Finite Group Databasebeta

← D61×#2023 #29707279

Subgroups — D61×#2023 #29707279

Order 15616.

1734 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2C2×#102×D61C212yesmaximal
3#390×D61C211yesmaximal, characteristic
4#21446956C211yesmaximal, characteristic, complemented
5#21446955C211yesmaximal, characteristic, complemented
6#21446954C212yesmaximal, complemented
7#21446953C212yesmaximal, complemented
8#21446952C211yesmaximal, characteristic, complemented
9#340×D61C212yesmaximal, complemented
10#336×D61C211yesmaximal, characteristic, complemented
11C61×#2023C211yesmaximal, characteristic, complemented
12C22×Q8×D61—21no—
13C22×D4×D61C2211yescharacteristic
14C22×C8×D61C2212yes—
15C2×#14519777C2211yescharacteristic, complemented
16C2×#14519776—21no—
17C2×#14519776C2212yescomplemented
18C2×#14519775—21no—
19C4⋊Q8×D61—28no—
20C2×C4⋊C4×D61—21no—
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2212yes—
23C2×C22⋊C4×D61—21no—
24C2×C22⋊C4×D61—21no—
25C2×C42×D61C2211yescharacteristic
26C2×#14519699C2212yes—
27C2×#14519698C2212yes—
28C2×#14519697C2212yes—
29#102×D61—28no—
30#16839665C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839663C2211yescharacteristic
33#16839662—21no—
34#16839662—21no—
35#16839525C2212yescomplemented
36#16839524C2212yescomplemented
37#16839524C2212yescomplemented
38#16839517C2211yescharacteristic, complemented
39#16839516C2212yescomplemented
40C2×C4⋊Q8×C61C2211yescharacteristic, complemented
41C2×#102×C61C2212yes—
42C61×#390C2211yescharacteristic
43C61×#340C2212yescomplemented
44C61×#336C2211yescharacteristic, complemented
45C24×D61—21no—
46C22×Dic122—21no—
47C22×Dic122—22no—
48C2×Q8×D61—28no—
49C2×Q8×D61—44no—
50C2×Q8×D61—44no—
51C22×D244C2311yescharacteristic
52C22×C22⋊D61—21no—
53C2×D4×D61—24no—
54C2×D4×D61—24no—
55C2×D4×D61—22no—
56C2×D4×D61Q814yescomplemented
57C22×C4×D61—22no—
58C22×C4×D61—21no—
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C22×#92418C2312yes—
63C2×C8×D61—24no—
64C2×C8×D61—24no—
65C2×C8×D61—24no—
66#14519777—24no—
67#14519776—28no—
68#14519776—24no—
69#14519776—24no—
70#14519775—28no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2312yes—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—21no—
77C4⋊C4×D61—28no—
78C4⋊C4×D61—24no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61D418yes—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C22⋊C4×D61—44no—
88C22⋊C4×D61—44no—
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C42×D61—24no—
93#14519699—24no—
94#14519698—24no—
95#14519697—24no—
96C22×Q8×C61—21no—
97C22×D4×C61C2311yescharacteristic
98C22×C8×C61C2312yes—
99C4⋊Q8×C61—24no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2312yes—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C42×C61C2311yescharacteristic
106#102×C61—24no—
107C24×C61—21no—
108C23×D61—21no—
109C23×D61—24no—
110C23×D61—42no—
111C23×D61—42no—
112C23×D61—42no—
113C23×D61—42no—
114C23×D61—42no—
115C23×D61—42no—
116C23×D61C2×D411yescharacteristic
117C2×Q8×C61—24no—
118C2×Q8×C61—42no—
119C2×Q8×C61—42no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—21no—
123C2×D4×C61C2×Q812yescomplemented
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C2×C22⋊D61—24no—
130C2×C22⋊D61—42no—
131C2×C22⋊D61—42no—
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61C2×D411yescharacteristic
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137Q8×D61—432no—
138D4×D61—216no—
139D4×D61—48no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—21no—
143C2×D244C2×Q812yescomplemented
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—28no—
149C2×C4×D61—44no—
150C2×C4×D61—44no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61D814yes—
155C2×C4×D61SD1614yes—
156C2×C4×D61C2×D414yes—
157C2×C4×D61C2×Q812yes—
158C2×C4×D61#4114yes—
159C2×C4×D61#4112yes—
160C2×Dic122—24no—
161C2×Dic122—28no—
162C2×Dic122—44no—
163C2×Dic122—42no—
164C2×Dic122—42no—
165C2×Dic122—44no—
166C2×C8×C61—22no—
167C2×C8×C61—22no—
168C2×C8×C61—22no—
169C4⋊C4×C61—24no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61C2×D414yes—
173C22⋊C4×C61—42no—
174C22⋊C4×C61—42no—
175C42×C61—22no—
176C22⋊Dic61—42no—
177C22⋊Dic61—42no—
178#11758198—42no—
179#11758198—42no—
180#11758198—42no—
181#11758198—42no—
182C4⋊Dic61—24no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61C2×D414yes—
186#11758196—28no—
187#11758196—28no—
188#11758196—42no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418—22no—
195C8×D61—48no—
196C23×C61—22no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61C22×D411yescharacteristic
204C22×D61—22no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—48no—
212C22×D61—48no—
213C22×D61—48no—
214C22×D61—84no—
215C22×D61—84no—
216C22×D61—84no—
217C22×D61—84no—
218C22×D61#12012yes—
219C22×D61C22⋊Q812yes—
220C22×D61#12412yes—
221C22×D61C2×D812yes—
222C22×D61C2×SD1612yes—
223C22×D61AGL(1,ℤ/8)12yes—
224C22×D61#13712yes—
225Q8×C61—48no—
226D4×C61—24no—
227D4×C61—42no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—24no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61C2×D812yes—
239C2×C4×C61C2×SD1612yes—
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×Q811yescharacteristic
242C2×C4×C61C2×#4112yes—
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—48no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—24no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61#12012yes—
256C2×Dic61C22⋊Q812yes—
257C2×Dic61#12412yes—
258C2×Dic61C2×D812yes—
259C2×Dic61C2×SD1612yes—
260D244—24no—
261D244—42no—
262C4×D61—28no—
263C4×D61—28no—
264C4×D61—416no—
265C4×D61—84no—
266C4×D61C22⋊Q818yes—
267C4×D61#12418yes—
268Dic122—416no—
269Dic122—48no—
270C8×C61—42no—
271#92418—42no—
272C2×#2023—611nomaximal, Sylow
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61C2×#12011yescharacteristic
281C22×C61C2×C22⋊Q811yescharacteristic
282C22×C61C2×#12411yescharacteristic
283C22×C61C22×D811yescharacteristic
284C22×C61C22×SD1611yescharacteristic
285C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C61C2×#13711yescharacteristic
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—81no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—816no—
295C2×D61#39314yes—
296C2×D61#44714yes—
297C2×D61#44814yes—
298C2×D61#47414yes—
299C2×D61#47614yes—
300C2×D61#48614yes—
301C2×D61#48914yes—
302C4×C61—22no—
303C4×C61—22no—
304C4×C61—44no—
305C4×C61—81no—
306C4×C61C2×C22⋊Q812yes—
307C4×C61C2×#12412yes—
308Dic61—22no—
309Dic61—22no—
310Dic61—44no—
311Dic61—81no—
312Dic61#39314yes—
313C22×C4⋊Q8—611no—
314C22×#102—612no—
315C2×#390—611no—
316#2023—612no—
317#2023—611no—
318#2023—612no—
319#2023—611no—
320#2023—611no—
321#2023D6111yescharacteristic, direct product factor
322C2×#340—612no—
323C2×#336—611no—
324C2×C61—82no—
325C2×C61C2×#39311yescharacteristic
326C2×C61C2×#44711yescharacteristic
327C2×C61C2×#44811yescharacteristic
328C2×C61C2×#47411yescharacteristic
329C2×C61C2×#47611yescharacteristic
330C2×C61C2×#48611yescharacteristic
331C2×C61C2×#48911yescharacteristic
332D61—82no—
333D61#202318yesdirect product factor
334C23×Q8—1221no—
335C23×D4—611no—
336C23×C8—612no—
337C2×C4⋊Q8—612no—
338C2×C4⋊Q8—611no—
339C2×C4⋊Q8—1221no—
340C2×C4⋊Q8—1221no—
341C2×C4⋊Q8—1228no—
342C2×C4⋊Q8C2×D6111yescharacteristic, complemented
343C22×C4⋊C4—612no—
344C22×C4⋊C4—611no—
345C22×C4⋊C4—1221no—
346C22×C22⋊C4—1221no—
347C22×C22⋊C4—1221no—
348C22×C42—611no—
349C2×#102—612no—
350C2×#102—612no—
351C2×#102—612no—
352C2×#102—1228no—
353C2×#102C2×D6112yes—
354#390—611no—
355#390—611no—
356#390—611no—
357#390—1221no—
358#390—1221no—
359#390C2×D6111yescharacteristic
360#340—612no—
361#340—612no—
362#340—612no—
363#340C2×D6112yescomplemented
364#336—612no—
365#336—611no—
366#336C2×D6111yescharacteristic, complemented
367C61C2×#202311yescharacteristic, complemented, Sylow
368C25—1221no—
369C22×Q8—21no—
370C22×Q8—1222no—
371C22×Q8—1228no—
372C22×Q8—1221no—
373C22×Q8—2444no—
374C22×Q8—2444no—
375C22×D4—614no—
376C22×D4—611no—
377C22×D4—1224no—
378C22×D4—1224no—
379C22×D4—1222no—
380C22×D4—1221no—
381C22×D4C22×D6111yescharacteristic
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—1222no—
386C23×C4—1221no—
387C22×C8—612no—
388C22×C8—1224no—
389C22×C8—1224no—
390C22×C8—1224no—
391C22×C8C22×D6112yes—
392C4⋊Q8—24no—
393C4⋊Q8—1224no—
394C4⋊Q8—1224no—
395C4⋊Q8—1228no—
396C4⋊Q8—1228no—
397C4⋊Q8—1224no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—618no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—1224no—
403C2×C4⋊C4—1228no—
404C2×C4⋊C4—1224no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6112yes—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—2444no—
420C2×C22⋊C4—2444no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—1224no—
425C2×C42C22×D6111yescharacteristic
426#102—24no—
427#102—1224no—
428#102—1224no—
429#102—1224no—
430C24—21no—
431C24—611no—
432C24—1224no—
433C24—1221no—
434C24—2442no—
435C24—2442no—
436C24—2442no—
437C24—2442no—
438C24—2442no—
439C24—2442no—
440C2×Q8—24no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—1224no—
444C2×Q8—1228no—
445C2×Q8—2442no—
446C2×Q8—2444no—
447C2×Q8—2444no—
448C2×Q8—24432no—
449C2×Q8—2442no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—612no—
454C2×D4—12216no—
455C2×D4—1224no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1221no—
459C2×D4—2448no—
460C2×D4—2442no—
461C2×D4—2442no—
462C2×D4Q8×D6112yescomplemented
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—611no—
466C22×C4—614no—
467C22×C4—612no—
468C22×C4—614no—
469C22×C4—612no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—614no—
473C22×C4—614no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1228no—
479C22×C4—1222no—
480C22×C4—1221no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2444no—
485C22×C4—2444no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—1222no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—2448no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—614no—
500C4⋊C4—1228no—
501C4⋊C4—1228no—
502C4⋊C4—1224no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—2442no—
506C4⋊C4D4×D6114yes—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—2442no—
510C22⋊C4—2442no—
511C22⋊C4—2442no—
512C22⋊C4—2442no—
513C22⋊C4—2442no—
514C22⋊C4—2442no—
515C42—22no—
516C42—1222no—
517C42—1222no—
518C42—1222no—
519C23—22no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—612no—
527C23—612no—
528C23—612no—
529C23—612no—
530C23—612no—
531C23—612no—
532C23—612no—
533C23—1222no—
534C23—4884no—
535C23—4884no—
536C23—4884no—
537C23—4884no—
538C23—2448no—
539C23—2448no—
540C23—2448no—
541C23—2441no—
542C23—2441no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23C2×D4×D6111yescharacteristic
548Q8—48no—
549Q8—2448no—
550Q8—24416no—
551D4—24no—
552D4—42no—
553D4—1224no—
554D4—2448no—
555D4—2442no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—24no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—618no—
570C2×C4—618no—
571C2×C4—612no—
572C2×C4—612no—
573C2×C4—1228no—
574C2×C4—1228no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1224no—
580C2×C4—4884no—
581C2×C4—24416no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4D8×D6112yes—
588C2×C4SD16×D6112yes—
589C2×C4C2×D4×D6112yes—
590C2×C4C2×Q8×D6111yescharacteristic
591C2×C4#41×D6112yes—
592C2×C4#41×D6111yescharacteristic
593C8—42no—
594C8—2442no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—614no—
603C22—614no—
604C22—614no—
605C22—614no—
606C22—614no—
607C22—614no—
608C22—614no—
609C22—48816no—
610C22—4881no—
611C22—4881no—
612C22—4881no—
613C22—4881no—
614C22—2442no—
615C22—2442no—
616C22—2442no—
617C22#120×D6111yescharacteristic
618C22C22⋊Q8×D6111yescharacteristic
619C22#124×D6111yescharacteristic
620C22C2×D8×D6111yescharacteristic
621C22C2×SD16×D6111yescharacteristic
622C22AGL(1,ℤ/8)×D6111yescharacteristic
623C22#137×D6111yescharacteristic
624C4—22no—
625C4—22no—
626C4—44no—
627C4—81no—
628C4—614no—
629C4—1222no—
630C4—1222no—
631C4—4881no—
632C4—2444no—
633C4C22⋊Q8×D6112yes—
634C4#124×D6112yes—
635C2—82no—
636C2—618no—
637C2—4882no—
638C2#393×D6111yescharacteristic
639C2#447×D6111yescharacteristic
640C2#448×D6111yescharacteristic
641C2#474×D6111yescharacteristic
642C2#476×D6111yescharacteristic
643C2#486×D6111yescharacteristic
644C2#489×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2023C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2023D61
hypocenterC61C2×#2023
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D61C2semidirect
4. #21446956C2semidirect
5. #21446955C2semidirect
6. #21446954C2semidirect
7. #21446953C2semidirect
8. #21446952C2semidirect
9. #340×D61C2semidirect
10. #336×D61C2semidirect
11. C61×#2023C2semidirect
15. C2×#14519777C22semidirect
17. C2×#14519776C22semidirect
35. #16839525C22semidirect
36. #16839524C22semidirect
37. #16839524C22semidirect
38. #16839517C22semidirect
39. #16839516C22semidirect
40. C2×C4⋊Q8×C61C22semidirect
43. C61×#340C22semidirect
44. C61×#336C22semidirect
56. C2×D4×D61Q8semidirect
123. C2×D4×C61C2×Q8semidirect
143. C2×D244C2×Q8semidirect
321. #2023D61direct (N × H)
333. D61#2023direct (N × H)
342. C2×C4⋊Q8C2×D61semidirect
363. #340C2×D61semidirect
366. #336C2×D61semidirect
367. C61C2×#2023semidirect
462. C2×D4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
C2×#102×D612
#390×D612
#214469562
#214469552
#214469542
#214469532
#214469522
#340×D612
#336×D612
C61×#20232
C2×#202361