Finite Group Databasebeta

← D61×#1493 #29646611

Subgroups — D61×#1493 #29646611

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#423×D61C211yesmaximal, characteristic
3C2×C4×C8×D61C211yesmaximal, characteristic
4#21444275C211yesmaximal, characteristic, complemented
5#21444274C211yesmaximal, characteristic, complemented
6#21444273C211yesmaximal, characteristic, complemented
7#21444272C214yesmaximal, complemented
8Q8⋊C8×D61C214yesmaximal, complemented
9C61×#1493C211yesmaximal, characteristic, complemented
10C2×M16×D61—21no—
11C22×C8×D61—21no—
12#16840319C2211yescharacteristic
13#16840318—21no—
14#16840317C411yescharacteristic
15#16840317C411yescharacteristic
16#16840316—21no—
17#16840316C2212yes—
18#16840315—21no—
19#16840314—21no—
20#16840314C412yes—
21C4⋊Q8×D61C411yescharacteristic
22C4⋊Q8×D61C411yescharacteristic
23#125×D61—21no—
24C22⋊Q8×D61—21no—
25C22⋊Q8×D61C412yes—
26C4×Q8×D61—21no—
27C4×Q8×D61C2212yes—
28#117×D61—21no—
29C2×C42×D61C2211yescharacteristic
30#16839786C2211yescharacteristic
31#16839785—21no—
32#16839784—21no—
33#16839784C2212yes—
34C4⋊C8×D61—21no—
35C4⋊C8×D61C2212yes—
36C2×C4×#92418C2211yescharacteristic
37C2×C8×Dic61—21no—
38C4×C8×D61—21no—
39C4×C8×D61—21no—
40C4×C8×D61C2212yes—
41C4×C8×D61C2212yes—
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C61×#533C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C2×C4×C8×C61C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×Q8×D61—21no—
50C2×Q8×D61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56M16×D61—44no—
57C22×#92418—21no—
58C2×C8×D61—28no—
59C2×C8×D61—22no—
60C2×C8×D61—22no—
61C2×C8×D61—22no—
62#14519777C2×C411yescharacteristic
63#14519777C2×C411yescharacteristic
64#14519776—21no—
65#14519776—21no—
66#14519776—21no—
67#14519776C2×C412yes—
68#14519775—21no—
69#14519775C2×C412yes—
70#14519769—21no—
71#14519768—21no—
72#14519768—21no—
73#14519767—22no—
74#14519767—22no—
75#14519757—21no—
76#14519757C2×C412yes—
77#14519756—21no—
78#14519756C2×C412yes—
79#14519755—22no—
80#14519755—22no—
81#14519754—22no—
82#14519754—22no—
83#14519753—21no—
84#14519753C2×C412yes—
85Q8×Dic61—21no—
86Q8×Dic61C2×C412yes—
87C4×Dic122—21no—
88C4×Dic122—22no—
89C4×Dic122—22no—
90C4×Dic122C2312yes—
91#14519742—21no—
92#14519742—22no—
93#14519742—22no—
94#14519742C2×C412yes—
95#14519736—21no—
96#14519735—21no—
97#14519735—21no—
98#14519734—22no—
99#14519733—22no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61C2×C412yes—
106C22⋊C4×D61—22no—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C42×D61—22no—
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61C2311yescharacteristic
118C42×D61C2311yescharacteristic
119C4⋊#92418—21no—
120C4⋊#92418C2312yes—
121#14519706—22no—
122#14519706—22no—
123C4×#92418—21no—
124C4×#92418C2312yes—
125C8×Dic61—22no—
126C8×Dic61—22no—
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129C4⋊Q8×C61C2×C411yescharacteristic
130C4⋊Q8×C61C2×C411yescharacteristic
131#125×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61C2×C412yes—
134C4×Q8×C61—21no—
135C4×Q8×C61C2312yes—
136#117×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2312yes—
140C4×C8×C61—21no—
141C4×C8×C61C2312yes—
142C23×D61C22⋊C411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61C22×C412yes—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C22⋊C411yescharacteristic
151Q8×D61—28no—
152Q8×D61—44no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61SD1614yes—
164C2×C4×D61Q1614yes—
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×Dic122—21no—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122C22×C412yes—
175M16×C61—42no—
176C2×C8×C61—24no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61C22×C412yes—
185C22⋊C4×C61—22no—
186C42×C61—22no—
187C42×C61C22×C411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2411yescharacteristic
191C22⋊Dic61—22no—
192#11758198—22no—
193#11758198—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61C22×C412yes—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223#11758194—42no—
224C2×#92418—24no—
225C2×#92418—22no—
226C2×#92418—22no—
227#11758189—44no—
228C8×D61—28no—
229C8×D61—28no—
230C8×D61—44no—
231C23×C61C2×C22⋊C411yescharacteristic
232C22×D61—22no—
233C22×D61—22no—
234C22×D61#10314yes—
235C22×D61C2×C22⋊C411yescharacteristic
236C22×D61C2×C22⋊C411yescharacteristic
237Q8×C61—24no—
238Q8×C61—42no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×SD1612yes—
247C2×C4×C61C2×Q1612yes—
248C2×C4×C61C23×C411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61#10314yes—
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61#10314yes—
271C4×D61#10314yes—
272C4×D61#10414yes—
273C4×D61#13114yes—
274C4×D61C2×SD1612yes—
275C4×D61C2×SD1612yes—
276C4×D61C2×Q1612yes—
277C4×D61C2×Q1612yes—
278Dic122—24no—
279Dic122—42no—
280Dic122—44no—
281Dic122—44no—
282C8×C61—24no—
283C8×C61—42no—
284#92418—24no—
285#92418—42no—
286C2×#1493—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61C2×#10312yes—
290C22×C61C22×C22⋊C411yescharacteristic
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—28no—
294C2×D61#40812yes—
295C2×D61C2×#10312yes—
296C2×D61C2×#10312yes—
297C2×D61C2×#10412yes—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61C2×#10312yes—
303C4×C61C2×#10412yes—
304C4×C61C2×#13112yes—
305C4×C61C22×SD1611yescharacteristic
306C4×C61C22×Q1611yescharacteristic
307Dic61—21no—
308Dic61—21no—
309Dic61—42no—
310Dic61—42no—
311Dic61#40812yes—
312Dic61C2×#10312yes—
313Dic61C2×#10312yes—
314Dic61C2×#10412yes—
315C2×#533—611no—
316C2×#423—611no—
317C22×C4×C8—611no—
318#1493—611no—
319#1493—611no—
320#1493—614no—
321#1493—611no—
322#1493D6111yescharacteristic, direct product factor
323C2×Q8⋊C8—614no—
324C2×C61—22no—
325C2×C61C2×#40811yescharacteristic
326C2×C61C22×#10311yescharacteristic
327C2×C61C22×#10411yescharacteristic
328D61—22no—
329D61#149314yesdirect product factor
330C22×M16—1221no—
331C23×C8—1221no—
332#533—611no—
333#533—611no—
334#533—612no—
335#533—612no—
336#533—611no—
337#533—1221no—
338#533—1221no—
339#533—1221no—
340#533—1221no—
341#533C2×D6111yescharacteristic
342C2×C4⋊Q8—611no—
343C2×C4⋊Q8—611no—
344C2×#125—1221no—
345C2×C22⋊Q8—612no—
346C2×C22⋊Q8—1221no—
347C2×C4×Q8—612no—
348C2×C4×Q8—1221no—
349C2×#117—1221no—
350C22×C42—611no—
351#423—611no—
352#423—612no—
353#423—1221no—
354#423—1221no—
355#423C2×D6111yescharacteristic
356C2×C4⋊C8—612no—
357C2×C4⋊C8—1221no—
358C2×C4×C8—611no—
359C2×C4×C8—612no—
360C2×C4×C8—612no—
361C2×C4×C8—1221no—
362C2×C4×C8—1221no—
363C2×C4×C8—1221no—
364C2×C4×C8C2×D6111yescharacteristic
365Q8⋊C8—614no—
366Q8⋊C8—614no—
367Q8⋊C8—614no—
368Q8⋊C8C2×D6114yescomplemented
369C61C2×#149311yescharacteristic, complemented, Sylow
370C22×Q8—612no—
371C22×Q8—1221no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C2×M16—21no—
376C2×M16—1222no—
377C2×M16—1221no—
378C2×M16—2444no—
379C22×C8—21no—
380C22×C8—1222no—
381C22×C8—1222no—
382C22×C8—1228no—
383C22×C8—1222no—
384C22×C8—1221no—
385C4⋊Q8—612no—
386C4⋊Q8—612no—
387C4⋊Q8—611no—
388C4⋊Q8—611no—
389C4⋊Q8—1221no—
390C4⋊Q8—1221no—
391C4⋊Q8—1221no—
392C4⋊Q8—1221no—
393C4⋊Q8C4×D6111yescharacteristic
394C4⋊Q8C4×D6111yescharacteristic
395#125—21no—
396#125—1222no—
397#125—1222no—
398#125—1221no—
399#125—1221no—
400#125—1221no—
401C22⋊Q8—21no—
402C22⋊Q8—612no—
403C22⋊Q8—612no—
404C22⋊Q8—612no—
405C22⋊Q8—1222no—
406C22⋊Q8—1222no—
407C22⋊Q8—1222no—
408C22⋊Q8—1222no—
409C22⋊Q8—1221no—
410C22⋊Q8—1221no—
411C22⋊Q8—1221no—
412C22⋊Q8C4×D6112yes—
413C4×Q8—21no—
414C4×Q8—612no—
415C4×Q8—612no—
416C4×Q8—612no—
417C4×Q8—1222no—
418C4×Q8—1222no—
419C4×Q8—1222no—
420C4×Q8—1221no—
421C4×Q8—1222no—
422C4×Q8—1221no—
423C4×Q8—1221no—
424C4×Q8C22×D6112yes—
425#117—21no—
426#117—1222no—
427#117—1222no—
428#117—1221no—
429#117—1221no—
430#117—1221no—
431C2×C4⋊C4—612no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4—1222no—
436C2×C4⋊C4—1221no—
437C2×C22⋊C4—1222no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—1222no—
450C2×C42C22×D6111yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—612no—
453C4⋊C8—1222no—
454C4⋊C8—1222no—
455C4⋊C8—1221no—
456C4⋊C8C22×D6112yes—
457C4×C8—21no—
458C4×C8—612no—
459C4×C8—1222no—
460C4×C8—1222no—
461C4×C8—1221no—
462C4×C8C22×D6112yes—
463C24—611no—
464C2×Q8—21no—
465C2×Q8—612no—
466C2×Q8—1222no—
467C2×Q8—1222no—
468C2×Q8—1228no—
469C2×Q8—1221no—
470C2×Q8—2444no—
471C2×Q8C2×C4×D6112yes—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—614no—
480C22×C4—614no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4D4×D6111yescharacteristic
495C22×C4D4×D6111yescharacteristic
496M16—42no—
497M16—2444no—
498M16—2442no—
499C2×C8—24no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—1228no—
503C2×C8—1228no—
504C2×C8—1224no—
505C2×C8—1222no—
506C2×C8—1222no—
507C2×C8—2444no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—612no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4C2×C4×D6112yes—
528C22⋊C4—22no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C42—22no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42C2×C4×D6111yescharacteristic
549C42D4×D6111yescharacteristic
550C42D4×D6111yescharacteristic
551C42C23×D6111yescharacteristic
552C23—611no—
553C23—611no—
554C23—614no—
555C23—1222no—
556C23—1222no—
557C23C22⋊C4×D6111yescharacteristic
558Q8—24no—
559Q8—42no—
560Q8—1224no—
561Q8—2444no—
562Q8—2444no—
563Q8—2442no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—614no—
573C2×C4—614no—
574C2×C4—614no—
575C2×C4—614no—
576C2×C4—612no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—614no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—2444no—
594C2×C4—2444no—
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C2×C4C22⋊C4×D6111yescharacteristic
598C2×C4SD16×D6112yes—
599C2×C4Q16×D6112yes—
600C2×C4C22×C4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C2×D4×D6111yescharacteristic
603C8—24no—
604C8—42no—
605C8—1224no—
606C8—2442no—
607C22—21no—
608C22—21no—
609C22—612no—
610C22—612no—
611C22—612no—
612C22—612no—
613C22—1228no—
614C22—1221no—
615C22—1221no—
616C22#103×D6112yes—
617C22C2×C22⋊C4×D6111yescharacteristic
618C4—21no—
619C4—21no—
620C4—42no—
621C4—42no—
622C4—612no—
623C4—612no—
624C4—612no—
625C4—612no—
626C4—1221no—
627C4—1221no—
628C4—2442no—
629C4—2442no—
630C4#103×D6112yes—
631C4#104×D6112yes—
632C4#131×D6112yes—
633C4C2×SD16×D6111yescharacteristic
634C4C2×Q16×D6111yescharacteristic
635C2—22no—
636C2—614no—
637C2—1222no—
638C2#408×D6111yescharacteristic
639C2C2×#103×D6111yescharacteristic
640C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1493C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1493D61
hypocenterC61C2×#1493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
4. #21444275C2semidirect
5. #21444274C2semidirect
6. #21444273C2semidirect
7. #21444272C2semidirect
8. Q8⋊C8×D61C2semidirect
9. C61×#1493C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
322. #1493D61direct (N × H)
329. D61#1493direct (N × H)
368. Q8⋊C8C2×D61semidirect
369. C61C2×#1493semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#423×D612
C2×C4×C8×D612
#214442752
#214442742
#214442732
#214442722
Q8⋊C8×D612
C61×#14932
C2×#149361