Finite Group Databasebeta

← D61⋊#1463 #30609940

Subgroups — D61⋊#1463 #30609940

Order 15616.

1718 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C212yesmaximal
2#21461069C212yesmaximal, complemented
3#21461068C214yesmaximal, complemented
4#21461067C212yesmaximal, complemented
5D61⋊#324C214yesmaximal, complemented
6C22×C4⋊C4×D61C211yesmaximal, characteristic
7C2×D61⋊M16—22no—
8#16840734—22no—
9#16840733—22no—
10#16840733C2214yes—
11#16840732C2214yes—
12D61⋊(C22⋊C8)—22no—
13D61⋊(C22⋊C8)C2214yes—
14#16840608C2218yescomplemented
15#16840607C2218yescomplemented
16C23×C4×D61C411yescharacteristic
17C23×C4×D61C411yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C411yescharacteristic
21C22×#11758196C2211yescharacteristic
22C2×C4⋊C4×D61—22no—
23C2×C4⋊C4×D61—22no—
24C2×C4⋊C4×D61—22no—
25C2×C4⋊C4×D61—22no—
26C2×C4⋊C4×D61C412yes—
27C2×C4⋊C4×D61C412yes—
28C2×C4⋊C4×D61C2212yes—
29C2×C4⋊C4×D61C2212yes—
30C22×C4⋊C4×C61C411yescharacteristic
31C2×#11758213—24no—
32D61⋊M16—48no—
33C2×#11758217—24no—
34C2×D61⋊C8—24no—
35#14519834—24no—
36#14519834—24no—
37C22⋊#92420—24no—
38C22⋊#92420C2318yes—
39C24×D61C2×C411yescharacteristic
40C23×Dic61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2311yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61—28no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C22×C4×D61—44no—
53C22×C4×D61—44no—
54C22×C4×D61C2×C412yes—
55C22×C4×D61C2×C412yes—
56C22×C4×D61C2×C412yes—
57C22×C4×D61C2×C412yes—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61D412yes—
61C22×C4×D61D412yes—
62C22×C4×D61D412yes—
63C22×C4×D61D412yes—
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61C2×C412yes—
69C2×C4⋊Dic61C2312yes—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196C2×C412yes—
75C2×#11758196C2×C412yes—
76C2×#11758196C2×C412yes—
77C2×#11758196C2312yes—
78C4⋊C4×D61—24no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—24no—
81C4⋊C4×D61—24no—
82C4⋊C4×D61—24no—
83C4⋊C4×D61—24no—
84C4⋊C4×D61—24no—
85C4⋊C4×D61—24no—
86C23×C4×C61C2×C411yescharacteristic
87C23×C4×C61C2×C411yescharacteristic
88C23×C4×C61C2×C411yescharacteristic
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61C2×C412yes—
92C2×C4⋊C4×C61C2×C412yes—
93C24×C61C22×C411yescharacteristic
94C23×D61—24no—
95C23×D61—24no—
96C23×D61—24no—
97C23×D61C22⋊C411yescharacteristic
98C23×D61C22⋊C411yescharacteristic
99C23×D61C22⋊C411yescharacteristic
100C23×D61C22⋊C411yescharacteristic
101C23×D61C22×C411yescharacteristic
102C23×D61C22×C411yescharacteristic
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—24no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61C22⋊C412yes—
111C22×C4×C61C22⋊C412yes—
112C22×C4×C61C22×C412yes—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C22×C411yescharacteristic
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—24no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—42no—
122C22×Dic61—42no—
123C22×Dic61C22×C412yes—
124C22×Dic61C22×C412yes—
125C22×Dic61C22×C411yescharacteristic
126C22×Dic61C2×D412yes—
127C22×Dic61C2×D412yes—
128C22×Dic61C2411yescharacteristic
129C2×C4×D61—28no—
130C2×C4×D61—28no—
131C2×C4×D61—28no—
132C2×C4×D61—28no—
133C2×C4×D61—28no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—24no—
139C2×C4×D61—24no—
140C2×C4×D61—24no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—42no—
146C2×C4×D61—42no—
147C2×C4×D61—44no—
148C2×C4×D61—44no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—44no—
152C2×C4×D61—44no—
153C2×C4×D61—44no—
154C2×C4×D61—44no—
155C2×C4×D61—44no—
156C2×C4×D61—44no—
157C2×C4×D61—44no—
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C22⋊C412yes—
160C2×C4×D61C22⋊C412yes—
161C2×C4×D61C22⋊C412yes—
162C2×C4×D61M1618yescomplemented
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×D412yes—
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D412yes—
167#11758217—48no—
168C2×#92420—28no—
169#11758213—48no—
170D61⋊C8—48no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—24no—
173C4⋊Dic61—24no—
174C4⋊Dic61—24no—
175#11758196—24no—
176#11758196—24no—
177#11758196—24no—
178#11758196—24no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61C23×C411yescharacteristic
185C22×D61—232no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—22no—
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61#9914yes—
202C22×D61#10114yes—
203C22×D61C2×C22⋊C411yescharacteristic
204C22×D61C2×C22⋊C411yescharacteristic
205C22×D61C2×C22⋊C411yescharacteristic
206C22×D61C2×C22⋊C411yescharacteristic
207C22×D61C2×M1614yes—
208C2×C4×C61—24no—
209C2×C4×C61—24no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—24no—
213C2×C4×C61—22no—
214C2×C4×C61—42no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61C2×C22⋊C412yes—
221C2×C4×C61C2×C22⋊C412yes—
222C2×C4×C61C2×M1614yescomplemented
223C2×Dic61—24no—
224C2×Dic61—24no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—24no—
228C2×Dic61—22no—
229C2×Dic61—41no—
230C2×Dic61—42no—
231C2×Dic61—41no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61C2×C22⋊C412yes—
236C2×Dic61C2×M1614yescomplemented
237C2×Dic61C22×D412yes—
238C4×D61—28no—
239C4×D61—28no—
240C4×D61—28no—
241C4×D61—28no—
242C4×D61—24no—
243C4×D61—24no—
244C4×D61—24no—
245C4×D61—24no—
246C4×D61—42no—
247C4×D61—42no—
248C4×D61—42no—
249C4×D61—42no—
250C4×D61—44no—
251C4×D61—44no—
252C4×D61—44no—
253C4×D61—44no—
254#92420—48no—
255C2×#1463—611nomaximal, Sylow
256C22×C61—28no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61C2×#9912yes—
264C22×C61C2×#10112yes—
265C22×C61C22×C22⋊C411yescharacteristic
266C22×C61C22×M1612yes—
267C2×D61—28no—
268C2×D61—28no—
269C2×D61—28no—
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—28no—
277C2×D61—28no—
278C2×D61—28no—
279C2×D61#40712yes—
280C2×D61#40712yes—
281C2×D61C2×#9912yes—
282C2×D61C2×#9912yes—
283C2×D61C2×#10112yes—
284C2×D61C2×#10112yes—
285C4×C61—24no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—42no—
289Dic61—24no—
290Dic61—22no—
291Dic61—22no—
292Dic61—42no—
293C23×C4⋊C4—611no—
294C2×#407—612no—
295#1463—612no—
296#1463—614no—
297#1463—612no—
298C2×#324—614no—
299C2×C61—22no—
300C2×C61—22no—
301C2×C61—22no—
302C2×C61C2×#40711yescharacteristic
303C2×C61C22×#9911yescharacteristic
304C2×C61C22×#10111yescharacteristic
305D61—22no—
306D61—22no—
307D61—22no—
308D61#146314yescomplemented
309C24×C4—611no—
310C24×C4—611no—
311C24×C4—611no—
312C22×M16—1222no—
313C22×C4⋊C4—611no—
314C22×C4⋊C4—611no—
315C22×C4⋊C4—611no—
316C22×C4⋊C4—612no—
317C22×C4⋊C4—612no—
318C22×C4⋊C4—612no—
319C22×C4⋊C4—612no—
320C22×C4⋊C4—1222no—
321C22×C4⋊C4—1222no—
322C22×C4⋊C4—1222no—
323C22×C4⋊C4—1222no—
324C22×C4⋊C4#692311yescharacteristic
325#407—614no—
326#407—614no—
327#407—1222no—
328#407—1222no—
329C2×C22⋊C8—614no—
330C2×C22⋊C8—1222no—
331#324—618no—
332#324—618no—
333C61C2×#146311yescharacteristic, complemented, Sylow
334C25—611no—
335C23×C4—611no—
336C23×C4—612no—
337C23×C4—612no—
338C23×C4—612no—
339C23×C4—612no—
340C23×C4—612no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—612no—
348C23×C4—612no—
349C23×C4—612no—
350C23×C4—1228no—
351C23×C4—1221no—
352C23×C4—1221no—
353C23×C4—1221no—
354C23×C4—1221no—
355C23×C4—1221no—
356C23×C4—1221no—
357C23×C4—1221no—
358C23×C4—1221no—
359C23×C4—2444no—
360C23×C4—2444no—
361C23×C4C2×#692311yescharacteristic
362C23×C4C2×#692311yescharacteristic
363C23×C4C2×#692311yescharacteristic
364C2×M16—1224no—
365C2×M16—1224no—
366C2×M16—2448no—
367C22×C8—1224no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—612no—
371C2×C4⋊C4—612no—
372C2×C4⋊C4—612no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—612no—
375C2×C4⋊C4—612no—
376C2×C4⋊C4—1224no—
377C2×C4⋊C4—1224no—
378C2×C4⋊C4—1224no—
379C2×C4⋊C4—1224no—
380C2×C4⋊C4—1224no—
381C2×C4⋊C4—1224no—
382C2×C4⋊C4—1224no—
383C2×C4⋊C4—1224no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4C2×#692312yes—
391C2×C4⋊C4C2×#692312yes—
392C22⋊C8—618no—
393C22⋊C8—1224no—
394C22⋊C8—1224no—
395C22⋊C8—1224no—
396C24—611no—
397C24—611no—
398C24—611no—
399C24—611no—
400C24—611no—
401C24—611no—
402C24—1224no—
403C24—1224no—
404C24—1224no—
405C24C22×#692311yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—612no—
414C22×C4—612no—
415C22×C4—612no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—612no—
419C22×C4—612no—
420C22×C4—612no—
421C22×C4—612no—
422C22×C4—618no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—1224no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1228no—
434C22×C4—1224no—
435C22×C4—1228no—
436C22×C4—1228no—
437C22×C4—1228no—
438C22×C4—1228no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1224no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1224no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—2444no—
450C22×C4—2444no—
451C22×C4—2444no—
452C22×C4—2442no—
453C22×C4—2442no—
454C22×C4—2442no—
455C22×C4—2442no—
456C22×C4—2444no—
457C22×C4—2444no—
458C22×C4—2444no—
459C22×C4—2444no—
460C22×C4—2444no—
461C22×C4—2444no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4C22⋊#692312yes—
465C22×C4C22⋊#692312yes—
466C22×C4C22×#692312yes—
467C22×C4C22×#692312yes—
468C22×C4C22×#692311yescharacteristic
469C22×C4C22×#692311yescharacteristic
470M16—2448no—
471M16—2448no—
472C2×C8—1228no—
473C2×C8—2448no—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—1224no—
477C4⋊C4—1224no—
478C4⋊C4—1224no—
479C4⋊C4—1224no—
480C4⋊C4—1224no—
481C4⋊C4—1224no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—611no—
486C23—614no—
487C23—614no—
488C23—611no—
489C23—611no—
490C23—611no—
491C23—614no—
492C23—1222no—
493C23—1222no—
494C23—1222no—
495C23—1222no—
496C23—1222no—
497C23—1222no—
498C23—1222no—
499C23—1222no—
500C23—1222no—
501C23—1222no—
502C23—1222no—
503C23—1222no—
504C23—12232no—
505C23—1222no—
506C23—1222no—
507C23—1222no—
508C23C2×C22⋊#692311yescharacteristic
509C23C2×C22⋊#692311yescharacteristic
510C23C23×#692311yescharacteristic
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—614no—
526C2×C4—1224no—
527C2×C4—1224no—
528C2×C4—1228no—
529C2×C4—1228no—
530C2×C4—1224no—
531C2×C4—1224no—
532C2×C4—1228no—
533C2×C4—1228no—
534C2×C4—1224no—
535C2×C4—1224no—
536C2×C4—1224no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2444no—
545C2×C4—2444no—
546C2×C4—2444no—
547C2×C4—2444no—
548C2×C4—2441no—
549C2×C4—2442no—
550C2×C4—2441no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4C2×C22⋊#692312yes—
555C2×C4C2×C22⋊#692312yes—
556C2×C4D61⋊M1614yescomplemented
557C8—2448no—
558C22—28no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—612no—
566C22—612no—
567C22—612no—
568C22—612no—
569C22—612no—
570C22—612no—
571C22—1228no—
572C22—1228no—
573C22—1228no—
574C22—1228no—
575C22—1228no—
576C22—1228no—
577C22—1221no—
578C22—1221no—
579C22—1221no—
580C22—1221no—
581C22—1221no—
582C22—1221no—
583C22D61⋊#9912yes—
584C22D61⋊#10112yes—
585C22C22×C22⋊#692311yescharacteristic
586C22C2×D61⋊M1612yes—
587C4—24no—
588C4—22no—
589C4—22no—
590C4—42no—
591C4—1224no—
592C4—1222no—
593C4—1222no—
594C4—2442no—
595C2—22no—
596C2—22no—
597C2—22no—
598C2—614no—
599C2—1222no—
600C2—1222no—
601C2—1222no—
602C2D61⋊#40711yescharacteristic
603C2C2×D61⋊#9911yescharacteristic
604C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1463
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21461069C2semidirect
3. #21461068C2semidirect
4. #21461067C2semidirect
5. D61⋊#324C2semidirect
14. #16840608C22semidirect
15. #16840607C22semidirect
162. C2×C4×D61M16semidirect
222. C2×C4×C61C2×M16semidirect
236. C2×Dic61C2×M16semidirect
308. D61#1463semidirect
333. C61C2×#1463semidirect
556. C2×C4D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214610692
#214610682
#214610672
D61⋊#3242
C22×C4⋊C4×D612
C2×#146361