Finite Group Databasebeta

← #30613623

Subgroups — #30613623

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#21462680C211yesmaximal, characteristic, complemented
2#21462675C211yesmaximal, characteristic, complemented
3#21461467C212yesmaximal, complemented
4#21461421C212yesmaximal, complemented
5#21461418C212yesmaximal, complemented
6#21461416C212yesmaximal, complemented
7#21461381C211yesmaximal, characteristic, complemented
8#21461160C211yesmaximal, characteristic, complemented
9#21461158C211yesmaximal, characteristic, complemented
10#21461028C211yesmaximal, characteristic, complemented
11C2×#16839842C211yesmaximal, characteristic
12#16840797C2212yescomplemented
13#16840796C2212yescomplemented
14#16840793—22no—
15#16840792—22no—
16#16840790C2212yescomplemented
17D4×#92420C2212yescomplemented
18#16840783C2211yescharacteristic
19#16840783C2211yescharacteristic
20#16840779C2211yescharacteristic
21#16840733—21no—
22#16840732—21no—
23D61⋊(C22⋊C8)—21no—
24C2×C22⋊#92420—21no—
25C4×#11758217C2211yescharacteristic
26#16840625C2212yescomplemented
27#16840624C2212yescomplemented
28#16840610C2212yescomplemented
29#16840610C2212yescomplemented
30D4⋊#92420C2212yescomplemented
31D4⋊#92420C2212yescomplemented
32#92420⋊C8C2212yescomplemented
33#16840603C2212yescomplemented
34C22×#11758199C411yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37#16839842C411yescharacteristic
38#16839842C411yescharacteristic
39#16839842C411yescharacteristic
40#16839842C411yescharacteristic
41#16839842C2211yescharacteristic
42#16839842C2211yescharacteristic
43#16839842C2211yescharacteristic
44#16839842C2211yescharacteristic
45C2×#14519710C411yescharacteristic
46C2×#14519699C411yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48C2×#102×C61C411yescharacteristic
49C2×#11758213—22no—
50C2×#11758217—21no—
51C2×#11758217—22no—
52C2×D61⋊C8—22no—
53C22×#92420—22no—
54#14519844D412yes—
55C4⋊#92420C2312yes—
56C4⋊#92420C2312yes—
57#14519834—22no—
58#14519834—22no—
59C22⋊#92420—21no—
60C22⋊#92420—21no—
61C22⋊#92420—22no—
62C22⋊#92420—22no—
63C22⋊#92420D411yescharacteristic
64C22⋊#92420D411yescharacteristic
65#14519832—21no—
66#14519832—21no—
67#14519832—21no—
68C4×#92420C2312yes—
69C4×#92420C2312yes—
70C22×D244C2×C411yescharacteristic
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C2×#11758199—24no—
74C2×#11758199C2×C411yescharacteristic
75C2×#11758199C2×C411yescharacteristic
76C2×#11758199C2×C411yescharacteristic
77C2×#11758199C2×C411yescharacteristic
78C22×#92418C2×C411yescharacteristic
79D4×Dic61—21no—
80D4×Dic61—21no—
81D4×Dic61C2×C411yescharacteristic
82D4×Dic61C2×C411yescharacteristic
83D4×Dic61C2311yescharacteristic
84D4×Dic61C2311yescharacteristic
85#14519739—21no—
86#14519739—21no—
87#14519739C2×C411yescharacteristic
88#14519739C2×C411yescharacteristic
89#14519739C2311yescharacteristic
90#14519739C2311yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×C4×Dic61C2311yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519699C2×C411yescharacteristic
100#14519699C2×C411yescharacteristic
101#14519699C2×C411yescharacteristic
102#14519699C2×C411yescharacteristic
103C8×Dic61C2×C411yescharacteristic
104C8×Dic61C2×C411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C8×Dic61C2311yescharacteristic
107C22×D4×C61C2×C411yescharacteristic
108C22×C8×C61C2×C411yescharacteristic
109C2×C4⋊C4×C61C2×C411yescharacteristic
110#102×C61C2×C411yescharacteristic
111#102×C61C2×C411yescharacteristic
112#102×C61C2×C411yescharacteristic
113#102×C61C2×C411yescharacteristic
114C24×C61—21no—
115C23×D61—21no—
116C2×D4×C61—22no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C2×D4×C61C22×C411yescharacteristic
120C2×D4×C61C22×C411yescharacteristic
121C22×C4×C61—21no—
122C22×C4×C61C22×C411yescharacteristic
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—82no—
129C22×Dic61C2×D411yescharacteristic
130C22×Dic61#4111yescharacteristic
131C2×D244—22no—
132C2×D244—21no—
133C2×D244—41no—
134C2×D244C22×C411yescharacteristic
135C2×D244C22×C411yescharacteristic
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—82no—
141#11758217—42no—
142#11758217—82no—
143C2×#92420—22no—
144C2×#92420—22no—
145C2×#92420—22no—
146C2×#92420—82no—
147C2×#92420C2×D412yes—
148C2×#92420C2×D412yes—
149#11758213—82no—
150D61⋊C8—82no—
151C2×C8×C61—41no—
152C2×C8×C61C22×C411yescharacteristic
153C2×C8×C61C22×C411yescharacteristic
154C4⋊C4×C61—21no—
155C4⋊C4×C61C22×C411yescharacteristic
156C4⋊C4×C61C22×C411yescharacteristic
157C22⋊Dic61—21no—
158C22⋊Dic61—21no—
159C22⋊Dic61—21no—
160C22⋊Dic61—21no—
161#11758199—22no—
162#11758199—22no—
163#11758199—22no—
164#11758199M1614yescomplemented
165#11758198—21no—
166#11758198—21no—
167#11758198—21no—
168#11758198—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61C22×C411yescharacteristic
171C4⋊Dic61C22×C411yescharacteristic
172C4×Dic61C22×C411yescharacteristic
173C4×Dic61C2×D411yescharacteristic
174C4×Dic61#4111yescharacteristic
175C4×Dic61C2411yescharacteristic
176C2×#92418—22no—
177C2×#92418C22×C411yescharacteristic
178C2×#92418C22×C411yescharacteristic
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—81no—
184C23×C61C4×D411yescharacteristic
185C22×D61—21no—
186C22×D61—21no—
187C22×D61—42no—
188C22×D61—42no—
189C22×D61—81no—
190D4×C61—21no—
191D4×C61—21no—
192D4×C61—21no—
193D4×C61—42no—
194D4×C61C2×M1612yes—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—81no—
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61C23×C411yescharacteristic
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—81no—
209C2×Dic61—81no—
210C2×Dic61—81no—
211C2×Dic61C4×D411yescharacteristic
212C2×Dic61C4×D411yescharacteristic
213C2×Dic61C22×D411yescharacteristic
214C2×Dic61C2×#4111yescharacteristic
215D244—21no—
216D244—21no—
217D244—21no—
218D244—42no—
219D244C2×M1612yes—
220C4×D61—42no—
221C4×D61—42no—
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—21no—
235C22×C61—21no—
236C22×C61—22no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61—41no—
242C22×C61—84no—
243C22×C61#44412yes—
244C22×C61C2×C4×D411yescharacteristic
245C2×D61—22no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—84no—
252C4×C61—21no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61C22×M1611yescharacteristic
256C4×C61#56811yescharacteristic
257Dic61—21no—
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—22no—
275C2×C61—42no—
276C2×C61—81no—
277C2×C61D4×M1611yescharacteristic
278C2×C61#294811yescharacteristic
279C2×C61C2×#44411yescharacteristic
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—611no—
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#692311yescharacteristic
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×D4C2×#692311yescharacteristic
322C23×C4—1221no—
323C23×C4—1221no—
324C2×D8—611no—
325C2×D8—611no—
326C2×D8—611no—
327C2×D8—611no—
328C2×D8—1224no—
329C2×M16—1222no—
330C2×M16—1222no—
331C2×M16—1221no—
332C22×C8—611no—
333C22×C8—1222no—
334C22×C8—1222no—
335C22×C8C2×#692311yescharacteristic
336C4×D4—611no—
337C4×D4—611no—
338C4×D4—611no—
339C4×D4—611no—
340C4×D4—611no—
341C4×D4—611no—
342C4×D4—611no—
343C4×D4—611no—
344C4×D4—1221no—
345C4×D4—1221no—
346C4×D4—1221no—
347C4×D4—1221no—
348C2×C4⋊C4—611no—
349C2×C4⋊C4C2×#692311yescharacteristic
350C2×C22⋊C4—1221no—
351C2×C22⋊C4—1221no—
352C2×C42—611no—
353#107—611no—
354#107—611no—
355#107—611no—
356#107—611no—
357C4⋊C8—612no—
358C4⋊C8—612no—
359C4⋊C8—612no—
360#102—611no—
361#102—611no—
362#102—611no—
363#102—611no—
364#102C2×#692311yescharacteristic
365#102C2×#692311yescharacteristic
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—611no—
383C4×C8—611no—
384C4×C8—612no—
385C24—21no—
386C24—1221no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—611no—
391C2×D4—611no—
392C2×D4—1222no—
393C2×D4—1221no—
394C2×D4—2441no—
395C2×D4C22×#692311yescharacteristic
396C2×D4C22×#692311yescharacteristic
397C22×C4—21no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—4882no—
410C22×C4—4882no—
411C22×C4C22×#692311yescharacteristic
412D8—614no—
413D8—1222no—
414D8—1222no—
415D8—1222no—
416M16—4882no—
417M16—4882no—
418M16—2442no—
419C2×C8—41no—
420C2×C8—611no—
421C2×C8—612no—
422C2×C8—612no—
423C2×C8—611no—
424C2×C8—1222no—
425C2×C8—1222no—
426C2×C8—1222no—
427C2×C8—1222no—
428C2×C8—4882no—
429C2×C8—4882no—
430C2×C8C22×#692311yescharacteristic
431C2×C8C22×#692311yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—611no—
434C4⋊C4—611no—
435C4⋊C4—1221no—
436C4⋊C4C22×#692311yescharacteristic
437C4⋊C4C22×#692311yescharacteristic
438C22⋊C4—1221no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C22⋊C4—1221no—
442C22⋊C4—1221no—
443C22⋊C4—1221no—
444C22⋊C4—1221no—
445C22⋊C4—1221no—
446C42—611no—
447C42—611no—
448C42—611no—
449C42—611no—
450C23—21no—
451C23—21no—
452C23—42no—
453C23—42no—
454C23—81no—
455C23—1221no—
456C23—1221no—
457C23—4881no—
458C23—2442no—
459C23—2442no—
460C23D4×#692311yescharacteristic
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—612no—
466D4—1221no—
467D4—1221no—
468D4—1221no—
469D4—2442no—
470D4D61⋊M1612yes—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—81no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—4881no—
485C2×C4—4881no—
486C2×C4—4881no—
487C2×C4—4881no—
488C2×C4—4881no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4—2442no—
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—21no—
505C22—21no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—84no—
513C22—1222no—
514C22—4884no—
515C22—2441no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22—2441no—
520C22#1684080712yes—
521C22C2×D4×#692311yescharacteristic
522C4—21no—
523C4—41no—
524C4—41no—
525C4—612no—
526C4—1221no—
527C4—1221no—
528C4—1221no—
529C4—2441no—
530C4—2441no—
531C4C2×D61⋊M1611yescharacteristic
532C4#1684084011yescharacteristic
533C2—22no—
534C2—42no—
535C2—81no—
536C2—4881no—
537C2—2442no—
538C2#2146255711yescharacteristic
539C2#2146257811yescharacteristic
540C2C2×#1684080711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#102×C61C4
socleC22×C61C2×C4×D4
prime radicalC22×#11758199C4
cosocleC4×Dic61C24
hypercenterC2×#102#6923
hypocenterC61#18064
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #21462680C2semidirect
2. #21462675C2semidirect
3. #21461467C2semidirect
4. #21461421C2semidirect
5. #21461418C2semidirect
6. #21461416C2semidirect
7. #21461381C2semidirect
8. #21461160C2semidirect
9. #21461158C2semidirect
10. #21461028C2semidirect
12. #16840797C22semidirect
13. #16840796C22semidirect
16. #16840790C22semidirect
17. D4×#92420C22semidirect
26. #16840625C22semidirect
27. #16840624C22semidirect
28. #16840610C22semidirect
29. #16840610C22semidirect
30. D4⋊#92420C22semidirect
31. D4⋊#92420C22semidirect
32. #92420⋊C8C22semidirect
33. #16840603C22semidirect
164. #11758199M16semidirect
319. C61#18064semidirect

Maximal subgroups

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

subgroupindex
#214626802
#214626752
#214614672
#214614212
#214614182
#214614162
#214613812
#214611602
#214611582
#214610282
C2×#168398422
#1806461