Finite Group Databasebeta

← #29611053

Subgroups — #29611053

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C2×#16839627C211yesmaximal, characteristic, complemented
3C2×#16839626C211yesmaximal, characteristic, complemented
4#21444089C212yesmaximal, complemented
5#21444065C211yesmaximal, characteristic, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444063C212yesmaximal, complemented
8#21444062C212yesmaximal, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444058C212yesmaximal
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C22⋊D61C2211yescharacteristic
14C2×#14519763—24no—
15C2×#14519763—24no—
16C2×#14519763C418yescomplemented
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×C4×Dic61C2211yescharacteristic
26#16839627—24no—
27#16839626—24no—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—42no—
44C22×Dic122—42no—
45C22×Dic122C2×C414yes—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—42no—
49C22×C22⋊D61—42no—
50C22×C22⋊D61C2×C414yes—
51C23×Dic61C2312yes—
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56#14519763—232no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—42no—
59C2×#11758196—24no—
60C2×#11758196—42no—
61C2×#11758196—42no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—42no—
65C2×C22⋊Dic61—42no—
66C2×C22⋊Dic61—42no—
67C2×C22⋊Dic61C2×C414yes—
68C2×#11758198—22no—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198C2×C414yes—
79C2×#11758198C2×C414yes—
80C2×C4×Dic61C2×C414yes—
81C2×C4×Dic61D414yes—
82C2×C4×Dic61D414yes—
83#14519684—22no—
84#14519684—24no—
85#14519684—24no—
86#14519684—24no—
87#14519684—42no—
88#14519684—42no—
89#14519684—42no—
90C25×C61C2311yescharacteristic
91C23×C4×C61C2312yes—
92C23×C4×C61C2312yes—
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—42no—
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—42no—
100C2×C22⋊C4×C61—42no—
101C2×C22⋊C4×C61—42no—
102C2×C22⋊C4×C61C2×C414yes—
103#95×C61—22no—
104#95×C61—42no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—22no—
111C24×C61—21no—
112C24×C61—22no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61C22×C412yes—
116C24×C61C2411yescharacteristic
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—22no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61C22×C412yes—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
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×C61C22×C412yes—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C2×C22⋊D61—28no—
153C2×C22⋊D61—48no—
154C2×C22⋊D61—44no—
155C2×C22⋊D61—48no—
156C2×C22⋊D61—44no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61C22×C412yes—
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C412yes—
184C22×Dic61C2×D412yes—
185C22×Dic61C2×D412yes—
186C22×Dic61C2×D412yes—
187C22×Dic61C2×D412yes—
188C2×Dic122—28no—
189C2×Dic122—48no—
190C2×Dic122—44no—
191C2×Dic122—48no—
192C2×Dic122—44no—
193C4⋊C4×C61—44no—
194C22⋊C4×C61—28no—
195C22⋊C4×C61—48no—
196C22⋊Dic61—28no—
197C22⋊Dic61—48no—
198#11758198—28no—
199#11758198—28no—
200#11758198—48no—
201#11758198—48no—
202C4⋊Dic61—44no—
203#11758196—48no—
204C4×Dic61C22⋊C4116yescomplemented
205C23×C61—22no—
206C23×C61—24no—
207C23×C61—24no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—41no—
211C23×C61—42no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—42no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61C23×C411yescharacteristic
229C23×C61C22×D411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61H(5,𝔽2)12yes—
232C23×C61H(5,𝔽2)12yes—
233C23×C61H(5,𝔽2)12yes—
234C23×C61H(5,𝔽2)11yescharacteristic
235C23×C61H(5,𝔽2)11yescharacteristic
236C23×C612−1+412yes—
237C23×C612−1+411yescharacteristic
238C23×C612−1+411yescharacteristic
239C22×D61—22no—
240C22×D61—24no—
241C22×D61—24no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—42no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—42no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C2×C4×C61—24no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—24no—
266C2×C4×C61—22no—
267C2×C4×C61—24no—
268C2×C4×C61—41no—
269C2×C4×C61—42no—
270C2×C4×C61—41no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61C2×C22⋊C414yes—
286C22⋊D61—416no—
287C2×Dic61—24no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—24no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—24no—
299C2×Dic61—41no—
300C2×Dic61—42no—
301C2×Dic61—41no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61C2×C22⋊C414yes—
317C2×Dic61C2×C22⋊C414yes—
318Dic122—416no—
319#14662—611nomaximal, Sylow
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—44no—
324C22×C61—44no—
325C22×C61—82no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—82no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61C22×C22⋊C411yescharacteristic
332C22×C61#51812yes—
333C22×C61#52012yes—
334C22×C61#52011yescharacteristic
335C22×C61#52011yescharacteristic
336C22×C61#53511yescharacteristic
337C22×C61#53511yescharacteristic
338C22×C61#53511yescharacteristic
339C22×C61#53512yes—
340C22×C61#53511yescharacteristic
341C22×C61#53611yescharacteristic
342C22×C61#53611yescharacteristic
343C22×C61#53712yes—
344C22×C61#53711yescharacteristic
345C22×C61#53711yescharacteristic
346C22×C61H(3,𝔽4)12yes—
347C22×C61H(3,𝔽4)12yes—
348C22×C61#56212yes—
349C22×C61#56212yes—
350C22×C61#56212yes—
351C22×C61#56212yes—
352C22×C61#56312yes—
353C22×C61#56312yes—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—44no—
358C2×D61—44no—
359C2×D61—82no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—82no—
363C2×D61—81no—
364C2×D61—81no—
365C4×C61—24no—
366C4×C61—42no—
367C4×C61—82no—
368C4×C61—82no—
369Dic61—24no—
370Dic61—24no—
371Dic61—42no—
372Dic61—82no—
373Dic61—82no—
374C22×#124—611no—
375C2×#382—611no—
376C2×#382—611no—
377#1446—612no—
378#1439—612no—
379#1439—611no—
380#1439—611no—
381#1439—612no—
382#1439—611no—
383#1439D6111yescharacteristic, complemented
384#1438—612no—
385C2×C61—82no—
386C2×C61#230911yescharacteristic
387C2×C61#231111yescharacteristic
388C2×C61#231111yescharacteristic
389C2×C61#237912yes—
390C2×C61#237912yes—
391C2×C61#281912yes—
392C2×C61#281911yescharacteristic
393C2×C61#281911yescharacteristic
394C2×C61#282012yes—
395C2×C61#282011yescharacteristic
396C2×C61#282011yescharacteristic
397D61—82no—
398C23×Q8—611no—
399C23×D4—611no—
400C2×#124—618no—
401C2×#124—1224no—
402C2×#124—1224no—
403C22×C4⋊C4—612no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4C2×D6111yescharacteristic
406C22×C22⋊C4—611no—
407C22×C22⋊C4—611no—
408C22×C22⋊C4—611no—
409C22×C22⋊C4—612no—
410C22×C22⋊C4—612no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4C2×D6111yescharacteristic
413C22×C22⋊C4C2×D6112yes—
414C22×C42—611no—
415#382—1224no—
416#382—1224no—
417C2×#95—612no—
418C2×#95—612no—
419C2×#95—612no—
420C2×#95—611no—
421C2×#95—612no—
422C2×#95—612no—
423C2×#95—612no—
424C2×#95C2×D6111yescharacteristic
425C2×#95C2×D6112yes—
426C61#1466211yescharacteristic, complemented, Sylow
427C25—611no—
428C25C22×D6111yescharacteristic
429C22×Q8—614no—
430C22×Q8—1222no—
431C22×Q8—1222no—
432C22×Q8—2442no—
433C22×Q8—2442no—
434C22×D4—614no—
435C22×D4—1222no—
436C22×D4—1222no—
437C22×D4—2442no—
438C22×D4—2442no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—612no—
443C23×C4—612no—
444C23×C4C22×D6112yes—
445C23×C4C22×D6112yes—
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448#124—12232no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—1224no—
452C2×C4⋊C4—1222no—
453C2×C4⋊C4—2442no—
454C2×C4⋊C4—2442no—
455C2×C4⋊C4—2442no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—614no—
462C2×C22⋊C4—614no—
463C2×C22⋊C4—614no—
464C2×C22⋊C4—1222no—
465C2×C22⋊C4—1222no—
466C2×C22⋊C4—1222no—
467C2×C22⋊C4—1222no—
468C2×C22⋊C4—1222no—
469C2×C22⋊C4—1222no—
470C2×C22⋊C4—2442no—
471C2×C22⋊C4—2442no—
472C2×C22⋊C4—2442no—
473C2×C22⋊C4—2442no—
474C2×C22⋊C4—2442no—
475C2×C22⋊C4—2442no—
476C2×C22⋊C4—2442no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4—2442no—
479C2×C22⋊C4C4×D6114yes—
480C2×C42—614no—
481C2×C42—614no—
482C2×C42—614no—
483#95—22no—
484#95—42no—
485#95—1224no—
486#95—1224no—
487#95—1224no—
488#95—1222no—
489#95—2442no—
490#95—2442no—
491#95—2442no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—612no—
503C24—1221no—
504C24—1221no—
505C24—1222no—
506C24—1221no—
507C24—1222no—
508C24—1221no—
509C24—1222no—
510C24—1222no—
511C24—1221no—
512C24—1221no—
513C24C2×C4×D6112yes—
514C24C23×D6111yescharacteristic
515C2×Q8—1228no—
516C2×Q8—2448no—
517C2×Q8—2444no—
518C2×Q8—2448no—
519C2×Q8—2444no—
520C2×D4—1228no—
521C2×D4—2448no—
522C2×D4—2444no—
523C2×D4—2448no—
524C2×D4—2444no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—1221no—
555C22×C4—1222no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4C2×C4×D6112yes—
577C22×C4C2×C4×D6112yes—
578C22×C4D4×D6112yes—
579C22×C4D4×D6112yes—
580C4⋊C4—44no—
581C4⋊C4—2444no—
582C4⋊C4—2448no—
583C22⋊C4—28no—
584C22⋊C4—48no—
585C22⋊C4—1228no—
586C22⋊C4—1228no—
587C22⋊C4—1228no—
588C22⋊C4—2448no—
589C22⋊C4—2448no—
590C22⋊C4—2448no—
591C42—6116no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—1222no—
616C23—1224no—
617C23—1224no—
618C23—1222no—
619C23—1222no—
620C23—2442no—
621C23—2442no—
622C23—2442no—
623C23—2442no—
624C23—2442no—
625C23—2442no—
626C23—2442no—
627C23—2442no—
628C23—2441no—
629C23—2441no—
630C23—2442no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2442no—
636C23—2441no—
637C23—2441no—
638C23C22×C4×D6111yescharacteristic
639C23C2×D4×D6111yescharacteristic
640C23C2×D4×D6111yescharacteristic
641C23#1451982212yes—
642C23#1451982212yes—
643C23#1451982211yescharacteristic
644C23#1451982312yes—
645C23#1451982311yescharacteristic
646C23#1451982412yes—
647C23#1451982411yescharacteristic
648C23#1451982511yescharacteristic
649Q8—24416no—
650D4—24416no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—614no—
675C2×C4—614no—
676C2×C4—1224no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1224no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1224no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2441no—
703C2×C4—2442no—
704C2×C4—2441no—
705C2×C4C22⋊C4×D6114yes—
706C22—44no—
707C22—44no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—82no—
712C22—81no—
713C22—81no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—4882no—
718C22—4881no—
719C22—4881no—
720C22—4882no—
721C22—4881no—
722C22—4881no—
723C22—2444no—
724C22—2444no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22C2×C22⋊C4×D6111yescharacteristic
729C22#1684023412yes—
730C22#1684024112yes—
731C22#1684024211yescharacteristic
732C22#1684024311yescharacteristic
733C22#1684032511yescharacteristic
734C22#1684032711yescharacteristic
735C22#1684032811yescharacteristic
736C22#1684032812yes—
737C22#1684033011yescharacteristic
738C22#1684033411yescharacteristic
739C22#1684033511yescharacteristic
740C22#1684033912yes—
741C22#1684034111yescharacteristic
742C22#1684034211yescharacteristic
743C22#1684050412yes—
744C22#1684050512yes—
745C22#1684050712yes—
746C22#1684050812yes—
747C22#1684050912yes—
748C22#1684050912yes—
749C22#1684051312yes—
750C22#1684051412yes—
751C4—24no—
752C4—42no—
753C4—82no—
754C4—82no—
755C4—1224no—
756C4—1224no—
757C4—4882no—
758C4—4882no—
759C4—2442no—
760C2—82no—
761C2—4882no—
762C2#2144839811yescharacteristic
763C2#2144840611yescharacteristic
764C2#2144840811yescharacteristic
765C2#2144898812yes—
766C2#2144899212yes—
767C2#2145386312yes—
768C2#2145386611yescharacteristic
769C2#2145386711yescharacteristic
770C2#2145386812yes—
771C2#2145387311yescharacteristic
772C2#2145387511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14662
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#16839627C2semidirect
3. C2×#16839626C2semidirect
4. #21444089C2semidirect
5. #21444065C2semidirect
6. #21444064C2semidirect
7. #21444063C2semidirect
8. #21444062C2semidirect
9. #21444061C2semidirect
11. C61×#1439C2semidirect
16. C2×#14519763C4semidirect
204. C4×Dic61C22⋊C4semidirect
383. #1439D61semidirect
426. C61#14662semidirect

Maximal subgroups

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

subgroupindex
C22×#145197632
C2×#168396272
C2×#168396262
#214440892
#214440652
#214440642
#214440632
#214440622
#214440612
#214440582
C61×#14392
#1466261