Finite Group Databasebeta

← D61⋊#1491 #30610435

Subgroups — D61⋊#1491 #30610435

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic
2C4×D61⋊M16C211yesmaximal, characteristic
3#21461163C212yesmaximal, complemented
4#21461162C214yesmaximal, complemented
5#21461161C212yesmaximal, complemented
6D61⋊(Q8⋊C8)C214yesmaximal, complemented
7C2×C4×Q8×D61C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840785—21no—
10#16840784C2212yes—
11#16840783C2212yes—
12#16840782—21no—
13D61⋊(C4⋊C8)C2212yes—
14D61⋊(C22⋊C8)—21no—
15C4×#11758213—21no—
16C4×#11758213C2212yes—
17C4×#11758217—21no—
18C4×#11758217C2212yes—
19#16840721—21no—
20#16840721—21no—
21C4×D61⋊C8C2212yes—
22#16840612C2218yescomplemented
23Q8⋊#92420C2218yescomplemented
24C22×Q8×D61C411yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×Dic122—21no—
27C2×C4×Dic122C411yescharacteristic
28C2×#14519742—21no—
29C2×#14519742C2211yescharacteristic
30C4×Q8×D61—21no—
31C4×Q8×D61—21no—
32C4×Q8×D61—21no—
33C4×Q8×D61—21no—
34C4×Q8×D61C412yes—
35C4×Q8×D61C412yes—
36C4×Q8×D61C2212yes—
37C4×Q8×D61C2212yes—
38C2×C4⋊C4×D61—21no—
39C2×C4⋊C4×D61C411yescharacteristic
40C2×C42×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44D61⋊M16—28no—
45C2×#11758217—22no—
46C2×D61⋊C8—22no—
47C2×D61⋊C8—22no—
48#14519844—22no—
49C4⋊#92420C2314yes—
50#14519834—22no—
51C22⋊#92420—22no—
52#14519832—22no—
53#14519832—22no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420—22no—
57C4×#92420C2314yes—
58C22×Dic122—21no—
59C22×Dic122C2×C411yescharacteristic
60C2×Q8×D61—28no—
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C2×Q8×D61C2×C412yes—
64C2×Q8×D61C2×C412yes—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70Q8×Dic61—21no—
71Q8×Dic61—21no—
72Q8×Dic61C2×C412yes—
73Q8×Dic61C2312yes—
74C4×Dic122—21no—
75C4×Dic122—21no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78C4×Dic122—22no—
79C4×Dic122—22no—
80C4×Dic122C2×C412yes—
81C4×Dic122C2×C412yes—
82#14519742—22no—
83#14519742—22no—
84#14519742—21no—
85#14519742—21no—
86#14519742—22no—
87#14519742—22no—
88#14519742C2×C412yes—
89#14519742C2312yes—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61C2×C412yes—
102C4⋊C4×D61C2×C412yes—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C42×D61—22no—
110C42×D61—22no—
111C42×D61—22no—
112C42×D61—22no—
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C22×Q8×C61C2×C411yescharacteristic
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61C2×C412yes—
125C4×Q8×C61C2×C412yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61C22⋊C411yescharacteristic
131C2×Q8×C61—24no—
132C2×Q8×C61—21no—
133C2×Q8×C61C22×C412yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144Q8×D61—28no—
145Q8×D61—28no—
146Q8×D61—24no—
147Q8×D61—24no—
148Q8×D61—24no—
149Q8×D61M1618yescomplemented
150C2×C4×D61—28no—
151C2×C4×D61—24no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—24no—
155C2×C4×D61—24no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—44no—
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×Dic122—28no—
172C2×Dic122—21no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175C2×Dic122—24no—
176C2×Dic122C22×C412yes—
177#11758217—28no—
178C2×#92420—24no—
179C2×#92420—24no—
180#11758213—28no—
181D61⋊C8—28no—
182D61⋊C8—44no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61C22×C412yes—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61C22⋊C411yescharacteristic
190C42×C61C22⋊C411yescharacteristic
191C42×C61C22×C411yescharacteristic
192C42×C61C22×C411yescharacteristic
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2411yescharacteristic
221C23×C61C2×C22⋊C411yescharacteristic
222C22×D61—22no—
223C22×D61—22no—
224C22×D61#10414yes—
225C22×D61C2×C22⋊C411yescharacteristic
226C22×D61C2×C22⋊C411yescharacteristic
227Q8×C61—24no—
228Q8×C61—22no—
229Q8×C61C2×M1614yescomplemented
230C2×C4×C61—24no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×Dic61—24no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—42no—
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C22×D411yescharacteristic
255C2×Dic61C22×D411yescharacteristic
256C4×D61—28no—
257C4×D61—28no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61C2×M1614yes—
271C4×D61#13714yes—
272Dic122—28no—
273Dic122—24no—
274Dic122—22no—
275Dic122—28no—
276Dic122C2×M1614yescomplemented
277#92420—28no—
278#92420—44no—
279C2×#1491—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61C2×#10412yes—
283C22×C61C22×C22⋊C411yescharacteristic
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—28no—
287C2×D61#40712yes—
288C2×D61#41912yes—
289C2×D61C2×#10412yes—
290C2×D61C2×#10412yes—
291C4×C61—24no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—42no—
297C4×C61#41912yes—
298C4×C61C22×M1612yes—
299Dic61—21no—
300Dic61—24no—
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61—42no—
305Dic61#40712yes—
306Dic61C2×#13712yes—
307C22×C4×Q8—611no—
308C2×#432—611no—
309C2×C4×M16—611no—
310#1491—612no—
311#1491—614no—
312#1491—612no—
313C2×Q8⋊C8—614no—
314C2×C61—22no—
315C2×C61C2×#40711yescharacteristic
316C2×C61C2×#41911yescharacteristic
317C2×C61C22×#10411yescharacteristic
318D61—22no—
319D61#149114yescomplemented
320C23×Q8—611no—
321C22×M16—1221no—
322C2×C4×Q8—611no—
323C2×C4×Q8—612no—
324C2×C4×Q8—612no—
325C2×C4×Q8—612no—
326C2×C4×Q8—612no—
327C2×C4×Q8—611no—
328C2×C4×Q8—611no—
329C2×C4×Q8—1221no—
330C2×C4×Q8—1221no—
331C2×C4×Q8—1221no—
332C2×C4×Q8—1221no—
333C2×C4×Q8—1221no—
334C2×C4×Q8—1221no—
335C2×C4×Q8#692311yescharacteristic
336C22×C4⋊C4—611no—
337C22×C4⋊C4—1221no—
338C22×C42—611no—
339C22×C42—1221no—
340#432—612no—
341#432—612no—
342#432—1221no—
343#432—1221no—
344C2×C4⋊C8—612no—
345C2×C22⋊C8—1221no—
346C4×M16—612no—
347C4×M16—612no—
348C4×M16—1221no—
349C4×M16—1221no—
350C2×#97—1221no—
351C2×#97—1221no—
352C2×C4×C8—612no—
353Q8⋊C8—618no—
354Q8⋊C8—618no—
355C61C2×#149111yescharacteristic, complemented, Sylow
356C22×Q8—612no—
357C22×Q8—612no—
358C22×Q8—611no—
359C22×Q8—1221no—
360C22×Q8—1221no—
361C22×Q8—1221no—
362C22×Q8—1228no—
363C22×Q8C2×#692311yescharacteristic
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—1221no—
368C23×C4—1221no—
369C2×M16—1222no—
370C2×M16—1222no—
371C2×M16—1228no—
372C22×C8—1222no—
373C22×C8—1222no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—612no—
377C4×Q8—612no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—612no—
381C4×Q8—612no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384C4×Q8—1222no—
385C4×Q8—1222no—
386C4×Q8—1222no—
387C4×Q8—1221no—
388C4×Q8—1221no—
389C4×Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392C4×Q8—1221no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8C2×#692312yes—
397C4×Q8C2×#692312yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—612no—
401C2×C4⋊C4—612no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4C2×#692311yescharacteristic
413C2×C42—21no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1222no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42—1222no—
429C2×C42—1221no—
430C2×C42—1221no—
431C2×C42—1221no—
432C2×C42C2×#692311yescharacteristic
433C4⋊C8—614no—
434C4⋊C8—1222no—
435C22⋊C8—1222no—
436C22⋊C8—1222no—
437#97—1222no—
438#97—1222no—
439#97—1222no—
440#97—1222no—
441C4×C8—614no—
442C4×C8—1222no—
443C24—611no—
444C2×Q8—24no—
445C2×Q8—21no—
446C2×Q8—618no—
447C2×Q8—612no—
448C2×Q8—1222no—
449C2×Q8—1222no—
450C2×Q8—1224no—
451C2×Q8—1228no—
452C2×Q8—1224no—
453C2×Q8—1224no—
454C2×Q8—1228no—
455C2×Q8—1228no—
456C2×Q8—1224no—
457C2×Q8—1221no—
458C2×Q8C22×#692312yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—611no—
462C22×C4—611no—
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—611no—
475C22×C4—611no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1224no—
481C22×C4—1228no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—2444no—
487C22×C4C22⋊#692311yescharacteristic
488C22×C4C22⋊#692311yescharacteristic
489C22×C4C22×#692311yescharacteristic
490M16—1228no—
491M16—1228no—
492C2×C8—1224no—
493C2×C8—1228no—
494C2×C8—1224no—
495C2×C8—2444no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1221no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4C22×#692312yes—
510C42—22no—
511C42—22no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—1222no—
525C42—1222no—
526C42—1222no—
527C42—1222no—
528C42—1222no—
529C42—1222no—
530C42C22⋊#692311yescharacteristic
531C42C22⋊#692311yescharacteristic
532C42C22×#692311yescharacteristic
533C42C22×#692311yescharacteristic
534C23—611no—
535C23—614no—
536C23—611no—
537C23—1222no—
538C23—1222no—
539C23C2×C22⋊#692311yescharacteristic
540Q8—24no—
541Q8—22no—
542Q8—614no—
543Q8—1228no—
544Q8—1228no—
545Q8—1224no—
546Q8—1222no—
547Q8D61⋊M1614yescomplemented
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—614no—
558C2×C4—614no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1228no—
572C2×C4—1228no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—2444no—
582C2×C4—2444no—
583C2×C4—2442no—
584C2×C4C2×C22⋊#692311yescharacteristic
585C2×C4C2×C22⋊#692311yescharacteristic
586C2×C4C2×C22⋊#692311yescharacteristic
587C2×C4C2×C22⋊#692311yescharacteristic
588C2×C4C2×C22⋊#692311yescharacteristic
589C2×C4C23×#692311yescharacteristic
590C8—1228no—
591C8—2444no—
592C22—21no—
593C22—21no—
594C22—612no—
595C22—612no—
596C22—612no—
597C22—612no—
598C22—1228no—
599C22—1221no—
600C22—1221no—
601C22D61⋊#10412yes—
602C22C22×C22⋊#692311yescharacteristic
603C4—24no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—612no—
610C4—612no—
611C4—1221no—
612C4—1224no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—2442no—
617C4#1684075512yes—
618C4C2×D61⋊M1612yes—
619C2—22no—
620C2—614no—
621C2—1222no—
622C2D61⋊#40711yescharacteristic
623C2C2×#1684075511yescharacteristic
624C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461163C2semidirect
4. #21461162C2semidirect
5. #21461161C2semidirect
6. D61⋊(Q8⋊C8)C2semidirect
22. #16840612C22semidirect
23. Q8⋊#92420C22semidirect
149. Q8×D61M16semidirect
229. Q8×C61C2×M16semidirect
276. Dic122C2×M16semidirect
319. D61#1491semidirect
355. C61C2×#1491semidirect
547. Q8D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
C4×D61⋊M162
#214611632
#214611622
#214611612
D61⋊(Q8⋊C8)2
C2×C4×Q8×D612
C2×#149161