Finite Group Databasebeta

← D61⋊#1527 #30611435

Subgroups — D61⋊#1527 #30611435

Order 15616.

1394 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2C4×D61⋊M16C211yesmaximal, characteristic, complemented
3#21461280C212yesmaximal, complemented
4#21461279C214yesmaximal, complemented
5#21461278C212yesmaximal, complemented
6D61⋊#329C214yesmaximal, complemented
7C2×#124×D61C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840785C2212yescomplemented
10#16840784—21no—
11#16840783C2212yescomplemented
12#16840782—21no—
13D61⋊(C4⋊C8)—21no—
14D61⋊(C22⋊C8)—21no—
15C4×#11758213—21no—
16C4×#11758213C2212yescomplemented
17C4×#11758217—21no—
18C4×#11758217C2212yescomplemented
19#16840721C2212yescomplemented
20#16840721C2212yescomplemented
21C4×D61⋊C8—21no—
22#16840618C2218yescomplemented
23#16840617C2218yescomplemented
24C22×Q8×D61C411yescharacteristic
25C22×D4×D61C411yescharacteristic
26C2×#14519766C2211yescharacteristic
27C2×#14519765C411yescharacteristic
28C2×#14519764C2211yescharacteristic
29C2×#14519763—21no—
30C2×#14519763—21no—
31#124×D61—21no—
32#124×D61—21no—
33#124×D61—21no—
34#124×D61—21no—
35#124×D61C412yes—
36#124×D61C412yes—
37#124×D61C2212yes—
38#124×D61C2212yes—
39C2×C22⋊C4×D61—21no—
40C2×C22⋊C4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×#124×C61C411yescharacteristic
43C2×#11758213—22no—
44D61⋊M16—28no—
45C2×#11758217—22no—
46C2×D61⋊C8—22no—
47C2×D61⋊C8—22no—
48#14519844—22no—
49C4⋊#92420—22no—
50#14519834—22no—
51C22⋊#92420—22no—
52#14519832—22no—
53#14519832—22no—
54#14519832C2314yescomplemented
55#14519832C2314yescomplemented
56C4×#92420—22no—
57C4×#92420—22no—
58C24×D61—21no—
59C22×Dic122—21no—
60C22×Dic122C2×C411yescharacteristic
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C2×Q8×D61—44no—
64C2×Q8×D61C2×C412yes—
65C2×Q8×D61C2×C412yes—
66C22×D244C2×C411yescharacteristic
67C22×C22⋊D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—44no—
71C2×D4×D61C2×C412yes—
72C2×D4×D61C2×C412yes—
73C22×C4×D61—21no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77#14519766—21no—
78#14519766—21no—
79#14519766C2×C412yes—
80#14519766C2312yes—
81#14519765—21no—
82#14519765—21no—
83#14519765C2×C412yes—
84#14519765C2×C412yes—
85#14519764—21no—
86#14519764—21no—
87#14519764C2×C412yes—
88#14519764C2312yes—
89#14519763—22no—
90#14519763—22no—
91#14519763—22no—
92#14519763—22no—
93#14519763—22no—
94#14519763—22no—
95#14519763—22no—
96#14519763—22no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
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—
110C22⋊C4×D61—22no—
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61C2311yescharacteristic
121C42×D61C2311yescharacteristic
122C22×Q8×C61C2×C411yescharacteristic
123C22×D4×C61C2×C411yescharacteristic
124#124×C61—21no—
125#124×C61—21no—
126#124×C61C2×C412yes—
127#124×C61C2×C412yes—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C42×C61C2×C411yescharacteristic
131C24×C61—21no—
132C23×D61—21no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—44no—
136C23×D61—44no—
137C23×D61—44no—
138C23×D61C22⋊C411yescharacteristic
139C2×Q8×C61—21no—
140C2×Q8×C61—42no—
141C2×Q8×C61C22×C412yes—
142C2×D4×C61—21no—
143C2×D4×C61—42no—
144C2×D4×C61C22×C412yes—
145C22×C4×C61—21no—
146C22×C4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22⋊C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—44no—
152C22×Dic61—21no—
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156Q8×D61—44no—
157Q8×D61—44no—
158Q8×D61—44no—
159Q8×D61—44no—
160D4×D61—44no—
161D4×D61—44no—
162D4×D61—44no—
163D4×D61—44no—
164C2×D244—21no—
165C2×D244—42no—
166C2×D244C22×C412yes—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—42no—
172C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×Dic122—21no—
186C2×Dic122—22no—
187C2×Dic122—22no—
188C2×Dic122—44no—
189C2×Dic122—42no—
190C2×Dic122C22×C412yes—
191#11758217—28no—
192C2×#92420—24no—
193C2×#92420—24no—
194#11758213—28no—
195D61⋊C8—28no—
196D61⋊C8—44no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C42×C61C22⋊C411yescharacteristic
202C42×C61C22⋊C411yescharacteristic
203C42×C61C22×C411yescharacteristic
204C42×C61C22×C411yescharacteristic
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22×C411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2411yescharacteristic
229C23×C61—22no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61C2×C22⋊C411yescharacteristic
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—44no—
238C22×D61—44no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—42no—
242C22×D61—44no—
243C22×D61—44no—
244C22×D61—44no—
245C22×D61—44no—
246C22×D61—816no—
247C22×D61#10414yes—
248C22×D61C2×C22⋊C411yescharacteristic
249C22×D61C2×C22⋊C411yescharacteristic
250Q8×C61—42no—
251Q8×C61—42no—
252D4×C61—42no—
253D4×C61—42no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—41no—
258C2×C4×C61—42no—
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C23×C411yescharacteristic
265C22⋊D61—44no—
266C22⋊D61—44no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—41no—
271C2×Dic61—42no—
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C22×D411yescharacteristic
277C2×Dic61C22×D411yescharacteristic
278D244—42no—
279D244—42no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—41no—
290C4×D61—41no—
291C4×D61—44no—
292C4×D61—44no—
293C4×D61#10014yes—
294Dic122—44no—
295Dic122—42no—
296Dic122—44no—
297Dic122—42no—
298#92420—28no—
299#92420—44no—
300C2×#1527—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—84no—
307C22×C61C2×#10412yes—
308C22×C61C22×C22⋊C411yescharacteristic
309C2×D61—21no—
310C2×D61—21no—
311C2×D61—28no—
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—42no—
315C2×D61—88no—
316C2×D61—84no—
317C2×D61—88no—
318C2×D61C2×#10012yes—
319C2×D61C2×#10412yes—
320C2×D61C2×#10412yes—
321C2×D61#42112yes—
322C4×C61—21no—
323C4×C61—21no—
324C4×C61—21no—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61—42no—
328C4×C61C2×#10012yes—
329Dic61—21no—
330Dic61—21no—
331Dic61—21no—
332Dic61—21no—
333Dic61—21no—
334Dic61—42no—
335Dic61C2×#10012yes—
336C22×#124—611no—
337C2×#432—611no—
338C2×C4×M16—611no—
339#1527—612no—
340#1527—614no—
341#1527—612no—
342C2×#329—614no—
343C2×C61—22no—
344C2×C61—82no—
345C2×C61C22×#10011yescharacteristic
346C2×C61C22×#10411yescharacteristic
347C2×C61C2×#42111yescharacteristic
348D61—22no—
349D61—82no—
350D61#152714yescomplemented
351C23×Q8—611no—
352C23×D4—611no—
353C22×M16—1221no—
354C2×#124—611no—
355C2×#124—611no—
356C2×#124—612no—
357C2×#124—612no—
358C2×#124—612no—
359C2×#124—612no—
360C2×#124—611no—
361C2×#124—1221no—
362C2×#124—1221no—
363C2×#124—1221no—
364C2×#124—1221no—
365C2×#124—1221no—
366C2×#124—1221no—
367C2×#124#692311yescharacteristic
368C22×C22⋊C4—1221no—
369C22×C22⋊C4—1221no—
370C22×C42—611no—
371#432—612no—
372#432—612no—
373#432—1221no—
374#432—1221no—
375C2×C4⋊C8—1221no—
376C2×C22⋊C8—1221no—
377C4×M16—612no—
378C4×M16—612no—
379C4×M16—1221no—
380C4×M16—1221no—
381C2×#97—612no—
382C2×#97—612no—
383C2×C4×C8—1221no—
384#329—618no—
385#329—618no—
386C61C2×#152711yescharacteristic, complemented, Sylow
387C25—1221no—
388C22×Q8—612no—
389C22×Q8—612no—
390C22×Q8—611no—
391C22×Q8—1221no—
392C22×Q8—1221no—
393C22×Q8—1221no—
394C22×Q8—2444no—
395C22×Q8C2×#692311yescharacteristic
396C22×D4—612no—
397C22×D4—612no—
398C22×D4—611no—
399C22×D4—1221no—
400C22×D4—1221no—
401C22×D4—1221no—
402C22×D4—2444no—
403C22×D4C2×#692311yescharacteristic
404C23×C4—611no—
405C23×C4—611no—
406C23×C4—611no—
407C23×C4—1221no—
408C2×M16—1222no—
409C2×M16—1222no—
410C2×M16—1228no—
411C22×C8—1222no—
412C22×C8—1222no—
413#124—21no—
414#124—21no—
415#124—612no—
416#124—612no—
417#124—612no—
418#124—612no—
419#124—612no—
420#124—612no—
421#124—1222no—
422#124—1222no—
423#124—1222no—
424#124—1222no—
425#124—1222no—
426#124—1222no—
427#124—1222no—
428#124—1222no—
429#124—1221no—
430#124—1221no—
431#124—1221no—
432#124—1221no—
433#124—1221no—
434#124—1221no—
435#124C2×#692312yes—
436#124C2×#692312yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
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⋊C4—1222no—
446C2×C22⋊C4—1222no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42C2×#692311yescharacteristic
465C4⋊C8—1222no—
466C4⋊C8—1222no—
467C22⋊C8—1222no—
468C22⋊C8—1222no—
469#97—614no—
470#97—614no—
471#97—1222no—
472#97—1222no—
473C4×C8—1222no—
474C4×C8—1222no—
475C24—21no—
476C24—611no—
477C24—1222no—
478C24—1222no—
479C24—1221no—
480C24—2444no—
481C24—2444no—
482C24—2444no—
483C2×Q8—21no—
484C2×Q8—42no—
485C2×Q8—612no—
486C2×Q8—1222no—
487C2×Q8—1222no—
488C2×Q8—1221no—
489C2×Q8—2442no—
490C2×Q8—2444no—
491C2×Q8—2444no—
492C2×Q8—2444no—
493C2×Q8—2444no—
494C2×Q8—2444no—
495C2×Q8C22×#692312yes—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—612no—
499C2×D4—1222no—
500C2×D4—1222no—
501C2×D4—1221no—
502C2×D4—2442no—
503C2×D4—2444no—
504C2×D4—2444no—
505C2×D4—2444no—
506C2×D4—2444no—
507C2×D4—2444no—
508C2×D4C22×#692312yes—
509C22×C4—21no—
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—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—1224no—
526C22×C4—1224no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1221no—
530C22×C4—2442no—
531C22×C4—2444no—
532C22×C4C22⋊#692311yescharacteristic
533C22×C4C22⋊#692311yescharacteristic
534C22×C4C22×#692311yescharacteristic
535M16—1228no—
536M16—1228no—
537C2×C8—1224no—
538C2×C8—1228no—
539C2×C8—1224no—
540C2×C8—2444no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—1222no—
553C22⋊C4—1222no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42C22⋊#692311yescharacteristic
570C42C22⋊#692311yescharacteristic
571C42C22×#692311yescharacteristic
572C42C22×#692311yescharacteristic
573C23—22no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—611no—
578C23—614no—
579C23—611no—
580C23—1222no—
581C23—1222no—
582C23—1222no—
583C23—48816no—
584C23—2442no—
585C23—2442no—
586C23—2444no—
587C23—2444no—
588C23—2444no—
589C23—2444no—
590C23—2444no—
591C23—2444no—
592C23—2442no—
593C23C2×C22⋊#692311yescharacteristic
594Q8—42no—
595Q8—42no—
596Q8—2442no—
597Q8—2444no—
598Q8—2444no—
599Q8—2442no—
600D4—42no—
601D4—42no—
602D4—2442no—
603D4—2444no—
604D4—2444no—
605D4—2442no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—611no—
612C2×C4—614no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—611no—
617C2×C4—611no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2444no—
633C2×C4—2444no—
634C2×C4—2441no—
635C2×C4—2442no—
636C2×C4C2×C22⋊#692311yescharacteristic
637C2×C4C2×C22⋊#692311yescharacteristic
638C2×C4C2×C22⋊#692311yescharacteristic
639C2×C4C2×C22⋊#692311yescharacteristic
640C2×C4C2×C22⋊#692311yescharacteristic
641C2×C4C23×#692311yescharacteristic
642C8—1228no—
643C8—2444no—
644C22—21no—
645C22—21no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—84no—
650C22—612no—
651C22—612no—
652C22—612no—
653C22—612no—
654C22—1228no—
655C22—1221no—
656C22—1221no—
657C22—4884no—
658C22—4888no—
659C22—4888no—
660C22—2442no—
661C22—2442no—
662C22—2442no—
663C22D61⋊#10412yes—
664C22C22×C22⋊#692311yescharacteristic
665C4—21no—
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—42no—
671C4—612no—
672C4—1221no—
673C4—1221no—
674C4—1221no—
675C4—1221no—
676C4—1221no—
677C4—2442no—
678C4D61⋊#10012yes—
679C2—22no—
680C2—82no—
681C2—614no—
682C2—1222no—
683C2—4882no—
684C2C2×D61⋊#10011yescharacteristic
685C2C2×D61⋊#10411yescharacteristic
686C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC4×Dic61C24
hypercenterC2×#124#6923
hypocenterC61C2×#1527
LCSG ▷ C2×C4×C61 ▷ C22×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. C4×D61⋊M16C2semidirect
3. #21461280C2semidirect
4. #21461279C2semidirect
5. #21461278C2semidirect
6. D61⋊#329C2semidirect
9. #16840785C22semidirect
11. #16840783C22semidirect
16. C4×#11758213C22semidirect
18. C4×#11758217C22semidirect
19. #16840721C22semidirect
20. #16840721C22semidirect
22. #16840618C22semidirect
23. #16840617C22semidirect
54. #14519832C23semidirect
55. #14519832C23semidirect
350. D61#1527semidirect
386. C61C2×#1527semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
C4×D61⋊M162
#214612802
#214612792
#214612782
D61⋊#3292
C2×#124×D612
C2×#152761