Finite Group Databasebeta

← D61×#2043 #29707691

Subgroups — D61×#2043 #29707691

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2C2×#103×D61C212yesmaximal
3C2×#103×D61C212yesmaximal
4#389×D61C211yesmaximal, characteristic
5#21447066C211yesmaximal, characteristic, complemented
6#21447065C211yesmaximal, characteristic, complemented
7#21447064C212yesmaximal, complemented
8#21447063C212yesmaximal, complemented
9#21447062C211yesmaximal, characteristic, complemented
10#336×D61C211yesmaximal, characteristic
11C61×#2043C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2212yes—
13C22×C8×D61C2212yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519776—21no—
16C2×#14519776—21no—
17C2×#14519775C2212yes—
18C4⋊Q8×D61—28no—
19C2×C4⋊C4×D61—21no—
20C2×C4⋊C4×D61—21no—
21C2×C4⋊C4×D61—21no—
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24C2×C42×D61C2211yescharacteristic
25C2×#14519702C2212yes—
26C2×#14519702C2212yes—
27C2×#14519701C2212yes—
28C2×#14519701C2212yes—
29C2×#14519700C2212yes—
30C2×#14519700C2212yes—
31#103×D61—28no—
32#103×D61—28no—
33#16839661C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839659—21no—
36#16839658C2211yescharacteristic
37#16839657—21no—
38#95×D61—21no—
39#16839517C2211yescharacteristic
40#16839516C2212yes—
41C2×C4⋊Q8×C61C2211yescharacteristic
42C2×#103×C61C2212yes—
43C2×#103×C61C2212yes—
44C61×#389C2211yescharacteristic
45C61×#336C2211yescharacteristic
46C22×Dic122—22no—
47C22×Dic122C2312yes—
48C2×Q8×D61—24no—
49C2×Q8×D61—24no—
50C2×Q8×D61—24no—
51C2×Q8×D61—24no—
52C2×Q8×D61—24no—
53C2×Q8×D61D418yes—
54C22×C4×D61—22no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C22×#92418C2312yes—
61C2×C8×D61—24no—
62C2×C8×D61—24no—
63C2×C8×D61—24no—
64#14519777—24no—
65#14519776—28no—
66#14519776—28no—
67#14519775—24no—
68#14519775—24no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C4⋊C4×D61—28no—
81C4⋊C4×D61—28no—
82C4⋊C4×D61—22no—
83C4⋊C4×D61—24no—
84C4⋊C4×D61—44no—
85C4⋊C4×D61D414yes—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C42×D61—24no—
90#14519702—24no—
91#14519702—24no—
92#14519701—24no—
93#14519701—24no—
94#14519700—24no—
95#14519700—24no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99C22×Q8×C61C2312yes—
100C22×C8×C61C2312yes—
101C4⋊Q8×C61—24no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C42×C61C2311yescharacteristic
108#103×C61—24no—
109#103×C61—24no—
110#95×C61—21no—
111C23×D61C2×D411yescharacteristic
112C2×Q8×C61—22no—
113C2×Q8×C61—22no—
114C2×Q8×C61—22no—
115C2×Q8×C61—22no—
116C2×Q8×C61—22no—
117C2×Q8×C61C2×D414yes—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2411yescharacteristic
124C22×Dic61—22no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61C2×D411yescharacteristic
128C22×Dic61C2×D411yescharacteristic
129C22×Dic61C2×D411yescharacteristic
130Q8×D61—216no—
131Q8×D61—216no—
132Q8×D61—48no—
133Q8×D61—48no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—28no—
139C2×C4×D61—24no—
140C2×C4×D61—44no—
141C2×C4×D61—44no—
142C2×C4×D61—42no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×C4×D61—42no—
146C2×C4×D61—42no—
147C2×C4×D61SD1614yes—
148C2×C4×D61Q1614yes—
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×D414yes—
151C2×C4×D61#4114yes—
152C2×C4×D61#4112yes—
153C2×Dic122—22no—
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122—28no—
159C2×Dic122—44no—
160C2×Dic122—44no—
161C2×Dic122C2×D414yes—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C4⋊C4×C61—24no—
166C4⋊C4×C61—24no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—42no—
170C4⋊C4×C61C2×D412yes—
171C42×C61—22no—
172C4⋊Dic61—24no—
173C4⋊Dic61—24no—
174C4⋊Dic61—21no—
175C4⋊Dic61—22no—
176C4⋊Dic61—42no—
177C4⋊Dic61C2×D412yes—
178#11758196—28no—
179#11758196—28no—
180#11758196—24no—
181#11758196—42no—
182#11758196—42no—
183#11758196—42no—
184C4×Dic61—22no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C2×#92418—22no—
188C2×#92418—22no—
189C2×#92418—22no—
190C8×D61—48no—
191C23×C61C22×D411yescharacteristic
192C22×D61#12012yes—
193C22×D61#12112yes—
194C22×D61#12412yes—
195C22×D61C2×SD1612yes—
196C22×D61C2×Q1612yes—
197C22×D61#13712yes—
198C22×D61#13712yes—
199Q8×C61—24no—
200Q8×C61—24no—
201Q8×C61—42no—
202Q8×C61—42no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—24no—
208C2×C4×C61—22no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61C2×SD1612yes—
217C2×C4×C61C2×Q1612yes—
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D412yes—
220C2×C4×C61C2×#4112yes—
221C2×C4×C61C2×#4111yescharacteristic
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—24no—
227C2×Dic61—22no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61#12012yes—
236C2×Dic61#12112yes—
237C2×Dic61#12412yes—
238C2×Dic61C2×SD1612yes—
239C2×Dic61C2×Q1612yes—
240C4×D61—28no—
241C4×D61—28no—
242C4×D61—416no—
243C4×D61—48no—
244C4×D61—84no—
245C4×D61#12118yes—
246C4×D61#12318yes—
247Dic122—24no—
248Dic122—24no—
249Dic122—42no—
250Dic122—42no—
251Dic122—416no—
252C8×C61—42no—
253#92418—42no—
254C2×#2043—611nomaximal, Sylow
255C22×C61C2×#12011yescharacteristic
256C22×C61C2×#12111yescharacteristic
257C22×C61C2×#12411yescharacteristic
258C22×C61C22×SD1611yescharacteristic
259C22×C61C22×Q1611yescharacteristic
260C22×C61C2×#13711yescharacteristic
261C22×C61C2×#13711yescharacteristic
262C2×D61#39414yes—
263C2×D61#44814yes—
264C2×D61#45114yes—
265C2×D61#46114yes—
266C2×D61#46214yes—
267C2×D61#48714yes—
268C2×D61#49114yes—
269C4×C61—22no—
270C4×C61—22no—
271C4×C61—44no—
272C4×C61—42no—
273C4×C61—81no—
274C4×C61C2×#12112yes—
275C4×C61C2×#12312yes—
276Dic61—22no—
277Dic61—22no—
278Dic61—44no—
279Dic61—42no—
280Dic61—81no—
281Dic61#39414yes—
282C22×C4⋊Q8—611no—
283C22×#103—612no—
284C22×#103—612no—
285C2×#389—611no—
286#2043—612no—
287#2043—612no—
288#2043—611no—
289#2043—611no—
290#2043—611no—
291#2043D6111yescharacteristic, direct product factor
292C2×#336—611no—
293C2×C61C2×#39411yescharacteristic
294C2×C61C2×#44811yescharacteristic
295C2×C61C2×#45111yescharacteristic
296C2×C61C2×#46111yescharacteristic
297C2×C61C2×#46211yescharacteristic
298C2×C61C2×#48711yescharacteristic
299C2×C61C2×#49111yescharacteristic
300D61#204318yesdirect product factor
301C23×Q8—612no—
302C23×C8—612no—
303C2×C4⋊Q8—612no—
304C2×C4⋊Q8—611no—
305C2×C4⋊Q8—1221no—
306C2×C4⋊Q8—1221no—
307C2×C4⋊Q8—1228no—
308C2×C4⋊Q8C2×D6111yescharacteristic
309C22×C4⋊C4—611no—
310C22×C4⋊C4—611no—
311C22×C4⋊C4—1221no—
312C22×C4⋊C4—1221no—
313C22×C4⋊C4—1221no—
314C22×C42—611no—
315C2×#103—612no—
316C2×#103—612no—
317C2×#103—612no—
318C2×#103—612no—
319C2×#103—612no—
320C2×#103—612no—
321C2×#103—1228no—
322C2×#103—1228no—
323C2×#103C2×D6112yes—
324C2×#103C2×D6112yes—
325#389—611no—
326#389—611no—
327#389—611no—
328#389—1221no—
329#389—1221no—
330#389C2×D6111yescharacteristic
331C2×#95—1221no—
332#336—612no—
333#336—611no—
334#336C2×D6111yescharacteristic
335C61C2×#204311yescharacteristic, complemented, Sylow
336C22×Q8—618no—
337C22×Q8—612no—
338C22×Q8—1222no—
339C22×Q8—1224no—
340C22×Q8—1224no—
341C22×Q8—1224no—
342C22×Q8—1224no—
343C22×Q8—1224no—
344C22×Q8C22×D6112yes—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—1221no—
349C23×C4—1222no—
350C23×C4—1221no—
351C22×C8—612no—
352C22×C8—1224no—
353C22×C8—1224no—
354C22×C8—1224no—
355C22×C8C22×D6112yes—
356C4⋊Q8—24no—
357C4⋊Q8—1224no—
358C4⋊Q8—1228no—
359C4⋊Q8—1228no—
360C4⋊Q8—1224no—
361C4⋊Q8—1224no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—614no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—1222no—
369C2×C4⋊C4—1228no—
370C2×C4⋊C4—1228no—
371C2×C4⋊C4—1224no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4—1222no—
374C2×C4⋊C4—1222no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—2444no—
382C2×C4⋊C4C22×D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—1224no—
388C2×C42C22×D6111yescharacteristic
389#103—24no—
390#103—24no—
391#103—1224no—
392#103—1224no—
393#103—1224no—
394#103—1224no—
395#103—1224no—
396#103—1224no—
397#95—21no—
398#95—1221no—
399#95—1221no—
400#95—1221no—
401C24—611no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—614no—
408C2×Q8—1228no—
409C2×Q8—12216no—
410C2×Q8—12216no—
411C2×Q8—1222no—
412C2×Q8—1222no—
413C2×Q8—1222no—
414C2×Q8—1222no—
415C2×Q8—1222no—
416C2×Q8—2444no—
417C2×Q8—2444no—
418C2×Q8—2448no—
419C2×Q8—2448no—
420C2×Q8D4×D6114yes—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—611no—
425C22×C4—614no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—614no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—614no—
432C22×C4—614no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1224no—
438C22×C4—1228no—
439C22×C4—1221no—
440C22×C4—1222no—
441C22×C4—1221no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4—2442no—
445C22×C4—2442no—
446C22×C4—2444no—
447C22×C4—2444no—
448C22×C4—2442no—
449C22×C4D4×D6111yescharacteristic
450C22×C4D4×D6111yescharacteristic
451C22×C4C23×D6111yescharacteristic
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—1222no—
456C2×C8—1222no—
457C2×C8—1222no—
458C2×C8—2448no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—612no—
465C4⋊C4—1224no—
466C4⋊C4—1228no—
467C4⋊C4—1228no—
468C4⋊C4—1224no—
469C4⋊C4—1224no—
470C4⋊C4—1221no—
471C4⋊C4—1222no—
472C4⋊C4—2442no—
473C4⋊C4—2442no—
474C4⋊C4—2442no—
475C4⋊C4—2442no—
476C4⋊C4D4×D6112yes—
477C42—22no—
478C42—1222no—
479C42—1222no—
480C42—1222no—
481C23—612no—
482C23—612no—
483C23—612no—
484C23—612no—
485C23—612no—
486C23—612no—
487C23—612no—
488C23C2×D4×D6111yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—42no—
492Q8—42no—
493Q8—1224no—
494Q8—1224no—
495Q8—24416no—
496Q8—2442no—
497Q8—2442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—612no—
512C2×C4—612no—
513C2×C4—612no—
514C2×C4—618no—
515C2×C4—618no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—1228no—
519C2×C4—1228no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1224no—
525C2×C4—1222no—
526C2×C4—4884no—
527C2×C4—2448no—
528C2×C4—24416no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4SD16×D6112yes—
537C2×C4Q16×D6112yes—
538C2×C4C2×D4×D6111yescharacteristic
539C2×C4C2×D4×D6112yes—
540C2×C4#41×D6112yes—
541C2×C4#41×D6111yescharacteristic
542C8—42no—
543C8—2442no—
544C22—614no—
545C22—614no—
546C22—614no—
547C22—614no—
548C22—614no—
549C22—614no—
550C22—614no—
551C22#120×D6111yescharacteristic
552C22#121×D6111yescharacteristic
553C22#124×D6111yescharacteristic
554C22C2×SD16×D6111yescharacteristic
555C22C2×Q16×D6111yescharacteristic
556C22#137×D6111yescharacteristic
557C22#137×D6111yescharacteristic
558C4—22no—
559C4—22no—
560C4—44no—
561C4—42no—
562C4—81no—
563C4—614no—
564C4—1222no—
565C4—1222no—
566C4—4881no—
567C4—2444no—
568C4—2442no—
569C4#121×D6112yes—
570C4#123×D6112yes—
571C2—618no—
572C2#394×D6111yescharacteristic
573C2#448×D6111yescharacteristic
574C2#451×D6111yescharacteristic
575C2#461×D6111yescharacteristic
576C2#462×D6111yescharacteristic
577C2#487×D6111yescharacteristic
578C2#491×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2043C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2043D61
hypocenterC61C2×#2043
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
5. #21447066C2semidirect
6. #21447065C2semidirect
7. #21447064C2semidirect
8. #21447063C2semidirect
9. #21447062C2semidirect
11. C61×#2043C2semidirect
291. #2043D61direct (N × H)
300. D61#2043direct (N × H)
335. C61C2×#2043semidirect

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×#103×D612
#389×D612
#214470662
#214470652
#214470642
#214470632
#214470622
#336×D612
C61×#20432
C2×#204361