Finite Group Databasebeta

← #29681711

Subgroups — #29681711

Order 15616.

1986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D61C211yesmaximal, characteristic, complemented
2C2×#16840269C211yesmaximal, characteristic
3C2×#16839763C211yesmaximal, characteristic, complemented
4C2×#16839619C211yesmaximal, characteristic, complemented
5#21446254C212yesmaximal, complemented
6#21446249C212yesmaximal, complemented
7#21446244C212yesmaximal, complemented
8#21446239C212yesmaximal, complemented
9#21445539C211yesmaximal, characteristic, complemented
10#21445538C211yesmaximal, characteristic, complemented
11C2×C61×#417C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×#11758194C2211yescharacteristic
14C22×#11758189C2212yes—
15C2×M16×D61—24no—
16C2×M16×D61—24no—
17C2×M16×D61—24no—
18C22×C8×D61C2212yes—
19#16840269—24no—
20#16840269C418yescomplemented
21C2×#14519758—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×#14519748C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×#14519745—21no—
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61—21no—
29C2×#14519736C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×#11758198—21no—
32#16839763—24no—
33C2×#14519701C2212yescomplemented
34C2×#14519698C2212yescomplemented
35#16839619—21no—
36#16839619—21no—
37#16839619C2212yes—
38#16839619C2212yes—
39C2×#14519684—21no—
40#16839525C2212yescomplemented
41#16839525C2212yescomplemented
42#16839524C2212yescomplemented
43#16839524C2212yescomplemented
44C22×#41×C61C2211yescharacteristic
45C22×M16×C61C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C61×#417—24no—
48C2×#103×C61C2212yescomplemented
49C2×#102×C61C2212yescomplemented
50C24×D61D411yescharacteristic
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C23×Dic61—21no—
54C23×Dic61D411yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61C2×C414yes—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D414yes—
63C22×C4×D61C2311yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194D414yescomplemented
68C2×#11758189—24no—
69C2×#11758189—24no—
70C2×#11758189—24no—
71M16×D61—232no—
72C22×#92418C2312yes—
73C2×C8×D61—24no—
74C2×C8×D61—24no—
75C2×C8×D61—24no—
76#14519758—28no—
77#14519753—22no—
78#14519753—22no—
79#14519753C2×C414yescomplemented
80#14519753C2×C414yescomplemented
81#14519748—22no—
82#14519748—22no—
83#14519748C2×C414yescomplemented
84#14519748C2×C414yescomplemented
85#14519745—28no—
86C4×C22⋊D61—28no—
87C4×C22⋊D61—28no—
88#14519736—22no—
89#14519736C2×C414yes—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2312yes—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—44no—
106C2×C4×Dic61—21no—
107#14519701—24no—
108#14519698—24no—
109#14519684—22no—
110#14519684—22no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—22no—
115C2×#41×C61—22no—
116C2×#41×C61C2×C414yes—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—21no—
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C2×M16×C61—22no—
124C2×M16×C61—22no—
125C2×M16×C61D414yescomplemented
126C22×C8×C61C2312yes—
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2312yes—
131#103×C61—24no—
132#102×C61—24no—
133C24×C61—21no—
134C24×C61C2×D411yescharacteristic
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—41no—
140C23×D61—41no—
141C23×D61C22⋊C414yes—
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144#41×C61—28no—
145#41×C61—28no—
146#41×C61—44no—
147#41×C61—44no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61C22×C412yes—
154C2×D4×C61—24no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61C22×C412yes—
163C22×C4×C61—21no—
164C22×C4×C61—24no—
165C22×C4×C61—22no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61C22×C412yes—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×D412yes—
176C22×C4×C61#4112yes—
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—24no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—22no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61C22⋊C414yes—
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C2×C4×D61—28no—
197C2×C4×D61—28no—
198C2×C4×D61—28no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—28no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61C22⋊C414yes—
213C2×C4×D61C22⋊C414yes—
214C2×C4×D61C22×C412yes—
215C2×C4×D61C22×C412yes—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2×D412yes—
218M16×C61—28no—
219C2×C8×C61—22no—
220C2×C8×C61—22no—
221C2×C8×C61C2×D414yes—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—42no—
225C22⋊Dic61—24no—
226C22⋊Dic61—24no—
227C22⋊Dic61—24no—
228#11758198—24no—
229#11758198—24no—
230#11758198—44no—
231#11758198—44no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—22no—
235C4⋊Dic61—22no—
236C4⋊Dic61—42no—
237C4⋊Dic61C22×C412yes—
238C4⋊Dic61C22×C412yes—
239#11758196—24no—
240#11758196—24no—
241C4×Dic61—24no—
242#11758194—28no—
243C2×#92418—22no—
244C2×#92418—22no—
245C2×#92418C2×D414yes—
246#11758189—216no—
247C8×D61—216no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—22no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C2×C22⋊C412yes—
260C23×C61#12112yes—
261C23×C61#12112yes—
262C23×C61C22×D411yescharacteristic
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—28no—
274C22×D61—28no—
275C22×D61—44no—
276C22×D61—44no—
277C22×D61—44no—
278C22×D61—44no—
279C22×D61—44no—
280C22×D61C2×C22⋊C412yes—
281C22×D61C2×C22⋊C412yes—
282C22×D61AGL(1,ℤ/8)12yes—
283C22×D61#13712yes—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—41no—
287Q8×C61—41no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—48no—
291D4×C61—41no—
292D4×C61—41no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—48no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—84no—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C4×D414yes—
303C2×C4×C61C4×D414yes—
304C2×C4×C61#12014yes—
305C2×C4×C61#12112yes—
306C2×C4×C61#12112yes—
307C2×C4×C61#12314yes—
308C2×C4×C61C23×C411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C22⋊D61—48no—
315C22⋊D61—48no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—28no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—84no—
331C2×Dic61C2×C22⋊C412yes—
332C2×Dic61C2×C22⋊C412yes—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—28no—
342C4×D61—28no—
343C8×C61—24no—
344#92418—24no—
345#20971—611nomaximal, Sylow
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61#38614yes—
360C22×C61C22×C22⋊C411yescharacteristic
361C22×C61C2×#12111yescharacteristic
362C22×C61C2×#12111yescharacteristic
363C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C61C2×#13711yescharacteristic
365C22×C61#57511yescharacteristic
366C22×C61#57511yescharacteristic
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—416no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61#41714yescomplemented
382C4×C61—42no—
383C4×C61—82no—
384C4×C61#38614yes—
385C4×C61C2×C4×D411yescharacteristic
386C4×C61C2×C4×D411yescharacteristic
387C4×C61C2×#12011yescharacteristic
388C4×C61C2×#12311yescharacteristic
389Dic61—22no—
390Dic61—22no—
391Dic61—42no—
392Dic61—42no—
393Dic61—82no—
394C23×M16—611no—
395C2×#525—611no—
396C2×#417—611no—
397C2×#417D6111yescharacteristic, complemented
398C2×#380—611no—
399#1895—612no—
400#1894—612no—
401#1893—612no—
402#1892—612no—
403#1736—611no—
404#1736—611no—
405C2×C61—24no—
406C2×C61—82no—
407C2×C61C2×#38611yescharacteristic
408C2×C61C2×#41711yescharacteristic
409C2×C61#289611yescharacteristic
410C2×C61#305511yescharacteristic
411C2×C61#305511yescharacteristic
412C2×C61#305611yescharacteristic
413C2×C61#305611yescharacteristic
414D61—24no—
415D61—42no—
416C22×#41C2×D6111yescharacteristic
417C24×C4—611no—
418C22×M16—611no—
419C22×M16—612no—
420C22×M16—1224no—
421C22×M16—1224no—
422C22×M16—1224no—
423C22×M16C2×D6111yescharacteristic
424C23×C8—612no—
425#525—618no—
426#525—1224no—
427C2×#123—1221no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—611no—
430C2×#121—611no—
431C2×#121—611no—
432C2×#120—1221no—
433C2×C4×D4—1221no—
434C2×C4×D4—1221no—
435C2×#117—611no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4C2×D6111yescharacteristic
438C22×C22⋊C4—1221no—
439#417—24no—
440#417—1224no—
441C2×#103—612no—
442C2×#103C2×D6112yescomplemented
443C2×#102—612no—
444C2×#102C2×D6112yescomplemented
445#380—612no—
446#380—612no—
447#380—1221no—
448#380—1221no—
449C2×#95—1221no—
450#340—612no—
451#340—612no—
452#340—612no—
453#340—612no—
454C61#2097111yescharacteristic, complemented, Sylow
455C25—611no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41C4×D6114yes—
462C22×Q8C22×D6111yescharacteristic
463C22×D4—21no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4C22×D6111yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—611no—
470C23×C4—614no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—614no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—1222no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1222no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C2×M16—22no—
483C2×M16—22no—
484C2×M16—614no—
485C2×M16—1224no—
486C2×M16—1224no—
487C2×M16—12232no—
488C2×M16—1222no—
489C2×M16—1222no—
490C2×M16—1224no—
491C2×M16C22⋊D6114yescomplemented
492C22×C8—612no—
493C22×C8—1224no—
494C22×C8—1224no—
495C22×C8—1224no—
496C22×C8C22×D6112yes—
497#123—1228no—
498C22⋊Q8—614no—
499C22⋊Q8—614no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502#121—614no—
503#121—614no—
504#121—1222no—
505#121—1222no—
506#120—1228no—
507C4×D4—1228no—
508C4×D4—1228no—
509#117—614no—
510#117—1222no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—612no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4C22×D6112yes—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—2444no—
531C2×C42—1221no—
532#103—24no—
533#103—1224no—
534#102—24no—
535#102—1224no—
536#95—1222no—
537#95—1222no—
538C24—21no—
539C24—611no—
540C24—611no—
541C24—614no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24—1222no—
546C24—2441no—
547C24—2441no—
548C24D4×D6111yescharacteristic
549#41—28no—
550#41—28no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C2×C4×D6112yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—1224no—
568C2×D4—1224no—
569C2×D4—2442no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4—2442no—
573C2×D4C2×C4×D6112yes—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—614no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—614no—
590C22×C4—614no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1228no—
602C22×C4—1228no—
603C22×C4—1228no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1228no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4C2×C4×D6112yes—
616C22×C4#1175822212yes—
617C22×C4D4×D6112yes—
618C22×C4D4×D6112yes—
619C22×C4D4×D6111yescharacteristic
620C22×C4#1175822412yes—
621C22×C4C2×C22⋊D6112yes—
622C22×C4C23×D6111yescharacteristic
623M16—28no—
624M16—12216no—
625M16—1228no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—614no—
629C2×C8—12216no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8C2×C22⋊D6114yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—42no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1222no—
643C4⋊C4—1222no—
644C4⋊C4—2442no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C22⋊C4—2444no—
651C22⋊C4—2444no—
652C42—1224no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—612no—
665C23—612no—
666C23—612no—
667C23—612no—
668C23—1228no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1228no—
680C23—2444no—
681C23—2444no—
682C23—2444no—
683C23—2444no—
684C23—2444no—
685C23C22⋊C4×D6112yes—
686C23#1451974812yes—
687C23#1451975012yes—
688C23C2×D4×D6111yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—2448no—
699D4—2448no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—48no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1228no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1228no—
724C2×C4—1228no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—4884no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4C22⋊C4×D6112yes—
736C2×C4#1451973714yes—
737C2×C4C4×C22⋊D6114yes—
738C2×C4#1451974514yes—
739C2×C4#1451974812yes—
740C2×C4#1451975012yes—
741C2×C4#1451975914yes—
742C2×C4C22×C4×D6111yescharacteristic
743C2×C4C2×D4×D6111yescharacteristic
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4C22×C22⋊D6111yescharacteristic
746C2×C4C2×#1175822411yescharacteristic
747C2×C4C2×#1175822211yescharacteristic
748C8—24no—
749C8—1224no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—614no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—24416no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22#1683963814yes—
779C22C2×C22⋊C4×D6111yescharacteristic
780C22C2×#1451974811yescharacteristic
781C22C2×#1451975011yescharacteristic
782C22AGL(1,ℤ/8)×D6111yescharacteristic
783C22#137×D6111yescharacteristic
784C22#1684055811yescharacteristic
785C22#1684056111yescharacteristic
786C4—42no—
787C4—82no—
788C4—1222no—
789C4—1222no—
790C4—4882no—
791C4—2442no—
792C4—2442no—
793C4#1683963814yes—
794C4C2×#1451973711yescharacteristic
795C4C2×C4×C22⋊D6111yescharacteristic
796C4C2×#1451974511yescharacteristic
797C4C2×#1451975911yescharacteristic
798C2—24no—
799C2—82no—
800C2—1224no—
801C2—2442no—
802C2C2×#1683963811yescharacteristic
803C2#417×D6111yescharacteristic
804C2#2145433511yescharacteristic
805C2#2145543211yescharacteristic
806C2#2145544111yescharacteristic
807C2#2145544311yescharacteristic
808C2#2145545211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840269C2
cosocleC22×C4×C61C24
hypercenterC2×#417D61
hypocenterC61#20971
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×M16×D61C2semidirect
3. C2×#16839763C2semidirect
4. C2×#16839619C2semidirect
5. #21446254C2semidirect
6. #21446249C2semidirect
7. #21446244C2semidirect
8. #21446239C2semidirect
9. #21445539C2semidirect
10. #21445538C2semidirect
11. C2×C61×#417C2semidirect
20. #16840269C4semidirect
33. C2×#14519701C22semidirect
34. C2×#14519698C22semidirect
40. #16839525C22semidirect
41. #16839525C22semidirect
42. #16839524C22semidirect
43. #16839524C22semidirect
48. C2×#103×C61C22semidirect
49. C2×#102×C61C22semidirect
67. C2×#11758194D4semidirect
79. #14519753C2×C4semidirect
80. #14519753C2×C4semidirect
83. #14519748C2×C4semidirect
84. #14519748C2×C4semidirect
125. C2×M16×C61D4semidirect
381. C2×D61#417semidirect
397. C2×#417D61semidirect
442. C2×#103C2×D61semidirect
444. C2×#102C2×D61semidirect
454. C61#20971semidirect
491. C2×M16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
C2×#168402692
C2×#168397632
C2×#168396192
#214462542
#214462492
#214462442
#214462392
#214455392
#214455382
C2×C61×#4172
#2097161