Finite Group Databasebeta

← D61⋊#2128 #30623963

Subgroups — D61⋊#2128 #30623963

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#410C212yesmaximal, complemented
2#21462100C212yesmaximal, complemented
3#21462099C214yesmaximal, complemented
4#21462098C212yesmaximal, complemented
5D61⋊#353C214yesmaximal, complemented
6#535×D61C211yesmaximal, characteristic
7C2×#14519856—22no—
8#16840743C2214yescomplemented
9#16840742—22no—
10#16840741—22no—
11#16840741C2214yescomplemented
12D61⋊#99—22no—
13D61⋊#99C2214yescomplemented
14#16840667C2218yescomplemented
15#16840666C2218yescomplemented
16C2×#41×D61C2211yescharacteristic
17C22×D4×D61C411yescharacteristic, complemented
18#16840331C2211yescharacteristic
19#16840330C2212yes—
20#16840329C2211yescharacteristic
21#16840328—22no—
22#16840327—22no—
23#16840326C411yescharacteristic, complemented
24#16840325C412yescomplemented
25#127×D61C2212yes—
26#124×D61C412yescomplemented
27#121×D61—22no—
28#120×D61—22no—
29#117×D61C411yescharacteristic, complemented
30C61×#535C411yescharacteristic, complemented
31#14519856—24no—
32#14519856—24no—
33#14519856—42no—
34#14519856—42no—
35C2×C4⋊#6923—42no—
36C2×C22⋊#6923—24no—
37C2×C4×#6923—42no—
38#14519836—24no—
39#14519836C2318yescomplemented
40#14519835—24no—
41#14519835—24no—
42C24×D61—21no—
43C2×#11758226C2311yescharacteristic
44C2×#11758222D412yes—
45C2×#11758222C2311yescharacteristic
46C2×#11758224C2×C411yescharacteristic
47C2×#11758224D412yes—
48#41×D61—42no—
49#41×D61—42no—
50C2×Q8×D61C2×C411yescharacteristic
51C22×D244C2×C411yescharacteristic, complemented
52C22×C22⋊D61—21no—
53C2×D4×D61—24no—
54C2×D4×D61—21no—
55C2×D4×D61—21no—
56C2×D4×D61—42no—
57C2×D4×D61—42no—
58C2×D4×D61C2×C412yes—
59C2×D4×D61C2×C412yescomplemented
60C2×D4×D61D412yes—
61C2×D4×D61C2311yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D412yes—
64#14519774C2312yes—
65#14519773—24no—
66#14519773C2×C412yes—
67#14519773C2312yes—
68#14519766C2×C412yescomplemented
69#14519765C2×C412yescomplemented
70#14519764C2×C412yescomplemented
71#14519763—24no—
72#14519752—22no—
73#14519751—22no—
74#14519750—24no—
75#14519749—24no—
76#14519748—22no—
77#14519747—22no—
78#14519747—24no—
79#14519746—22no—
80#14519745—22no—
81#14519745—24no—
82#14519736C2×C411yescharacteristic, complemented
83#14519735—21no—
84#14519734C2×C412yescomplemented
85#14519733—21no—
86C4⋊C4×D61—21no—
87C22⋊C4×D61—21no—
88C22⋊C4×D61—24no—
89C42×D61C2×C412yes—
90C2×#41×C61C2×C411yescharacteristic
91C22×D4×C61C2×C411yescharacteristic, complemented
92#127×C61C2×C412yes—
93#124×C61C2×C412yescomplemented
94#121×C61—22no—
95#120×C61—22no—
96#117×C61C2×C411yescharacteristic, complemented
97C24×C61—21no—
98C23×D61—21no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—42no—
102C23×D61—42no—
103C23×D61—84no—
104C23×D61C22⋊C411yescharacteristic
105C23×D61C2×D412yes—
106C22×#6923—44no—
107#41×C61—42no—
108C2×Q8×C61C22×C411yescharacteristic
109C2×D4×C61—24no—
110C2×D4×C61—21no—
111C2×D4×C61—42no—
112C2×D4×C61C22⋊C412yes—
113C2×D4×C61C22×C412yes—
114C2×D4×C61C22×C411yescharacteristic
115C22×C4×C61C22⋊C412yes—
116C22×C4×C61C22×C411yescharacteristic
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—44no—
122C2×C22⋊D61C22⋊C412yes—
123C2×C22⋊D61C2×D412yes—
124C2×C22⋊D61C2×D412yes—
125C22×Dic61C22⋊C411yescharacteristic
126C22×Dic61C22⋊C412yes—
127#11758226—42no—
128Q8×D61—41no—
129Q8×D61—41no—
130#11758224—42no—
131#11758224—42no—
132#11758224—42no—
133D4×D61—42no—
134D4×D61—42no—
135D4×D61—41no—
136D4×D61—41no—
137D4×D61—44no—
138D4×D61—42no—
139D4×D61—42no—
140D4×D61—44no—
141D4×D61—42no—
142D4×D61—42no—
143D4×D61—88no—
144#11758222—42no—
145#11758222—42no—
146#11758222—42no—
147C2×D244—21no—
148C2×D244—24no—
149C2×D244—42no—
150C2×D244C22×C412yes—
151C2×D244C2×D412yes—
152C2×D244C2411yescharacteristic
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C412yes—
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D412yes—
167C2×Dic122C22⋊C412yes—
168C2×Dic122C22×C411yescharacteristic
169C22⋊#6923—28no—
170C22⋊#6923—44no—
171C4⋊#6923—44no—
172C4⋊#6923—44no—
173C4×#6923—44no—
174C4×#6923—44no—
175C4⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—24no—
178C42×C61C22×C412yes—
179C22⋊Dic61—21no—
180C22⋊Dic61—24no—
181#11758198—22no—
182#11758198—24no—
183#11758198—24no—
184C4⋊Dic61—21no—
185#11758196—22no—
186C4×Dic61—22no—
187C4×Dic61C22×C412yes—
188C23×C61—22no—
189C23×C61—42no—
190C23×C61—82no—
191C23×C61C2×C22⋊C411yescharacteristic
192C23×C61C2×C22⋊C412yes—
193C22×D61—22no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—42no—
199C22×D61—44no—
200C22×D61—44no—
201C22×D61—48no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—84no—
206C22×D61—82no—
207C22×D61—88no—
208C22×D61—88no—
209C22×D61C2×C22⋊C411yescharacteristic
210C22×D61C2×C22⋊C411yescharacteristic
211C22×D61C22×D412yes—
212C2×#6923—48no—
213C2×#6923—88no—
214Q8×C61—41no—
215D4×C61—42no—
216D4×C61—41no—
217D4×C61—42no—
218D4×C61—42no—
219D4×C61—84no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61C2×C22⋊C412yes—
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C22⋊D61—42no—
228C22⋊D61—42no—
229C22⋊D61—42no—
230C22⋊D61—44no—
231C22⋊D61—44no—
232C22⋊D61—84no—
233C22⋊D61—84no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61C2×C22⋊C411yescharacteristic
239C2×Dic61C2×C22⋊C412yes—
240C2×Dic61C2×C22⋊C411yescharacteristic
241D244—42no—
242D244—41no—
243D244—42no—
244D244—42no—
245D244—84no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—44no—
257C4×D61#9912yes—
258C4×D61#9912yes—
259Dic122—42no—
260Dic122—41no—
261C2×#2128—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—22no—
264C22×C61—42no—
265C22×C61—41no—
266C22×C61—44no—
267C22×C61—42no—
268C22×C61—84no—
269C22×C61C22×C22⋊C411yescharacteristic
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—21no—
273C2×D61—42no—
274C2×D61—44no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—41no—
278C2×D61—44no—
279C2×D61—42no—
280C2×D61—82no—
281C2×D61—84no—
282C2×D61—88no—
283C2×D61—84no—
284C2×D61—84no—
285C2×D61C2×#9911yescharacteristic
286C2×D61C2×#9911yescharacteristic
287#6923—88no—
288C4×C61—21no—
289C4×C61—22no—
290C4×C61—42no—
291C4×C61C2×#9912yes—
292Dic61—22no—
293Dic61—21no—
294Dic61—42no—
295Dic61C2×#9912yes—
296C2×#535—611no—
297C2×#410—612no—
298#2128—612no—
299#2128—614no—
300#2128—612no—
301C2×#353—614no—
302C2×C61—21no—
303C2×C61—41no—
304C2×C61—42no—
305C2×C61—82no—
306C2×C61C22×#9911yescharacteristic
307D61—21no—
308D61—42no—
309D61—41no—
310D61—82no—
311D61#212812yescomplemented
312C22×#41—611no—
313C23×D4—611no—
314#535—611no—
315#535—611no—
316#535—612no—
317#535—612no—
318#535—611no—
319#535—1222no—
320#535—1222no—
321#535#692311yescharacteristic, complemented
322C2×#127—612no—
323C2×#124—612no—
324C2×#121—1222no—
325C2×#120—1222no—
326C2×#117—611no—
327C2×#117—1222no—
328#410—614no—
329#410—614no—
330#410—1222no—
331#410—1222no—
332C2×#99—614no—
333C2×#99—1222no—
334#353—618no—
335#353—618no—
336C61C2×#212811yescharacteristic, complemented, Sylow
337C25—1221no—
338C2×#41—611no—
339C2×#41—612no—
340C2×#41—611no—
341C2×#41—612no—
342C2×#41—611no—
343C2×#41—2442no—
344C2×#41—2442no—
345C2×#41C2×#692311yescharacteristic
346C22×Q8—611no—
347C22×D4—612no—
348C22×D4—611no—
349C22×D4—612no—
350C22×D4—612no—
351C22×D4—611no—
352C22×D4—1221no—
353C22×D4—1221no—
354C22×D4—1221no—
355C22×D4—1224no—
356C22×D4—2442no—
357C22×D4—2442no—
358C22×D4C2×#692311yescharacteristic, complemented
359C23×C4—612no—
360C23×C4—611no—
361#127—612no—
362#127—612no—
363#127—612no—
364#127—1224no—
365#127C2×#692312yes—
366#124—612no—
367#124—612no—
368#124—612no—
369#124—1224no—
370#124C2×#692312yescomplemented
371#121—22no—
372#121—1224no—
373#121—1222no—
374#121—1222no—
375#121—1224no—
376#121—1222no—
377#120—22no—
378#120—1222no—
379#120—1224no—
380#120—1224no—
381#120—1222no—
382#120—1222no—
383#117—611no—
384#117—612no—
385#117—1221no—
386#117—1221no—
387#117—1224no—
388#117—1224no—
389#117—2442no—
390#117—2442no—
391#117C2×#692311yescharacteristic, complemented
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—2442no—
394C2×C22⋊C4—1224no—
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1224no—
397C2×C42—612no—
398C2×C42—2442no—
399#99—618no—
400#99—1224no—
401#99—1224no—
402#99—1224no—
403C24—21no—
404C24—612no—
405C24—611no—
406C24—1222no—
407C24—1222no—
408C24—1221no—
409C24—4884no—
410C24—2442no—
411C24—2442no—
412#41—42no—
413#41—2442no—
414#41—2442no—
415#41—2442no—
416#41—2442no—
417#41—2442no—
418#41—2442no—
419#41—2442no—
420C2×Q8—612no—
421C2×Q8—611no—
422C2×Q8—2441no—
423C2×Q8—2441no—
424C2×Q8C22×#692311yescharacteristic
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—42no—
428C2×D4—612no—
429C2×D4—612no—
430C2×D4—612no—
431C2×D4—612no—
432C2×D4—611no—
433C2×D4—612no—
434C2×D4—1224no—
435C2×D4—1222no—
436C2×D4—1222no—
437C2×D4—1224no—
438C2×D4—1224no—
439C2×D4—1221no—
440C2×D4—4888no—
441C2×D4—2442no—
442C2×D4—2442no—
443C2×D4—2442no—
444C2×D4—2441no—
445C2×D4—2441no—
446C2×D4—2442no—
447C2×D4—2442no—
448C2×D4—2442no—
449C2×D4—2442no—
450C2×D4—2444no—
451C2×D4—2444no—
452C2×D4—2444no—
453C2×D4C22⋊#692312yes—
454C2×D4C22×#692312yes—
455C2×D4C22×#692311yescharacteristic
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—2444no—
473C22×C4C22⋊#692312yes—
474C22×C4C22×#692311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—1222no—
477C4⋊C4—1221no—
478C4⋊C4—2444no—
479C4⋊C4—2444no—
480C22⋊C4—21no—
481C22⋊C4—24no—
482C22⋊C4—1224no—
483C22⋊C4—1222no—
484C22⋊C4—1224no—
485C22⋊C4—1221no—
486C22⋊C4—1224no—
487C22⋊C4—1228no—
488C22⋊C4—2444no—
489C42—612no—
490C42—1222no—
491C42—2444no—
492C42—2444no—
493C42C22×#692312yes—
494C23—22no—
495C23—42no—
496C23—82no—
497C23—611no—
498C23—611no—
499C23—612no—
500C23—1222no—
501C23—1222no—
502C23—1221no—
503C23—1221no—
504C23—1222no—
505C23—4882no—
506C23—4884no—
507C23—4888no—
508C23—4888no—
509C23—2442no—
510C23—2442no—
511C23—2442no—
512C23—2448no—
513C23—2444no—
514C23—2444no—
515C23—2442no—
516C23C2×C22⋊#692311yescharacteristic
517C23C2×C22⋊#692312yes—
518Q8—41no—
519Q8—2442no—
520Q8—2441no—
521D4—42no—
522D4—41no—
523D4—42no—
524D4—42no—
525D4—84no—
526D4—4884no—
527D4—4884no—
528D4—4884no—
529D4—2442no—
530D4—2441no—
531D4—2442no—
532D4—2444no—
533D4—2442no—
534D4—2442no—
535D4—2442no—
536D4—2444no—
537D4—2442no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—611no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—611no—
546C2×C4—612no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—4888no—
562C2×C4—2444no—
563C2×C4—2448no—
564C2×C4C2×C22⋊#692312yes—
565C2×C4C2×C22⋊#692311yescharacteristic
566C2×C4C23×#692311yescharacteristic
567C22—21no—
568C22—22no—
569C22—42no—
570C22—41no—
571C22—44no—
572C22—42no—
573C22—84no—
574C22—611no—
575C22—611no—
576C22—1222no—
577C22—1222no—
578C22—1221no—
579C22—4882no—
580C22—4884no—
581C22—4884no—
582C22—4884no—
583C22—4888no—
584C22—2444no—
585C22—2442no—
586C22—2441no—
587C22—2444no—
588C22—2442no—
589C22—2442no—
590C22—2442no—
591C22C22×C22⋊#692311yescharacteristic
592C4—22no—
593C4—21no—
594C4—42no—
595C4—612no—
596C4—1221no—
597C4—1222no—
598C4—4888no—
599C4—2442no—
600C4D61⋊#9912yes—
601C2—21no—
602C2—41no—
603C2—42no—
604C2—82no—
605C2—612no—
606C2—1221no—
607C2—4882no—
608C2—2442no—
609C2—2441no—
610C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#535C4
socleC2×C61C22×#99
prime radical#535×D61C2
cosocleC2×D244C24
hypercenter#535#6923
hypocenterC61C2×#2128
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. D61⋊#410C2semidirect
2. #21462100C2semidirect
3. #21462099C2semidirect
4. #21462098C2semidirect
5. D61⋊#353C2semidirect
8. #16840743C22semidirect
11. #16840741C22semidirect
13. D61⋊#99C22semidirect
14. #16840667C22semidirect
15. #16840666C22semidirect
17. C22×D4×D61C4semidirect
23. #16840326C4semidirect
24. #16840325C4semidirect
26. #124×D61C4semidirect
29. #117×D61C4semidirect
30. C61×#535C4semidirect
39. #14519836C23semidirect
51. C22×D244C2×C4semidirect
59. C2×D4×D61C2×C4semidirect
68. #14519766C2×C4semidirect
69. #14519765C2×C4semidirect
70. #14519764C2×C4semidirect
82. #14519736C2×C4semidirect
84. #14519734C2×C4semidirect
91. C22×D4×C61C2×C4semidirect
93. #124×C61C2×C4semidirect
96. #117×C61C2×C4semidirect
311. D61#2128semidirect
321. #535#6923semidirect
336. C61C2×#2128semidirect
358. C22×D4C2×#6923semidirect
370. #124C2×#6923semidirect
391. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4102
#214621002
#214620992
#214620982
D61⋊#3532
#535×D612
C2×#212861