Finite Group Databasebeta

← D61×#1549 #29648356

Subgroups — D61×#1549 #29648356

Order 15616.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic
3#423×D61C211yesmaximal, characteristic
4#21444505C211yesmaximal, characteristic, complemented
5#21444504C211yesmaximal, characteristic, complemented
6#21444503C211yesmaximal, characteristic, complemented
7#21444502C214yesmaximal, complemented
8#332×D61C214yesmaximal, complemented
9C61×#1549C211yesmaximal, characteristic, complemented
10C22×Q8×D61—21no—
11C2×M16×D61—21no—
12C2×#14519777C2211yescharacteristic
13C2×#14519776—21no—
14C2×#14519776C412yes—
15C2×#14519775—21no—
16C4⋊Q8×D61—21no—
17C4⋊Q8×D61—21no—
18C4⋊Q8×D61—21no—
19C4⋊Q8×D61—21no—
20C4⋊Q8×D61C412yes—
21C4⋊Q8×D61C412yes—
22C4⋊Q8×D61C2212yes—
23C4⋊Q8×D61C2212yes—
24C2×C4⋊C4×D61—21no—
25C2×C4⋊C4×D61C412yes—
26C2×C42×D61C2211yescharacteristic
27#16839815C2211yescharacteristic
28#16839814C2212yes—
29#16839813—21no—
30#16839812—21no—
31#16839786C2211yescharacteristic
32#16839785—21no—
33#16839784—21no—
34#16839784C2212yes—
35C4⋊C8×D61—21no—
36C4⋊C8×D61C2212yes—
37C4⋊C8×D61C2212yes—
38C22⋊C8×D61—21no—
39C4×C8×D61—21no—
40#16839509C2214yescomplemented
41#16839508C2214yescomplemented
42#16839507C2214yescomplemented
43C2×C4⋊Q8×C61C2211yescharacteristic
44C61×#431C2211yescharacteristic
45C61×#423C2211yescharacteristic
46C61×#332C2214yescomplemented
47C22×Dic122—21no—
48C22×Dic122—22no—
49C2×Q8×D61—22no—
50C2×Q8×D61—22no—
51C2×Q8×D61—22no—
52C2×Q8×D61—22no—
53C2×Q8×D61—48no—
54C22×C4×D61—22no—
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C2×#11758194—21no—
59C2×#11758189—22no—
60M16×D61—44no—
61C2×C8×D61—22no—
62C2×C8×D61—22no—
63#14519777—21no—
64#14519777—21no—
65#14519777C2×C412yes—
66#14519777C2312yes—
67#14519776—22no—
68#14519776—22no—
69#14519776—22no—
70#14519776—22no—
71#14519776—22no—
72#14519776—22no—
73#14519776C2×C414yes—
74#14519776C2×C414yes—
75#14519775—22no—
76#14519775—22no—
77#14519775—22no—
78#14519775—22no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61C2×C412yes—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C4⋊C4×D61—22no—
84C4⋊C4×D61—22no—
85C4⋊C4×D61—22no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61C2×C414yes—
90C4⋊C4×D61C2×C414yes—
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C42×D61C2×C411yescharacteristic
95C42×D61C2×C411yescharacteristic
96C42×D61D411yescharacteristic
97C42×D61D411yescharacteristic
98C42×D61D411yescharacteristic
99C42×D61D411yescharacteristic
100C42×D61C2311yescharacteristic
101C42×D61C2311yescharacteristic
102C4⋊#92418—21no—
103C4⋊#92418C2312yes—
104C4⋊#92418C2312yes—
105#14519706—22no—
106#14519706—22no—
107#14519706—22no—
108C22⋊#92418—21no—
109#14519689—22no—
110C4×#92418—21no—
111C8×Dic61—22no—
112C22×Q8×C61—21no—
113C2×M16×C61—21no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61C2×C412yes—
117C4⋊Q8×C61C2312yes—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61C2×C412yes—
120C2×C42×C61C2311yescharacteristic
121C4⋊C8×C61—21no—
122C4⋊C8×C61C2312yes—
123C4⋊C8×C61C2312yes—
124C22⋊C8×C61—21no—
125C4×C8×C61—21no—
126C23×D61C22⋊C411yescharacteristic
127C2×Q8×C61—22no—
128C2×Q8×C61—22no—
129C2×Q8×C61—44no—
130C22×C4×C61—22no—
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×Dic61—22no—
135C22×Dic61C22⋊C411yescharacteristic
136C22×Dic61C22⋊C411yescharacteristic
137C22×Dic61C22⋊C411yescharacteristic
138Q8×D61—48no—
139Q8×D61—48no—
140Q8×D61—48no—
141Q8×D61—48no—
142C2×C4×D61—24no—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—48no—
147C2×C4×D61C22⋊C411yescharacteristic
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61SD1614yes—
154C2×C4×D61Q1614yes—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C22×C411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×Dic122—22no—
162C2×Dic122—22no—
163C2×Dic122—24no—
164C2×Dic122—24no—
165C2×Dic122—48no—
166C2×Dic122—44no—
167M16×C61—42no—
168C2×C8×C61—22no—
169C2×C8×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61C22×C414yes—
174C42×C61C22×C411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61C2411yescharacteristic
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61C22×C414yes—
182#11758196—24no—
183#11758196—24no—
184#11758196—24no—
185#11758196—24no—
186C4×Dic61C22⋊C411yescharacteristic
187C4×Dic61C22⋊C411yescharacteristic
188C4×Dic61C22⋊C411yescharacteristic
189C4×Dic61C22⋊C411yescharacteristic
190C4×Dic61C22⋊C411yescharacteristic
191C4×Dic61C22⋊C411yescharacteristic
192C4×Dic61C22×C411yescharacteristic
193C4×Dic61C22×C411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198#11758194—42no—
199C2×#92418—22no—
200C2×#92418—22no—
201#11758189—44no—
202C8×D61—44no—
203C8×D61—44no—
204C23×C61C2×C22⋊C411yescharacteristic
205C22×D61—22no—
206C22×D61—22no—
207C22×D61#10314yes—
208C22×D61C2×C22⋊C411yescharacteristic
209C22×D61C2×C22⋊C411yescharacteristic
210Q8×C61—44no—
211Q8×C61—44no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—44no—
216C2×C4×C61C2×C22⋊C411yescharacteristic
217C2×C4×C61C2×C22⋊C411yescharacteristic
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×SD1612yes—
220C2×C4×C61C2×Q1612yes—
221C2×C4×C61C23×C411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—24no—
227C2×Dic61—44no—
228C2×Dic61#10314yes—
229C2×Dic61C2×C22⋊C411yescharacteristic
230C2×Dic61C2×C22⋊C411yescharacteristic
231C2×Dic61C2×C22⋊C411yescharacteristic
232C2×Dic61C2×C22⋊C411yescharacteristic
233C2×Dic61C2×C22⋊C411yescharacteristic
234C2×Dic61C2×C22⋊C411yescharacteristic
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—22no—
238C4×D61—22no—
239C4×D61—22no—
240C4×D61—22no—
241C4×D61—48no—
242C4×D61—48no—
243C4×D61#10114yes—
244C4×D61#10314yes—
245C4×D61#10314yes—
246C4×D61C2×SD1612yes—
247C4×D61C2×SD1612yes—
248C4×D61C2×Q1612yes—
249C4×D61C2×Q1612yes—
250C4×D61AGL(1,ℤ/8)14yes—
251Dic122—48no—
252Dic122—44no—
253Dic122—44no—
254Dic122—48no—
255C8×C61—42no—
256C8×C61—42no—
257#92418—42no—
258#92418—42no—
259C2×#1549—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61C2×#10312yes—
263C22×C61C22×C22⋊C411yescharacteristic
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—28no—
267C2×D61C2×#10112yes—
268C2×D61C2×#10312yes—
269C2×D61C2×#10312yes—
270C2×D61#41812yes—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—44no—
274C4×C61C2×#10112yes—
275C4×C61C2×#10312yes—
276C4×C61C22×SD1611yescharacteristic
277C4×C61C22×Q1611yescharacteristic
278C4×C61C2×AGL(1,ℤ/8)12yes—
279Dic61—21no—
280Dic61—21no—
281Dic61—44no—
282Dic61C2×#10112yes—
283Dic61C2×#10312yes—
284Dic61C2×#10312yes—
285Dic61#41812yes—
286C22×C4⋊Q8—611no—
287C2×#431—611no—
288C2×#423—611no—
289#1549—611no—
290#1549—611no—
291#1549—614no—
292#1549—611no—
293#1549D6111yescharacteristic, direct product factor
294C2×#332—614no—
295C2×C61—22no—
296C2×C61C22×#10111yescharacteristic
297C2×C61C22×#10311yescharacteristic
298C2×C61C2×#41811yescharacteristic
299D61—22no—
300D61#154914yesdirect product factor
301C23×Q8—1221no—
302C22×M16—1221no—
303C2×C4⋊Q8—612no—
304C2×C4⋊Q8—612no—
305C2×C4⋊Q8—612no—
306C2×C4⋊Q8—612no—
307C2×C4⋊Q8—612no—
308C2×C4⋊Q8—611no—
309C2×C4⋊Q8—1221no—
310C2×C4⋊Q8—1221no—
311C2×C4⋊Q8—1221no—
312C2×C4⋊Q8—1221no—
313C2×C4⋊Q8—1221no—
314C2×C4⋊Q8—1221no—
315C2×C4⋊Q8C2×D6111yescharacteristic
316C22×C4⋊C4—612no—
317C22×C4⋊C4—1221no—
318C22×C42—611no—
319#431—611no—
320#431—612no—
321#431—1221no—
322#431—1221no—
323#431C2×D6111yescharacteristic
324#423—611no—
325#423—612no—
326#423—1221no—
327#423—1221no—
328#423C2×D6111yescharacteristic
329C2×C4⋊C8—612no—
330C2×C4⋊C8—612no—
331C2×C4⋊C8—1221no—
332C2×C22⋊C8—1221no—
333C2×C4×C8—1221no—
334#332—614no—
335#332—614no—
336#332—614no—
337#332C2×D6114yescomplemented
338C61C2×#154911yescharacteristic, complemented, Sylow
339C22×Q8—21no—
340C22×Q8—1222no—
341C22×Q8—1222no—
342C22×Q8—1222no—
343C22×Q8—1222no—
344C22×Q8—1222no—
345C22×Q8—1221no—
346C22×Q8—2448no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—1222no—
351C2×M16—21no—
352C2×M16—1222no—
353C2×M16—1221no—
354C2×M16—2444no—
355C22×C8—1222no—
356C22×C8—1222no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—614no—
360C4⋊Q8—614no—
361C4⋊Q8—612no—
362C4⋊Q8—612no—
363C4⋊Q8—1222no—
364C4⋊Q8—1222no—
365C4⋊Q8—1222no—
366C4⋊Q8—1222no—
367C4⋊Q8—1222no—
368C4⋊Q8—1222no—
369C4⋊Q8—1222no—
370C4⋊Q8—1222no—
371C4⋊Q8—1222no—
372C4⋊Q8—1222no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C4⋊Q8C4×D6112yes—
376C4⋊Q8C22×D6112yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—612no—
379C2×C4⋊C4—614no—
380C2×C4⋊C4—614no—
381C2×C4⋊C4—1222no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4—1222no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4C4×D6112yes—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42C22×D6111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—612no—
405C4⋊C8—612no—
406C4⋊C8—1222no—
407C4⋊C8—1222no—
408C4⋊C8—1222no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6112yes—
411C4⋊C8C22×D6112yes—
412C22⋊C8—21no—
413C22⋊C8—1222no—
414C22⋊C8—1221no—
415C4×C8—21no—
416C4×C8—1222no—
417C4×C8—1221no—
418C24—611no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—44no—
422C2×Q8—1224no—
423C2×Q8—1224no—
424C2×Q8—1222no—
425C2×Q8—1222no—
426C2×Q8—2444no—
427C2×Q8—2448no—
428C2×Q8—2448no—
429C2×Q8—2448no—
430C2×Q8—2448no—
431C2×Q8—2448no—
432C22×C4—22no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—614no—
441C22×C4—614no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—1224no—
451C22×C4—1224no—
452C22×C4—1224no—
453C22×C4—1224no—
454C22×C4—1222no—
455C22×C4—2448no—
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459M16—42no—
460M16—2444no—
461M16—2442no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—1222no—
465C2×C8—1222no—
466C2×C8—2444no—
467C2×C8—2444no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—614no—
472C4⋊C4—1224no—
473C4⋊C4—1224no—
474C4⋊C4—1224no—
475C4⋊C4—1224no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4C2×C4×D6114yes—
480C42—611no—
481C42—611no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42C2×C4×D6111yescharacteristic
493C42D4×D6111yescharacteristic
494C42D4×D6111yescharacteristic
495C42C23×D6111yescharacteristic
496C23—611no—
497C23—611no—
498C23—614no—
499C23—1222no—
500C23—1222no—
501C23C22⋊C4×D6111yescharacteristic
502Q8—44no—
503Q8—44no—
504Q8—2444no—
505Q8—2448no—
506Q8—2448no—
507Q8—2444no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—614no—
517C2×C4—614no—
518C2×C4—614no—
519C2×C4—614no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—614no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1224no—
536C2×C4—2448no—
537C2×C4—2448no—
538C2×C4—2444no—
539C2×C4C22⋊C4×D6111yescharacteristic
540C2×C4C22⋊C4×D6111yescharacteristic
541C2×C4C22⋊C4×D6111yescharacteristic
542C2×C4SD16×D6112yes—
543C2×C4Q16×D6112yes—
544C2×C4C22×C4×D6111yescharacteristic
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C8—42no—
548C8—42no—
549C8—2442no—
550C8—2442no—
551C22—21no—
552C22—21no—
553C22—612no—
554C22—612no—
555C22—612no—
556C22—612no—
557C22—1228no—
558C22—1221no—
559C22—1221no—
560C22#103×D6112yes—
561C22C2×C22⋊C4×D6111yescharacteristic
562C4—21no—
563C4—21no—
564C4—44no—
565C4—612no—
566C4—612no—
567C4—612no—
568C4—612no—
569C4—1221no—
570C4—1221no—
571C4—2444no—
572C4#101×D6112yes—
573C4#103×D6112yes—
574C4C2×SD16×D6111yescharacteristic
575C4C2×Q16×D6111yescharacteristic
576C4AGL(1,ℤ/8)×D6112yes—
577C2—22no—
578C2—614no—
579C2—1222no—
580C2C2×#101×D6111yescharacteristic
581C2C2×#103×D6111yescharacteristic
582C2#418×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1549C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1549D61
hypocenterC61C2×#1549
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #21444505C2semidirect
5. #21444504C2semidirect
6. #21444503C2semidirect
7. #21444502C2semidirect
8. #332×D61C2semidirect
9. C61×#1549C2semidirect
40. #16839509C22semidirect
41. #16839508C22semidirect
42. #16839507C22semidirect
46. C61×#332C22semidirect
293. #1549D61direct (N × H)
300. D61#1549direct (N × H)
337. #332C2×D61semidirect
338. C61C2×#1549semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
#431×D612
#423×D612
#214445052
#214445042
#214445032
#214445022
#332×D612
C61×#15492
C2×#154961