Finite Group Databasebeta

← D61×#2024 #29707291

Subgroups — D61×#2024 #29707291

Order 15616.

1518 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2C2×#103×D61C212yesmaximal
3#391×D61C211yesmaximal, characteristic
4#21446961C211yesmaximal, characteristic, complemented
5#21446960C211yesmaximal, characteristic, complemented
6#21446959C212yesmaximal, complemented
7#21446958C212yesmaximal, complemented
8#21446957C211yesmaximal, characteristic, complemented
9#340×D61C212yesmaximal
10#336×D61C211yesmaximal, characteristic
11C61×#2024C211yesmaximal, characteristic, complemented
12C22×Q8×D61—21no—
13C22×Q8×D61C2211yescharacteristic
14C22×C8×D61C2212yes—
15C2×#14519777C2211yescharacteristic
16C2×#14519776—21no—
17C2×#14519776C2212yes—
18C2×#14519775—21no—
19C4⋊Q8×D61—28no—
20C2×C4⋊C4×D61—21no—
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2212yes—
23C2×C42×D61C2211yescharacteristic
24C2×#14519702C2212yes—
25C2×#14519701C2212yes—
26C2×#14519700C2212yes—
27#103×D61—28no—
28#16839669C2211yescharacteristic
29#16839668C2211yescharacteristic
30#16839667C2211yescharacteristic
31#16839666—21no—
32#16839666—21no—
33#95×D61—21no—
34#95×D61—21no—
35#16839525C2212yes—
36#16839524C2212yes—
37#16839524C2212yes—
38#16839517C2211yescharacteristic
39#16839516C2212yes—
40C2×C4⋊Q8×C61C2211yescharacteristic
41C2×#103×C61C2212yes—
42C61×#391C2211yescharacteristic
43C61×#340C2212yes—
44C61×#336C2211yescharacteristic
45C22×Dic122—21no—
46C22×Dic122—22no—
47C22×Dic122—21no—
48C22×Dic122C2311yescharacteristic
49C2×Q8×D61—28no—
50C2×Q8×D61—22no—
51C2×Q8×D61—24no—
52C2×Q8×D61—24no—
53C2×Q8×D61—44no—
54C2×Q8×D61—44no—
55C2×Q8×D61Q814yescomplemented
56C22×C4×D61—22no—
57C22×C4×D61—21no—
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×C4×Dic61D411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C42×D61—24no—
85#14519702—24no—
86#14519701—24no—
87#14519700—24no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94C22×Q8×C61—21no—
95C22×Q8×C61C2311yescharacteristic
96C22×C8×C61C2312yes—
97C4⋊Q8×C61—24no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2312yes—
101C2×C42×C61C2311yescharacteristic
102#103×C61—24no—
103#95×C61—21no—
104#95×C61—21no—
105C23×D61C2×D411yescharacteristic
106C2×Q8×C61—24no—
107C2×Q8×C61—21no—
108C2×Q8×C61—22no—
109C2×Q8×C61—22no—
110C2×Q8×C61—42no—
111C2×Q8×C61—42no—
112C2×Q8×C61C2×Q812yescomplemented
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2411yescharacteristic
119C22×Dic61—22no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61C2×D411yescharacteristic
123C22×Dic61C2×D411yescharacteristic
124C22×Dic61C2×D411yescharacteristic
125Q8×D61—216no—
126Q8×D61—432no—
127Q8×D61—48no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—28no—
133C2×C4×D61—24no—
134C2×C4×D61—42no—
135C2×C4×D61—42no—
136C2×C4×D61—44no—
137C2×C4×D61—44no—
138C2×C4×D61—42no—
139C2×C4×D61—42no—
140C2×C4×D61—42no—
141C2×C4×D61SD1614yes—
142C2×C4×D61Q1614yes—
143C2×C4×D61C2×D414yes—
144C2×C4×D61C2×Q812yes—
145C2×C4×D61#4114yes—
146C2×C4×D61#4112yes—
147C2×Dic122—22no—
148C2×Dic122—22no—
149C2×Dic122—24no—
150C2×Dic122—28no—
151C2×Dic122—21no—
152C2×Dic122—24no—
153C2×Dic122—44no—
154C2×Dic122—42no—
155C2×Dic122—42no—
156C2×Dic122—42no—
157C2×Dic122—42no—
158C2×Dic122—44no—
159C2×Dic122C2×Q812yescomplemented
160C2×C8×C61—22no—
161C2×C8×C61—22no—
162C2×C8×C61—22no—
163C4⋊C4×C61—24no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61C2×D414yes—
167C42×C61—22no—
168C4⋊Dic61—24no—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171C4⋊Dic61C2×D414yes—
172#11758196—28no—
173#11758196—28no—
174#11758196—42no—
175C4×Dic61—22no—
176C4×Dic61—22no—
177C4×Dic61—22no—
178C2×#92418—22no—
179C2×#92418—22no—
180C2×#92418—22no—
181C8×D61—48no—
182C23×C61C22×D411yescharacteristic
183C22×D61#12012yes—
184C22×D61C22⋊Q812yes—
185C22×D61#12412yes—
186C22×D61C2×SD1612yes—
187C22×D61C2×Q1612yes—
188C22×D61AGL(1,ℤ/8)12yes—
189C22×D61#13712yes—
190Q8×C61—24no—
191Q8×C61—48no—
192Q8×C61—42no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—24no—
198C2×C4×C61—22no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61C2×SD1612yes—
207C2×C4×C61C2×Q1612yes—
208C2×C4×C61C22×D412yes—
209C2×C4×C61C22×Q811yescharacteristic
210C2×C4×C61C2×#4112yes—
211C2×C4×C61C2×#4111yescharacteristic
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—24no—
217C2×Dic61—22no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61#12012yes—
226C2×Dic61C22⋊Q812yes—
227C2×Dic61#12412yes—
228C2×Dic61C2×SD1612yes—
229C2×Dic61C2×Q1612yes—
230C4×D61—28no—
231C4×D61—28no—
232C4×D61—48no—
233C4×D61—416no—
234C4×D61—84no—
235C4×D61C22⋊Q818yes—
236C4×D61#12418yes—
237Dic122—24no—
238Dic122—416no—
239Dic122—48no—
240Dic122—42no—
241Dic122—48no—
242C8×C61—42no—
243#92418—42no—
244C2×#2024—611nomaximal, Sylow
245C22×C61C2×#12011yescharacteristic
246C22×C61C2×C22⋊Q811yescharacteristic
247C22×C61C2×#12411yescharacteristic
248C22×C61C22×SD1611yescharacteristic
249C22×C61C22×Q1611yescharacteristic
250C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C61C2×#13711yescharacteristic
252C2×D61#39314yes—
253C2×D61#45014yes—
254C2×D61#45114yes—
255C2×D61#47514yes—
256C2×D61#47714yes—
257C2×D61#48714yes—
258C2×D61#48914yes—
259C4×C61—22no—
260C4×C61—22no—
261C4×C61—42no—
262C4×C61—44no—
263C4×C61—81no—
264C4×C61C2×C22⋊Q812yes—
265C4×C61C2×#12412yes—
266Dic61—22no—
267Dic61—22no—
268Dic61—42no—
269Dic61—44no—
270Dic61—81no—
271Dic61#39314yes—
272C22×C4⋊Q8—611no—
273C22×#103—612no—
274C2×#391—611no—
275#2024—612no—
276#2024—611no—
277#2024—612no—
278#2024—611no—
279#2024—611no—
280#2024D6111yescharacteristic, direct product factor
281C2×#340—612no—
282C2×#336—611no—
283C2×C61C2×#39311yescharacteristic
284C2×C61C2×#45011yescharacteristic
285C2×C61C2×#45111yescharacteristic
286C2×C61C2×#47511yescharacteristic
287C2×C61C2×#47711yescharacteristic
288C2×C61C2×#48711yescharacteristic
289C2×C61C2×#48911yescharacteristic
290D61#202418yesdirect product factor
291C23×Q8—611no—
292C23×Q8—1221no—
293C23×C8—612no—
294C2×C4⋊Q8—612no—
295C2×C4⋊Q8—611no—
296C2×C4⋊Q8—1221no—
297C2×C4⋊Q8—1221no—
298C2×C4⋊Q8—1228no—
299C2×C4⋊Q8C2×D6111yescharacteristic
300C22×C4⋊C4—612no—
301C22×C4⋊C4—611no—
302C22×C4⋊C4—1221no—
303C22×C42—611no—
304C2×#103—612no—
305C2×#103—612no—
306C2×#103—612no—
307C2×#103—1228no—
308C2×#103C2×D6112yes—
309#391—611no—
310#391—611no—
311#391—611no—
312#391—1221no—
313#391—1221no—
314#391C2×D6111yescharacteristic
315C2×#95—1221no—
316C2×#95—1221no—
317#340—612no—
318#340—612no—
319#340—612no—
320#340C2×D6112yes—
321#336—612no—
322#336—611no—
323#336C2×D6111yescharacteristic
324C61C2×#202411yescharacteristic, complemented, Sylow
325C22×Q8—21no—
326C22×Q8—614no—
327C22×Q8—611no—
328C22×Q8—1222no—
329C22×Q8—1221no—
330C22×Q8—1222no—
331C22×Q8—1224no—
332C22×Q8—1224no—
333C22×Q8—1228no—
334C22×Q8—1221no—
335C22×Q8—2444no—
336C22×Q8—2444no—
337C22×Q8C22×D6111yescharacteristic
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—1222no—
342C23×C4—1221no—
343C23×C4—1221no—
344C22×C8—612no—
345C22×C8—1224no—
346C22×C8—1224no—
347C22×C8—1224no—
348C22×C8C22×D6112yes—
349C4⋊Q8—24no—
350C4⋊Q8—1224no—
351C4⋊Q8—1224no—
352C4⋊Q8—1228no—
353C4⋊Q8—1228no—
354C4⋊Q8—1224no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—618no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4—1228no—
361C2×C4⋊C4—1224no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4C22×D6111yescharacteristic
367C2×C4⋊C4C22×D6112yes—
368C2×C42—611no—
369C2×C42—611no—
370C2×C42—611no—
371C2×C42—1224no—
372C2×C42C22×D6111yescharacteristic
373#103—24no—
374#103—1224no—
375#103—1224no—
376#103—1224no—
377#95—21no—
378#95—21no—
379#95—1221no—
380#95—1221no—
381#95—1221no—
382#95—1221no—
383#95—1221no—
384#95—1221no—
385C24—611no—
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8—612no—
393C2×Q8—1224no—
394C2×Q8—1224no—
395C2×Q8—1228no—
396C2×Q8—12216no—
397C2×Q8—1221no—
398C2×Q8—1222no—
399C2×Q8—1222no—
400C2×Q8—2442no—
401C2×Q8—2442no—
402C2×Q8—2442no—
403C2×Q8—2444no—
404C2×Q8—2444no—
405C2×Q8—2448no—
406C2×Q8—24432no—
407C2×Q8—2442no—
408C2×Q8Q8×D6112yescomplemented
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—611no—
413C22×C4—614no—
414C22×C4—612no—
415C22×C4—614no—
416C22×C4—612no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—614no—
420C22×C4—614no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1228no—
426C22×C4—1224no—
427C22×C4—1221no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4—2442no—
434C22×C4—2442no—
435C22×C4—2444no—
436C22×C4—2444no—
437C22×C4D4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439C22×C4C23×D6111yescharacteristic
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—1222no—
444C2×C8—1222no—
445C2×C8—1222no—
446C2×C8—2448no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—614no—
451C4⋊C4—1228no—
452C4⋊C4—1228no—
453C4⋊C4—1224no—
454C4⋊C4—1222no—
455C4⋊C4—1222no—
456C4⋊C4—2442no—
457C4⋊C4D4×D6114yes—
458C42—22no—
459C42—1222no—
460C42—1222no—
461C42—1222no—
462C23—612no—
463C23—612no—
464C23—612no—
465C23—612no—
466C23—612no—
467C23—612no—
468C23—612no—
469C23C2×D4×D6111yescharacteristic
470Q8—24no—
471Q8—48no—
472Q8—42no—
473Q8—1224no—
474Q8—2448no—
475Q8—2448no—
476Q8—24416no—
477Q8—2442no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—618no—
495C2×C4—618no—
496C2×C4—612no—
497C2×C4—612no—
498C2×C4—1228no—
499C2×C4—1228no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1224no—
505C2×C4—1222no—
506C2×C4—4884no—
507C2×C4—2448no—
508C2×C4—24416no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4SD16×D6112yes—
517C2×C4Q16×D6112yes—
518C2×C4C2×D4×D6112yes—
519C2×C4C2×Q8×D6111yescharacteristic
520C2×C4#41×D6112yes—
521C2×C4#41×D6111yescharacteristic
522C8—42no—
523C8—2442no—
524C22—614no—
525C22—614no—
526C22—614no—
527C22—614no—
528C22—614no—
529C22—614no—
530C22—614no—
531C22#120×D6111yescharacteristic
532C22C22⋊Q8×D6111yescharacteristic
533C22#124×D6111yescharacteristic
534C22C2×SD16×D6111yescharacteristic
535C22C2×Q16×D6111yescharacteristic
536C22AGL(1,ℤ/8)×D6111yescharacteristic
537C22#137×D6111yescharacteristic
538C4—22no—
539C4—22no—
540C4—42no—
541C4—44no—
542C4—81no—
543C4—614no—
544C4—1222no—
545C4—1222no—
546C4—4881no—
547C4—2442no—
548C4—2444no—
549C4C22⋊Q8×D6112yes—
550C4#124×D6112yes—
551C2—618no—
552C2#393×D6111yescharacteristic
553C2#450×D6111yescharacteristic
554C2#451×D6111yescharacteristic
555C2#475×D6111yescharacteristic
556C2#477×D6111yescharacteristic
557C2#487×D6111yescharacteristic
558C2#489×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2024C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2024D61
hypocenterC61C2×#2024
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
4. #21446961C2semidirect
5. #21446960C2semidirect
6. #21446959C2semidirect
7. #21446958C2semidirect
8. #21446957C2semidirect
11. C61×#2024C2semidirect
55. C2×Q8×D61Q8semidirect
112. C2×Q8×C61C2×Q8semidirect
159. C2×Dic122C2×Q8semidirect
280. #2024D61direct (N × H)
290. D61#2024direct (N × H)
324. C61C2×#2024semidirect
408. C2×Q8Q8×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×#103×D612
#391×D612
#214469612
#214469602
#214469592
#214469582
#214469572
#340×D612
#336×D612
C61×#20242
C2×#202461