Finite Group Databasebeta

← #30610016

Subgroups — #30610016

Order 15616.

1210 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462674C212yesmaximal, complemented
2#21461082C212yesmaximal, complemented
3#21461076C212yesmaximal, complemented
4#21461072C212yesmaximal, complemented
5#21461068C212yesmaximal, complemented
6#21461056C212yesmaximal, complemented
7D61⋊#324C212yesmaximal, complemented
8C2×#16840244C211yesmaximal, characteristic
9#16840792—28no—
10#16840782C2214yes—
11#16840733C2214yes—
12D61⋊(C22⋊C8)C2214yes—
13#16840608C2214yes—
14#16840607C2214yes—
15#16840607C2214yes—
16#16840606C2214yes—
17C22×#11758226C411yescharacteristic
18#16840244—28no—
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×D244C411yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519739C411yescharacteristic
24C2×#14519739C411yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×#14519734C411yescharacteristic
27C2×#14519734C411yescharacteristic
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61C411yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C4×Q8×C61C411yescharacteristic
33C2×#11758213—24no—
34C2×D61⋊C8—24no—
35#14519844—24no—
36#14519834—24no—
37#14519834—24no—
38C22⋊#92420C2318yes—
39#14519832—24no—
40C2×#11758226—24no—
41C2×#11758226—24no—
42C2×#11758226—24no—
43C22×D244C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×D244C2×C411yescharacteristic
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C22×C4×D61C2311yescharacteristic
55Q8×Dic61—24no—
56C4×D244—24no—
57C4×D244—24no—
58C4×D244—24no—
59#14519739—24no—
60#14519739—24no—
61#14519739D418yes—
62#14519734—24no—
63#14519734—24no—
64#14519734—24no—
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×#11758196C2×C411yescharacteristic
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2311yescharacteristic
72C4⋊C4×D61—24no—
73C4⋊C4×D61—24no—
74C4⋊C4×D61—24no—
75C2×#11758198C2×C411yescharacteristic
76C2×#11758198C2×C411yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2311yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C22×Q8×C61C2×C411yescharacteristic
85C4×Q8×C61—24no—
86C2×C4⋊C4×C61C2×C411yescharacteristic
87C2×C4⋊C4×C61C2×C411yescharacteristic
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C42×C61C2×C411yescharacteristic
90C2×C42×C61C2×C411yescharacteristic
91C2×C42×C61C2×C411yescharacteristic
92C23×D61C22×C411yescharacteristic
93C23×D61C22×C411yescharacteristic
94C23×D61C22×C411yescharacteristic
95C2×Q8×C61—22no—
96C2×Q8×C61—22no—
97C2×Q8×C61—22no—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×Dic61C22×C411yescharacteristic
106C22×Dic61C22×C411yescharacteristic
107C22×Dic61C22×C411yescharacteristic
108C22×Dic61C22×C411yescharacteristic
109C22×Dic61C2411yescharacteristic
110#11758226—232no—
111C2×D244—22no—
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244C22⋊C414yes—
119C2×D244M1614yescomplemented
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—81no—
133C2×C4×D61—81no—
134C2×C4×D61—81no—
135C2×C4×D61—81no—
136C2×C4×D61—81no—
137C2×C4×D61—81no—
138C2×C4×D61M1614yescomplemented
139C2×C4×D61C2×D414yes—
140C2×C4×D61C2×D414yes—
141C2×#92420—28no—
142#11758213—84no—
143D61⋊C8—84no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61C22⋊C414yes—
147C42×C61—22no—
148C42×C61—22no—
149C42×C61—22no—
150#11758198—22no—
151#11758198—22no—
152#11758198—22no—
153#11758198—22no—
154#11758198C22⋊C414yes—
155#11758198C22⋊C414yes—
156C4⋊Dic61—22no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159#11758196—22no—
160#11758196—22no—
161#11758196—22no—
162#11758196—22no—
163C4×Dic61—22no—
164C4×Dic61—22no—
165C4×Dic61C2×D414yes—
166C23×C61C23×C411yescharacteristic
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61C2×C22⋊C412yes—
178C22×D61C2×C22⋊C412yes—
179C22×D61C2×M1612yes—
180C22×D61C2×M1612yes—
181C22×D61C2×M1612yes—
182Q8×C61—28no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61C2×C22⋊C412yes—
196C2×C4×C61C2×C22⋊C412yes—
197C2×C4×C61C2×C22⋊C412yes—
198C2×C4×C61C2×M1612yes—
199C2×C4×C61C2×M1612yes—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61C2×C22⋊C412yes—
209C2×Dic61C2×M1612yes—
210C2×Dic61C22×D412yes—
211D244—28no—
212D244—28no—
213D244—28no—
214C4×D61—28no—
215C4×D61—28no—
216C4×D61—28no—
217C4×D61—44no—
218C4×D61—44no—
219C4×D61—82no—
220C4×D61—82no—
221C4×D61—82no—
222C4×D61—82no—
223#92420—48no—
224#17368—611nomaximal, Sylow
225C22×C61—21no—
226C22×C61—21no—
227C22×C61C22×C22⋊C411yescharacteristic
228C22×C61C22×M1611yescharacteristic
229C22×C61C22×M1611yescharacteristic
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—42no—
237C2×D61—42no—
238C2×D61—42no—
239C2×D61—42no—
240C2×D61—42no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—42no—
244C2×D61#40714yes—
245C4×C61—22no—
246C4×C61—22no—
247C4×C61—22no—
248C4×C61—22no—
249C4×C61—22no—
250C4×C61—41no—
251C4×C61—41no—
252Dic61—22no—
253Dic61—22no—
254Dic61—22no—
255Dic61—41no—
256Dic61—41no—
257C2×#520—611no—
258#2973—612no—
259#1467—612no—
260#1465—612no—
261#1464—612no—
262#1463—612no—
263#1459—612no—
264C2×#324—612no—
265C2×C61—21no—
266C2×C61—21no—
267C2×C61C2×#40711yescharacteristic
268C2×C61#288311yescharacteristic
269C2×C61#288911yescharacteristic
270D61—24no—
271D61—42no—
272D61—42no—
273C22×#41—611no—
274#520—1228no—
275C2×C4×Q8—611no—
276C2×C4×Q8#692311yescharacteristic
277C2×C4×D4—611no—
278C2×C4×D4—611no—
279C2×C4×D4—611no—
280C2×C4×D4—611no—
281C2×C4×D4—611no—
282C2×C4×D4—611no—
283C2×#117—611no—
284C2×#117—611no—
285C2×#117—611no—
286C22×C4⋊C4—611no—
287C22×C4⋊C4—611no—
288C22×C4⋊C4—611no—
289#435—1228no—
290#432—614no—
291#407—614no—
292C2×C22⋊C8—614no—
293#324—614no—
294#324—614no—
295#324—614no—
296#323—614no—
297C61#1736811yescharacteristic, complemented, Sylow
298C2×#41—1224no—
299C2×#41—1224no—
300C2×#41—1224no—
301C22×Q8C2×#692311yescharacteristic
302C22×D4—611no—
303C22×D4—611no—
304C22×D4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C2×M16—1224no—
315C22×C8—1224no—
316C4×Q8—24no—
317C4×Q8—1224no—
318C4×D4—618no—
319C4×D4—1224no—
320C4×D4—1224no—
321C4×D4—1224no—
322C4×D4—1224no—
323C4×D4—1224no—
324#117—1224no—
325#117—1224no—
326#117—1224no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—611no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—1224no—
335C2×C4⋊C4—1224no—
336C2×C4⋊C4—1224no—
337C2×C4⋊C4C2×#692311yescharacteristic
338C2×C4⋊C4C2×#692311yescharacteristic
339C2×C4⋊C4C2×#692311yescharacteristic
340C2×C22⋊C4—611no—
341C2×C22⋊C4—611no—
342C2×C22⋊C4—611no—
343C2×C22⋊C4—611no—
344C2×C22⋊C4—611no—
345C2×C22⋊C4—611no—
346C2×C42—611no—
347C2×C42—611no—
348C2×C42—611no—
349C2×C42C2×#692311yescharacteristic
350C2×C42C2×#692311yescharacteristic
351C2×C42C2×#692311yescharacteristic
352C4⋊C8—1224no—
353C22⋊C8—618no—
354C22⋊C8—1224no—
355C22⋊C8—1224no—
356#97—1224no—
357C24—611no—
358C24—611no—
359C24—611no—
360#41—12232no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×D4—614no—
365C2×D4—614no—
366C2×D4—1222no—
367C2×D4—1222no—
368C2×D4—1222no—
369C2×D4—1222no—
370C2×D4—1222no—
371C2×D4—1222no—
372C2×D4—1222no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—614no—
377C22×C4—614no—
378C22×C4—614no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—4881no—
394C22×C4—4881no—
395C22×C4—4881no—
396C22×C4—4881no—
397C22×C4—4881no—
398C22×C4—4881no—
399C22×C4C22×#692311yescharacteristic
400C22×C4C22×#692311yescharacteristic
401C22×C4C22×#692311yescharacteristic
402C22×C4C22×#692311yescharacteristic
403C22×C4C22×#692311yescharacteristic
404C22×C4C22×#692311yescharacteristic
405C22×C4C22×#692311yescharacteristic
406M16—4884no—
407C2×C8—1228no—
408C2×C8—4884no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—1222no—
412C4⋊C4—1222no—
413C4⋊C4—1222no—
414C4⋊C4—1222no—
415C4⋊C4—1222no—
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C4⋊C4C22⋊#692314yes—
419C22⋊C4—614no—
420C22⋊C4—614no—
421C22⋊C4—1222no—
422C22⋊C4—1222no—
423C22⋊C4—1222no—
424C22⋊C4—1222no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42—614no—
429C42—1222no—
430C42—1222no—
431C23—612no—
432C23—612no—
433C23—612no—
434C23—612no—
435C23—612no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—1221no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23C23×#692311yescharacteristic
447Q8—28no—
448D4—1228no—
449D4—1228no—
450D4—1228no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—1228no—
467C2×C4—1228no—
468C2×C4—1228no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—4882no—
474C2×C4—4882no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—2444no—
478C2×C4—2444no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4C2×C22⋊#692312yes—
484C2×C4C2×C22⋊#692312yes—
485C2×C4C2×C22⋊#692312yes—
486C2×C4D61⋊M1612yes—
487C2×C4D61⋊M1612yes—
488C8—2448no—
489C22—21no—
490C22—21no—
491C22—614no—
492C22—1222no—
493C22—1222no—
494C22—1222no—
495C22—1222no—
496C22—1222no—
497C22—1222no—
498C22—2442no—
499C22—2442no—
500C22—2442no—
501C22—2442no—
502C22—2442no—
503C22—2442no—
504C22—2441no—
505C22—2441no—
506C22C22×C22⋊#692311yescharacteristic
507C22C2×D61⋊M1611yescharacteristic
508C22C2×D61⋊M1611yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—22no—
514C4—41no—
515C4—41no—
516C4—1222no—
517C4—1222no—
518C4—1222no—
519C4—2441no—
520C4—2441no—
521C2—21no—
522C2—21no—
523C2—1224no—
524C2—2442no—
525C2—2442no—
526C2D61⋊#40711yescharacteristic
527C2#2146241911yescharacteristic
528C2#2146243211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC22×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17368
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462674C2semidirect
2. #21461082C2semidirect
3. #21461076C2semidirect
4. #21461072C2semidirect
5. #21461068C2semidirect
6. #21461056C2semidirect
7. D61⋊#324C2semidirect
119. C2×D244M16semidirect
138. C2×C4×D61M16semidirect
297. C61#17368semidirect

Maximal subgroups

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

subgroupindex
#214626742
#214610822
#214610762
#214610722
#214610682
#214610562
D61⋊#3242
C2×#168402442
#1736861