Finite Group Databasebeta

← D61⋊#1868 #30615542

Subgroups — D61⋊#1868 #30615542

Order 15616.

1342 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#568C211yesmaximal, characteristic
2D61⋊#424C212yesmaximal, complemented
3D61⋊#408C211yesmaximal, characteristic
4#21461791C218yesmaximal, complemented
5#21461527C212yesmaximal, complemented
6#410×D61C211yesmaximal, characteristic
7#16840842—21no—
8#16840841—24no—
9#16840840—21no—
10#16840840C2214yes—
11D61⋊#131—24no—
12C2×D61⋊M16—22no—
13C2×D61⋊M16C2211yescharacteristic
14C2×D61⋊M16C2212yes—
15C22×D61⋊C8C2211yescharacteristic
16#16840769—24no—
17#16840768C2218yescomplemented
18D61⋊(C4⋊C8)—24no—
19#16840737—21no—
20#16840736—21no—
21#16840735C2214yes—
22D61⋊(C22⋊C8)—22no—
23#16840643C2218yescomplemented
24C2×#41×D61C2211yescharacteristic
25#117×D61C2212yes—
26#16839736C411yescharacteristic
27#16839735C412yes—
28#16839734C2214yes—
29#99×D61C414yes—
30C61×#410C411yescharacteristic
31#14519865—28no—
32#14519864—28no—
33#14519864—216no—
34C2×#11758213—24no—
35C2×#11758213—21no—
36C2×#11758213D414yes—
37D61⋊M16—24no—
38D61⋊M16—24no—
39D61⋊M16—22no—
40D61⋊M16—24no—
41D61⋊M16—22no—
42D61⋊M16—22no—
43D61⋊M16—22no—
44D61⋊M16—22no—
45D61⋊M16—22no—
46C2×#11758217—24no—
47C2×#11758217C2312yes—
48C2×#11758217C2314yes—
49C2×D61⋊C8—24no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8—21no—
52C2×D61⋊C8—21no—
53C2×D61⋊C8—22no—
54C2×D61⋊C8—22no—
55C2×D61⋊C8D414yes—
56C22×#92420C2312yes—
57#14519844—28no—
58C4⋊#92420—28no—
59#14519834—24no—
60C22⋊#92420—24no—
61C2×#11758226D411yescharacteristic
62C2×#11758222C2×C411yescharacteristic
63C2×#11758222Q812yes—
64C2×#11758224D411yescharacteristic
65C2×#11758224C2312yes—
66#41×D61—22no—
67#41×D61—22no—
68#41×D61—22no—
69#41×D61—22no—
70C2×Q8×D61Q811yescharacteristic
71C2×D4×D61C2×C412yes—
72C2×D4×D61Q811yescharacteristic
73C22×C4×D61D412yes—
74C22×C4×D61C2311yescharacteristic
75#14519736C2×C412yes—
76#14519735—22no—
77#14519734—22no—
78#14519733C2314yes—
79C4⋊C4×D61—22no—
80C22⋊C4×D61C2×C414yes—
81C42×D61—22no—
82#14519692C2×C414yes—
83#14519691C2×C418yes—
84C2×#41×C61C2×C411yescharacteristic
85#117×C61C2×C412yes—
86#99×C61C2×C414yes—
87C23×D61C4⋊C412yes—
88C23×D61C22×C411yescharacteristic
89#41×C61—22no—
90#41×C61—22no—
91C2×Q8×C61C4⋊C411yescharacteristic
92C2×D4×C61C4⋊C411yescharacteristic
93C2×D4×C61C22×C412yes—
94C22×C4×C61C4⋊C412yes—
95C22×C4×C61C22×C411yescharacteristic
96C2×C22⋊D61C4⋊C412yes—
97C2×C22⋊D61C22×C412yes—
98C2×C22⋊D61C2×Q812yes—
99C22×Dic61C2×D412yes—
100C22×Dic61C2411yescharacteristic
101#11758226—22no—
102#11758226—22no—
103Q8×D61—22no—
104Q8×D61—22no—
105#11758224—24no—
106#11758224—24no—
107#11758224—22no—
108#11758224—22no—
109D4×D61—24no—
110D4×D61—24no—
111D4×D61—22no—
112D4×D61—22no—
113#11758222—22no—
114#11758222—22no—
115#11758222—24no—
116#11758222—24no—
117C2×D244C4⋊C412yes—
118C2×D244C4⋊C411yescharacteristic
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—24no—
124C2×C4×D61C4⋊C412yes—
125C2×C4×D61C4⋊C412yes—
126C2×C4×D61C2×D412yes—
127C2×C4×D61C2×D412yes—
128C2×C4×D61C2×D412yes—
129C2×C4×D61C2×D411yescharacteristic
130C2×C4×D61C2×D411yescharacteristic
131C2×C4×D61C2×Q811yescharacteristic
132C2×C4×D61C2×Q811yescharacteristic
133C2×C4×D61#4112yes—
134C2×C4×D61#4112yes—
135C2×Dic122C4⋊C411yescharacteristic
136C2×Dic122C2×Q812yes—
137#11758217—28no—
138#11758217—24no—
139#11758217—24no—
140#11758217—24no—
141C2×#92420—28no—
142C2×#92420—22no—
143C2×#92420—22no—
144C2×#92420—24no—
145C2×#92420C2×D418yes—
146#11758213—28no—
147#11758213—24no—
148#11758213—24no—
149#11758213—42no—
150D61⋊C8—28no—
151D61⋊C8—24no—
152D61⋊C8—24no—
153D61⋊C8—41no—
154D61⋊C8—42no—
155D61⋊C8—41no—
156D61⋊C8—41no—
157D61⋊C8—41no—
158C4⋊C4×C61—22no—
159C22⋊C4×C61C22×C414yes—
160C42×C61—22no—
161C22⋊Dic61C22×C414yes—
162#11758198—24no—
163C4⋊Dic61—22no—
164#11758196—24no—
165C4×Dic61—22no—
166C4×Dic61—24no—
167C23×C61C2×C4⋊C412yes—
168C23×C61C23×C411yescharacteristic
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—42no—
172C22×D61—44no—
173C22×D61C2×C4⋊C411yescharacteristic
174C22×D61C2×C4⋊C412yes—
175C22×D61C2×C4⋊C411yescharacteristic
176C22×D61C4×D412yes—
177C22×D61C4×D412yes—
178Q8×C61—22no—
179D4×C61—24no—
180D4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—24no—
184C2×C4×C61C2×C4⋊C412yes—
185C2×C4×C61C2×C4⋊C411yescharacteristic
186C2×C4×C61C2×C4⋊C411yescharacteristic
187C2×C4×C61C4×D412yes—
188C2×C4×C61C4×D412yes—
189C22⋊D61—24no—
190C22⋊D61—24no—
191C22⋊D61—24no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—24no—
195C2×Dic61C2×C4⋊C412yes—
196C2×Dic61C22×D412yes—
197C2×Dic61C22×D411yescharacteristic
198C2×Dic61C22×Q811yescharacteristic
199C2×Dic61C2×#4112yes—
200D244—24no—
201D244—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—48no—
209C4×D61#12011yescharacteristic
210C4×D61#12012yes—
211C4×D61#12011yescharacteristic
212C4×D61C22⋊Q812yes—
213C4×D61C22⋊Q812yes—
214C4×D61C22⋊Q812yes—
215C4×D61C22⋊Q812yes—
216C4×D61#12311yescharacteristic
217C4×D61#12311yescharacteristic
218C4×D61#12312yes—
219Dic122—22no—
220Dic122—24no—
221#92420—28no—
222#92420—42no—
223#92420—42no—
224C2×#1868—611nomaximal, Sylow
225C22×C61—22no—
226C22×C61—41no—
227C22×C61—42no—
228C22×C61C22×C4⋊C411yescharacteristic
229C22×C61C2×C4×D412yes—
230C2×D61—24no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—41no—
234C2×D61—42no—
235C2×D61—44no—
236C2×D61—42no—
237C2×D61—82no—
238C2×D61#38511yescharacteristic
239C2×D61#38512yes—
240C2×D61#38511yescharacteristic
241C4×C61—22no—
242C4×C61—44no—
243C4×C61#38512yes—
244C4×C61#38511yescharacteristic
245C4×C61#38511yescharacteristic
246Dic61—22no—
247Dic61—44no—
248Dic61C2×#12011yescharacteristic
249Dic61C2×C22⋊Q812yes—
250Dic61C2×#12311yescharacteristic
251C2×#568—611no—
252C2×#424—612no—
253C2×#410—611no—
254C2×#408—611no—
255#1868—618no—
256C2×#344—612no—
257C2×C61—22no—
258C2×C61—21no—
259C2×C61—42no—
260C2×C61C2×#38511yescharacteristic
261D61—21no—
262D61—22no—
263D61—42no—
264D61#186812yescomplemented
265C22×#41—611no—
266#568—614no—
267#568—1224no—
268#568—1221no—
269#568—1221no—
270C2×#131—1224no—
271C22×M16—612no—
272C22×M16—611no—
273C22×M16—1222no—
274C23×C8—611no—
275C2×#117—612no—
276#424—618no—
277#424—1224no—
278C2×C4⋊C8—1224no—
279#410—611no—
280#410—612no—
281#410—614no—
282#410#692311yescharacteristic
283C2×#99—614no—
284#408—614no—
285#408—1221no—
286#408—1221no—
287C2×C22⋊C8—1222no—
288#344—618no—
289C61C2×#186811yescharacteristic, complemented, Sylow
290C2×#41—611no—
291C2×#41—611no—
292C2×#41—612no—
293C2×#41—612no—
294C2×#41—611no—
295C2×#41—1222no—
296C2×#41—1222no—
297C2×#41—1222no—
298C2×#41—1222no—
299C2×#41C2×#692311yescharacteristic
300C22×Q8—611no—
301C22×D4—611no—
302C22×D4—612no—
303C23×C4—611no—
304C23×C4—612no—
305#131—12216no—
306#131—1228no—
307#131—1228no—
308C2×M16—614no—
309C2×M16—614no—
310C2×M16—612no—
311C2×M16—1224no—
312C2×M16—1222no—
313C2×M16—1222no—
314C2×M16—1222no—
315C2×M16—1222no—
316C2×M16—1224no—
317C2×M16—1224no—
318C2×M16—1224no—
319C2×M16—1224no—
320C2×M16—1221no—
321C2×M16—1222no—
322C2×M16—1222no—
323C22×C8—614no—
324C22×C8—612no—
325C22×C8—1224no—
326C22×C8—1221no—
327C22×C8—1221no—
328C22×C8—1222no—
329C22×C8—1222no—
330C22×C8—1221no—
331#117—612no—
332#117—614no—
333#117—1222no—
334#117—1222no—
335#117C2×#692312yes—
336C2×C4⋊C4—1222no—
337C2×C22⋊C4—614no—
338C2×C42—1222no—
339C4⋊C8—1228no—
340C4⋊C8—1228no—
341#99—614no—
342#99—618no—
343#99C2×#692314yes—
344C22⋊C8—1224no—
345C22⋊C8—1224no—
346C24—611no—
347C24—612no—
348#41—22no—
349#41—22no—
350#41—1224no—
351#41—1224no—
352#41—1224no—
353#41—1222no—
354#41—1224no—
355#41—1222no—
356#41—1222no—
357#41—1222no—
358#41—1222no—
359#41—1222no—
360C2×Q8—611no—
361C2×Q8—612no—
362C2×Q8—1222no—
363C2×Q8—1222no—
364C2×Q8C4⋊#692311yescharacteristic
365C2×D4—612no—
366C2×D4—612no—
367C2×D4—612no—
368C2×D4—612no—
369C2×D4—611no—
370C2×D4—1222no—
371C2×D4—1222no—
372C2×D4—1224no—
373C2×D4—1224no—
374C2×D4C4⋊#692311yescharacteristic
375C2×D4C22×#692312yes—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—612no—
382C22×C4—612no—
383C22×C4—612no—
384C22×C4—612no—
385C22×C4—612no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—1224no—
394C22×C4C4⋊#692312yes—
395C22×C4C22×#692311yescharacteristic
396M16—1224no—
397M16—1224no—
398M16—1224no—
399M16—1224no—
400M16—1228no—
401M16—1228no—
402M16—1224no—
403M16—2442no—
404C2×C8—618no—
405C2×C8—1224no—
406C2×C8—1224no—
407C2×C8—1228no—
408C2×C8—1228no—
409C2×C8—1222no—
410C2×C8—1222no—
411C2×C8—1224no—
412C2×C8—2442no—
413C2×C8—2441no—
414C2×C8—2441no—
415C2×C8—2441no—
416C2×C8—2441no—
417C4⋊C4—22no—
418C4⋊C4—1224no—
419C4⋊C4—1222no—
420C22⋊C4—614no—
421C22⋊C4—1224no—
422C22⋊C4C22×#692314yes—
423C42—22no—
424C42—1224no—
425C42—1222no—
426C23—611no—
427C23—612no—
428C23—611no—
429C23—612no—
430C23—612no—
431C23—1222no—
432C23—1222no—
433C23—2442no—
434C23—2444no—
435C23C2×C4⋊#692312yes—
436C23C23×#692311yescharacteristic
437Q8—22no—
438Q8—1224no—
439Q8—1222no—
440D4—24no—
441D4—22no—
442D4—1224no—
443D4—1224no—
444D4—1224no—
445D4—1224no—
446D4—1222no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—612no—
453C2×C4—612no—
454C2×C4—612no—
455C2×C4—611no—
456C2×C4—612no—
457C2×C4—612no—
458C2×C4—612no—
459C2×C4—611no—
460C2×C4—612no—
461C2×C4—611no—
462C2×C4—612no—
463C2×C4—611no—
464C2×C4—612no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1224no—
474C2×C4—2448no—
475C2×C4C2×C4⋊#692312yes—
476C2×C4C2×C4⋊#692311yescharacteristic
477C2×C4C2×C4⋊#692311yescharacteristic
478C2×C4D4×#692312yes—
479C2×C4D4×#692312yes—
480C8—1228no—
481C8—2442no—
482C8—2442no—
483C22—22no—
484C22—41no—
485C22—42no—
486C22—611no—
487C22—611no—
488C22—612no—
489C22—1224no—
490C22—1222no—
491C22—1222no—
492C22—4882no—
493C22—2442no—
494C22—2441no—
495C22—2442no—
496C22—2444no—
497C22C22×C4⋊#692311yescharacteristic
498C22C2×D4×#692312yes—
499C4—22no—
500C4—44no—
501C4—611no—
502C4—612no—
503C4—611no—
504C4—1222no—
505C4—2444no—
506C4#1684070911yescharacteristic
507C4#1684070912yes—
508C4#1684070911yescharacteristic
509C2—22no—
510C2—21no—
511C2—42no—
512C2—612no—
513C2—1221no—
514C2—1222no—
515C2—2442no—
516C2C2×#1684070911yescharacteristic
subgroupG/H
centerC4#16840709
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#410C4
socleC2×C61C2×#385
prime radicalC2×#41×D61C22
cosocleC22×Dic61C24
hypercenter#410#6923
hypocenterC61C2×#1868
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. D61⋊#424C2semidirect
4. #21461791C2semidirect
5. #21461527C2semidirect
17. #16840768C22semidirect
23. #16840643C22semidirect
264. D61#1868semidirect
289. C61C2×#1868semidirect

Maximal subgroups

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

subgroupindex
D61⋊#5682
D61⋊#4242
D61⋊#4082
#214617912
#214615272
#410×D612
C2×#186861