Finite Group Databasebeta

← #30612463

Subgroups — #30612463

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462682C211yesmaximal, characteristic, complemented
2#21462667C211yesmaximal, characteristic, complemented
3#21461441C212yesmaximal, complemented
4#21461438C212yesmaximal, complemented
5#21461420C212yesmaximal, complemented
6#21461419C212yesmaximal, complemented
7#21461367C211yesmaximal, characteristic, complemented
8#21461119C211yesmaximal, characteristic, complemented
9#21461119C211yesmaximal, characteristic, complemented
10#21461033C211yesmaximal, characteristic, complemented
11C4×D8×D61C211yesmaximal, characteristic
12#16840797C2212yescomplemented
13#16840796C2212yescomplemented
14#16840795—22no—
15#16840790C2212yescomplemented
16#16840789—22no—
17D4×#92420C2212yescomplemented
18#16840781C2211yescharacteristic
19#16840781C2211yescharacteristic
20#16840780C2211yescharacteristic
21#16840780C2211yescharacteristic
22#16840734—21no—
23#16840733—21no—
24C2×#14519834—21no—
25D61⋊(C22⋊C8)—21no—
26#16840626C2212yescomplemented
27#16840623C2212yescomplemented
28#16840610C2212yescomplemented
29#16840610C2212yescomplemented
30D4⋊#92420C2212yescomplemented
31D4⋊#92420C2212yescomplemented
32#92420⋊C8C2212yescomplemented
33#92420⋊C8C2212yescomplemented
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—22no—
50C2×#11758217—22no—
51C2×D61⋊C8—22no—
52C22×#92420—22no—
53#14519844—21no—
54#14519844D412yes—
55C4⋊#92420C2312yes—
56C4⋊#92420C2312yes—
57#14519834—21no—
58#14519834—21no—
59#14519834—21no—
60#14519834—22no—
61#14519834—22no—
62#14519834D411yescharacteristic
63#14519834D411yescharacteristic
64C22⋊#92420—22no—
65C22⋊#92420—22no—
66C4×#92420—21no—
67C4×#92420—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—22no—
127D4×D61M1614yescomplemented
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—82no—
149D61⋊C8—82no—
150D8×C61—22no—
151C2×C8×C61C22×C411yescharacteristic
152C2×C8×C61C22×C411yescharacteristic
153C4⋊C4×C61C22×C411yescharacteristic
154C4⋊C4×C61C22×C411yescharacteristic
155C22⋊C4×C61—21no—
156C22⋊C4×C61—21no—
157C42×C61C22×C411yescharacteristic
158C22⋊Dic61—21no—
159C22⋊Dic61—21no—
160#11758199—22no—
161#11758199—22no—
162#11758198—21no—
163#11758198—21no—
164#11758198—21no—
165#11758198—21no—
166C4⋊Dic61C22×C411yescharacteristic
167C4⋊Dic61C22×C411yescharacteristic
168#11758196—21no—
169#11758196—21no—
170C4×Dic61C2×D411yescharacteristic
171C4×Dic61#4111yescharacteristic
172C4×Dic61C2411yescharacteristic
173C2×#92418C22×C411yescharacteristic
174C2×#92418C22×C411yescharacteristic
175D488—22no—
176C8×D61—22no—
177C8×D61—22no—
178C23×C61—21no—
179C23×C61—21no—
180C22×D61—21no—
181C22×D61—24no—
182C22×D61—21no—
183C22×D61—42no—
184C22×D61—81no—
185C22×D61—81no—
186C22×D61—81no—
187C22×D61—81no—
188C22×D61C4×D411yescharacteristic
189D4×C61—21no—
190D4×C61—21no—
191D4×C61—21no—
192D4×C61C2×M1612yes—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—81no—
196C2×C4×C61—81no—
197C2×C4×C61C4×D411yescharacteristic
198C2×C4×C61C4×D411yescharacteristic
199C2×C4×C61C23×C411yescharacteristic
200C22⋊D61—24no—
201C22⋊D61—42no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61C4×D411yescharacteristic
207C2×Dic61C22×D411yescharacteristic
208C2×Dic61C2×#4111yescharacteristic
209D244—21no—
210D244—21no—
211D244—21no—
212D244C2×M1612yes—
213C4×D61—22no—
214C4×D61—41no—
215C4×D61—42no—
216C4×D61—42no—
217C4×D61—81no—
218C4×D61—81no—
219C4×D61—81no—
220C4×D61—81no—
221C4×D61C2×M1612yes—
222C4×D61#13112yes—
223#92420—22no—
224#92420—22no—
225#92420—42no—
226#92420—42no—
227#92420—42no—
228C8×C61—21no—
229C8×C61—21no—
230#92418—21no—
231#92418—21no—
232#17877—611nomaximal, Sylow
233C22×C61—22no—
234C22×C61—41no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61C2×C4×D411yescharacteristic
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—22no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—84no—
249C2×D61—84no—
250C2×D61#43512yes—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61C22×M1611yescharacteristic
256C4×C61C2×#13111yescharacteristic
257Dic61—21no—
258Dic61—41no—
259Dic61—41no—
260Dic61#43512yes—
261Dic61#57612yes—
262#2975—611no—
263#2972—611no—
264C2×C4×D8—611no—
265#1586—612no—
266#1586—612no—
267#1581—612no—
268#1581—612no—
269#1564—611no—
270#1478—611no—
271#1478—611no—
272#1452—611no—
273C2×C61—42no—
274C2×C61—81no—
275C2×C61C2×#43511yescharacteristic
276C2×C61#294811yescharacteristic
277C2×C61#295711yescharacteristic
278D61—22no—
279D61—42no—
280D61—81no—
281C22×D8—611no—
282C2×C4×D4—611no—
283C2×C4×D4—611no—
284C4×D8—611no—
285C4×D8—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8—611no—
289C4×D8—611no—
290C4×D8—611no—
291C4×D8#692311yescharacteristic
292#436—612no—
293#436—612no—
294#436—1222no—
295C8×D4—612no—
296C8×D4—612no—
297C8×D4—1222no—
298#431—611no—
299#431—611no—
300#431—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—
309C2×C4×C8—611no—
310#335—612no—
311#334—612no—
312D4⋊C8—612no—
313D4⋊C8—612no—
314D4⋊C8—612no—
315D4⋊C8—612no—
316#322—612no—
317#322—612no—
318C61#1787711yescharacteristic, complemented, Sylow
319C22×D4—611no—
320C22×D4—611no—
321C23×C4—1221no—
322C23×C4—1221no—
323C2×D8—611no—
324C2×D8—611no—
325C2×D8—611no—
326C2×D8—1224no—
327C2×D8C2×#692311yescharacteristic
328C2×M16—1222no—
329C2×M16—1222no—
330C22×C8—611no—
331C22×C8—611no—
332C22×C8—1222no—
333C22×C8—1222no—
334C4×D4—611no—
335C4×D4—611no—
336C4×D4—611no—
337C4×D4—611no—
338C4×D4—611no—
339C4×D4—611no—
340C4×D4—1221no—
341C4×D4—1221no—
342C4×D4—1221no—
343C4×D4—1221no—
344C4×D4C2×#692311yescharacteristic
345C4×D4C2×#692311yescharacteristic
346C2×C4⋊C4—611no—
347C2×C4⋊C4—611no—
348C2×C22⋊C4—1221no—
349C2×C22⋊C4—1221no—
350C2×C42—611no—
351#107—611no—
352#107—611no—
353#107—611no—
354#107C2×#692311yescharacteristic
355C4⋊C8—612no—
356C4⋊C8—612no—
357C4⋊C8—612no—
358C4⋊C8—1221no—
359#102—611no—
360#102—611no—
361#102—611no—
362#102—611no—
363#102—611no—
364#102—611no—
365#102C2×#692311yescharacteristic
366#102C2×#692311yescharacteristic
367C22⋊C8—611no—
368C22⋊C8—611no—
369C22⋊C8—1222no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372C22⋊C8—1222no—
373C22⋊C8—1221no—
374C22⋊C8—1221no—
375C22⋊C8—1221no—
376C4×C8—612no—
377C4×C8—611no—
378C4×C8—611no—
379C4×C8—612no—
380C4×C8—611no—
381C4×C8—1221no—
382C4×C8—1221no—
383C4×C8C2×#692311yescharacteristic
384C24—1221no—
385C24—1221no—
386C2×D4—614no—
387C2×D4—611no—
388C2×D4—611no—
389C2×D4—1222no—
390C2×D4—1222no—
391C2×D4—1222no—
392C2×D4—1221no—
393C2×D4—1221no—
394C2×D4C22×#692311yescharacteristic
395C2×D4C22×#692311yescharacteristic
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
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—
411D8—22no—
412D8—1222no—
413D8—1222no—
414D8—1222no—
415M16—4882no—
416M16—4882no—
417C2×C8—612no—
418C2×C8—612no—
419C2×C8—611no—
420C2×C8—611no—
421C2×C8—1222no—
422C2×C8—1222no—
423C2×C8—1222no—
424C2×C8—1222no—
425C2×C8—1222no—
426C2×C8—4882no—
427C2×C8—4882no—
428C2×C8C22×#692311yescharacteristic
429C2×C8C22×#692311yescharacteristic
430C4⋊C4—611no—
431C4⋊C4—611no—
432C4⋊C4—1221no—
433C4⋊C4—1221no—
434C4⋊C4C22×#692311yescharacteristic
435C4⋊C4C22×#692311yescharacteristic
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—1221no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C22⋊C4—1221no—
442C22⋊C4—1221no—
443C22⋊C4—1221no—
444C42—611no—
445C42—611no—
446C42—611no—
447C42C22×#692311yescharacteristic
448C23—21no—
449C23—21no—
450C23—611no—
451C23—1224no—
452C23—1221no—
453C23—1221no—
454C23—4881no—
455C23—4881no—
456C23—4881no—
457C23—4881no—
458C23—2442no—
459D4—21no—
460D4—21no—
461D4—21no—
462D4—612no—
463D4—1224no—
464D4—1221no—
465D4—1221no—
466D4—1221no—
467D4—2442no—
468D4D61⋊M1612yes—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—611no—
474C2×C4—611no—
475C2×C4—612no—
476C2×C4—612no—
477C2×C4—611no—
478C2×C4—1222no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—2441no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4D4×#692311yescharacteristic
491C2×C4D4×#692311yescharacteristic
492C2×C4C23×#692311yescharacteristic
493C8—21no—
494C8—21no—
495C8—1222no—
496C8—1222no—
497C8—1221no—
498C8—1221no—
499C8—2442no—
500C8—2442no—
501C8—2442no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—612no—
509C22—1221no—
510C22—1221no—
511C22—1222no—
512C22—4884no—
513C22—4884no—
514C22—2441no—
515C22—2441no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22C2×D4×#692311yescharacteristic
520C4—21no—
521C4—21no—
522C4—41no—
523C4—41no—
524C4—612no—
525C4—612no—
526C4—1221no—
527C4—2441no—
528C4—2441no—
529C4C2×D61⋊M1611yescharacteristic
530C4D61⋊#13111yescharacteristic
531C2—42no—
532C2—81no—
533C2—1222no—
534C2—4881no—
535C2—2442no—
536C2D61⋊#43511yescharacteristic
537C2#2146257811yescharacteristic
538C2#2146259811yescharacteristic
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#17877
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. #21462682C2semidirect
2. #21462667C2semidirect
3. #21461441C2semidirect
4. #21461438C2semidirect
5. #21461420C2semidirect
6. #21461419C2semidirect
7. #21461367C2semidirect
8. #21461119C2semidirect
9. #21461119C2semidirect
10. #21461033C2semidirect
12. #16840797C22semidirect
13. #16840796C22semidirect
15. #16840790C22semidirect
17. D4×#92420C22semidirect
26. #16840626C22semidirect
27. #16840623C22semidirect
28. #16840610C22semidirect
29. #16840610C22semidirect
30. D4⋊#92420C22semidirect
31. D4⋊#92420C22semidirect
32. #92420⋊C8C22semidirect
33. #92420⋊C8C22semidirect
127. D4×D61M16semidirect
318. C61#17877semidirect

Maximal subgroups

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

subgroupindex
#214626822
#214626672
#214614412
#214614382
#214614202
#214614192
#214613672
#214611192
#214610332
C4×D8×D612
#1787761