Finite Group Databasebeta

← D61⋊#1469 #30610047

Subgroups — D61⋊#1469 #30610047

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2D61⋊#431C211yesmaximal, characteristic, complemented
3#21461090C212yesmaximal, complemented
4#21461089C212yesmaximal, complemented
5#21461088C214yesmaximal, complemented
6D61⋊#323C214yesmaximal, complemented
7C2×#124×D61C211yesmaximal, characteristic
8#16840785—21no—
9#16840784—21no—
10#16840783C2212yescomplemented
11#16840782C2212yescomplemented
12#16840781—21no—
13#16840780—21no—
14#16840779C2212yescomplemented
15#16840778C2212yescomplemented
16D61⋊(C4⋊C8)—21no—
17D61⋊(C4⋊C8)—21no—
18D61⋊(C22⋊C8)C2212yes—
19D61⋊(C22⋊C8)C2212yes—
20#16840721—21no—
21C4×D61⋊C8—21no—
22#16840606C2218yescomplemented
23#16840605C2218yescomplemented
24C22×Q8×D61C411yescharacteristic
25C22×D4×D61C411yescharacteristic
26C2×#14519766C2211yescharacteristic
27C2×#14519765C411yescharacteristic
28C2×#14519764C2211yescharacteristic
29C2×#14519763C412yes—
30C2×#14519763C2212yes—
31#124×D61—21no—
32#124×D61—21no—
33#124×D61—21no—
34#124×D61—21no—
35#124×D61—21no—
36#124×D61—21no—
37#124×D61—21no—
38#124×D61—21no—
39C2×C22⋊C4×D61C412yes—
40C2×C22⋊C4×D61C2212yes—
41C2×C42×D61C2211yescharacteristic
42C2×#124×C61C411yescharacteristic
43C2×D61⋊C8—22no—
44C2×D61⋊C8—22no—
45#14519844—22no—
46#14519844—22no—
47C4⋊#92420—22no—
48C4⋊#92420—22no—
49#14519834—22no—
50#14519834—22no—
51C22⋊#92420C2314yes—
52C22⋊#92420C2314yes—
53#14519832—22no—
54#14519832—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57C24×D61C2×C412yes—
58C22×Dic122C2×C412yes—
59C22×Dic122C2×C411yescharacteristic
60C2×Q8×D61—21no—
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C2×Q8×D61—21no—
64C2×Q8×D61—44no—
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61C2×C412yes—
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61—44no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C412yes—
75C22×C4×D61C2311yescharacteristic
76#14519766—21no—
77#14519766—21no—
78#14519766—21no—
79#14519766—21no—
80#14519765—21no—
81#14519765—21no—
82#14519765—21no—
83#14519765—21no—
84#14519764—21no—
85#14519764—21no—
86#14519764—21no—
87#14519764—21no—
88#14519763—22no—
89#14519763—22no—
90#14519763—22no—
91#14519763—22no—
92#14519763—22no—
93#14519763—22no—
94#14519763—22no—
95#14519763—22no—
96C2×C22⋊Dic61C2×C412yes—
97C2×C22⋊Dic61C2312yes—
98C2×#11758198C2×C412yes—
99C2×#11758198C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×#11758198C2312yes—
102C22⋊C4×D61—22no—
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C22⋊C4×D61—22no—
107C22⋊C4×D61—22no—
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C22×Q8×C61C2×C411yescharacteristic
122C22×D4×C61C2×C411yescharacteristic
123#124×C61—21no—
124#124×C61—21no—
125#124×C61—21no—
126#124×C61—21no—
127C2×C22⋊C4×C61C2×C412yes—
128C2×C22⋊C4×C61C2×C412yes—
129C2×C42×C61C2×C411yescharacteristic
130C24×C61C22×C412yes—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—28no—
134C23×D61—44no—
135C23×D61—44no—
136C23×D61C22×C411yescharacteristic
137C23×D61C22×C412yes—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—42no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—42no—
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C412yes—
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—44no—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C412yes—
154C22×Dic61C2411yescharacteristic
155Q8×D61—44no—
156Q8×D61—44no—
157Q8×D61—44no—
158Q8×D61—44no—
159D4×D61—44no—
160D4×D61—44no—
161D4×D61—44no—
162D4×D61—44no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—42no—
166C2×C4×D61—24no—
167C2×C4×D61—24no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—42no—
171C2×C4×D61—44no—
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22⋊C411yescharacteristic
177C2×C4×D61C22⋊C411yescharacteristic
178C2×C4×D61C22⋊C411yescharacteristic
179C2×C4×D61C22⋊C411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2×D411yescharacteristic
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—22no—
187C2×Dic122—22no—
188C2×Dic122—44no—
189C2×Dic122—42no—
190C2×#92420—24no—
191C2×#92420—24no—
192D61⋊C8—44no—
193D61⋊C8—44no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C42×C61C22⋊C411yescharacteristic
199C42×C61C22⋊C411yescharacteristic
200C42×C61C22⋊C411yescharacteristic
201C42×C61C22⋊C411yescharacteristic
202C22⋊Dic61—22no—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C23×C61—22no—
227C23×C61—24no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61C23×C411yescharacteristic
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—24no—
235C22×D61—44no—
236C22×D61—44no—
237C22×D61—44no—
238C22×D61—44no—
239C22×D61—44no—
240C22×D61—44no—
241C22×D61—42no—
242C22×D61—42no—
243C22×D61—816no—
244C22×D61C2×C22⋊C411yescharacteristic
245C22×D61C2×C22⋊C411yescharacteristic
246C22×D61#13114yes—
247Q8×C61—42no—
248Q8×C61—42no—
249D4×C61—42no—
250D4×C61—42no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—41no—
255C2×C4×C61—42no—
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C22⋊D61—44no—
263C22⋊D61—44no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—41no—
268C2×Dic61—42no—
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C22×D411yescharacteristic
274C2×Dic61C22×D411yescharacteristic
275D244—42no—
276D244—42no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—44no—
289C4×D61—44no—
290C4×D61#10014yes—
291Dic122—44no—
292Dic122—42no—
293Dic122—42no—
294Dic122—44no—
295#92420—44no—
296#92420—44no—
297C2×#1469—611nomaximal, Sylow
298C22×C61—21no—
299C22×C61—21no—
300C22×C61—42no—
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—84no—
304C22×C61C22×C22⋊C411yescharacteristic
305C22×C61C2×#13112yes—
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—28no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—88no—
313C2×D61—88no—
314C2×D61—84no—
315C2×D61#40812yes—
316C2×D61#40812yes—
317C2×D61#41012yes—
318C2×D61C2×#10012yes—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—21no—
324C4×C61—42no—
325C4×C61C2×#10012yes—
326Dic61—21no—
327Dic61—21no—
328Dic61—21no—
329Dic61—21no—
330Dic61—21no—
331Dic61—42no—
332Dic61C2×#10012yes—
333C22×#124—611no—
334C2×#432—611no—
335C2×#431—611no—
336#1469—614no—
337#1469—612no—
338#1469—612no—
339C2×#323—614no—
340C2×C61—22no—
341C2×C61—82no—
342C2×C61C2×#40811yescharacteristic
343C2×C61C2×#41011yescharacteristic
344C2×C61C22×#10011yescharacteristic
345D61—22no—
346D61—82no—
347D61#146914yescomplemented
348C23×Q8—611no—
349C23×D4—611no—
350C2×#124—611no—
351C2×#124—611no—
352C2×#124—612no—
353C2×#124—612no—
354C2×#124—611no—
355C2×#124—1221no—
356C2×#124—1221no—
357C2×#124—1221no—
358C2×#124—1221no—
359C2×#124—1221no—
360C2×#124—1221no—
361C2×#124—1221no—
362C2×#124—1221no—
363C2×#124#692311yescharacteristic
364C22×C22⋊C4—612no—
365C22×C22⋊C4—612no—
366C22×C42—611no—
367#432—612no—
368#432—612no—
369#432—1221no—
370#432—1221no—
371#431—612no—
372#431—612no—
373#431—1221no—
374#431—1221no—
375C2×C4⋊C8—1221no—
376C2×C4⋊C8—1221no—
377C2×C22⋊C8—612no—
378C2×C22⋊C8—612no—
379C2×#97—1221no—
380C2×C4×C8—1221no—
381#323—618no—
382#323—618no—
383C61C2×#146911yescharacteristic, complemented, Sylow
384C25—612no—
385C22×Q8—612no—
386C22×Q8—611no—
387C22×Q8—1221no—
388C22×Q8—1221no—
389C22×Q8—1221no—
390C22×Q8—1221no—
391C22×Q8—2444no—
392C22×Q8C2×#692311yescharacteristic
393C22×D4—612no—
394C22×D4—611no—
395C22×D4—1221no—
396C22×D4—1221no—
397C22×D4—1221no—
398C22×D4—1221no—
399C22×D4—2444no—
400C22×D4C2×#692311yescharacteristic
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—612no—
405C22×C8—1222no—
406C22×C8—1222no—
407#124—21no—
408#124—21no—
409#124—21no—
410#124—21no—
411#124—1222no—
412#124—1222no—
413#124—1222no—
414#124—1222no—
415#124—1222no—
416#124—1222no—
417#124—1222no—
418#124—1222no—
419#124—1221no—
420#124—1221no—
421#124—1221no—
422#124—1221no—
423#124—1221no—
424#124—1221no—
425#124—1221no—
426#124—1221no—
427#124—1221no—
428#124—1221no—
429#124—1221no—
430#124—1221no—
431C2×C22⋊C4—612no—
432C2×C22⋊C4—612no—
433C2×C22⋊C4—612no—
434C2×C22⋊C4—612no—
435C2×C22⋊C4—612no—
436C2×C22⋊C4—612no—
437C2×C22⋊C4—1222no—
438C2×C22⋊C4—1222no—
439C2×C22⋊C4—1222no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C22⋊C4—1222no—
443C2×C22⋊C4—1222no—
444C2×C22⋊C4—1222no—
445C2×C22⋊C4C2×#692312yes—
446C2×C22⋊C4C2×#692312yes—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42C2×#692311yescharacteristic
459C4⋊C8—1222no—
460C4⋊C8—1222no—
461C4⋊C8—1222no—
462C4⋊C8—1222no—
463C22⋊C8—614no—
464C22⋊C8—614no—
465C22⋊C8—1222no—
466C22⋊C8—1222no—
467#97—1222no—
468#97—1222no—
469C4×C8—1222no—
470C4×C8—1222no—
471C24—611no—
472C24—612no—
473C24—1228no—
474C24—1222no—
475C24—1222no—
476C24—2444no—
477C24—2444no—
478C24C22×#692312yes—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—42no—
482C2×Q8—1222no—
483C2×Q8—1222no—
484C2×Q8—1221no—
485C2×Q8—1221no—
486C2×Q8—2442no—
487C2×Q8—2444no—
488C2×Q8—2444no—
489C2×Q8—2444no—
490C2×Q8—2444no—
491C2×Q8—2444no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—1222no—
496C2×D4—1222no—
497C2×D4—1221no—
498C2×D4—1221no—
499C2×D4—2442no—
500C2×D4—2444no—
501C2×D4—2444no—
502C2×D4—2444no—
503C2×D4—2444no—
504C2×D4—2444no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—612no—
521C22×C4—1224no—
522C22×C4—1224no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—2442no—
526C22×C4—2444no—
527C22×C4C22×#692311yescharacteristic
528C22×C4C22×#692311yescharacteristic
529C22×C4C22×#692312yes—
530C22×C4C22×#692311yescharacteristic
531C2×C8—1224no—
532C2×C8—1224no—
533C2×C8—2444no—
534C2×C8—2444no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42C22⋊#692311yescharacteristic
564C42C22⋊#692311yescharacteristic
565C42C22⋊#692311yescharacteristic
566C42C22⋊#692311yescharacteristic
567C23—22no—
568C23—24no—
569C23—42no—
570C23—42no—
571C23—611no—
572C23—611no—
573C23—614no—
574C23—1222no—
575C23—1222no—
576C23—1224no—
577C23—1222no—
578C23—48816no—
579C23—2442no—
580C23—2442no—
581C23—2444no—
582C23—2444no—
583C23—2444no—
584C23—2444no—
585C23—2444no—
586C23—2444no—
587C23C23×#692311yescharacteristic
588Q8—42no—
589Q8—42no—
590Q8—2442no—
591Q8—2444no—
592Q8—2444no—
593Q8—2442no—
594D4—42no—
595D4—42no—
596D4—2442no—
597D4—2444no—
598D4—2444no—
599D4—2442no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—611no—
606C2×C4—614no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2444no—
627C2×C4—2444no—
628C2×C4—2441no—
629C2×C4—2442no—
630C2×C4C2×C22⋊#692311yescharacteristic
631C2×C4C2×C22⋊#692311yescharacteristic
632C2×C4C2×C22⋊#692311yescharacteristic
633C2×C4C2×C22⋊#692311yescharacteristic
634C2×C4C2×C22⋊#692311yescharacteristic
635C2×C4C2×C22⋊#692311yescharacteristic
636C8—2444no—
637C8—2444no—
638C22—21no—
639C22—21no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—84no—
644C22—612no—
645C22—612no—
646C22—612no—
647C22—612no—
648C22—1228no—
649C22—1221no—
650C22—1221no—
651C22—4884no—
652C22—4888no—
653C22—4888no—
654C22—2442no—
655C22—2442no—
656C22—2442no—
657C22C22×C22⋊#692311yescharacteristic
658C22D61⋊#13112yes—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—21no—
663C4—21no—
664C4—42no—
665C4—612no—
666C4—1221no—
667C4—1221no—
668C4—1221no—
669C4—1221no—
670C4—1221no—
671C4—2442no—
672C4D61⋊#10012yes—
673C2—22no—
674C2—82no—
675C2—614no—
676C2—1222no—
677C2—4882no—
678C2D61⋊#40811yescharacteristic
679C2D61⋊#41011yescharacteristic
680C2C2×D61⋊#10011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×Dic61C24
hypercenterC2×#124#6923
hypocenterC61C2×#1469
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. D61⋊#431C2semidirect
3. #21461090C2semidirect
4. #21461089C2semidirect
5. #21461088C2semidirect
6. D61⋊#323C2semidirect
10. #16840783C22semidirect
11. #16840782C22semidirect
14. #16840779C22semidirect
15. #16840778C22semidirect
22. #16840606C22semidirect
23. #16840605C22semidirect
347. D61#1469semidirect
383. C61C2×#1469semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
D61⋊#4312
#214610902
#214610892
#214610882
D61⋊#3232
C2×#124×D612
C2×#146961