Finite Group Databasebeta

← D61×#1983 #29684067

Subgroups — D61×#1983 #29684067

Order 15616.

1814 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
1C2×#124×D61C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#103×D61C212yesmaximal, complemented
4C2×#102×D61C212yesmaximal
5C4×C4⋊C4×D61C211yesmaximal, characteristic, complemented
6#21446752C211yesmaximal, characteristic, complemented
7#21446751C211yesmaximal, characteristic, complemented
8#21446750C212yesmaximal, complemented
9#21446749C211yesmaximal, characteristic, complemented
10#21446748C212yesmaximal, complemented
11C61×#1983C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2211yescharacteristic
13C22×D4×D61C2211yescharacteristic
14C22×C8×D61C2212yes—
15C2×#14519766C2211yescharacteristic
16C2×#14519765C2211yescharacteristic
17C2×#14519764C2211yescharacteristic
18C2×#14519763—21no—
19C2×#14519763—21no—
20#124×D61—24no—
21#124×D61C418yescomplemented
22C2×C4⋊C4×D61C2212yes—
23C2×C22⋊C4×D61—21no—
24C2×C22⋊C4×D61—21no—
25C2×C42×D61—21no—
26C2×C42×D61C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic, complemented
28C2×#14519706C2212yescomplemented
29C4⋊C8×D61—24no—
30C2×#14519702C2212yescomplemented
31C2×#14519701C2212yescomplemented
32C2×#14519700C2212yescomplemented
33#103×D61—28no—
34C2×#14519699C2212yes—
35C2×#14519698C2212yes—
36C2×#14519697C2212yes—
37#102×D61—28no—
38C4⋊C4×Dic61C2212yescomplemented
39C4×#11758196—21no—
40C4×C4⋊Dic61C2211yescharacteristic, complemented
41#16839613—21no—
42#95×D61—21no—
43C2×#124×C61C2211yescharacteristic
44C2×C4⋊C8×C61C2211yescharacteristic, complemented
45C2×#103×C61C2212yescomplemented
46C2×#102×C61C2212yes—
47C4×C4⋊C4×C61C2211yescharacteristic, complemented
48C24×D61—21no—
49C22×Dic122—21no—
50C22×Dic122C2311yescharacteristic
51C2×Q8×D61—22no—
52C2×Q8×D61—24no—
53C2×Q8×D61—24no—
54C2×Q8×D61C2×C414yes—
55C22×D244C2311yescharacteristic
56C22×C22⋊D61—21no—
57C2×D4×D61—24no—
58C2×D4×D61—22no—
59C2×D4×D61—24no—
60C2×D4×D61C2×C414yes—
61C22×C4×D61—22no—
62C22×C4×D61—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C22×#92418C2312yes—
67C2×C8×D61—24no—
68C2×C8×D61—24no—
69C2×C8×D61—24no—
70#14519766—22no—
71#14519766C2×C414yescomplemented
72#14519765—22no—
73#14519765C2×C414yescomplemented
74#14519764—22no—
75#14519764C2×C414yescomplemented
76#14519763—28no—
77#14519763—28no—
78C2×C4⋊Dic61C2312yes—
79C2×#11758196—22no—
80C4⋊C4×D61—24no—
81C4⋊C4×D61D418yes—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C22⋊C4×D61—28no—
89C22⋊C4×D61—28no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C42×D61—44no—
96C42×D61C2×C414yes—
97C42×D61D414yes—
98C4⋊#92418—22no—
99#14519706—24no—
100#14519702—24no—
101#14519701—24no—
102#14519700—24no—
103#14519699—24no—
104#14519698—24no—
105#14519697—24no—
106#14519684—21no—
107#14519684—22no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C22×C8×C61C2312yes—
111#124×C61—22no—
112#124×C61C2×C414yescomplemented
113C2×C4⋊C4×C61C2312yes—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118C4⋊C8×C61—22no—
119#103×C61—24no—
120#102×C61—24no—
121#95×C61—21no—
122C24×C61—21no—
123C23×D61—21no—
124C23×D61—24no—
125C23×D61—44no—
126C23×D61—44no—
127C23×D61—42no—
128C23×D61—42no—
129C23×D61C2×D411yescharacteristic
130C2×Q8×C61—21no—
131C2×Q8×C61—22no—
132C2×Q8×C61—22no—
133C2×Q8×C61C22×C412yes—
134C2×D4×C61—22no—
135C2×D4×C61—21no—
136C2×D4×C61—22no—
137C2×D4×C61C22×C412yes—
138C22×C4×C61—21no—
139C22×C4×C61—22no—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2411yescharacteristic
143C2×C22⋊D61—24no—
144C2×C22⋊D61—44no—
145C22×Dic61—21no—
146C22×Dic61—22no—
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150Q8×D61—216no—
151Q8×D61—44no—
152Q8×D61—44no—
153D4×D61—216no—
154D4×D61—44no—
155D4×D61—44no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—21no—
159C2×D244C22×C412yes—
160C2×C4×D61—24no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—24no—
164C2×C4×D61—28no—
165C2×C4×D61—44no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61C22⋊C414yes—
169C2×C4×D61C22⋊C414yes—
170C2×C4×D61C22×C412yes—
171C2×C4×D61C2×D414yes—
172C2×C4×D61C2×D412yes—
173C2×C4×D61#4114yes—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—21no—
177C2×Dic122—24no—
178C2×Dic122—44no—
179C2×Dic122C22×C412yes—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C2×C8×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61C2×D414yes—
185C22⋊C4×C61—24no—
186C22⋊C4×C61—24no—
187C42×C61—42no—
188C42×C61C22×C412yes—
189C42×C61C2×D412yes—
190C22⋊Dic61—24no—
191C22⋊Dic61—24no—
192#11758198—24no—
193#11758198—24no—
194#11758198—24no—
195#11758198—24no—
196C4⋊Dic61—22no—
197C4⋊Dic61C2×D414yes—
198#11758196—28no—
199C4×Dic61—44no—
200C4×Dic61—42no—
201C4×Dic61C22⋊C414yes—
202C4×Dic61C22⋊C414yes—
203C4×Dic61C22×C412yes—
204C4×Dic61C2×D412yes—
205C2×#92418—22no—
206C2×#92418—22no—
207C2×#92418—22no—
208C8×D61—48no—
209C23×C61—22no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61C22×D411yescharacteristic
215C22×D61—22no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—48no—
221C22×D61—48no—
222C22×D61—48no—
223C22×D61—88no—
224C22×D61—88no—
225C22×D61C2×C22⋊C412yes—
226C22×D61#12114yes—
227C22×D61#13514yes—
228C22×D61AGL(1,ℤ/8)12yes—
229C22×D61#13712yes—
230Q8×C61—24no—
231Q8×C61—41no—
232Q8×C61—41no—
233D4×C61—24no—
234D4×C61—41no—
235D4×C61—41no—
236C2×C4×C61—22no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—22no—
240C2×C4×C61—24no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61C2×C22⋊C412yes—
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D412yes—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C2×#4112yes—
250C22⋊D61—48no—
251C2×Dic61—22no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61C2×C22⋊C412yes—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61#12114yes—
263D244—24no—
264D244—41no—
265D244—41no—
266C4×D61—28no—
267C4×D61—28no—
268C4×D61—48no—
269C4×D61—416no—
270C4×D61C4×D418yes—
271C4×D61#12414yes—
272C4×D61#12714yes—
273Dic122—24no—
274Dic122—41no—
275Dic122—41no—
276Dic122—48no—
277C8×C61—42no—
278#92418—42no—
279C2×#1983—611nomaximal, Sylow
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—82no—
284C22×C61—82no—
285C22×C61C22×C22⋊C411yescharacteristic
286C22×C61C2×#12112yes—
287C22×C61C2×#13512yes—
288C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C61C2×#13711yescharacteristic
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—82no—
294C2×D61—82no—
295C2×D61—816no—
296C2×D61#39014yes—
297C2×D61#41614yes—
298C2×D61#41714yes—
299C2×D61#46318yes—
300C2×D61#46418yes—
301C4×C61—22no—
302C4×C61—22no—
303C4×C61—44no—
304C4×C61—42no—
305C4×C61C2×C4×D412yes—
306C4×C61C2×#12411yescharacteristic
307C4×C61C2×#12711yescharacteristic
308Dic61—22no—
309Dic61—22no—
310Dic61—44no—
311Dic61—42no—
312Dic61#39014yes—
313C22×#124—611no—
314C22×C4⋊C8—611no—
315C22×#103—612no—
316C22×#102—612no—
317C2×C4×C4⋊C4—611no—
318#1983—611no—
319#1983—612no—
320#1983—612no—
321#1983—611no—
322#1983—611no—
323#1983D6111yescharacteristic, direct product factor
324C2×C61—82no—
325C2×C61C2×#39011yescharacteristic
326C2×C61C2×#41611yescharacteristic
327C2×C61C2×#41711yescharacteristic
328C2×C61C2×#46312yes—
329C2×C61C2×#46412yes—
330D61—82no—
331D61#198318yesdirect product factor
332C23×Q8—611no—
333C23×D4—611no—
334C23×C8—612no—
335C2×#124—611no—
336C2×#124—611no—
337C2×#124—618no—
338C2×#124—611no—
339C2×#124—1221no—
340C2×#124—1221no—
341C2×#124—1224no—
342C2×#124C2×D6111yescharacteristic
343C22×C4⋊C4—612no—
344C22×C22⋊C4—1221no—
345C22×C22⋊C4—1221no—
346C22×C42—611no—
347C22×C42—1221no—
348C2×C4⋊C8—612no—
349C2×C4⋊C8—611no—
350C2×C4⋊C8—1224no—
351C2×C4⋊C8C2×D6111yescharacteristic, complemented
352C2×#103—612no—
353C2×#103—612no—
354C2×#103—612no—
355C2×#103—1228no—
356C2×#103C2×D6112yescomplemented
357C2×#102—612no—
358C2×#102—612no—
359C2×#102—612no—
360C2×#102—1228no—
361C2×#102C2×D6112yes—
362C4×C4⋊C4—612no—
363C4×C4⋊C4—611no—
364C4×C4⋊C4—1221no—
365C4×C4⋊C4—1221no—
366C4×C4⋊C4C2×D6111yescharacteristic, complemented
367C2×#95—1221no—
368C61C2×#198311yescharacteristic, complemented, Sylow
369C25—1221no—
370C22×Q8—614no—
371C22×Q8—611no—
372C22×Q8—1221no—
373C22×Q8—1222no—
374C22×Q8—1224no—
375C22×Q8—1224no—
376C22×Q8C22×D6111yescharacteristic
377C22×D4—614no—
378C22×D4—611no—
379C22×D4—1224no—
380C22×D4—1224no—
381C22×D4—1222no—
382C22×D4—1221no—
383C22×D4C22×D6111yescharacteristic
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—611no—
387C23×C4—1221no—
388C23×C4—1222no—
389C22×C8—612no—
390C22×C8—1224no—
391C22×C8—1224no—
392C22×C8—1224no—
393C22×C8C22×D6112yes—
394#124—22no—
395#124—614no—
396#124—614no—
397#124—614no—
398#124—1228no—
399#124—1228no—
400#124—1222no—
401#124—1222no—
402#124—1222no—
403#124C4×D6114yescomplemented
404C2×C4⋊C4—612no—
405C2×C4⋊C4—618no—
406C2×C4⋊C4—1224no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4C22×D6112yes—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—1228no—
412C2×C22⋊C4—1228no—
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×C42—21no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—614no—
424C2×C42—614no—
425C2×C42—1222no—
426C2×C42—1221no—
427C2×C42—2444no—
428C2×C42C22×D6111yescharacteristic
429C4⋊C8—22no—
430C4⋊C8—1224no—
431C4⋊C8—1222no—
432#103—24no—
433#103—1224no—
434#103—1224no—
435#103—1224no—
436#102—24no—
437#102—1224no—
438#102—1224no—
439#102—1224no—
440#95—21no—
441#95—1222no—
442#95—1221no—
443C24—21no—
444C24—611no—
445C24—1224no—
446C24—1221no—
447C24—2444no—
448C24—2444no—
449C24—2442no—
450C24—2442no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—612no—
455C2×Q8—1224no—
456C2×Q8—12216no—
457C2×Q8—1221no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×Q8—2444no—
461C2×Q8—2444no—
462C2×Q8—2444no—
463C2×Q8C2×C4×D6112yes—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—612no—
468C2×D4—12216no—
469C2×D4—1224no—
470C2×D4—1222no—
471C2×D4—1221no—
472C2×D4—1222no—
473C2×D4—2444no—
474C2×D4—2444no—
475C2×D4—2444no—
476C2×D4C2×C4×D6112yes—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—611no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—614no—
483C22×C4—614no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—614no—
487C22×C4—614no—
488C22×C4—1222no—
489C22×C4—1224no—
490C22×C4—1222no—
491C22×C4—1224no—
492C22×C4—1228no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—2444no—
496C22×C4—2444no—
497C22×C4—2444no—
498C22×C4D4×D6111yescharacteristic
499C22×C4D4×D6111yescharacteristic
500C22×C4C23×D6111yescharacteristic
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—1222no—
505C2×C8—1222no—
506C2×C8—1222no—
507C2×C8—2448no—
508C4⋊C4—22no—
509C4⋊C4—614no—
510C4⋊C4—1228no—
511C4⋊C4—1222no—
512C4⋊C4D4×D6114yes—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—1224no—
516C22⋊C4—1224no—
517C22⋊C4—1224no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C42—42no—
522C42—612no—
523C42—612no—
524C42—614no—
525C42—614no—
526C42—2442no—
527C42—2444no—
528C42C2×C4×D6112yes—
529C42D4×D6112yes—
530C23—22no—
531C23—42no—
532C23—42no—
533C23—41no—
534C23—41no—
535C23—612no—
536C23—614no—
537C23—614no—
538C23—612no—
539C23—612no—
540C23—1222no—
541C23—4888no—
542C23—4888no—
543C23—2448no—
544C23—2448no—
545C23—2448no—
546C23—2442no—
547C23—2442no—
548C23—2441no—
549C23—2441no—
550C23C2×D4×D6111yescharacteristic
551Q8—24no—
552Q8—41no—
553Q8—41no—
554Q8—1224no—
555Q8—2448no—
556Q8—2441no—
557Q8—2441no—
558D4—24no—
559D4—41no—
560D4—41no—
561D4—1224no—
562D4—2448no—
563D4—2441no—
564D4—2441no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—612no—
574C2×C4—614no—
575C2×C4—618no—
576C2×C4—614no—
577C2×C4—614no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—1228no—
581C2×C4—1228no—
582C2×C4—1222no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1222no—
586C2×C4—1224no—
587C2×C4—24416no—
588C2×C4—2448no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4C22⋊C4×D6112yes—
593C2×C4C22⋊C4×D6112yes—
594C2×C4C22×C4×D6111yescharacteristic
595C2×C4C2×D4×D6112yes—
596C2×C4C2×D4×D6111yescharacteristic
597C2×C4#41×D6112yes—
598C8—42no—
599C8—2442no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—82no—
604C22—82no—
605C22—614no—
606C22—618no—
607C22—618no—
608C22—614no—
609C22—614no—
610C22—48816no—
611C22—4882no—
612C22—4882no—
613C22—2442no—
614C22—2442no—
615C22—2442no—
616C22C2×C22⋊C4×D6111yescharacteristic
617C22#121×D6112yes—
618C22#135×D6112yes—
619C22AGL(1,ℤ/8)×D6111yescharacteristic
620C22#137×D6111yescharacteristic
621C4—22no—
622C4—22no—
623C4—42no—
624C4—44no—
625C4—614no—
626C4—1222no—
627C4—1222no—
628C4—2442no—
629C4—2444no—
630C4C4×D4×D6112yes—
631C4#124×D6111yescharacteristic
632C4#127×D6111yescharacteristic
633C2—82no—
634C2—618no—
635C2—4882no—
636C2#390×D6111yescharacteristic
637C2#416×D6111yescharacteristic
638C2#417×D6111yescharacteristic
639C2#463×D6112yes—
640C2#464×D6112yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61C2×#1983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D61C2semidirect
3. C2×#103×D61C2semidirect
5. C4×C4⋊C4×D61C2semidirect
6. #21446752C2semidirect
7. #21446751C2semidirect
8. #21446750C2semidirect
9. #21446749C2semidirect
10. #21446748C2semidirect
11. C61×#1983C2semidirect
21. #124×D61C4semidirect
27. C2×C4⋊#92418C22semidirect
28. C2×#14519706C22semidirect
30. C2×#14519702C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519700C22semidirect
38. C4⋊C4×Dic61C22semidirect
40. C4×C4⋊Dic61C22semidirect
44. C2×C4⋊C8×C61C22semidirect
45. C2×#103×C61C22semidirect
47. C4×C4⋊C4×C61C22semidirect
71. #14519766C2×C4semidirect
73. #14519765C2×C4semidirect
75. #14519764C2×C4semidirect
112. #124×C61C2×C4semidirect
323. #1983D61direct (N × H)
331. D61#1983direct (N × H)
351. C2×C4⋊C8C2×D61semidirect
356. C2×#103C2×D61semidirect
366. C4×C4⋊C4C2×D61semidirect
368. C61C2×#1983semidirect
403. #124C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D612
C2×C4⋊C8×D612
C2×#103×D612
C2×#102×D612
C4×C4⋊C4×D612
#214467522
#214467512
#214467502
#214467492
#214467482
C61×#19832
C2×#198361