Finite Group Databasebeta

← #29611467

Subgroups — #29611467

Order 15616.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic, complemented
2C22×C4×D244C211yesmaximal, characteristic
3C2×#16839683C211yesmaximal, characteristic, complemented
4C2×#16839675C211yesmaximal, characteristic, complemented
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×#16839633C211yesmaximal, characteristic, complemented
7#21444071C211yesmaximal, characteristic, complemented
8#21444065C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444059C211yesmaximal, characteristic
12#21444059C211yesmaximal, characteristic
13#21444052C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519755—24no—
21C2×#14519755—24no—
22C2×#14519755—24no—
23C2×C4×D244—24no—
24C2×C4×D244—24no—
25C2×C4×D244—24no—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41#16839683—24no—
42#16839675—24no—
43#16839636—24no—
44#16839633—24no—
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C22×C4⋊C4×C61C2211yescharacteristic
55C22×C42×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C24×D61C2311yescharacteristic
62C24×D61C2311yescharacteristic
63C22×Dic122—22no—
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—22no—
68C22×Dic122—41no—
69C22×Dic122—41no—
70C22×D244—22no—
71C22×D244—22no—
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—22no—
75C22×D244—22no—
76C22×D244Q814yescomplemented
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
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—41no—
93C22×C4×D61—41no—
94C22×C4×D61—41no—
95C22×C4×D61—41no—
96C22×C4×D61D414yes—
97#14519755—232no—
98C4×D244—232no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—22no—
103C2×C4⋊Dic61—41no—
104C2×C4⋊Dic61D414yes—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196—22no—
108C2×#11758196—22no—
109C2×#11758196—22no—
110C2×#11758196—22no—
111C2×#11758196—22no—
112C2×#11758196—41no—
113C2×#11758196D414yescomplemented
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×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198—22no—
137C2×#11758198—22no—
138C2×#11758198—22no—
139C2×#11758198—41no—
140C2×#11758198—41no—
141C2×#11758198—41no—
142C2×#11758198—41no—
143C2×#11758198D414yes—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—22no—
151#14519684—22no—
152#14519684—22no—
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C2×C4⋊C4×C61—22no—
161C2×C4⋊C4×C61—22no—
162C2×C4⋊C4×C61D414yescomplemented
163C2×C42×C61—22no—
164C2×C42×C61—22no—
165C2×C42×C61—22no—
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—22no—
169#95×C61—22no—
170#95×C61—22no—
171C24×C61C2411yescharacteristic
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×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61C2×D412yes—
197C23×D61C2×D412yes—
198C23×D61C2×Q812yes—
199C23×D61C2×Q812yes—
200C23×D61#4112yes—
201C23×D61#4112yes—
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×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×Q812yes—
249C22×C4×C61#4112yes—
250C22×C4×C61#4112yes—
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×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61C2×D412yes—
287C22×Dic61C2×D412yes—
288C22×Dic61C2×D412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61C2×D412yes—
291C22×Dic61C2×D412yes—
292C22×Dic61#4112yes—
293C2×D244—28no—
294C2×D244—28no—
295C2×D244—28no—
296C2×D244—28no—
297C2×D244—28no—
298C2×D244—28no—
299C2×D244—28no—
300C2×C4×D61—28no—
301C2×C4×D61—28no—
302C2×C4×D61—28no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C2×C4×D61—44no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×C4×D61—44no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×Dic122—28no—
315C2×Dic122—44no—
316C2×Dic122—44no—
317C2×Dic122—44no—
318C2×Dic122—44no—
319C2×Dic122—44no—
320C2×Dic122—44no—
321C4⋊C4×C61—28no—
322C42×C61—28no—
323#11758198—28no—
324#11758198—28no—
325#11758198—28no—
326#11758198—28no—
327#11758198—28no—
328#11758198—28no—
329#11758198—44no—
330#11758198—44no—
331#11758198—44no—
332#11758198—44no—
333C4⋊Dic61—28no—
334C4⋊Dic61—44no—
335#11758196—28no—
336#11758196—28no—
337#11758196—44no—
338C23×C61C22×D411yescharacteristic
339C23×C61C22×D411yescharacteristic
340C23×C61C22×D411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C22×Q811yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61C2×#4111yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C61H(5,𝔽2)11yescharacteristic
351C23×C612−1+411yescharacteristic
352C23×C612−1+411yescharacteristic
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—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
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—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61C22⋊Q814yes—
422C22×D61C22⋊Q814yescomplemented
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—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
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×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61#12014yes—
471C2×C4×C61C22⋊Q814yescomplemented
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—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
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×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61#12014yes—
514D244—232no—
515C4×D61—416no—
516C4×D61—416no—
517Dic122—416no—
518#14723—611nomaximal, Sylow
519C22×C61C2×#12011yescharacteristic
520C22×C61C2×#12011yescharacteristic
521C22×C61C2×C22⋊Q811yescharacteristic
522C22×C61C2×C22⋊Q811yescharacteristic
523C22×C61C2×C22⋊Q811yescharacteristic
524C22×C61#52511yescharacteristic
525C22×C61#52511yescharacteristic
526C22×C61#52511yescharacteristic
527C22×C61#52511yescharacteristic
528C22×C61#52511yescharacteristic
529C22×C61#53211yescharacteristic
530C22×C61#53211yescharacteristic
531C22×C61#53211yescharacteristic
532C22×C61#53411yescharacteristic
533C22×C61#53611yescharacteristic
534C22×C61#53911yescharacteristic
535C22×C61#53911yescharacteristic
536C22×C61#54211yescharacteristic
537C22×C61#54211yescharacteristic
538C22×C61D4211yescharacteristic
539C22×C61D4211yescharacteristic
540C22×C61D4211yescharacteristic
541C22×C61D4211yescharacteristic
542C22×C61#54711yescharacteristic
543C22×C61#54711yescharacteristic
544C22×C61#54811yescharacteristic
545C22×C61#54811yescharacteristic
546C22×C61#54811yescharacteristic
547C22×C61#54811yescharacteristic
548C22×C61D4×Q811yescharacteristic
549C22×C61D4×Q811yescharacteristic
550C22×C61#55111yescharacteristic
551C22×C61#55111yescharacteristic
552C22×C61#55411yescharacteristic
553C22×C61#55411yescharacteristic
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—42no—
568C2×D61—42no—
569C2×D61—42no—
570C2×D61—42no—
571C2×D61—42no—
572C2×D61—42no—
573C2×D61—42no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C4×C61—24no—
585C4×C61—24no—
586C4×C61—42no—
587C4×C61—42no—
588C4×C61—42no—
589C4×C61—42no—
590C4×C61—81no—
591Dic61—24no—
592Dic61—42no—
593Dic61—42no—
594Dic61—42no—
595Dic61—42no—
596Dic61—81no—
597C22×C22⋊Q8—611no—
598C22×C4×D4—611no—
599C2×#395—611no—
600C2×#393—611no—
601C2×#385—611no—
602C2×#385—611no—
603#1441—611no—
604#1439—611no—
605#1439—611no—
606#1439—611no—
607#1438—611no—
608#1438—611no—
609#1436—611no—
610#1436D6111yescharacteristic, complemented
611C22⋊#95—611no—
612C2×C61#238811yescharacteristic
613C2×C61#240311yescharacteristic
614C2×C61#240911yescharacteristic
615C2×C61#243211yescharacteristic
616C2×C61#244911yescharacteristic
617C2×C61#244911yescharacteristic
618C2×C61#245211yescharacteristic
619C2×C61#245211yescharacteristic
620C2×C61#246111yescharacteristic
621C2×C61#246111yescharacteristic
622C2×C61#246311yescharacteristic
623C2×C61#246311yescharacteristic
624C2×C61#256411yescharacteristic
625C2×C61#263811yescharacteristic
626C2×C61#284811yescharacteristic
627D61—44no—
628D61—44no—
629C23×Q8—611no—
630C23×D4—611no—
631C24×C4—611no—
632C24×C4—611no—
633C2×C22⋊Q8—1224no—
634C2×C22⋊Q8—1224no—
635C2×C22⋊Q8—1224no—
636C2×C4×D4—1224no—
637C2×C4×D4—1224no—
638C2×C4×D4—1224no—
639C22×C4⋊C4—611no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4—611no—
644C22×C4⋊C4C2×D6111yescharacteristic
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4—611no—
651C22×C22⋊C4—611no—
652C22×C22⋊C4—611no—
653C22×C22⋊C4—611no—
654C22×C22⋊C4—611no—
655C22×C42C2×D6111yescharacteristic
656#395—1224no—
657#393—1224no—
658#385—1224no—
659#385—1224no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95C2×D6111yescharacteristic
670C2×#95C2×D6111yescharacteristic
671C2×#95C2×D6111yescharacteristic
672C2×#95C2×D6111yescharacteristic
673C2×#95C2×D6111yescharacteristic
674C61#1472311yescharacteristic, complemented, Sylow
675C25—611no—
676C25—611no—
677C22×Q8—1222no—
678C22×Q8—1222no—
679C22×Q8—1222no—
680C22×Q8—1222no—
681C22×Q8—1222no—
682C22×Q8—2441no—
683C22×Q8—2441no—
684C22×D4—614no—
685C22×D4—1222no—
686C22×D4—1222no—
687C22×D4—1222no—
688C22×D4—1222no—
689C22×D4—1222no—
690C22×D4—1222no—
691C23×C4—611no—
692C23×C4—611no—
693C23×C4—611no—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—614no—
697C23×C4—611no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—2441no—
708C23×C4—2441no—
709C23×C4—2441no—
710C23×C4—2441no—
711C23×C4C22×D6111yescharacteristic
712C23×C4C22×D6111yescharacteristic
713C23×C4C22×D6111yescharacteristic
714C23×C4C22×D6111yescharacteristic
715C23×C4C22×D6111yescharacteristic
716C23×C4C22×D6111yescharacteristic
717C23×C4C22×D6111yescharacteristic
718C22⋊Q8—12232no—
719C4×D4—12232no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—614no—
723C2×C4⋊C4—614no—
724C2×C4⋊C4—1222no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4—1222no—
727C2×C4⋊C4—1222no—
728C2×C4⋊C4—1222no—
729C2×C4⋊C4—1222no—
730C2×C4⋊C4—1222no—
731C2×C4⋊C4—1222no—
732C2×C4⋊C4—1222no—
733C2×C4⋊C4—1222no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—2441no—
736C2×C4⋊C4—2441no—
737C2×C4⋊C4D24414yescomplemented
738C2×C22⋊C4—614no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—1222no—
750C2×C22⋊C4—1222no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—1222no—
763C2×C22⋊C4—1222no—
764C2×C22⋊C4—2441no—
765C2×C22⋊C4—2441no—
766C2×C22⋊C4—2441no—
767C2×C22⋊C4—2441no—
768C2×C42—22no—
769C2×C42—22no—
770C2×C42—22no—
771#95—22no—
772#95—22no—
773#95—22no—
774#95—22no—
775#95—22no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—1222no—
784#95—1222no—
785C24—612no—
786C24—612no—
787C24—612no—
788C24—612no—
789C24—612no—
790C24—612no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24—1221no—
804C24—1221no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24—1221no—
810C24—1221no—
811C24—1221no—
812C24—1221no—
813C24—1221no—
814C24—1221no—
815C24C23×D6111yescharacteristic
816C2×Q8—1228no—
817C2×Q8—2444no—
818C2×Q8—2444no—
819C2×Q8—2444no—
820C2×Q8—2444no—
821C2×Q8—2444no—
822C2×Q8—2444no—
823C2×D4—1228no—
824C2×D4—1228no—
825C2×D4—1228no—
826C2×D4—1228no—
827C2×D4—1228no—
828C2×D4—1228no—
829C2×D4—1228no—
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—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—612no—
870C22×C4—612no—
871C22×C4—612no—
872C22×C4—612no—
873C22×C4—612no—
874C22×C4—612no—
875C22×C4—612no—
876C22×C4—1228no—
877C22×C4—1228no—
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—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
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—1228no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—2444no—
915C22×C4—2444no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4C2×D24412yes—
926C22×C4C2×D24412yes—
927C22×C4C2×D24412yes—
928C22×C4#1175822212yes—
929C22×C4#1175822212yes—
930C22×C4D4×D6112yes—
931C22×C4D4×D6112yes—
932C22×C4D4×D6112yes—
933C22×C4D4×D6112yes—
934C22×C4Q8×D6112yes—
935C4⋊C4—28no—
936C4⋊C4—1228no—
937C4⋊C4—1228no—
938C4⋊C4—1228no—
939C4⋊C4—2444no—
940C4⋊C4—2444no—
941C22⋊C4—1228no—
942C22⋊C4—1228no—
943C22⋊C4—1228no—
944C22⋊C4—1228no—
945C22⋊C4—1228no—
946C22⋊C4—1228no—
947C22⋊C4—2444no—
948C22⋊C4—2444no—
949C22⋊C4—2444no—
950C22⋊C4—2444no—
951C42—28no—
952C23—614no—
953C23—614no—
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—1222no—
979C23—1222no—
980C23—1222no—
981C23—1222no—
982C23—1222no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
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—
1006C23—2441no—
1007C23—2441no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23—2441no—
1017C23—2441no—
1018C23—2441no—
1019C23—2441no—
1020C23—2441no—
1021C23—2441no—
1022C23C2×D4×D6111yescharacteristic
1023C23C2×D4×D6111yescharacteristic
1024C23C2×D4×D6111yescharacteristic
1025C23C2×D4×D6111yescharacteristic
1026C23C22×D24411yescharacteristic
1027C23C2×Q8×D6111yescharacteristic
1028C23#41×D6111yescharacteristic
1029C23#41×D6111yescharacteristic
1030C23#41×D6111yescharacteristic
1031C23C2×#1175822211yescharacteristic
1032C23C2×#1175822211yescharacteristic
1033C23#1451982311yescharacteristic
1034C23#1451982311yescharacteristic
1035C23#1451982411yescharacteristic
1036C23#1451982511yescharacteristic
1037Q8—24416no—
1038D4—12232no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—614no—
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—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—24416no—
1106C2×C4—24416no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4#1451974714yes—
1131C2×C4#1451975514yescomplemented
1132C22—1224no—
1133C22—1224no—
1134C22—1224no—
1135C22—1224no—
1136C22—1224no—
1137C22—1224no—
1138C22—2442no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2442no—
1143C22—2442no—
1144C22—2442no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22—2442no—
1149C22—2442no—
1150C22—2442no—
1151C22—2442no—
1152C22—2442no—
1153C22—2442no—
1154C22—2442no—
1155C22—2442no—
1156C22—2442no—
1157C22—2442no—
1158C22—2442no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22#120×D6111yescharacteristic
1163C22C2×#1451974711yescharacteristic
1164C22C22⋊Q8×D6111yescharacteristic
1165C22C22⋊Q8×D6111yescharacteristic
1166C22C2×#1451975511yescharacteristic
1167C22#1684027011yescharacteristic
1168C22#1684027111yescharacteristic
1169C22#1684027111yescharacteristic
1170C22#1684027111yescharacteristic
1171C22#1684027411yescharacteristic
1172C22#1684030911yescharacteristic
1173C22#1684030911yescharacteristic
1174C22#1684031211yescharacteristic
1175C22#1684032311yescharacteristic
1176C22#1684033511yescharacteristic
1177C22#1684035311yescharacteristic
1178C22#1684036011yescharacteristic
1179C22#1684038311yescharacteristic
1180C22#1684038411yescharacteristic
1181C22#1684039611yescharacteristic
1182C22#1684039611yescharacteristic
1183C22D4×D24411yescharacteristic
1184C22D4×D24411yescharacteristic
1185C22#1684041011yescharacteristic
1186C22#1684041311yescharacteristic
1187C22#1684042011yescharacteristic
1188C22#1684042111yescharacteristic
1189C22#1684042211yescharacteristic
1190C22#1684042411yescharacteristic
1191C22#1684042711yescharacteristic
1192C22Q8×D24411yescharacteristic
1193C22#1684043611yescharacteristic
1194C22#1684043711yescharacteristic
1195C22#1684046811yescharacteristic
1196C22#1684047211yescharacteristic
1197C4—24no—
1198C4—24no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—81no—
1204C4—1224no—
1205C4—4881no—
1206C4—2442no—
1207C4—2442no—
1208C4—2442no—
1209C4—2442no—
1210C2—2444no—
1211C2—2444no—
1212C2#2144903511yescharacteristic
1213C2#2144913111yescharacteristic
1214C2#2144918211yescharacteristic
1215C2#2144944511yescharacteristic
1216C2#2144963311yescharacteristic
1217C2#2144963511yescharacteristic
1218C2#2144966911yescharacteristic
1219C2#2144967011yescharacteristic
1220C2#2144978611yescharacteristic
1221C2#2144978811yescharacteristic
1222C2#2144981311yescharacteristic
1223C2#2144981411yescharacteristic
1224C2#2145099811yescharacteristic
1225C2#2145174311yescharacteristic
1226C2#2145410511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC61×#1436C2
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#14723
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#14519755C2semidirect
3. C2×#16839683C2semidirect
4. C2×#16839675C2semidirect
5. C2×#16839636C2semidirect
6. C2×#16839633C2semidirect
7. #21444071C2semidirect
8. #21444065C2semidirect
9. #21444063C2semidirect
10. #21444063C2semidirect
13. #21444052C2semidirect
14. #21444040C2semidirect
15. C61×#1436C2semidirect
76. C22×D244Q8semidirect
113. C2×#11758196D4semidirect
162. C2×C4⋊C4×C61D4semidirect
422. C22×D61C22⋊Q8semidirect
471. C2×C4×C61C22⋊Q8semidirect
610. #1436D61semidirect
674. C61#14723semidirect
737. C2×C4⋊C4D244semidirect
1131. C2×C4#14519755semidirect

Maximal subgroups

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

subgroupindex
C22×#145197552
C22×C4×D2442
C2×#168396832
C2×#168396752
C2×#168396362
C2×#168396332
#214440712
#214440652
#214440632
#214440592
#214440522
#214440402
C61×#14362
#1472361