Finite Group Databasebeta

← D61⋊#1505 #30610948

Subgroups — D61⋊#1505 #30610948

Order 15616.

1410 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21461210C212yesmaximal, complemented
4#21461209C214yesmaximal, complemented
5#21461208C212yesmaximal, complemented
6D61⋊#327C214yesmaximal, complemented
7#532×D61C211yesmaximal, characteristic
8C22×C4×#6923—21no—
9#16840785C2212yescomplemented
10#16840784C2212yescomplemented
11#16840783—21no—
12#16840782—21no—
13D61⋊(C4⋊C8)—21no—
14D61⋊(C22⋊C8)C2212yes—
15#16840721—21no—
16#16840698—21no—
17#16840698—21no—
18#16840698C2212yescomplemented
19#16840698C2212yescomplemented
20C2×(C2×#6923)⋊C4—21no—
21C2×(C2×#6923)⋊C4C2212yes—
22#16840614C2218yescomplemented
23#16840613C2218yescomplemented
24C2×#41×D61—21no—
25#16840313C2211yescharacteristic
26#16840312C411yescharacteristic, complemented
27#16840311—21no—
28#16840310C2211yescharacteristic
29#16840309—21no—
30#16840309C2212yes—
31#16840308—21no—
32#16840307—21no—
33#16840307C412yescomplemented
34C4⋊Q8×D61C411yescharacteristic, complemented
35#127×D61C411yescharacteristic, complemented
36#124×D61—21no—
37#121×D61—21no—
38#121×D61C2212yes—
39C4×D4×D61—21no—
40C4×D4×D61C412yescomplemented
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×D61⋊C8—22no—
45C2×C4×#6923—28no—
46C2×C4×#6923—22no—
47C2×C4×#6923—22no—
48#14519844—22no—
49C4⋊#92420—22no—
50#14519834C2314yes—
51C22⋊#92420—22no—
52#14519832—22no—
53#14519832—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4C2314yes—
58C2×#11758226—21no—
59C2×#11758222—21no—
60C2×#11758222—22no—
61C2×#11758224—22no—
62C2×#11758224—21no—
63#41×D61—48no—
64C2×Q8×D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—21no—
67C2×D4×D61—21no—
68C2×D4×D61C2×C412yes—
69C22×C4×D61—22no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73#14519777C2×C411yescharacteristic, complemented
74#14519776—21no—
75#14519776C2×C412yescomplemented
76#14519775—21no—
77#14519774C2×C411yescharacteristic, complemented
78#14519773—21no—
79#14519773—21no—
80#14519773C2×C412yescomplemented
81#14519766—21no—
82#14519765—21no—
83#14519764—21no—
84#14519763—22no—
85#14519763—22no—
86#14519752—21no—
87#14519752C2312yes—
88#14519751—21no—
89#14519751C2×C412yes—
90#14519750—22no—
91#14519750—22no—
92#14519749—22no—
93#14519749—22no—
94#14519748—21no—
95#14519748C2312yes—
96C4×D244—21no—
97C4×D244C2×C412yescomplemented
98D4×Dic61—21no—
99D4×Dic61C2×C412yescomplemented
100#14519739—21no—
101#14519739C2×C412yescomplemented
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104#14519737—22no—
105#14519737—22no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61C2×C412yes—
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C2×#41×C61—21no—
122C4⋊Q8×C61C2×C411yescharacteristic, complemented
123#127×C61C2×C411yescharacteristic, complemented
124#124×C61—21no—
125#121×C61—21no—
126#121×C61C2×C412yes—
127C4×D4×C61—21no—
128C4×D4×C61C2×C412yescomplemented
129C2×C42×C61C2×C411yescharacteristic
130C23×D61—22no—
131C23×D61C2×D411yescharacteristic
132C22×#6923—28no—
133C22×#6923—24no—
134C22×#6923—44no—
135C22×#6923—44no—
136#41×C61—44no—
137C2×Q8×C61—21no—
138C2×D4×C61—22no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61C22×C412yes—
142C22×C4×C61—22no—
143C22×C4×C61C22⋊C411yescharacteristic
144C22×C4×C61C22⋊C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C22×Dic61—22no—
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155#11758226—44no—
156Q8×D61—44no—
157#11758224—44no—
158#11758224—48no—
159D4×D61—44no—
160D4×D61—44no—
161D4×D61—48no—
162D4×D61—44no—
163#11758222—48no—
164#11758222—44no—
165C2×D244—22no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244C22×C412yes—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—42no—
175C2×C4×D61—48no—
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×C4×D61C2×D411yescharacteristic
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2411yescharacteristic
188C2×Dic122—21no—
189C2×Dic122—22no—
190C2×#92420—24no—
191C4×#6923—28no—
192C4×#6923—28no—
193D61⋊C8—44no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61C22×C412yes—
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—
204#11758198—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208C4⋊Dic61—21no—
209C4⋊Dic61C22×C412yes—
210#11758196—22no—
211#11758196—22no—
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C23×C61—22no—
225C23×C61C2×C22⋊C411yescharacteristic
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—44no—
230C22×D61—44no—
231C22×D61—44no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61AGL(1,ℤ/8)14yes—
234C22×D61C22×D411yescharacteristic
235C2×#6923—28no—
236C2×#6923—44no—
237C2×#6923—416no—
238C2×#6923—44no—
239Q8×C61—42no—
240D4×C61—42no—
241D4×C61—42no—
242D4×C61—44no—
243D4×C61—42no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—41no—
248C2×C4×C61—44no—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C23×C411yescharacteristic
255C22⋊D61—44no—
256C22⋊D61—44no—
257C22⋊D61—44no—
258C22⋊D61—44no—
259C22⋊D61—44no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—44no—
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C22×D411yescharacteristic
271D244—42no—
272D244—42no—
273D244—44no—
274D244—42no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—44no—
287C4×D61—44no—
288C4×D61—44no—
289C4×D61#10414yes—
290Dic122—44no—
291Dic122—42no—
292#92420—44no—
293C2×#1505—611nomaximal, Sylow
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61#41812yes—
300C22×C61C22×C22⋊C411yescharacteristic
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—28no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—42no—
307C2×D61—88no—
308C2×D61#41012yes—
309C2×D61#41812yes—
310C2×D61C2×#10412yes—
311C2×D61C2×AGL(1,ℤ/8)12yes—
312#6923—48no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—42no—
319C4×C61C2×#10412yes—
320Dic61—21no—
321Dic61—21no—
322Dic61—21no—
323Dic61—21no—
324Dic61—21no—
325Dic61—42no—
326Dic61C2×#10412yes—
327C2×#532—611no—
328C2×#432—611no—
329C2×#376—611no—
330#1505—612no—
331#1505—614no—
332#1505—612no—
333C2×#327—614no—
334C2×C61—22no—
335C2×C61—82no—
336C2×C61C2×#41011yescharacteristic
337C2×C61C2×#41811yescharacteristic
338C2×C61C22×#10411yescharacteristic
339D61—22no—
340D61—82no—
341D61#150514yescomplemented
342C22×#41—1221no—
343#532—611no—
344#532—611no—
345#532—612no—
346#532—612no—
347#532—611no—
348#532—1221no—
349#532—1221no—
350#532—1221no—
351#532—1221no—
352#532#692311yescharacteristic, complemented
353C2×C4⋊Q8—611no—
354C2×#127—611no—
355C2×#124—1221no—
356C2×#121—612no—
357C2×#121—1221no—
358C2×C4×D4—612no—
359C2×C4×D4—1221no—
360C22×C42—611no—
361C22×C42—1221no—
362#432—612no—
363#432—612no—
364#432—1221no—
365#432—1221no—
366C2×C4⋊C8—1221no—
367C2×C22⋊C8—612no—
368C2×#97—1221no—
369#376—612no—
370#376—612no—
371#376—1221no—
372#376—1221no—
373C2×#95—612no—
374C2×#95—1221no—
375#327—618no—
376#327—618no—
377C61C2×#150511yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C2×#41—1222no—
380C2×#41—1222no—
381C2×#41—1221no—
382C2×#41—1221no—
383C2×#41—1221no—
384C2×#41—2448no—
385C22×Q8—1221no—
386C22×D4—612no—
387C22×D4—1221no—
388C22×D4—1221no—
389C22×D4—1222no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—1222no—
394C23×C4—1222no—
395C22×C8—1222no—
396C4⋊Q8—612no—
397C4⋊Q8—611no—
398C4⋊Q8—1221no—
399C4⋊Q8—1221no—
400C4⋊Q8C2×#692311yescharacteristic, complemented
401#127—612no—
402#127—611no—
403#127—1221no—
404#127—1221no—
405#127C2×#692311yescharacteristic, complemented
406#124—21no—
407#124—1222no—
408#124—1222no—
409#124—1221no—
410#124—1221no—
411#124—1221no—
412#121—21no—
413#121—612no—
414#121—612no—
415#121—612no—
416#121—1222no—
417#121—1222no—
418#121—1221no—
419#121—1222no—
420#121—1221no—
421#121—1222no—
422#121—1221no—
423#121C2×#692312yes—
424C4×D4—21no—
425C4×D4—612no—
426C4×D4—612no—
427C4×D4—612no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1221no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4C2×#692312yescomplemented
436C2×C4⋊C4—612no—
437C2×C4⋊C4—1221no—
438C2×C22⋊C4—1222no—
439C2×C22⋊C4—1222no—
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—611no—
450C2×C42—611no—
451C2×C42—1222no—
452C2×C42—1222no—
453C2×C42—1228no—
454C2×C42C2×#692311yescharacteristic
455C4⋊C8—1222no—
456C4⋊C8—1222no—
457C22⋊C8—614no—
458C22⋊C8—1222no—
459#97—1222no—
460#97—1222no—
461#95—614no—
462#95—1222no—
463#95—1222no—
464#95—1222no—
465C24—611no—
466C24—1222no—
467#41—44no—
468#41—2444no—
469#41—2448no—
470#41—2444no—
471#41—2448no—
472#41—2444no—
473C2×Q8—21no—
474C2×Q8—1222no—
475C2×Q8—1221no—
476C2×Q8—2444no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—612no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1222no—
484C2×D4—1222no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1221no—
488C2×D4—1221no—
489C2×D4—2444no—
490C2×D4—2444no—
491C2×D4—2444no—
492C2×D4—2448no—
493C2×D4C22×#692312yes—
494C22×C4—22no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—1224no—
511C22×C4—1222no—
512C22×C4—1224no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1224no—
516C22×C4—1228no—
517C22×C4—1222no—
518C22×C4—2442no—
519C22×C4—2448no—
520C22×C4—2444no—
521C22×C4—2444no—
522C22×C4C22⋊#692311yescharacteristic
523C22×C4C22⋊#692311yescharacteristic
524C22×C4C22×#692311yescharacteristic
525C2×C8—1224no—
526C2×C8—2444no—
527C4⋊C4—21no—
528C4⋊C4—612no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1221no—
532C4⋊C4C22×#692312yes—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—1228no—
554C42—1228no—
555C42C22⋊#692311yescharacteristic
556C42C22⋊#692311yescharacteristic
557C42C22×#692311yescharacteristic
558C42C22×#692311yescharacteristic
559C23—22no—
560C23—611no—
561C23—614no—
562C23—611no—
563C23—1222no—
564C23—1222no—
565C23—1222no—
566C23—2444no—
567C23—2444no—
568C23—2444no—
569C23C2×C22⋊#692311yescharacteristic
570Q8—42no—
571Q8—2442no—
572Q8—2444no—
573D4—42no—
574D4—42no—
575D4—44no—
576D4—42no—
577D4—2442no—
578D4—2442no—
579D4—2444no—
580D4—2444no—
581D4—2444no—
582D4—2444no—
583D4—2444no—
584D4—2444no—
585D4—2442no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—44no—
591C2×C4—611no—
592C2×C4—614no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1228no—
610C2×C4—1222no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2444no—
614C2×C4—2444no—
615C2×C4—2444no—
616C2×C4—2441no—
617C2×C4—2444no—
618C2×C4—2444no—
619C2×C4—24416no—
620C2×C4—2444no—
621C2×C4C2×C22⋊#692311yescharacteristic
622C2×C4C2×C22⋊#692311yescharacteristic
623C2×C4C2×C22⋊#692311yescharacteristic
624C2×C4C2×C22⋊#692311yescharacteristic
625C2×C4C2×C22⋊#692311yescharacteristic
626C2×C4C23×#692311yescharacteristic
627C8—2444no—
628C22—21no—
629C22—21no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—612no—
634C22—612no—
635C22—612no—
636C22—612no—
637C22—1228no—
638C22—1221no—
639C22—1221no—
640C22—4888no—
641C22—2442no—
642C22—2442no—
643C22—2442no—
644C22#1684075412yes—
645C22C22×C22⋊#692311yescharacteristic
646C4—21no—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—21no—
651C4—42no—
652C4—612no—
653C4—1221no—
654C4—1221no—
655C4—1221no—
656C4—1221no—
657C4—1221no—
658C4—2448no—
659C4—2442no—
660C4D61⋊#10412yes—
661C2—22no—
662C2—82no—
663C2—614no—
664C2—1222no—
665C2—4882no—
666C2D61⋊#41011yescharacteristic
667C2C2×#1684075411yescharacteristic
668C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#532C4
socleC22×C61C22×C22⋊C4
prime radical#532×D61C2
cosocleC2×C4×D61C24
hypercenter#532#6923
hypocenterC61C2×#1505
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. C2×#16840698C2semidirect
3. #21461210C2semidirect
4. #21461209C2semidirect
5. #21461208C2semidirect
6. D61⋊#327C2semidirect
9. #16840785C22semidirect
10. #16840784C22semidirect
18. #16840698C22semidirect
19. #16840698C22semidirect
22. #16840614C22semidirect
23. #16840613C22semidirect
26. #16840312C4semidirect
33. #16840307C4semidirect
34. C4⋊Q8×D61C4semidirect
35. #127×D61C4semidirect
40. C4×D4×D61C4semidirect
42. C61×#532C4semidirect
73. #14519777C2×C4semidirect
75. #14519776C2×C4semidirect
77. #14519774C2×C4semidirect
80. #14519773C2×C4semidirect
97. C4×D244C2×C4semidirect
99. D4×Dic61C2×C4semidirect
101. #14519739C2×C4semidirect
122. C4⋊Q8×C61C2×C4semidirect
123. #127×C61C2×C4semidirect
128. C4×D4×C61C2×C4semidirect
341. D61#1505semidirect
352. #532#6923semidirect
377. C61C2×#1505semidirect
400. C4⋊Q8C2×#6923semidirect
405. #127C2×#6923semidirect
435. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
C2×#168406982
#214612102
#214612092
#214612082
D61⋊#3272
#532×D612
C2×#150561