Finite Group Databasebeta

← #29681715

Subgroups — #29681715

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×#16840274C211yesmaximal, characteristic
3C2×#16839764C211yesmaximal, characteristic, complemented
4C2×#16839761C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6#21446256C212yesmaximal, complemented
7#21446251C212yesmaximal, complemented
8#21446246C212yesmaximal, complemented
9#21446241C212yesmaximal, complemented
10#21445540C211yesmaximal, characteristic, complemented
11C61×#1736C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758194C2211yescharacteristic
15C22×#11758189C2212yes—
16C2×M16×D61—24no—
17C2×M16×D61—24no—
18C2×M16×D61—24no—
19C22×C8×D61C2212yes—
20#16840274—24no—
21#16840274C418yescomplemented
22C2×#14519761—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519752C2211yescharacteristic
27C2×#14519747—21no—
28C2×C4×D244—21no—
29C2×C4×D244—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31C22×#11758198—21no—
32#16839764—24no—
33#16839761—24no—
34C2×#14519702C2212yescomplemented
35C2×#14519700C2212yescomplemented
36C2×#14519699C2212yescomplemented
37C2×#14519697C2212yescomplemented
38#16839619—21no—
39#16839619—21no—
40#16839619C2212yes—
41#16839619C2212yes—
42C2×#14519684—21no—
43#16839524C2212yescomplemented
44#16839524C2212yescomplemented
45C22×M16×C61C2211yescharacteristic
46C2×#117×C61C2211yescharacteristic
47C22×C4⋊C4×C61C2211yescharacteristic
48C61×#340C2212yescomplemented
49C61×#340C2212yescomplemented
50C24×D61D411yescharacteristic
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—22no—
54C2×#11758222—22no—
55C2×#11758222—22no—
56C2×#11758222C2×C414yes—
57C22×Dic122C2311yescharacteristic
58C22×D244—21no—
59C22×D244—21no—
60C22×D244C2311yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C23×Dic61D411yescharacteristic
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—21no—
69C22×C4×D61C2×C414yes—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D414yes—
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758194—22no—
76C2×#11758194—22no—
77C2×#11758194D414yescomplemented
78C2×#11758189—24no—
79C2×#11758189—24no—
80C2×#11758189—24no—
81M16×D61—232no—
82C22×#92418C2312yes—
83C2×C8×D61—24no—
84C2×C8×D61—24no—
85C2×C8×D61—24no—
86#14519761—28no—
87#14519757—22no—
88#14519757—22no—
89#14519757C2×C414yescomplemented
90#14519757C2×C414yescomplemented
91#14519752—22no—
92#14519752—22no—
93#14519752C2×C414yescomplemented
94#14519752C2×C414yescomplemented
95#14519747—28no—
96C4×D244—28no—
97C4×D244—28no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2312yes—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—44no—
111#14519702—24no—
112#14519700—24no—
113#14519699—24no—
114#14519697—24no—
115#14519684—22no—
116#14519684—22no—
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C2×M16×C61—22no—
120C2×M16×C61—22no—
121C2×M16×C61D414yescomplemented
122C22×C8×C61C2312yes—
123#117×C61—22no—
124#117×C61C2×C414yes—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61—22no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2312yes—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C42×C61—21no—
133C24×C61C2×D411yescharacteristic
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—21no—
139C23×D61—41no—
140C23×D61—41no—
141C23×D61C22⋊C414yes—
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61#4112yes—
156C22×C4×C61#4112yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—21no—
164C22×Dic61—22no—
165C22×Dic61—42no—
166C22×Dic61—42no—
167C22×Dic61—42no—
168C22×Dic61C22⋊C414yes—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171#11758222—28no—
172#11758222—28no—
173#11758222—44no—
174#11758222—44no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—24no—
180C2×D244—24no—
181C2×D244—21no—
182C2×D244—42no—
183C2×D244—42no—
184C2×D244—42no—
185C2×D244—42no—
186C2×D244C22×C412yes—
187C2×C4×D61—28no—
188C2×C4×D61—28no—
189C2×C4×D61—28no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—28no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—24no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22⋊C414yes—
207C2×C4×D61C22⋊C414yes—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C22×C412yes—
210C2×C4×D61C2×D412yes—
211C2×C4×D61C2×D412yes—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C22×C412yes—
218M16×C61—28no—
219C2×C8×C61—22no—
220C2×C8×C61—22no—
221C2×C8×C61C2×D414yes—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—42no—
227C4⋊C4×C61C22×C412yes—
228C4⋊C4×C61C22×C412yes—
229C22⋊C4×C61—24no—
230C42×C61—24no—
231#11758198—24no—
232#11758198—24no—
233#11758198—24no—
234#11758198—24no—
235#11758198—44no—
236#11758198—44no—
237C4⋊Dic61—24no—
238C4⋊Dic61—24no—
239C4⋊Dic61—22no—
240C4⋊Dic61—22no—
241C4⋊Dic61—42no—
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×C61C2×C22⋊C412yes—
253C23×C61#12112yes—
254C23×C61#12112yes—
255C23×C61C22×D411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—28no—
267C22×D61—28no—
268C22×D61—22no—
269C22×D61—44no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61C2×C22⋊C412yes—
281C22×D61C2×C22⋊C412yes—
282C22×D61AGL(1,ℤ/8)12yes—
283C22×D61#13712yes—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—84no—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C4×D414yes—
296C2×C4×C61C4×D414yes—
297C2×C4×C61#12014yes—
298C2×C4×C61#12112yes—
299C2×C4×C61#12112yes—
300C2×C4×C61#12314yes—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C22⋊D61—48no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—28no—
313C2×Dic61—22no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—84no—
320C2×Dic61C2×C22⋊C412yes—
321C2×Dic61C2×C22⋊C412yes—
322D244—22no—
323D244—22no—
324D244—48no—
325D244—48no—
326D244—41no—
327D244—41no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—28no—
337C4×D61—28no—
338C4×D61—48no—
339Dic122—22no—
340Dic122—22no—
341Dic122—41no—
342Dic122—41no—
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#38614yes—
353C22×C61C22×C22⋊C411yescharacteristic
354C22×C61C2×#12111yescharacteristic
355C22×C61C2×#12111yescharacteristic
356C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C61C2×#13711yescharacteristic
358C22×C61#57511yescharacteristic
359C22×C61#57511yescharacteristic
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—416no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61#41714yescomplemented
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—82no—
385C4×C61#38614yes—
386C4×C61C2×C4×D411yescharacteristic
387C4×C61C2×C4×D411yescharacteristic
388C4×C61C2×#12011yescharacteristic
389C4×C61C2×#12311yescharacteristic
390Dic61—22no—
391Dic61—22no—
392Dic61—42no—
393Dic61—82no—
394C23×M16—611no—
395C2×#525—611no—
396C2×#417—611no—
397C2×#417—611no—
398C2×#380—611no—
399#1895—612no—
400#1894—612no—
401#1893—612no—
402#1892—612no—
403#1736—611no—
404#1736D6111yescharacteristic, complemented
405C2×C61—24no—
406C2×C61C2×#38611yescharacteristic
407C2×C61C2×#41711yescharacteristic
408C2×C61#289611yescharacteristic
409C2×C61#305511yescharacteristic
410C2×C61#305511yescharacteristic
411C2×C61#305611yescharacteristic
412C2×C61#305611yescharacteristic
413D61—24no—
414D61—42no—
415D61—82no—
416C22×#41—611no—
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×#117C2×D6111yescharacteristic
436C22×C4⋊C4—611no—
437C22×C4⋊C4C2×D6111yescharacteristic
438C22×C22⋊C4—1221no—
439#417—1224no—
440#417—1224no—
441C2×#103—612no—
442C2×#103—612no—
443C2×#102—612no—
444C2×#102—612no—
445#380—612no—
446#380—612no—
447#380—1221no—
448#380—1221no—
449C2×#95—1221no—
450#340—612no—
451#340—612no—
452#340C2×D6112yescomplemented
453#340C2×D6112yescomplemented
454C61#2097111yescharacteristic, complemented, Sylow
455C25—611no—
456C2×#41—614no—
457C2×#41—1222no—
458C2×#41—1222no—
459C2×#41—1222no—
460C2×#41—1222no—
461C2×#41—1222no—
462C22×Q8—611no—
463C22×D4—611no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4—1221no—
467C23×C4—21no—
468C23×C4—611no—
469C23×C4—614no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—614no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—1222no—
476C23×C4—1222no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1221no—
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×M16D24414yescomplemented
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—22no—
510#117C4×D6114yes—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—612no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4C22×D6112yes—
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C22⋊C4—21no—
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—21no—
532#103—1224no—
533#103—1224no—
534#102—1224no—
535#102—1224no—
536#95—1222no—
537#95—1222no—
538C24—611no—
539C24—611no—
540C24—614no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24—1221no—
546C24—2441no—
547C24—2441no—
548C24D4×D6111yescharacteristic
549#41—1228no—
550#41—1228no—
551#41—2444no—
552#41—2444no—
553C2×Q8—612no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×D4—612no—
560C2×D4—1224no—
561C2×D4—1224no—
562C2×D4—1224no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—2442no—
569C2×D4—2442no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4—2442no—
573C2×D4—2442no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—614no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—614no—
588C22×C4—614no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1228no—
600C22×C4—1228no—
601C22×C4—1228no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1228no—
607C22×C4—1221no—
608C22×C4—1224no—
609C22×C4—1222no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4C2×C4×D6112yes—
616C22×C4C2×D24412yes—
617C22×C4#1175822212yes—
618C22×C4D4×D6112yes—
619C22×C4D4×D6112yes—
620C22×C4D4×D6111yescharacteristic
621C22×C4#1175822612yes—
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×D24414yes—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—42no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4—2442no—
643C4⋊C4C2×C4×D6112yes—
644C4⋊C4C2×C4×D6112yes—
645C22⋊C4—24no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C22⋊C4—2444no—
651C22⋊C4—2444no—
652C42—24no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—612no—
658C23—612no—
659C23—612no—
660C23—612no—
661C23—1228no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1228no—
673C23—1222no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2444no—
678C23—2444no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23C22⋊C4×D6112yes—
686C23#1451975012yes—
687C23#1451975212yes—
688C23C2×D4×D6111yescharacteristic
689Q8—1222no—
690Q8—1222no—
691Q8—2441no—
692Q8—2441no—
693D4—1222no—
694D4—1222no—
695D4—2448no—
696D4—2448no—
697D4—2448no—
698D4—2441no—
699D4—2441no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—84no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1228no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1228no—
726C2×C4—1228no—
727C2×C4—1222no—
728C2×C4—4884no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2448no—
735C2×C4C22⋊C4×D6112yes—
736C2×C4#1451973914yes—
737C2×C4C4×D24414yes—
738C2×C4#1451974714yes—
739C2×C4#1451975012yes—
740C2×C4#1451975212yes—
741C2×C4#1451976214yes—
742C2×C4C22×C4×D6111yescharacteristic
743C2×C4C2×D4×D6111yescharacteristic
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4C22×D24411yescharacteristic
746C2×C4C2×#1175822211yescharacteristic
747C2×C4C2×#1175822611yescharacteristic
748C8—24no—
749C8—1224no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—614no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—1222no—
764C22—1222no—
765C22—1222no—
766C22—4881no—
767C22—4881no—
768C22—4881no—
769C22—4881no—
770C22—24416no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22#1683964014yes—
779C22C2×C22⋊C4×D6111yescharacteristic
780C22C2×#1451975011yescharacteristic
781C22C2×#1451975211yescharacteristic
782C22AGL(1,ℤ/8)×D6111yescharacteristic
783C22#137×D6111yescharacteristic
784C22#1684055811yescharacteristic
785C22#1684056111yescharacteristic
786C4—42no—
787C4—42no—
788C4—82no—
789C4—1222no—
790C4—1222no—
791C4—4882no—
792C4—2442no—
793C4#1683964014yes—
794C4C2×#1451973911yescharacteristic
795C4C2×C4×D24411yescharacteristic
796C4C2×#1451974711yescharacteristic
797C4C2×#1451976211yescharacteristic
798C2—24no—
799C2—1224no—
800C2—4882no—
801C2—2442no—
802C2C2×#1683964011yescharacteristic
803C2#417×D6111yescharacteristic
804C2#2145433511yescharacteristic
805C2#2145543611yescharacteristic
806C2#2145543911yescharacteristic
807C2#2145544711yescharacteristic
808C2#2145545011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1736C2
socleC23×C61C22×D4
prime radicalC2×#16840274C2
cosocleC22×C4×C61C24
hypercenter#1736D61
hypocenterC61#20971
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C22×M16×D61C2semidirect
3. C2×#16839764C2semidirect
4. C2×#16839761C2semidirect
5. C2×#16839619C2semidirect
6. #21446256C2semidirect
7. #21446251C2semidirect
8. #21446246C2semidirect
9. #21446241C2semidirect
10. #21445540C2semidirect
11. C61×#1736C2semidirect
21. #16840274C4semidirect
34. C2×#14519702C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519699C22semidirect
37. C2×#14519697C22semidirect
43. #16839524C22semidirect
44. #16839524C22semidirect
48. C61×#340C22semidirect
49. C61×#340C22semidirect
77. C2×#11758194D4semidirect
89. #14519757C2×C4semidirect
90. #14519757C2×C4semidirect
93. #14519752C2×C4semidirect
94. #14519752C2×C4semidirect
121. C2×M16×C61D4semidirect
381. C2×D61#417semidirect
404. #1736D61semidirect
452. #340C2×D61semidirect
453. #340C2×D61semidirect
454. C61#20971semidirect
491. C2×M16D244semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
C2×#168402742
C2×#168397642
C2×#168397612
C2×#168396192
#214462562
#214462512
#214462462
#214462412
#214455402
C61×#17362
#2097161