×D61—81no—
189C22×D61C4×D411yescharacteristic
190D4×C61—21no—
191D4×C61—21no—
192D4×C61—21no—
193D4×C61C2×M1612yes—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—81no—
197C2×C4×C61—81no—
198C2×C4×C61C4×D411yescharacteristic
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61C23×C411yescharacteristic
201C22⋊D61—42no—
202C22⋊D61—42no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61C4×D411yescharacteristic
208C2×Dic61C22×D411yescharacteristic
209C2×Dic61C2×#4111yescharacteristic
210D244—21no—
211D244—21no—
212D244—21no—
213D244C2×M1612yes—
214C4×D61—22no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—22no—
218C4×D61—42no—
219C4×D61—42no—
220C4×D61—81no—
221C4×D61—81no—
222C4×D61—81no—
223C4×D61—81no—
224#92420—22no—
225#92420—22no—
226#92420—42no—
227#92420—42no—
228#92420—42no—
229C8×C61—21no—
230C8×C61—21no—
231#92418—21no—
232#92418C2×M1612yes—
233#18064—611nomaximal, Sylow
234C22×C61—22no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61C2×C4×D411yescharacteristic
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—22no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—84no—
250C2×D61—84no—
251C2×D61#44412yes—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61C22×M1611yescharacteristic
257C4×C61#56811yescharacteristic
258Dic61—21no—
259Dic61—21no—
260Dic61—41no—
261Dic61—41no—
262Dic61#57612yes—
263#2974—611no—
264#2974—611no—
265C2×C4×D8—611no—
266#1594—612no—
267#1581—612no—
268#1581—612no—
269#1580—612no—
270#1568—611no—
271#1490—611no—
272#1490—611no—
273#1451—611no—
274C2×C61—42no—
275C2×C61—81no—
276C2×C61D4×M1611yescharacteristic
277C2×C61#294811yescharacteristic
278C2×C61C2×#44411yescharacteristic
279D61—22no—
280D61—42no—
281D61—81no—
282C22×D8—611no—
283C2×C4×D4—611no—
284C2×C4×D4—611no—
285C4×D8—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8—611no—
289C4×D8—611no—
290C4×D8—611no—
291C4×D8—611no—
292C4×D8#692311yescharacteristic
293#436—612no—
294#436—612no—
295#435—1222no—
296#435—1222no—
297C8×D4—612no—
298C8×D4—612no—
299#432—611no—
300#432—611no—
301#431—611no—
302C2×#107—611no—
303C2×#102—611no—
304C2×#102—611no—
305#407—1221no—
306#407—1221no—
307C2×C22⋊C8—1221no—
308C2×C22⋊C8—1221no—
309C4×M16—611no—
310C2×C4×C8—611no—
311#335—612no—
312#334—612no—
313D4⋊C8—612no—
314D4⋊C8—612no—
315D4⋊C8—612no—
316D4⋊C8—612no—
317#322—612no—
318#322—612no—
319C61#1806411yescharacteristic, complemented, Sylow
320C22×D4—611no—
321C22×D4—611no—
322C23×C4—1221no—
323C23×C4—1221no—
324C2×D8—611no—
325C2×D8—611no—
326C2×D8—611no—
327C2×D8—1224no—
328C2×D8C2×#692311yescharacteristic
329C2×M16—1222no—
330C2×M16—1222no—
331C2×M16—1221no—
332C22×C8—611no—
333C22×C8—611no—
334C22×C8—1222no—
335C22×C8—1222no—
336C4×D4—611no—
337C4×D4—611no—
338C4×D4—611no—
339C4×D4—611no—
340C4×D4—611no—
341C4×D4—611no—
342C4×D4—1221no—
343C4×D4—1221no—
344C4×D4—1221no—
345C4×D4—1221no—
346C4×D4C2×#692311yescharacteristic
347C4×D4C2×#692311yescharacteristic
348C2×C4⋊C4—611no—
349C2×C4⋊C4—611no—
350C2×C22⋊C4—1221no—
351C2×C22⋊C4—1221no—
352C2×C42—611no—
353#107—611no—
354#107—611no—
355#107—611no—
356#107C2×#692311yescharacteristic
357C4⋊C8—612no—
358C4⋊C8—612no—
359C4⋊C8—612no—
360#102—611no—
361#102—611no—
362#102—611no—
363#102—611no—
364#102—611no—
365#102—611no—
366#102C2×#692311yescharacteristic
367#102C2×#692311yescharacteristic
368C22⋊C8—611no—
369C22⋊C8—611no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372C22⋊C8—1222no—
373C22⋊C8—1222no—
374C22⋊C8—1221no—
375C22⋊C8—1221no—
376#97—1221no—
377#97—1221no—
378#97—1221no—
379C4×C8—612no—
380C4×C8—611no—
381C4×C8—611no—
382C4×C8—612no—
383C4×C8—611no—
384C4×C8C2×#692311yescharacteristic
385C24—1221no—
386C24—1221no—
387C2×D4—611no—
388C2×D4—611no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—1222no—
392C2×D4—1222no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4C22×#692311yescharacteristic
396C2×D4C22×#692311yescharacteristic
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—1221no—
410C22×C4—4882no—
411C22×C4—4882no—
412D8—22no—
413D8—614no—
414D8—1222no—
415D8—1222no—
416M16—4882no—
417M16—4882no—
418M16—2442no—
419C2×C8—611no—
420C2×C8—612no—
421C2×C8—612no—
422C2×C8—611no—
423C2×C8—1222no—
424C2×C8—1222no—
425C2×C8—1222no—
426C2×C8—1222no—
427C2×C8—4882no—
428C2×C8—4882no—
429C2×C8—2441no—
430C2×C8C22×#692311yescharacteristic
431C2×C8C22×#692311yescharacteristic
432C4⋊C4—611no—
433C4⋊C4—611no—
434C4⋊C4—1221no—
435C4⋊C4—1221no—
436C4⋊C4C22×#692311yescharacteristic
437C4⋊C4C22×#692311yescharacteristic
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—1221no—
441C22⋊C4—1221no—
442C22⋊C4—1221no—
443C22⋊C4—1221no—
444C22⋊C4—1221no—
445C22⋊C4—1221no—
446C42—611no—
447C42—611no—
448C42—611no—
449C42C22×#692311yescharacteristic
450C23—21no—
451C23—21no—
452C23—611no—
453C23—1221no—
454C23—1221no—
455C23—4881no—
456C23—4881no—
457C23—2442no—
458C23—2442no—
459C23—2442no—
460C23—2442no—
461D4—21no—
462D4—21no—
463D4—21no—
464D4—612no—
465D4—1221no—
466D4—1221no—
467D4—1221no—
468D4—2442no—
469D4—2442no—
470D4D61⋊M1612yes—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—611no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—4881no—
485C2×C4—4881no—
486C2×C4—4881no—
487C2×C4—4881no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4D4×#692311yescharacteristic
493C2×C4D4×#692311yescharacteristic
494C2×C4C23×#692311yescharacteristic
495C8—21no—
496C8—21no—
497C8—612no—
498C8—1222no—
499C8—1222no—
500C8—1221no—
501C8—2442no—
502C8—2442no—
503C8—2442no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—612no—
511C22—1221no—
512C22—1221no—
513C22—1222no—
514C22—4884no—
515C22—4884no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22—2441no—
520C22—2441no—
521C22C2×D4×#692311yescharacteristic
522C4—21no—
523C4—21no—
524C4—41no—
525C4—41no—
526C4—612no—
527C4—1221no—
528C4—1221no—
529C4—2441no—
530C4—2441no—
531C4C2×D61⋊M1611yescharacteristic
532C4#1684084111yescharacteristic
533C2—42no—
534C2—81no—
535C2—1222no—
536C2—4881no—
537C2—2442no—
538C2#2146255811yescharacteristic
539C2#2146257811yescharacteristic
540C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×D8×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C4
cosocleC4×Dic61C24
hypercenterC4×D8#6923
hypocenterC61#18064
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462679C2semidirect
2. #21462677C2semidirect
3. #21461467C2semidirect
4. #21461420C2semidirect
5. #21461419C2semidirect
6. #21461416C2semidirect
7. #21461382C2semidirect
8. #21461159C2semidirect
9. #21461159C2semidirect
10. #21461029C2semidirect
12. #16840797C22semidirect
13. #16840796C22semidirect
16. #16840790C22semidirect
17. D4×#92420C22semidirect
26. #16840626C22semidirect
27. #16840624C22semidirect
28. #16840610C22semidirect
29. #16840610C22semidirect
30. D4⋊#92420C22semidirect
31. D4⋊#92420C22semidirect
32. #92420⋊C8C22semidirect
33. #16840603C22semidirect
162. #11758199M16semidirect
319. C61#18064semidirect

Maximal subgroups

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

subgroupindex
#214626792
#214626772
#214614672
#214614202
#214614192
#214614162
#214613822
#214611592
#214610292
C4×D8×D612
#1806461