Finite Group Databasebeta

← D61⋊#1986 #30616451

Subgroups — D61⋊#1986 #30616451

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D61⋊M16C211yesmaximal, characteristic
2C2×C4×C4⋊#6923C211yesmaximal, characteristic
3#21461996C214yesmaximal, complemented
4#21461995C212yesmaximal, complemented
5#21461994C212yesmaximal, complemented
6#21461495C214yesmaximal
7#533×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C22×C4⋊#6923—21no—
10C22×C4×#6923C2212yes—
11C4×#11758213C2212yes—
12C4×#11758213C2212yes—
13C4×#11758217—21no—
14C4×#11758217—21no—
15#16840721—21no—
16C4×D61⋊C8—21no—
17C4×C4⋊#6923—21no—
18C4×C4⋊#6923—21no—
19C4×C4⋊#6923C2212yes—
20C4×C4⋊#6923C2212yes—
21C2×(C2×#6923)⋊C4—21no—
22#16840632C2218yes—
23#16840632C2218yes—
24#16840319C411yescharacteristic, complemented
25#16840318C2212yes—
26#16840317C2211yescharacteristic
27#16840317C2211yescharacteristic
28#16840316—21no—
29#16840316—21no—
30#16840315C412yescomplemented
31#16840314—21no—
32#16840314—21no—
33C4⋊Q8×D61C411yescharacteristic, complemented
34C4⋊Q8×D61C411yescharacteristic, complemented
35#125×D61C412yescomplemented
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61—21no—
38C4×Q8×D61—21no—
39C4×Q8×D61—21no—
40#117×D61C2212yes—
41C2×C42×D61C2211yescharacteristic
42C61×#533C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758213C2314yes—
45D61⋊M16—24no—
46D61⋊M16Q818yescomplemented
47C2×#11758217—22no—
48C2×D61⋊C8—22no—
49C2×C4⋊#6923—28no—
50C2×C4⋊#6923—22no—
51C2×C4⋊#6923—22no—
52C2×C4×#6923—28no—
53C2×C4×#6923—22no—
54C2×C4×#6923C2314yes—
55#14519832—22no—
56#14519832—22no—
57C4×#92420—22no—
58C4×#92420—22no—
59(C2×#6923)⋊C4—22no—
60(C2×#6923)⋊C4—22no—
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66#14519777C2×C411yescharacteristic, complemented
67#14519777C2×C411yescharacteristic, complemented
68#14519776—21no—
69#14519776—21no—
70#14519776C2×C412yescomplemented
71#14519776C2×C412yescomplemented
72#14519775—21no—
73#14519775—21no—
74#14519769C2×C412yescomplemented
75#14519768C2×C412yescomplemented
76#14519768C2×C412yescomplemented
77#14519767—22no—
78#14519767—22no—
79#14519757—21no—
80#14519757—21no—
81#14519756—21no—
82#14519756—21no—
83#14519755—22no—
84#14519755—22no—
85#14519754—22no—
86#14519754—22no—
87#14519753—21no—
88#14519753—21no—
89Q8×Dic61—21no—
90Q8×Dic61—21no—
91C4×Dic122—21no—
92C4×Dic122—21no—
93C4×Dic122—22no—
94C4×Dic122—22no—
95#14519742—21no—
96#14519742—21no—
97#14519742—22no—
98#14519742—22no—
99#14519736C2×C412yes—
100#14519735C2312yes—
101#14519735C2312yes—
102#14519734—22no—
103#14519733—22no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61C2×C412yes—
109C4⋊C4×D61C2×C412yes—
110C22⋊C4×D61—22no—
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C42×D61—22no—
115C42×D61C2×C411yescharacteristic
116C42×D61C2×C411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61C2311yescharacteristic
122C42×D61C2311yescharacteristic
123C4⋊Q8×C61C2×C411yescharacteristic, complemented
124C4⋊Q8×C61C2×C411yescharacteristic, complemented
125#125×C61C2×C412yescomplemented
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130#117×C61C2×C412yes—
131C2×C42×C61C2×C411yescharacteristic
132C23×D61C2×D411yescharacteristic
133C22×#6923—28no—
134C22×#6923—24no—
135C22×#6923—44no—
136C22×#6923—44no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145Q8×D61—44no—
146Q8×D61—44no—
147C2×C4×D61—24no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—42no—
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×Q814yes—
163C2×C4×D61#4114yes—
164C2×C4×D61C2411yescharacteristic
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—22no—
168C2×Dic122—22no—
169#11758217—28no—
170C2×#92420—24no—
171C4⋊#6923—28no—
172C4⋊#6923—28no—
173C4×#6923—28no—
174C4×#6923—44no—
175#11758213—24no—
176#11758213C2×Q818yescomplemented
177D61⋊C8—28no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C412yes—
183C4⋊C4×C61C22×C412yes—
184C22⋊C4×C61—22no—
185C42×C61—22no—
186C42×C61C22⋊C411yescharacteristic
187C42×C61C22⋊C411yescharacteristic
188C42×C61C22×C411yescharacteristic
189C42×C61C22×C411yescharacteristic
190C22⋊Dic61—22no—
191#11758198—22no—
192#11758198—22no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61C22×C412yes—
198C4⋊Dic61C22×C412yes—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C23×C61C2×C22⋊C411yescharacteristic
223C22×D61—22no—
224C22×D61—22no—
225C22×D61C2×C22⋊C411yescharacteristic
226C22×D61#12412yes—
227C22×D61C4⋊Q812yes—
228C22×D61C22×D411yescharacteristic
229C2×#6923—28no—
230C2×#6923—44no—
231C2×#6923—416no—
232C2×#6923—44no—
233Q8×C61—42no—
234Q8×C61—42no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C4×Q814yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—41no—
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C22⋊Q814yes—
256C2×Dic61C22×D411yescharacteristic
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—44no—
265C4×D61—44no—
266C4×D61#10414yes—
267C4×D61C4×Q814yes—
268C4×D61C22⋊Q814yes—
269C4×D61#12412yes—
270C4×D61C4⋊Q812yes—
271C4×D61C22×Q812yes—
272C4×D61C2×#4112yes—
273Dic122—44no—
274Dic122—42no—
275Dic122—42no—
276Dic122—44no—
277#92420—28no—
278C2×#1986—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—21no—
281C22×C61#39112yes—
282C22×C61C22×C22⋊C411yescharacteristic
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—24no—
286C2×D61—24no—
287C2×D61#39112yes—
288C2×D61C2×#10412yes—
289C2×D61#42112yes—
290C2×D61C2×#12411yescharacteristic
291C2×D61C2×C4⋊Q811yescharacteristic
292#6923—48no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—42no—
297C4×C61—42no—
298C4×C61#39112yes—
299C4×C61C2×#10412yes—
300C4×C61C2×C4×Q812yes—
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61—42no—
305Dic61—42no—
306Dic61#39112yes—
307Dic61C2×#10412yes—
308Dic61C2×C22⋊Q812yes—
309C2×#533—611no—
310C2×C4×M16—611no—
311C2×C4×C4⋊C4—611no—
312#1986—612no—
313#1986—612no—
314#1986—614no—
315C2×#339—614no—
316C2×C61—22no—
317C2×C61C2×#39111yescharacteristic
318C2×C61C22×#10411yescharacteristic
319C2×C61C2×#42111yescharacteristic
320D61—21no—
321D61—21no—
322D61#198614yescomplemented
323C22×M16—612no—
324#533—611no—
325#533—611no—
326#533—612no—
327#533—612no—
328#533—611no—
329#533—1221no—
330#533—1221no—
331#533—1221no—
332#533—1221no—
333#533#692311yescharacteristic, complemented
334C2×C4⋊Q8—611no—
335C2×C4⋊Q8—611no—
336C2×#125—612no—
337C2×C22⋊Q8—1221no—
338C2×C22⋊Q8—1221no—
339C2×C4×Q8—1221no—
340C2×C4×Q8—1221no—
341C2×#117—612no—
342C22×C4⋊C4—1221no—
343C22×C42—611no—
344C22×C42—612no—
345C4×M16—612no—
346C4×M16—612no—
347C4×M16—1221no—
348C4×M16—1221no—
349C2×#97—1221no—
350C2×C4×C8—1221no—
351C4×C4⋊C4—612no—
352C4×C4⋊C4—612no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4—1221no—
355C2×#95—1221no—
356#339—618no—
357#339—618no—
358C61C2×#198611yescharacteristic, complemented, Sylow
359C22×Q8—1221no—
360C22×Q8—1221no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—1222no—
365C2×M16—618no—
366C2×M16—614no—
367C2×M16—1222no—
368C2×M16—1224no—
369C22×C8—1222no—
370C4⋊Q8—612no—
371C4⋊Q8—612no—
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8—1221no—
377C4⋊Q8—1221no—
378C4⋊Q8C2×#692311yescharacteristic, complemented
379C4⋊Q8C2×#692311yescharacteristic, complemented
380#125—612no—
381#125—612no—
382#125—612no—
383#125—1222no—
384#125—1222no—
385#125C2×#692312yescomplemented
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1222no—
391C22⋊Q8—1222no—
392C22⋊Q8—1221no—
393C22⋊Q8—1221no—
394C22⋊Q8—1221no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—1222no—
401C4×Q8—1222no—
402C4×Q8—1222no—
403C4×Q8—1221no—
404C4×Q8—1222no—
405C4×Q8—1221no—
406C4×Q8—1221no—
407C4×Q8—1221no—
408C4×Q8—1221no—
409C4×Q8—1221no—
410#117—612no—
411#117—612no—
412#117—612no—
413#117—1222no—
414#117—1222no—
415#117C2×#692312yes—
416C2×C4⋊C4—612no—
417C2×C4⋊C4—612no—
418C2×C4⋊C4—1222no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1222no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1228no—
425C2×C22⋊C4—1222no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—614no—
438C2×C42—1222no—
439C2×C42—1228no—
440C2×C42—1222no—
441C2×C42C2×#692311yescharacteristic
442#97—1222no—
443#97—1222no—
444C4×C8—1222no—
445C4×C8—1222no—
446#95—1222no—
447#95—1222no—
448C24—611no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—1222no—
452C2×Q8—1222no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×Q8—2444no—
456C2×Q8—2444no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—614no—
462C22×C4—614no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—1224no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1224no—
478C22×C4—1228no—
479C22×C4—2442no—
480C22×C4—2444no—
481C22×C4—2444no—
482C22×C4C22⋊#692311yescharacteristic
483C22×C4C22⋊#692311yescharacteristic
484C22×C4C22×#692311yescharacteristic
485M16—618no—
486M16—1224no—
487M16—1228no—
488C2×C8—1224no—
489C2×C8—1228no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—612no—
495C4⋊C4—612no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1228no—
505C4⋊C4—1228no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4C22×#692312yes—
511C4⋊C4C22×#692312yes—
512C22⋊C4—22no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C42—22no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—1222no—
530C42—1222no—
531C42—1228no—
532C42—1222no—
533C42—2444no—
534C42C22⋊#692311yescharacteristic
535C42C22⋊#692311yescharacteristic
536C42C22×#692311yescharacteristic
537C42C22×#692311yescharacteristic
538C23—611no—
539C23—612no—
540C23—612no—
541C23—611no—
542C23—1222no—
543C23—1222no—
544C23C2×C22⋊#692311yescharacteristic
545Q8—42no—
546Q8—42no—
547Q8—2442no—
548Q8—2444no—
549Q8—2444no—
550Q8—2442no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—614no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—614no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—614no—
563C2×C4—614no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1228no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2444no—
581C2×C4—2444no—
582C2×C4—2441no—
583C2×C4—2444no—
584C2×C4—24416no—
585C2×C4—2444no—
586C2×C4C2×C22⋊#692311yescharacteristic
587C2×C4C2×C22⋊#692311yescharacteristic
588C2×C4C2×C22⋊#692311yescharacteristic
589C2×C4C2×C22⋊#692311yescharacteristic
590C2×C4C2×C22⋊#692311yescharacteristic
591C2×C4Q8×#692314yes—
592C2×C4C23×#692311yescharacteristic
593C8—1228no—
594C22—21no—
595C22—21no—
596C22—612no—
597C22—612no—
598C22—612no—
599C22—611no—
600C22—611no—
601C22—1224no—
602C22—1224no—
603C22—1221no—
604C22—1221no—
605C22(C2×#6923)⋊Q812yes—
606C22C22×C22⋊#692311yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—42no—
611C4—42no—
612C4—612no—
613C4—612no—
614C4—612no—
615C4—1221no—
616C4—1221no—
617C4—1221no—
618C4—2448no—
619C4—2442no—
620C4—2442no—
621C4(C2×#6923)⋊Q812yes—
622C4D61⋊#10412yes—
623C4C2×Q8×#692312yes—
624C2—22no—
625C2—614no—
626C2—1221no—
627C2—1221no—
628C2C2×(C2×#6923)⋊Q811yescharacteristic
629C2C2×D61⋊#10411yescharacteristic
630C2D61⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#533C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#533#6923
hypocenterC61C2×#1986
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #21461996C2semidirect
4. #21461995C2semidirect
5. #21461994C2semidirect
24. #16840319C4semidirect
30. #16840315C4semidirect
33. C4⋊Q8×D61C4semidirect
34. C4⋊Q8×D61C4semidirect
35. #125×D61C4semidirect
42. C61×#533C4semidirect
46. D61⋊M16Q8semidirect
66. #14519777C2×C4semidirect
67. #14519777C2×C4semidirect
70. #14519776C2×C4semidirect
71. #14519776C2×C4semidirect
74. #14519769C2×C4semidirect
75. #14519768C2×C4semidirect
76. #14519768C2×C4semidirect
123. C4⋊Q8×C61C2×C4semidirect
124. C4⋊Q8×C61C2×C4semidirect
125. #125×C61C2×C4semidirect
176. #11758213C2×Q8semidirect
322. D61#1986semidirect
333. #533#6923semidirect
358. C61C2×#1986semidirect
378. C4⋊Q8C2×#6923semidirect
379. C4⋊Q8C2×#6923semidirect
385. #125C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C4×D61⋊M162
C2×C4×C4⋊#69232
#214619962
#214619952
#214619942
#214614952
#533×D612
C2×#198661