Finite Group Databasebeta

← #29606373

Subgroups — #29606373

Order 15616.

2554 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519759C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16839638C212yesmaximal
4C2×#16839624C211yesmaximal, characteristic, complemented
5#21444073C211yesmaximal, characteristic, complemented
6#21444071C212yesmaximal, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444062C212yesmaximal, complemented
10#21444040C212yesmaximal, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C2×#14519759—24no—
16C2×#14519759—24no—
17C2×#14519759C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758196C2211yescharacteristic
22C2×C4⋊C4×D61—28no—
23C2×C4⋊C4×D61—24no—
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2212yes—
26C22×#11758198C2212yes—
27C22×#11758198C2211yescharacteristic
28#16839638—28no—
29#16839624—24no—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C2×#95×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C24×D61C2311yescharacteristic
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61—24no—
46C22×C22⋊D61—24no—
47C22×C22⋊D61C2×C414yes—
48C23×Dic61C2312yes—
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2312yes—
52C23×Dic61C2311yescharacteristic
53C22×C4×D61—24no—
54C22×C4×D61—24no—
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—42no—
58C22×C4×D61—42no—
59C22×C4×D61—42no—
60C22×C4×D61—42no—
61C22×C4×D61C2×C414yes—
62C22×C4×D61D414yes—
63C22×C4×D61D414yes—
64C22×C4×D61D418yes—
65#14519759—232no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—24no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61C2×C414yescomplemented
71C2×#11758196—24no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196C2×C414yescomplemented
77C4⋊C4×D61—232no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—24no—
81C2×C22⋊Dic61—42no—
82C2×C22⋊Dic61—42no—
83C2×C22⋊Dic61C2×C414yescomplemented
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198C2×C414yes—
90#14519684—22no—
91#14519684—24no—
92#14519684—24no—
93#14519684—24no—
94#14519684—42no—
95#14519684—42no—
96#14519684—42no—
97C25×C61C2311yescharacteristic
98C23×C4×C61C2312yes—
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2312yes—
101C23×C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61—24no—
103C2×C4⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—24no—
107C2×C22⋊C4×C61—42no—
108C2×C22⋊C4×C61—42no—
109C2×C22⋊C4×C61C2×C414yescomplemented
110#95×C61—22no—
111#95×C61—42no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—21no—
117C24×C61—22no—
118C24×C61—21no—
119C24×C61—22no—
120C24×C61—21no—
121C24×C61—21no—
122C24×C61C22×C412yes—
123C24×C61C2411yescharacteristic
124C23×D61—22no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—22no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61C22×C412yes—
131C23×D61C2×D412yes—
132C23×D61C2×D412yes—
133C23×D61C2×D414yes—
134C23×D61#4114yes—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C2×D414yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C2×C22⋊D61—28no—
160C2×C22⋊D61—216no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—48no—
163C2×C22⋊D61—44no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61C22×C412yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C2×D414yes—
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195C2×C4×D61—216no—
196C2×C4×D61—28no—
197C2×C4×D61—216no—
198C2×C4×D61—28no—
199C2×C4×D61—216no—
200C2×C4×D61—48no—
201C2×C4×D61—48no—
202C2×C4×D61—48no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C2×C4×D61C22⋊C4116yescomplemented
207C4⋊C4×C61—28no—
208C22⋊C4×C61—28no—
209C22⋊C4×C61—48no—
210C22⋊Dic61—28no—
211C22⋊Dic61—48no—
212#11758198—28no—
213#11758198—48no—
214C4⋊Dic61—28no—
215C4⋊Dic61—28no—
216#11758196—216no—
217#11758196—28no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—41no—
224C23×C61—42no—
225C23×C61—41no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—41no—
235C23×C61—42no—
236C23×C61—41no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61C23×C411yescharacteristic
242C23×C61C22×D411yescharacteristic
243C23×C61C22×D411yescharacteristic
244C23×C61C22×D412yes—
245C23×C61C2×#4112yes—
246C23×C61H(5,𝔽2)12yes—
247C23×C61H(5,𝔽2)11yescharacteristic
248C23×C61H(5,𝔽2)11yescharacteristic
249C23×C612−1+412yes—
250C23×C612−1+411yescharacteristic
251C23×C612−1+411yescharacteristic
252C22×D61—24no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—22no—
264C22×D61—24no—
265C22×D61—22no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—24no—
269C22×D61—24no—
270C22×D61C2×C22⋊C414yes—
271C22×D61C4×D418yes—
272C22×D61#12014yes—
273C22×D61#12118yes—
274C22×D61#12314yes—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61C2×C22⋊C414yes—
299C22⋊D61—416no—
300C2×Dic61—24no—
301C2×Dic61—22no—
302C2×Dic61—24no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—24no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—41no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61C2×C22⋊C414yes—
331C4×D61—232no—
332C4×D61—432no—
333#14256—611nomaximal, Sylow
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—44no—
337C22×C61—44no—
338C22×C61—42no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—82no—
342C22×C61—82no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61C2×C4×D412yes—
347C22×C61#52012yes—
348C22×C61#52011yescharacteristic
349C22×C61#52011yescharacteristic
350C22×C61C2×#12011yescharacteristic
351C22×C61C2×#12112yes—
352C22×C61C2×#12311yescharacteristic
353C22×C61#53412yes—
354C22×C61#53412yes—
355C22×C61#53511yescharacteristic
356C22×C61#53511yescharacteristic
357C22×C61#53611yescharacteristic
358C22×C61#53612yes—
359C22×C61#53611yescharacteristic
360C22×C61#53612yes—
361C22×C61#53711yescharacteristic
362C22×C61#53712yes—
363C22×C61#53711yescharacteristic
364C22×C61#53912yes—
365C22×C61#53912yes—
366C22×C61#53912yes—
367C22×C61#53912yes—
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—28no—
371C2×D61—28no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61—28no—
375C2×D61—28no—
376C2×D61—24no—
377C2×D61—24no—
378C2×D61#38618yes—
379C4×C61—24no—
380C4×C61—42no—
381C4×C61—44no—
382C4×C61—82no—
383Dic61—24no—
384Dic61—42no—
385Dic61—44no—
386Dic61—42no—
387Dic61—82no—
388C22×#123—611no—
389C23×C4⋊C4—611no—
390C2×#386—612no—
391C2×#381—611no—
392#1441—612no—
393#1441—611no—
394#1441—611no—
395#1439—612no—
396#1439—611no—
397#1439D6111yescharacteristic, complemented
398C22⋊#95—612no—
399C2×C61—82no—
400C2×C61C2×#38611yescharacteristic
401C2×C61#231111yescharacteristic
402C2×C61#231111yescharacteristic
403C2×C61#232212yes—
404C2×C61#232212yes—
405C2×C61#261311yescharacteristic
406C2×C61#261411yescharacteristic
407C2×C61#261812yes—
408C2×C61#261812yes—
409C2×C61#262311yescharacteristic
410C2×C61#262311yescharacteristic
411D61—28no—
412C23×D4—611no—
413C24×C4—611no—
414C24×C4—612no—
415C2×#123—618no—
416C2×#123—1224no—
417C2×#123—1224no—
418C22×C4⋊C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—612no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—1224no—
423C22×C4⋊C4—1228no—
424C22×C4⋊C4C2×D6111yescharacteristic
425C22×C22⋊C4—611no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—612no—
428C22×C22⋊C4—612no—
429C22×C22⋊C4C2×D6111yescharacteristic
430C22×C22⋊C4C2×D6112yes—
431#386—1228no—
432#381—1224no—
433C2×#95—612no—
434C2×#95—611no—
435C2×#95—612no—
436C2×#95—612no—
437C2×#95—612no—
438C2×#95—612no—
439C2×#95—612no—
440C2×#95C2×D6111yescharacteristic
441C2×#95C2×D6112yes—
442C61#1425611yescharacteristic, complemented, Sylow
443C25—611no—
444C25C22×D6111yescharacteristic
445C22×D4—614no—
446C22×D4—1222no—
447C22×D4—1222no—
448C22×D4—1224no—
449C22×D4—1224no—
450C23×C4—611no—
451C23×C4—614no—
452C23×C4—614no—
453C23×C4—614no—
454C23×C4—611no—
455C23×C4—612no—
456C23×C4—611no—
457C23×C4—618no—
458C23×C4—612no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4—1224no—
462C23×C4—1224no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4—2442no—
466C23×C4—2442no—
467C23×C4C22×D6112yes—
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6112yes—
470C23×C4C22×D6111yescharacteristic
471#123—12232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—614no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—12232no—
477C2×C4⋊C4—1224no—
478C2×C4⋊C4—1224no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—614no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—1222no—
494C2×C22⋊C4—1222no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—2442no—
502C2×C22⋊C4—2442no—
503C2×C22⋊C4C4×D6114yescomplemented
504#95—22no—
505#95—42no—
506#95—1224no—
507#95—1224no—
508#95—1222no—
509#95—1224no—
510#95—2442no—
511#95—2442no—
512#95—2442no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—22no—
519C24—21no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—612no—
524C24—612no—
525C24—612no—
526C24—614no—
527C24—614no—
528C24—1222no—
529C24—1221no—
530C24—1221no—
531C24—1222no—
532C24—1221no—
533C24—1221no—
534C24C2×C4×D6112yes—
535C24C23×D6111yescharacteristic
536C2×D4—1228no—
537C2×D4—12216no—
538C2×D4—2444no—
539C2×D4—2448no—
540C2×D4—2444no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—6116no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—614no—
567C22×C4—1228no—
568C22×C4—12216no—
569C22×C4—12216no—
570C22×C4—1228no—
571C22×C4—12216no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—2448no—
598C22×C4—2448no—
599C22×C4—2448no—
600C22×C4—2448no—
601C22×C4—2448no—
602C22×C4—2448no—
603C22×C4C2×C4×D6112yes—
604C22×C4C2×C4×D6112yes—
605C22×C4D4×D6114yes—
606C22×C4D4×D6112yes—
607C22×C4D4×D6112yes—
608C4⋊C4—28no—
609C4⋊C4—1228no—
610C4⋊C4—12216no—
611C4⋊C4—1228no—
612C4⋊C4—1228no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—1228no—
616C22⋊C4—1228no—
617C22⋊C4—2448no—
618C22⋊C4—2448no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—41no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—614no—
643C23—618no—
644C23—614no—
645C23—618no—
646C23—614no—
647C23—1224no—
648C23—1222no—
649C23—1222no—
650C23—1224no—
651C23—1224no—
652C23—1222no—
653C23—1222no—
654C23—1224no—
655C23—1222no—
656C23—1224no—
657C23—1222no—
658C23—1222no—
659C23—1224no—
660C23—1222no—
661C23—1224no—
662C23—1224no—
663C23—1224no—
664C23—1224no—
665C23C22×C4×D6111yescharacteristic
666C23C2×D4×D6111yescharacteristic
667C23C2×D4×D6111yescharacteristic
668C23C2×D4×D6112yes—
669C23#41×D6112yes—
670C23#1451982212yes—
671C23#1451982211yescharacteristic
672C23#1451982311yescharacteristic
673C23#1451982412yes—
674C23#1451982411yescharacteristic
675C23#1451982511yescharacteristic
676D4—24416no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—614no—
701C2×C4—12232no—
702C2×C4—1224no—
703C2×C4—1222no—
704C2×C4—1224no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1224no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1224no—
712C2×C4—1224no—
713C2×C4—1224no—
714C2×C4—24432no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2441no—
723C2×C4—2442no—
724C2×C4—2441no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2441no—
729C2×C4—2442no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4C22⋊C4×D6114yes—
734C22—44no—
735C22—42no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—81no—
740C22—81no—
741C22—82no—
742C22—82no—
743C22—81no—
744C22—81no—
745C22—618no—
746C22—1224no—
747C22—1224no—
748C22—1228no—
749C22—1228no—
750C22—1228no—
751C22—1228no—
752C22—1224no—
753C22—1224no—
754C22—1224no—
755C22—1224no—
756C22C2×C22⋊C4×D6111yescharacteristic
757C22C4×D4×D6112yes—
758C22#1684024112yes—
759C22#1684024211yescharacteristic
760C22#1684024311yescharacteristic
761C22#120×D6111yescharacteristic
762C22#121×D6112yes—
763C22#123×D6111yescharacteristic
764C22#1684032012yes—
765C22#1684032212yes—
766C22#1684032511yescharacteristic
767C22#1684032811yescharacteristic
768C22#1684033212yes—
769C22#1684033211yescharacteristic
770C22#1684033512yes—
771C22#1684033511yescharacteristic
772C22#1684034111yescharacteristic
773C22#1684034112yes—
774C22#1684034211yescharacteristic
775C22#1684035312yes—
776C22#1684035512yes—
777C22#1684035512yes—
778C22#1684035812yes—
779C4—24no—
780C4—44no—
781C4—42no—
782C4—82no—
783C4—1224no—
784C4—4882no—
785C4—2444no—
786C4—2442no—
787C4—2442no—
788C2—82no—
789C2—1228no—
790C2#386×D6111yescharacteristic
791C2#2144840811yescharacteristic
792C2#2144840911yescharacteristic
793C2#2144848612yes—
794C2#2144848912yes—
795C2#2145153011yescharacteristic
796C2#2145153711yescharacteristic
797C2#2145156012yes—
798C2#2145156612yes—
799C2#2145159811yescharacteristic
800C2#2145160411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14256
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
4. C2×#16839624C2semidirect
5. #21444073C2semidirect
6. #21444071C2semidirect
7. #21444069C2semidirect
8. #21444064C2semidirect
9. #21444062C2semidirect
10. #21444040C2semidirect
11. C61×#1439C2semidirect
17. C2×#14519759C4semidirect
70. C2×C4⋊Dic61C2×C4semidirect
76. C2×#11758196C2×C4semidirect
83. C2×C22⋊Dic61C2×C4semidirect
109. C2×C22⋊C4×C61C2×C4semidirect
206. C2×C4×D61C22⋊C4semidirect
397. #1439D61semidirect
442. C61#14256semidirect
503. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197592
C22×C4⋊C4×D612
C2×#168396382
C2×#168396242
#214440732
#214440712
#214440692
#214440642
#214440622
#214440402
C61×#14392
#1425661