Finite Group Databasebeta

← D61×#1464 #29645855

Subgroups — D61×#1464 #29645855

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2#432×D61C212yesmaximal, complemented
3#21444153C211yesmaximal, characteristic, complemented
4#21444152C212yesmaximal, complemented
5#21444151C212yesmaximal, complemented
6#21444150C212yesmaximal, complemented
7#324×D61C212yesmaximal, complemented
8#323×D61C212yesmaximal
9C61×#1464C211yesmaximal, characteristic, complemented
10C23×C4×D61C411yescharacteristic
11C2×#14519736C411yescharacteristic
12C2×#14519735C411yescharacteristic
13C2×#14519735C2211yescharacteristic
14C2×#14519734C411yescharacteristic
15C2×#14519734C2211yescharacteristic
16C2×#14519733C411yescharacteristic
17C2×#14519733C2211yescharacteristic
18#117×D61—22no—
19#117×D61—22no—
20#117×D61—22no—
21#117×D61—22no—
22C2×C4⋊C4×D61C411yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24C2×C22⋊C4×D61C411yescharacteristic
25C2×C22⋊C4×D61C2211yescharacteristic
26C2×C42×D61C411yescharacteristic
27C2×C42×D61C2211yescharacteristic
28#16839819C2212yescomplemented
29#16839818—22no—
30#16839817—22no—
31#16839816C2214yescomplemented
32C4⋊C8×D61—22no—
33C22⋊C8×D61C2214yes—
34#97×D61—22no—
35#16839488C2212yescomplemented
36#16839487C2214yescomplemented
37#16839486C2212yes—
38#16839485C2214yes—
39C2×#117×C61C2211yescharacteristic
40C61×#432C2212yescomplemented
41C61×#324C2212yescomplemented
42C61×#323C2212yes—
43C24×D61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C22×C4×D61—24no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—24no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×C8×D61—24no—
60#14519736—22no—
61#14519736—22no—
62#14519735—22no—
63#14519735—22no—
64#14519735—22no—
65#14519735—22no—
66#14519734—22no—
67#14519734—22no—
68#14519734—22no—
69#14519734—22no—
70#14519733—22no—
71#14519733—22no—
72#14519733—22no—
73#14519733—22no—
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2311yescharacteristic
80C4⋊C4×D61—22no—
81C4⋊C4×D61—22no—
82C4⋊C4×D61—22no—
83C4⋊C4×D61—22no—
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2311yescharacteristic
90C22⋊C4×D61—22no—
91C22⋊C4×D61—22no—
92C22⋊C4×D61—22no—
93C22⋊C4×D61—22no—
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C42×D61—21no—
101C42×D61—21no—
102C42×D61—21no—
103C42×D61—21no—
104C42×D61D412yes—
105C42×D61D412yes—
106C42×D61D412yes—
107C42×D61D412yes—
108C4⋊#92418—22no—
109#14519706—24no—
110C22⋊#92418C2314yes—
111#14519689—24no—
112#14519688—22no—
113#14519687—24no—
114C23×C4×C61C2×C411yescharacteristic
115#117×C61—22no—
116#117×C61—22no—
117C2×C4⋊C4×C61C2×C411yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2311yescharacteristic
121C2×C42×C61C2×C411yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C4⋊C8×C61—22no—
124C22⋊C8×C61C2314yes—
125#97×C61—22no—
126C24×C61C22×C411yescharacteristic
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—22no—
130C23×D61—42no—
131C23×D61—42no—
132C23×D61M1614yes—
133C23×D61C22×C411yescharacteristic
134C23×D61C22×C411yescharacteristic
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C22×Dic61—22no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—22no—
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C2×C4×D61—28no—
156C2×C4×D61—28no—
157C2×C4×D61—28no—
158C2×C4×D61—28no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—22no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—22no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61C22⋊C411yescharacteristic
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C411yescharacteristic
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C412yes—
185C2×C4×D61C22⋊C412yes—
186C2×C4×D61M1614yes—
187C2×C4×D61C2×D412yes—
188C2×C4×D61C2×D412yes—
189C2×C8×C61—24no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C42×C61—21no—
195C42×C61—21no—
196C42×C61C2×D412yes—
197C42×C61C2×D412yes—
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61C22⋊C412yes—
217C4×Dic61C22⋊C412yes—
218C4×Dic61C22⋊C412yes—
219C4×Dic61C22⋊C412yes—
220C4×Dic61C2×D412yes—
221C4×Dic61C2×D412yes—
222C2×#92418—24no—
223C8×D61—48no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61C2×M1612yes—
229C23×C61C23×C411yescharacteristic
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—24no—
235C22×D61—24no—
236C22×D61—42no—
237C22×D61—42no—
238C22×D61—48no—
239C22×D61—48no—
240C22×D61—42no—
241C22×D61—42no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61C2×C22⋊C411yescharacteristic
245C22×D61C2×C22⋊C411yescharacteristic
246C22×D61C2×M1612yes—
247C22×D61C2×M1612yes—
248C22×D61C2×M1612yes—
249C2×C4×C61—24no—
250C2×C4×C61—24no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C412yes—
264C2×C4×C61C2×M1612yes—
265C2×C4×C61C22×D412yes—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C412yes—
281C2×Dic61C2×C22⋊C412yes—
282C2×Dic61C2×M1612yes—
283C4×D61—24no—
284C4×D61—24no—
285C4×D61—24no—
286C4×D61—24no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—24no—
292C4×D61—24no—
293C4×D61—24no—
294C4×D61—24no—
295C4×D61—42no—
296C4×D61—42no—
297C4×D61—42no—
298C4×D61—42no—
299C4×D61—42no—
300C4×D61—42no—
301C8×C61—44no—
302#92418—44no—
303C2×#1464—611nomaximal, Sylow
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—22no—
307C22×C61—42no—
308C22×C61—42no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C22×C22⋊C411yescharacteristic
312C22×C61C22×M1611yescharacteristic
313C22×C61C22×M1611yescharacteristic
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—24no—
317C2×D61—24no—
318C2×D61—22no—
319C2×D61—48no—
320C2×D61—42no—
321C2×D61—41no—
322C2×D61—41no—
323C2×D61—48no—
324C2×D61—42no—
325C2×D61#40712yes—
326C2×D61#40712yes—
327C2×D61#41012yes—
328C2×D61#41312yes—
329C4×C61—21no—
330C4×C61—21no—
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—41no—
335C4×C61—41no—
336Dic61—21no—
337Dic61—21no—
338Dic61—22no—
339Dic61—22no—
340Dic61—22no—
341Dic61—41no—
342Dic61—41no—
343C22×#117—611no—
344C2×#432—612no—
345#1464—612no—
346#1464—612no—
347#1464—612no—
348#1464—611no—
349#1464D6111yescharacteristic, direct product factor
350C2×#324—612no—
351C2×#323—612no—
352C2×C61—21no—
353C2×C61—21no—
354C2×C61—42no—
355C2×C61C2×#40711yescharacteristic
356C2×C61C2×#41011yescharacteristic
357C2×C61C2×#41311yescharacteristic
358D61—22no—
359D61—42no—
360D61#146414yesdirect product factor
361C24×C4—611no—
362C2×#117—611no—
363C2×#117—611no—
364C2×#117—611no—
365C2×#117—611no—
366C2×#117—611no—
367C2×#117—611no—
368C2×#117—611no—
369C2×#117—1222no—
370C2×#117—1222no—
371C2×#117—1222no—
372C2×#117—1222no—
373C2×#117C2×D6111yescharacteristic
374C22×C4⋊C4—611no—
375C22×C4⋊C4—611no—
376C22×C22⋊C4—611no—
377C22×C22⋊C4—611no—
378C22×C42—611no—
379C22×C42—611no—
380#432—612no—
381#432—614no—
382#432—1222no—
383#432—1222no—
384#432C2×D6112yescomplemented
385C2×C4⋊C8—1222no—
386C2×C22⋊C8—614no—
387C2×#97—1222no—
388#324—612no—
389#324—614no—
390#324C2×D6112yescomplemented
391#323—612no—
392#323—614no—
393#323C2×D6112yes—
394C61C2×#146411yescharacteristic, complemented, Sylow
395C25—611no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—611no—
405C23×C4—1221no—
406C23×C4—1221no—
407C23×C4—1221no—
408C23×C4—1221no—
409C23×C4—1224no—
410C23×C4—1224no—
411C23×C4C4×D6111yescharacteristic
412C22×C8—1224no—
413#117—22no—
414#117—22no—
415#117—1222no—
416#117—1222no—
417#117—1222no—
418#117—1222no—
419#117—1222no—
420#117—1222no—
421#117—1222no—
422#117—1222no—
423#117—1222no—
424#117—1222no—
425#117—1222no—
426#117—1222no—
427#117—1222no—
428#117—1222no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—1222no—
436C2×C4⋊C4—1222no—
437C2×C4⋊C4—1222no—
438C2×C4⋊C4—1222no—
439C2×C4⋊C4C4×D6111yescharacteristic
440C2×C4⋊C4C22×D6111yescharacteristic
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—1222no—
448C2×C22⋊C4—1222no—
449C2×C22⋊C4—1222no—
450C2×C22⋊C4—1222no—
451C2×C22⋊C4C4×D6111yescharacteristic
452C2×C22⋊C4C22×D6111yescharacteristic
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—612no—
457C2×C42—612no—
458C2×C42—612no—
459C2×C42—612no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—1221no—
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42—1221no—
467C2×C42C4×D6111yescharacteristic
468C2×C42C22×D6111yescharacteristic
469C4⋊C8—22no—
470C4⋊C8—1224no—
471C4⋊C8—1222no—
472C22⋊C8—614no—
473C22⋊C8—1224no—
474C22⋊C8C22×D6114yes—
475#97—22no—
476#97—1224no—
477#97—1222no—
478C24—611no—
479C24—611no—
480C24—614no—
481C24—1221no—
482C24—1221no—
483C24—1222no—
484C24—2442no—
485C24—2442no—
486C24C2×C4×D6111yescharacteristic
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—612no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—612no—
501C22×C4—614no—
502C22×C4—612no—
503C22×C4—612no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1222no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1228no—
517C22×C4—1228no—
518C22×C4—1228no—
519C22×C4—1228no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1222no—
531C22×C4—2442no—
532C22×C4—2442no—
533C22×C4—2442no—
534C22×C4—2442no—
535C22×C4C2×C4×D6111yescharacteristic
536C22×C4C2×C4×D6111yescharacteristic
537C22×C4C2×C4×D6111yescharacteristic
538C22×C4C2×C4×D6111yescharacteristic
539C22×C4C2×C4×D6111yescharacteristic
540C22×C4C23×D6111yescharacteristic
541C2×C8—24no—
542C2×C8—1224no—
543C2×C8—2448no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—1222no—
547C4⋊C4—1222no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—1222no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C42—21no—
561C42—21no—
562C42—612no—
563C42—612no—
564C42—612no—
565C42—612no—
566C42—612no—
567C42—612no—
568C42—1221no—
569C42—1221no—
570C42—1221no—
571C42—1221no—
572C42—1221no—
573C42—1221no—
574C42D4×D6112yes—
575C42D4×D6112yes—
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—611no—
581C23—611no—
582C23—612no—
583C23—612no—
584C23—612no—
585C23—1222no—
586C23—1222no—
587C23—1224no—
588C23—1224no—
589C23—1221no—
590C23—1221no—
591C23—2441no—
592C23—2441no—
593C23—2442no—
594C23—2442no—
595C23—2448no—
596C23—2448no—
597C23—2442no—
598C23—2442no—
599C23M16×D6112yes—
600C23C22×C4×D6111yescharacteristic
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—1224no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1224no—
624C2×C4—1224no—
625C2×C4—1224no—
626C2×C4—1224no—
627C2×C4—1224no—
628C2×C4—1224no—
629C2×C4—1224no—
630C2×C4—1224no—
631C2×C4—1224no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—2442no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4—2442no—
642C2×C4—2442no—
643C2×C4—2442no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4C22⋊C4×D6111yescharacteristic
649C2×C4C22⋊C4×D6111yescharacteristic
650C2×C4C22⋊C4×D6112yes—
651C2×C4M16×D6112yes—
652C2×C4C2×D4×D6112yes—
653C8—44no—
654C8—2444no—
655C22—21no—
656C22—21no—
657C22—22no—
658C22—42no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—612no—
663C22—612no—
664C22—612no—
665C22—612no—
666C22—1224no—
667C22—1224no—
668C22—1221no—
669C22—1221no—
670C22—1222no—
671C22—2442no—
672C22—2442no—
673C22—2448no—
674C22—2448no—
675C22—2441no—
676C22—2441no—
677C22C2×C22⋊C4×D6111yescharacteristic
678C22C2×M16×D6111yescharacteristic
679C22C2×M16×D6111yescharacteristic
680C4—21no—
681C4—21no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—41no—
687C4—1221no—
688C4—1221no—
689C4—1222no—
690C4—1222no—
691C4—1222no—
692C4—2441no—
693C4—2441no—
694C2—21no—
695C2—21no—
696C2—42no—
697C2—614no—
698C2—1222no—
699C2—2442no—
700C2#407×D6111yescharacteristic
701C2#410×D6111yescharacteristic
702C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1464C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1464D61
hypocenterC61C2×#1464
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #432×D61C2semidirect
3. #21444153C2semidirect
4. #21444152C2semidirect
5. #21444151C2semidirect
6. #21444150C2semidirect
7. #324×D61C2semidirect
9. C61×#1464C2semidirect
28. #16839819C22semidirect
31. #16839816C22semidirect
35. #16839488C22semidirect
36. #16839487C22semidirect
40. C61×#432C22semidirect
41. C61×#324C22semidirect
349. #1464D61direct (N × H)
360. D61#1464direct (N × H)
384. #432C2×D61semidirect
390. #324C2×D61semidirect
394. C61C2×#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
#432×D612
#214441532
#214441522
#214441512
#214441502
#324×D612
#323×D612
C61×#14642
C2×#146461