Finite Group Databasebeta

← #29611247

Subgroups — #29611247

Order 15616.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D61C211yesmaximal, characteristic, complemented
2C2×#16839654C211yesmaximal, characteristic, complemented
3C2×#16839653C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839640C211yesmaximal, characteristic
6C2×#16839640C211yesmaximal, characteristic
7C2×#16839636C211yesmaximal, characteristic, complemented
8#21444055C211yesmaximal, characteristic, complemented
9#21444055C211yesmaximal, characteristic, complemented
10#21444054C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444043C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C2×C42×D61—24no—
35C2×C42×D61—24no—
36C2×C42×D61—24no—
37#16839654—24no—
38#16839653—24no—
39#16839640—24no—
40#16839640—24no—
41#16839640C418yescomplemented
42#16839636—24no—
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244C2×C414yes—
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61C2×C414yes—
94C22×C4×D61D414yes—
95C22×C4×D61D414yes—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198C2×C414yes—
127C2×#11758198C2×C414yescomplemented
128C2×#11758198C2×C414yescomplemented
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—22no—
132C2×C4×Dic61—22no—
133C2×C4×Dic61—22no—
134C2×C4×Dic61—22no—
135C2×C4×Dic61—22no—
136C2×C4×Dic61—22no—
137C2×C4×Dic61D414yescomplemented
138C42×D61—232no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684C2×C414yescomplemented
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C2×C42×C61—22no—
157C2×C42×C61—22no—
158C2×C42×C61D414yescomplemented
159#95×C61—22no—
160#95×C61—22no—
161#95×C61—22no—
162#95×C61—22no—
163#95×C61—22no—
164#95×C61C2×C414yescomplemented
165C24×C61C2411yescharacteristic
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61C22×C412yes—
189C23×D61C22×C412yes—
190C23×D61C2×D412yes—
191C23×D61C2×D412yes—
192C23×D61#4112yes—
193C23×D61#4112yes—
194C23×D61#4112yes—
195C23×D61#4112yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61C22×C412yes—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61#4112yes—
244C22×C4×C61#4112yes—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61C22×C412yes—
278C22×Dic61C22×C412yes—
279C22×Dic61C2×D412yes—
280C22×Dic61C2×D412yes—
281C22×Dic61C2×D412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61#4112yes—
284C22×Dic61#4112yes—
285C22×Dic61#4112yes—
286C22×Dic61#4112yes—
287C2×D244—28no—
288C2×D244—28no—
289C2×D244—28no—
290C2×D244—44no—
291C2×D244—44no—
292C2×D244—44no—
293C2×D244—44no—
294C2×C4×D61—28no—
295C2×C4×D61—28no—
296C2×C4×D61—28no—
297C2×C4×D61—28no—
298C2×C4×D61—28no—
299C2×C4×D61—28no—
300C2×C4×D61—28no—
301C2×C4×D61—28no—
302C2×C4×D61—28no—
303C2×C4×D61—28no—
304C2×C4×D61—28no—
305C2×C4×D61—28no—
306C2×C4×D61—28no—
307C2×C4×D61—28no—
308C2×C4×D61—28no—
309C2×C4×D61—28no—
310C2×C4×D61—28no—
311C2×C4×D61—28no—
312C2×C4×D61—28no—
313C2×C4×D61—28no—
314C2×C4×D61—28no—
315C42×C61—28no—
316#11758198—28no—
317#11758198—28no—
318#11758198—28no—
319#11758198—44no—
320#11758198—44no—
321#11758198—44no—
322#11758198—44no—
323#11758198—44no—
324#11758198—44no—
325C4⋊Dic61—44no—
326#11758196—44no—
327C4×Dic61—28no—
328C4×Dic61—28no—
329C4×Dic61—28no—
330C23×C61C23×C411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C23×C61C2×#4111yescharacteristic
336C23×C61C2×#4111yescharacteristic
337C23×C61C2×#4111yescharacteristic
338C23×C61C2×#4111yescharacteristic
339C23×C61C2×#4111yescharacteristic
340C23×C61C2×#4111yescharacteristic
341C23×C61C2×#4111yescharacteristic
342C23×C61C2×#4111yescharacteristic
343C23×C61C2×#4111yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61#11714yes—
409C22×D61C4×D414yes—
410C22×D61C4×D414yes—
411C22×D61#12114yes—
412C22×D61#12314yes—
413C22×D61#12414yes—
414C22×D61#12614yes—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61C4×D414yes—
462C2×C4×C61#12014yes—
463C2×C4×C61#12114yes—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61C4×D414yes—
504C2×Dic61#12114yes—
505C2×Dic61#12314yes—
506D244—416no—
507C4×D61—232no—
508C4×D61—232no—
509C4×D61—232no—
510#14696—611nomaximal, Sylow
511C22×C61C2×#11711yescharacteristic
512C22×C61C2×C4×D411yescharacteristic
513C22×C61C2×C4×D411yescharacteristic
514C22×C61C2×C4×D411yescharacteristic
515C22×C61C2×C4×D411yescharacteristic
516C22×C61C4×#4111yescharacteristic
517C22×C61C4×#4111yescharacteristic
518C22×C61C2×#12011yescharacteristic
519C22×C61C2×#12111yescharacteristic
520C22×C61C2×#12111yescharacteristic
521C22×C61C2×#12111yescharacteristic
522C22×C61C2×#12311yescharacteristic
523C22×C61C2×#12311yescharacteristic
524C22×C61#52511yescharacteristic
525C22×C61#52511yescharacteristic
526C22×C61#52511yescharacteristic
527C22×C61#52511yescharacteristic
528C22×C61#52511yescharacteristic
529C22×C61#52511yescharacteristic
530C22×C61#52511yescharacteristic
531C22×C61#52511yescharacteristic
532C22×C61#52511yescharacteristic
533C22×C61#52511yescharacteristic
534C22×C61C2×#12411yescharacteristic
535C22×C61C2×#12611yescharacteristic
536C22×C61#52911yescharacteristic
537C22×C61#52911yescharacteristic
538C22×C61#52911yescharacteristic
539C22×C61#52911yescharacteristic
540C22×C61#52911yescharacteristic
541C22×C61#52911yescharacteristic
542C22×C61#52911yescharacteristic
543C22×C61#52911yescharacteristic
544C22×C61#53211yescharacteristic
545C22×C61#53211yescharacteristic
546C2×D61—24no—
547C2×D61—24no—
548C2×D61—24no—
549C2×D61—24no—
550C2×D61—24no—
551C2×D61—24no—
552C2×D61—24no—
553C2×D61—24no—
554C2×D61—24no—
555C2×D61—24no—
556C2×D61—24no—
557C2×D61—24no—
558C2×D61—24no—
559C2×D61—24no—
560C2×D61—42no—
561C2×D61—42no—
562C2×D61—42no—
563C2×D61—42no—
564C2×D61—42no—
565C2×D61—42no—
566C2×D61—42no—
567C2×D61—81no—
568C2×D61—81no—
569C2×D61—81no—
570C2×D61—81no—
571C2×D61—81no—
572C2×D61—81no—
573C2×D61—81no—
574C2×D61—81no—
575C2×D61#38818yescomplemented
576C4×C61—24no—
577C4×C61—24no—
578C4×C61—24no—
579C4×C61—42no—
580C4×C61—42no—
581C4×C61—81no—
582C4×C61—81no—
583Dic61—24no—
584Dic61—24no—
585Dic61—24no—
586Dic61—42no—
587Dic61—81no—
588Dic61—81no—
589C23×C42—611no—
590C2×#388—611no—
591C2×#388—611no—
592C2×#386—611no—
593C2×#386—611no—
594C2×#386—611no—
595C2×#385—611no—
596#1437—611no—
597#1437—611no—
598#1436—611no—
599#1436—611no—
600#1434—611no—
601#1434D6111yescharacteristic, complemented
602C22⋊#95—611no—
603C22⋊#95—611no—
604C2×C61C2×#38811yescharacteristic
605C2×C61#229011yescharacteristic
606C2×C61#229011yescharacteristic
607C2×C61C4×#12011yescharacteristic
608C2×C61C4×#12111yescharacteristic
609C2×C61C4×#12111yescharacteristic
610C2×C61C4×#12311yescharacteristic
611C2×C61#284711yescharacteristic
612C2×C61#284911yescharacteristic
613C2×C61#285011yescharacteristic
614C2×C61#285011yescharacteristic
615C2×C61#285211yescharacteristic
616C2×C61#285211yescharacteristic
617C2×C61#285311yescharacteristic
618C2×C61#285411yescharacteristic
619D61—28no—
620D61—82no—
621C23×D4—611no—
622C24×C4—611no—
623C24×C4—611no—
624C24×C4—611no—
625C22×C4⋊C4—611no—
626C22×C4⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C42—611no—
637C22×C42—611no—
638C22×C42—611no—
639C22×C42—1224no—
640C22×C42—1224no—
641C22×C42—1224no—
642C22×C42C2×D6111yescharacteristic
643#388—1224no—
644#388—1224no—
645#386—618no—
646#386—1224no—
647#386—1224no—
648#385—1224no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95—611no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95C2×D6111yescharacteristic
660C2×#95C2×D6111yescharacteristic
661C2×#95C2×D6111yescharacteristic
662C2×#95C2×D6111yescharacteristic
663C2×#95C2×D6111yescharacteristic
664C2×#95C2×D6111yescharacteristic
665C61#1469611yescharacteristic, complemented, Sylow
666C25—611no—
667C25—611no—
668C22×D4—614no—
669C22×D4—1222no—
670C22×D4—1222no—
671C22×D4—1222no—
672C22×D4—1222no—
673C22×D4—1222no—
674C22×D4—1222no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—614no—
680C23×C4—614no—
681C23×C4—614no—
682C23×C4—611no—
683C23×C4—611no—
684C23×C4—1222no—
685C23×C4—1222no—
686C23×C4—1222no—
687C23×C4—1222no—
688C23×C4—1222no—
689C23×C4—1222no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—1222no—
693C23×C4—1222no—
694C23×C4—1222no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4C22×D6111yescharacteristic
703C23×C4C22×D6111yescharacteristic
704C23×C4C22×D6111yescharacteristic
705C23×C4C22×D6111yescharacteristic
706C23×C4C22×D6111yescharacteristic
707C23×C4C22×D6111yescharacteristic
708C23×C4C22×D6111yescharacteristic
709C2×C4⋊C4—1222no—
710C2×C4⋊C4—1222no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C22⋊C4—614no—
716C2×C22⋊C4—614no—
717C2×C22⋊C4—614no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—1222no—
732C2×C22⋊C4—1222no—
733C2×C22⋊C4—1222no—
734C2×C22⋊C4—1222no—
735C2×C22⋊C4—1222no—
736C2×C22⋊C4—1222no—
737C2×C22⋊C4—1222no—
738C2×C22⋊C4—1222no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—614no—
745C2×C42—12232no—
746C2×C42—1222no—
747C2×C42—1222no—
748C2×C42—1222no—
749C2×C42—1222no—
750C2×C42—1222no—
751C2×C42—1222no—
752C2×C42—1222no—
753C2×C42—1222no—
754C2×C42D24414yescomplemented
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—614no—
761#95—1222no—
762#95—1222no—
763#95—1222no—
764#95—1222no—
765#95—1222no—
766#95—1222no—
767#95—1222no—
768#95—1222no—
769#95—1222no—
770#95C4×D6114yescomplemented
771C24—612no—
772C24—612no—
773C24—612no—
774C24—612no—
775C24—612no—
776C24—612no—
777C24—612no—
778C24—612no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—1221no—
790C24—1221no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24C23×D6111yescharacteristic
802C2×D4—1228no—
803C2×D4—1228no—
804C2×D4—1228no—
805C2×D4—2444no—
806C2×D4—2444no—
807C2×D4—2444no—
808C2×D4—2444no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—612no—
848C22×C4—612no—
849C22×C4—612no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
855C22×C4—612no—
856C22×C4—612no—
857C22×C4—1228no—
858C22×C4—1228no—
859C22×C4—1228no—
860C22×C4—1228no—
861C22×C4—1228no—
862C22×C4—1228no—
863C22×C4—1228no—
864C22×C4—1228no—
865C22×C4—1228no—
866C22×C4—1228no—
867C22×C4—1228no—
868C22×C4—1228no—
869C22×C4—1228no—
870C22×C4—1228no—
871C22×C4—1228no—
872C22×C4—1228no—
873C22×C4—1228no—
874C22×C4—1228no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1228no—
888C22×C4—1228no—
889C22×C4—1228no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4C2×C4×D6112yes—
911C22×C4C2×C4×D6112yes—
912C22×C4C2×C4×D6112yes—
913C22×C4C2×D24412yes—
914C22×C4C2×D24412yes—
915C22×C4C2×D24412yes—
916C22×C4#1175822212yes—
917C22×C4D4×D6112yes—
918C22×C4D4×D6112yes—
919C22×C4D4×D6112yes—
920C22×C4#1175822612yes—
921C4⋊C4—2444no—
922C4⋊C4—2444no—
923C22⋊C4—1228no—
924C22⋊C4—1228no—
925C22⋊C4—1228no—
926C22⋊C4—2444no—
927C22⋊C4—2444no—
928C22⋊C4—2444no—
929C22⋊C4—2444no—
930C22⋊C4—2444no—
931C22⋊C4—2444no—
932C42—28no—
933C42—1228no—
934C42—1228no—
935C42—1228no—
936C23—614no—
937C23—614no—
938C23—614no—
939C23—614no—
940C23—614no—
941C23—614no—
942C23—614no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—1222no—
954C23—1222no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
964C23—1222no—
965C23—1222no—
966C23—1222no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23—2441no—
991C23—2441no—
992C23—2441no—
993C23—2441no—
994C23—2441no—
995C23—2441no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23—2441no—
1002C23—2441no—
1003C23—2441no—
1004C23—2441no—
1005C23—2441no—
1006C23C22×C4×D6111yescharacteristic
1007C23C2×D4×D6111yescharacteristic
1008C23C2×D4×D6111yescharacteristic
1009C23C2×D4×D6111yescharacteristic
1010C23C22×D24411yescharacteristic
1011C23#41×D6111yescharacteristic
1012C23#41×D6111yescharacteristic
1013C23#41×D6111yescharacteristic
1014C23#41×D6111yescharacteristic
1015C23#41×D6111yescharacteristic
1016C23#41×D6111yescharacteristic
1017C23#41×D6111yescharacteristic
1018C23#41×D6111yescharacteristic
1019C23C2×#1175822211yescharacteristic
1020C23C2×#1175822611yescharacteristic
1021D4—24416no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—614no—
1069C2×C4—614no—
1070C2×C4—614no—
1071C2×C4—12232no—
1072C2×C4—12232no—
1073C2×C4—12232no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—1222no—
1085C2×C4—1222no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4C4×D24414yes—
1114C2×C4#1451974714yes—
1115C2×C4#1451975214yes—
1116C22—618no—
1117C22—1224no—
1118C22—1224no—
1119C22—1224no—
1120C22—1224no—
1121C22—1224no—
1122C22—1224no—
1123C22—1224no—
1124C22—1224no—
1125C22—1224no—
1126C22—1224no—
1127C22—1224no—
1128C22—1224no—
1129C22—1224no—
1130C22—1224no—
1131C22—4881no—
1132C22—4881no—
1133C22—4881no—
1134C22—4881no—
1135C22—4881no—
1136C22—4881no—
1137C22—4881no—
1138C22—4881no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2442no—
1143C22—2442no—
1144C22—2442no—
1145C22—2442no—
1146C22#117×D6111yescharacteristic
1147C22C4×D4×D6111yescharacteristic
1148C22C4×D4×D6111yescharacteristic
1149C22C4×D4×D6111yescharacteristic
1150C22C2×C4×D24411yescharacteristic
1151C22#1684023011yescharacteristic
1152C22C4×#1175822611yescharacteristic
1153C22C2×#1451974711yescharacteristic
1154C22#121×D6111yescharacteristic
1155C22#121×D6111yescharacteristic
1156C22C2×#1451975211yescharacteristic
1157C22#123×D6111yescharacteristic
1158C22#123×D6111yescharacteristic
1159C22#1684027011yescharacteristic
1160C22#1684027011yescharacteristic
1161C22#1684027111yescharacteristic
1162C22#1684027111yescharacteristic
1163C22#1684027411yescharacteristic
1164C22#1684027411yescharacteristic
1165C22#1684027411yescharacteristic
1166C22#1684027411yescharacteristic
1167C22#1684027511yescharacteristic
1168C22#1684027511yescharacteristic
1169C22#124×D6111yescharacteristic
1170C22#126×D6111yescharacteristic
1171C22#1684029011yescharacteristic
1172C22#1684029011yescharacteristic
1173C22#1684029511yescharacteristic
1174C22#1684029511yescharacteristic
1175C22#1684029511yescharacteristic
1176C22#1684029711yescharacteristic
1177C22#1684029711yescharacteristic
1178C22#1684029911yescharacteristic
1179C22#1684030911yescharacteristic
1180C22#1684031111yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—81no—
1187C4—81no—
1188C4—1224no—
1189C4—1224no—
1190C4—1224no—
1191C4—4881no—
1192C4—4881no—
1193C4—2442no—
1194C2—1228no—
1195C2—4882no—
1196C2#388×D6111yescharacteristic
1197C2#2144825711yescharacteristic
1198C2#2144826311yescharacteristic
1199C2C4×#1451974711yescharacteristic
1200C2#2144833111yescharacteristic
1201C2C4×#1451975211yescharacteristic
1202C2#2144834011yescharacteristic
1203C2#2145410211yescharacteristic
1204C2#2145411211yescharacteristic
1205C2#2145411711yescharacteristic
1206C2#2145412111yescharacteristic
1207C2#2145413511yescharacteristic
1208C2#2145413711yescharacteristic
1209C2#2145414311yescharacteristic
1210C2#2145414611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#14696
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×C42×D61C2semidirect
2. C2×#16839654C2semidirect
3. C2×#16839653C2semidirect
7. C2×#16839636C2semidirect
8. #21444055C2semidirect
9. #21444055C2semidirect
10. #21444054C2semidirect
11. #21444053C2semidirect
12. #21444043C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1434C2semidirect
41. #16839640C4semidirect
127. C2×#11758198C2×C4semidirect
128. C2×#11758198C2×C4semidirect
137. C2×C4×Dic61D4semidirect
148. #14519684C2×C4semidirect
158. C2×C42×C61D4semidirect
164. #95×C61C2×C4semidirect
575. C2×D61#388semidirect
601. #1434D61semidirect
665. C61#14696semidirect
754. C2×C42D244semidirect
770. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D612
C2×#168396542
C2×#168396532
C2×#168396402
C2×#168396362
#214440552
#214440542
#214440532
#214440432
#214440402
C61×#14342
#1469661