Finite Group Databasebeta

← D61×#1512 #29647251

Subgroups — D61×#1512 #29647251

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#432×D61C211yesmaximal, characteristic, complemented
3#382×D61C211yesmaximal, characteristic, complemented
4#21444358C211yesmaximal, characteristic, complemented
5#21444357C211yesmaximal, characteristic, complemented
6#21444356C212yesmaximal, complemented
7#21444355C211yesmaximal, characteristic, complemented
8#21444354C212yesmaximal, complemented
9#328×D61C212yesmaximal, complemented
10#327×D61C212yesmaximal
11C61×#1512C211yesmaximal, characteristic, complemented
12#16840299C411yescharacteristic, complemented
13#16840298C2211yescharacteristic
14#16840297C411yescharacteristic, complemented
15#16840296C2211yescharacteristic
16#16840295—21no—
17#16840294C411yescharacteristic, complemented
18#16840293C2211yescharacteristic
19#16840292—21no—
20#16840291C411yescharacteristic, complemented
21#16840290—21no—
22#16840289—21no—
23#126×D61—21no—
24#125×D61C411yescharacteristic, complemented
25#124×D61C411yescharacteristic, complemented
26#123×D61—21no—
27C22⋊Q8×D61C2211yescharacteristic
28#121×D61C2211yescharacteristic
29C4×Q8×D61C411yescharacteristic, complemented
30C4×D4×D61—21no—
31C4×D4×D61C411yescharacteristic, complemented
32#117×D61—21no—
33C2×C4⋊C4×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839819C2211yescharacteristic, complemented
36#16839818—21no—
37#16839817—21no—
38#16839816C2212yescomplemented
39C4⋊C8×D61—21no—
40C22⋊C8×D61C2212yes—
41#97×D61—21no—
42#16839628C2211yescharacteristic, complemented
43#16839627—21no—
44#16839626—21no—
45#16839626C2212yescomplemented
46#95×D61—21no—
47#95×D61C2212yes—
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic, complemented
56C61×#382C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yes—
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—22no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×C8×D61—22no—
68#14519772—21no—
69#14519772—21no—
70#14519772—21no—
71#14519771—21no—
72#14519770—21no—
73#14519770—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic, complemented
76#14519768C2×C411yescharacteristic, complemented
77#14519768C2×C411yescharacteristic, complemented
78#14519767—21no—
79#14519767—21no—
80#14519766C2×C411yescharacteristic, complemented
81#14519765C2×C411yescharacteristic, complemented
82#14519764C2×C411yescharacteristic, complemented
83#14519763—21no—
84#14519763—21no—
85#14519762—21no—
86#14519762—21no—
87#14519761—21no—
88#14519760—21no—
89#14519759—21no—
90#14519759—21no—
91#14519758—21no—
92#14519757C2×C411yescharacteristic
93#14519756C2311yescharacteristic
94#14519755—21no—
95#14519754—21no—
96#14519753C2×C411yescharacteristic
97#14519752C2×C411yescharacteristic
98#14519751C2311yescharacteristic
99#14519750—21no—
100#14519749—21no—
101#14519748C2×C411yescharacteristic
102Q8×Dic61C2×C411yescharacteristic, complemented
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic, complemented
105#14519742—21no—
106#14519742C2×C411yescharacteristic, complemented
107C4×D244—21no—
108C4×D244C2×C411yescharacteristic, complemented
109D4×Dic61—21no—
110D4×Dic61C2×C411yescharacteristic, complemented
111#14519739—21no—
112#14519739C2×C411yescharacteristic, complemented
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116#14519737—21no—
117#14519737—21no—
118#14519737—21no—
119#14519736—21no—
120#14519735—21no—
121#14519735—21no—
122#14519734—21no—
123#14519734—21no—
124#14519733—21no—
125#14519733—21no—
126C2×C4⋊Dic61—21no—
127C2×#11758196—22no—
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—44no—
133C4⋊C4×D61C2×C411yescharacteristic
134C4⋊C4×D61C2×C411yescharacteristic
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143C42×D61—21no—
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C4⋊#92418—21no—
153#14519706—22no—
154C22⋊#92418C2312yes—
155#14519689—22no—
156#14519688—21no—
157#14519687—22no—
158#14519684—21no—
159#14519684—22no—
160#14519684—22no—
161#14519684C2312yes—
162#126×C61—21no—
163#125×C61C2×C411yescharacteristic, complemented
164#124×C61C2×C411yescharacteristic, complemented
165#123×C61—21no—
166C22⋊Q8×C61C2311yescharacteristic
167#121×C61C2311yescharacteristic
168C4×Q8×C61C2×C411yescharacteristic, complemented
169C4×D4×C61—21no—
170C4×D4×C61C2×C411yescharacteristic, complemented
171#117×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C22⋊C8×C61C2312yes—
176#97×C61—21no—
177#95×C61—21no—
178#95×C61C2312yes—
179C23×D61—21no—
180C23×D61C2×D411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—22no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197Q8×D61—42no—
198D4×D61—42no—
199D4×D61—42no—
200D4×D61—42no—
201C2×D244—21no—
202C2×D244C22×C411yescharacteristic
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22×C411yescharacteristic
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×Dic122—21no—
229C2×Dic122C22×C411yescharacteristic
230C2×C8×C61—22no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—42no—
236C4⋊C4×C61C22×C411yescharacteristic
237C4⋊C4×C61C22×C411yescharacteristic
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C42×C61—21no—
244C42×C61C22×C411yescharacteristic
245C42×C61C22×C411yescharacteristic
246C42×C61C2×D411yescharacteristic
247C42×C61C2×D411yescharacteristic
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—42no—
268C4⋊Dic61C22×C411yescharacteristic
269C4⋊Dic61C22×C411yescharacteristic
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—44no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22⋊C411yescharacteristic
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22⋊C411yescharacteristic
292C4×Dic61C22×C411yescharacteristic
293C4×Dic61C22×C411yescharacteristic
294C4×Dic61C2×D411yescharacteristic
295C4×Dic61C2×D411yescharacteristic
296C2×#92418—22no—
297C8×D61—44no—
298C23×C61—21no—
299C23×C61C22×D411yescharacteristic
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—21no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61C2×C22⋊C411yescharacteristic
307C22×D61C2×C22⋊C411yescharacteristic
308C22×D61AGL(1,ℤ/8)12yes—
309C22×D61#13712yes—
310Q8×C61—41no—
311D4×C61—41no—
312D4×C61—41no—
313D4×C61—41no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C22⋊D61—42no—
332C22⋊D61—41no—
333C22⋊D61—41no—
334C22⋊D61—42no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352D244—41no—
353D244—42no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—42no—
369C4×D61—42no—
370C4×D61—42no—
371C4×D61—88no—
372Dic122—42no—
373Dic122—41no—
374C8×C61—42no—
375#92418—42no—
376C2×#1512—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61C22×C22⋊C411yescharacteristic
383C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C61C2×#13711yescharacteristic
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—84no—
393C2×D61#41012yes—
394C2×D61#41712yes—
395C2×D61#41712yes—
396C2×D61#42112yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61—82no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—41no—
414Dic61—41no—
415Dic61—41no—
416Dic61—82no—
417C2×#529—611no—
418C2×#432—611no—
419C2×#382—611no—
420#1512—611no—
421#1512—611no—
422#1512—612no—
423#1512—612no—
424#1512—611no—
425#1512D6111yescharacteristic, direct product factor
426C2×#328—612no—
427C2×#327—612no—
428C2×C61—21no—
429C2×C61—21no—
430C2×C61—81no—
431C2×C61C2×#41011yescharacteristic
432C2×C61C2×#41711yescharacteristic
433C2×C61C2×#42111yescharacteristic
434D61—22no—
435D61—81no—
436D61#151214yesdirect product factor
437#529—611no—
438#529—611no—
439#529—611no—
440#529—611no—
441#529—611no—
442#529—611no—
443#529—611no—
444#529—1221no—
445#529—1221no—
446#529—1221no—
447#529—1221no—
448#529C2×D6111yescharacteristic
449C2×#126—1221no—
450C2×#125—611no—
451C2×#124—611no—
452C2×#123—1221no—
453C2×C22⋊Q8—611no—
454C2×#121—611no—
455C2×C4×Q8—611no—
456C2×C4×D4—611no—
457C2×C4×D4—1221no—
458C2×#117—1221no—
459C22×C4⋊C4—1221no—
460C22×C42—611no—
461#432—611no—
462#432—612no—
463#432—1221no—
464#432—1221no—
465#432C2×D6111yescharacteristic, complemented
466C2×C4⋊C8—1221no—
467C2×C22⋊C8—612no—
468C2×#97—1221no—
469#382—611no—
470#382—612no—
471#382—1221no—
472#382—1221no—
473#382C2×D6111yescharacteristic, complemented
474C2×#95—612no—
475C2×#95—1221no—
476#328—612no—
477#328—612no—
478#328—612no—
479#328C2×D6112yescomplemented
480#327—612no—
481#327—612no—
482#327—612no—
483#327C2×D6112yes—
484C61C2×#151211yescharacteristic, complemented, Sylow
485C22×Q8—611no—
486C22×D4—611no—
487C22×D4—1221no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—1221no—
492C23×C4—1222no—
493C22×C8—1222no—
494#126—21no—
495#126—1221no—
496#126—1221no—
497#126—1221no—
498#126—1221no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#125—611no—
503#125—611no—
504#125—611no—
505#125—1221no—
506#125—1221no—
507#125C4×D6111yescharacteristic, complemented
508#124—611no—
509#124—611no—
510#124—611no—
511#124—1221no—
512#124—1221no—
513#124C4×D6111yescharacteristic, complemented
514#123—21no—
515#123—1221no—
516#123—1221no—
517#123—1221no—
518#123—1221no—
519#123—1221no—
520#123—1221no—
521#123—1221no—
522C22⋊Q8—611no—
523C22⋊Q8—611no—
524C22⋊Q8—611no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527C22⋊Q8C22×D6111yescharacteristic
528#121—611no—
529#121—611no—
530#121—611no—
531#121—1221no—
532#121—1221no—
533#121C22×D6111yescharacteristic
534C4×Q8—611no—
535C4×Q8—611no—
536C4×Q8—611no—
537C4×Q8—1221no—
538C4×Q8—1221no—
539C4×Q8C4×D6111yescharacteristic, complemented
540C4×D4—21no—
541C4×D4—611no—
542C4×D4—611no—
543C4×D4—611no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4C4×D6111yescharacteristic, complemented
554#117—21no—
555#117—1221no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—2444no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—1221no—
589C2×C42C22×D6111yescharacteristic
590C4⋊C8—21no—
591C4⋊C8—1222no—
592C4⋊C8—1221no—
593C22⋊C8—612no—
594C22⋊C8—1222no—
595C22⋊C8C22×D6112yes—
596#97—21no—
597#97—1222no—
598#97—1221no—
599#95—21no—
600#95—612no—
601#95—1222no—
602#95—1222no—
603#95—1221no—
604#95C22×D6112yes—
605C24—611no—
606C24—1221no—
607C2×Q8—611no—
608C2×Q8—1221no—
609C2×Q8—2442no—
610C2×Q8C2×C4×D6111yescharacteristic
611C2×D4—21no—
612C2×D4—611no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4—2442no—
620C2×D4C2×C4×D6111yescharacteristic
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—1221no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1222no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656C2×C8—22no—
657C2×C8—1222no—
658C2×C8—2444no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—611no—
665C4⋊C4—611no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—2442no—
681C4⋊C4—2444no—
682C4⋊C4C2×C4×D6111yescharacteristic
683C4⋊C4C2×C4×D6111yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C42—21no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—1221no—
718C42—1221no—
719C42—1221no—
720C42C2×C4×D6111yescharacteristic
721C42C2×C4×D6111yescharacteristic
722C42D4×D6111yescharacteristic
723C42D4×D6111yescharacteristic
724C23—21no—
725C23—611no—
726C23—611no—
727C23—612no—
728C23—612no—
729C23—1222no—
730C23—1222no—
731C23—1221no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23C2×D4×D6111yescharacteristic
736Q8—41no—
737Q8—2441no—
738Q8—2442no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—2441no—
743D4—2442no—
744D4—2442no—
745D4—2442no—
746D4—2441no—
747D4—2441no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—4888no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4C22⋊C4×D6111yescharacteristic
795C2×C4C22⋊C4×D6111yescharacteristic
796C2×C4C22⋊C4×D6111yescharacteristic
797C2×C4C22⋊C4×D6111yescharacteristic
798C2×C4C22×C4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C8—42no—
801C8—2442no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—612no—
808C22—612no—
809C22—612no—
810C22—612no—
811C22—1224no—
812C22—1224no—
813C22—1221no—
814C22—1221no—
815C22—4884no—
816C22—2441no—
817C22—2441no—
818C22—2441no—
819C22C2×C22⋊C4×D6111yescharacteristic
820C22AGL(1,ℤ/8)×D6111yescharacteristic
821C22#137×D6111yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—82no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—4882no—
839C4—2441no—
840C4—2441no—
841C4—2441no—
842C2—21no—
843C2—21no—
844C2—81no—
845C2—614no—
846C2—1222no—
847C2—4881no—
848C2#410×D6111yescharacteristic
849C2#417×D6111yescharacteristic
850C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1512C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC22×C4×C61C24
hypercenter#1512D61
hypocenterC61C2×#1512
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #432×D61C2semidirect
3. #382×D61C2semidirect
4. #21444358C2semidirect
5. #21444357C2semidirect
6. #21444356C2semidirect
7. #21444355C2semidirect
8. #21444354C2semidirect
9. #328×D61C2semidirect
11. C61×#1512C2semidirect
12. #16840299C4semidirect
14. #16840297C4semidirect
17. #16840294C4semidirect
20. #16840291C4semidirect
24. #125×D61C4semidirect
25. #124×D61C4semidirect
29. C4×Q8×D61C4semidirect
31. C4×D4×D61C4semidirect
35. #16839819C22semidirect
38. #16839816C22semidirect
42. #16839628C22semidirect
45. #16839626C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
55. C61×#432C22semidirect
56. C61×#382C22semidirect
57. C61×#328C22semidirect
75. #14519769C2×C4semidirect
76. #14519768C2×C4semidirect
77. #14519768C2×C4semidirect
80. #14519766C2×C4semidirect
81. #14519765C2×C4semidirect
82. #14519764C2×C4semidirect
102. Q8×Dic61C2×C4semidirect
104. C4×Dic122C2×C4semidirect
106. #14519742C2×C4semidirect
108. C4×D244C2×C4semidirect
110. D4×Dic61C2×C4semidirect
112. #14519739C2×C4semidirect
163. #125×C61C2×C4semidirect
164. #124×C61C2×C4semidirect
168. C4×Q8×C61C2×C4semidirect
170. C4×D4×C61C2×C4semidirect
425. #1512D61direct (N × H)
436. D61#1512direct (N × H)
465. #432C2×D61semidirect
473. #382C2×D61semidirect
479. #328C2×D61semidirect
484. C61C2×#1512semidirect
507. #125C4×D61semidirect
513. #124C4×D61semidirect
539. C4×Q8C4×D61semidirect
553. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#432×D612
#382×D612
#214443582
#214443572
#214443562
#214443552
#214443542
#328×D612
#327×D612
C61×#15122
C2×#151261