Finite Group Databasebeta

← #29606538

Subgroups — #29606538

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C2×#16839666C212yesmaximal, complemented
3C2×#16839662C212yesmaximal
4C2×#16839631C211yesmaximal, characteristic, complemented
5C2×#16839607C211yesmaximal, characteristic, complemented
6#21444065C211yesmaximal, characteristic, complemented
7#21444064C211yesmaximal, characteristic, complemented
8#21444063C212yesmaximal, complemented
9#21444062C212yesmaximal, complemented
10#21444061C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C22⋊D61C2211yescharacteristic
14C2×#14519763—24no—
15C2×#14519763—24no—
16C2×#14519763C418yescomplemented
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×#11758196C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2212yes—
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×C4×Dic61C2212yes—
27C22×C4×Dic61C2211yescharacteristic
28#16839666—28no—
29#16839662—28no—
30#16839631—24no—
31#16839607—24no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2212yes—
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C2×#95×C61C2212yes—
41C2×#95×C61C2211yescharacteristic
42C24×D61C2311yescharacteristic
43C22×Dic122—22no—
44C22×Dic122—22no—
45C22×Dic122—24no—
46C22×Dic122—24no—
47C22×Dic122C2×C414yes—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—24no—
51C22×C22⋊D61—24no—
52C22×C22⋊D61C2×C414yes—
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58#14519763—232no—
59C2×C4⋊Dic61—22no—
60C2×C4⋊Dic61—42no—
61C2×#11758196—24no—
62C2×#11758196—24no—
63C2×#11758196—24no—
64C2×#11758196—24no—
65C2×#11758196—42no—
66C2×#11758196—42no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—24no—
70C2×C22⋊Dic61—42no—
71C2×C22⋊Dic61—42no—
72C2×C22⋊Dic61C2×C414yes—
73C2×#11758198—22no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—42no—
80C2×#11758198—42no—
81C2×#11758198—42no—
82C2×#11758198—42no—
83C2×#11758198C2×C414yes—
84C2×#11758198C2×C414yes—
85C2×C4×Dic61—24no—
86C2×C4×Dic61—24no—
87C2×C4×Dic61C2×C414yes—
88C2×C4×Dic61D418yes—
89C2×C4×Dic61D414yes—
90C2×C4×Dic61D414yes—
91#14519684—22no—
92#14519684—24no—
93#14519684—24no—
94#14519684—24no—
95#14519684—24no—
96C25×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2312yes—
100C23×C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—42no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—24no—
106C2×C22⋊C4×C61—42no—
107C2×C22⋊C4×C61—42no—
108C2×C22⋊C4×C61C2×C414yes—
109#95×C61—22no—
110#95×C61—24no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—21no—
116C24×C61—22no—
117C24×C61—21no—
118C24×C61—22no—
119C24×C61—21no—
120C24×C61—21no—
121C24×C61C22×C412yes—
122C24×C61C2411yescharacteristic
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—22no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61C22×C412yes—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
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×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C2×D414yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D412yes—
158C2×C22⋊D61—28no—
159C2×C22⋊D61—216no—
160C2×C22⋊D61—48no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—21no—
169C22×Dic61—21no—
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×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61C22×C412yes—
185C22×Dic61C22×C412yes—
186C22×Dic61C22×C412yes—
187C22×Dic61C2×D414yes—
188C22×Dic61C2×D412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2×D412yes—
192C22×Dic61C2×D414yes—
193C22×Dic61#4114yes—
194C2×Dic122—28no—
195C2×Dic122—216no—
196C2×Dic122—48no—
197C2×Dic122—44no—
198C2×Dic122—44no—
199C4⋊C4×C61—44no—
200C22⋊C4×C61—28no—
201C22⋊C4×C61—48no—
202C22⋊Dic61—28no—
203C22⋊Dic61—48no—
204#11758198—28no—
205#11758198—28no—
206#11758198—48no—
207#11758198—48no—
208C4⋊Dic61—44no—
209#11758196—48no—
210#11758196—48no—
211C4×Dic61—216no—
212C4×Dic61C22⋊C4116yescomplemented
213C23×C61—22no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—42no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61C23×C411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C23×C61C22×D411yescharacteristic
239C23×C61C22×D412yes—
240C23×C61C2×#4112yes—
241C23×C61H(5,𝔽2)12yes—
242C23×C61H(5,𝔽2)11yescharacteristic
243C23×C61H(5,𝔽2)11yescharacteristic
244C23×C612−1+412yes—
245C23×C612−1+411yescharacteristic
246C23×C612−1+411yescharacteristic
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—42no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C2×C4×C61—24no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—22no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—42no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61C2×C22⋊C414yes—
294C22⋊D61—416no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—42no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61C2×C22⋊C414yes—
321C2×Dic61C2×C22⋊C414yes—
322C2×Dic61C4×D418yes—
323C2×Dic61#12118yes—
324C2×Dic61#12414yes—
325C2×Dic61#12714yes—
326Dic122—416no—
327#14273—611nomaximal, Sylow
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—44no—
331C22×C61—44no—
332C22×C61—42no—
333C22×C61—82no—
334C22×C61—82no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C22×C22⋊C411yescharacteristic
340C22×C61C2×C4×D412yes—
341C22×C61#52012yes—
342C22×C61#52011yescharacteristic
343C22×C61#52011yescharacteristic
344C22×C61C2×#12112yes—
345C22×C61C2×#12411yescharacteristic
346C22×C61C2×#12711yescharacteristic
347C22×C61#53511yescharacteristic
348C22×C61#53512yes—
349C22×C61#53511yescharacteristic
350C22×C61#53512yes—
351C22×C61#53611yescharacteristic
352C22×C61#53612yes—
353C22×C61#53611yescharacteristic
354C22×C61#53612yes—
355C22×C61#53712yes—
356C22×C61#53711yescharacteristic
357C22×C61#53711yescharacteristic
358C22×C61#54212yes—
359C22×C61#54212yes—
360C22×C61#54212yes—
361C22×C61#54212yes—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—42no—
367C2×D61—82no—
368C2×D61—82no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C4×C61—24no—
374C4×C61—44no—
375C4×C61—42no—
376C4×C61—82no—
377Dic61—24no—
378Dic61—44no—
379Dic61—42no—
380Dic61—82no—
381Dic61#39018yes—
382C22×#124—611no—
383C2×#391—612no—
384C2×#390—612no—
385C2×#384—611no—
386C2×#376—611no—
387#1439—612no—
388#1439—611no—
389#1439—611no—
390#1439—612no—
391#1439—611no—
392#1439D6111yescharacteristic, complemented
393C2×C61—82no—
394C2×C61C2×#39011yescharacteristic
395C2×C61#231111yescharacteristic
396C2×C61#231111yescharacteristic
397C2×C61#232612yes—
398C2×C61#232612yes—
399C2×C61#262012yes—
400C2×C61#262012yes—
401C2×C61#264011yescharacteristic
402C2×C61#264011yescharacteristic
403C2×C61#265711yescharacteristic
404C2×C61#265811yescharacteristic
405D61—82no—
406C23×Q8—611no—
407C23×D4—611no—
408C2×#124—618no—
409C2×#124—1224no—
410C2×#124—1224no—
411C22×C4⋊C4—612no—
412C22×C4⋊C4—612no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4C2×D6111yescharacteristic
415C22×C22⋊C4—611no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—611no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4—612no—
420C22×C22⋊C4—612no—
421C22×C22⋊C4C2×D6111yescharacteristic
422C22×C22⋊C4C2×D6112yes—
423C22×C42—611no—
424C22×C42—612no—
425#391—1228no—
426#390—1228no—
427#384—1224no—
428#376—1224no—
429C2×#95—612no—
430C2×#95—611no—
431C2×#95—612no—
432C2×#95—612no—
433C2×#95—612no—
434C2×#95C2×D6111yescharacteristic
435C2×#95C2×D6112yes—
436C61#1427311yescharacteristic, complemented, Sylow
437C25—611no—
438C25C22×D6111yescharacteristic
439C22×Q8—614no—
440C22×Q8—1222no—
441C22×Q8—1222no—
442C22×Q8—1224no—
443C22×Q8—1224no—
444C22×D4—614no—
445C22×D4—1222no—
446C22×D4—1222no—
447C22×D4—1224no—
448C22×D4—1224no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—612no—
453C23×C4—612no—
454C23×C4C22×D6112yes—
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6112yes—
457C23×C4C22×D6111yescharacteristic
458#124—12232no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—1224no—
462C2×C4⋊C4—1224no—
463C2×C4⋊C4—1224no—
464C2×C4⋊C4—1224no—
465C2×C4⋊C4—1222no—
466C2×C4⋊C4—2442no—
467C2×C4⋊C4—2442no—
468C2×C4⋊C4—2442no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—614no—
475C2×C22⋊C4—614no—
476C2×C22⋊C4—614no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1222no—
480C2×C22⋊C4—1222no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—1222no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C22⋊C4—1224no—
486C2×C22⋊C4—2442no—
487C2×C22⋊C4—2442no—
488C2×C22⋊C4—2442no—
489C2×C22⋊C4—2442no—
490C2×C22⋊C4—2442no—
491C2×C22⋊C4—2442no—
492C2×C22⋊C4C4×D6114yes—
493C2×C42—614no—
494C2×C42—614no—
495C2×C42—614no—
496C2×C42—618no—
497C2×C42—1224no—
498C2×C42—1224no—
499#95—22no—
500#95—24no—
501#95—1224no—
502#95—1224no—
503#95—1224no—
504#95—1222no—
505#95—1224no—
506C24—21no—
507C24—21no—
508C24—22no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—21no—
513C24—22no—
514C24—21no—
515C24—21no—
516C24—612no—
517C24—1221no—
518C24—1221no—
519C24—1222no—
520C24—1222no—
521C24—1222no—
522C24—1221no—
523C24—1221no—
524C24—1222no—
525C24—1221no—
526C24—1221no—
527C24C2×C4×D6112yes—
528C24C23×D6111yescharacteristic
529C2×Q8—1228no—
530C2×Q8—12216no—
531C2×Q8—2448no—
532C2×Q8—2444no—
533C2×Q8—2444no—
534C2×D4—1228no—
535C2×D4—12216no—
536C2×D4—2448no—
537C2×D4—2444no—
538C2×D4—2444no—
539C22×C4—22no—
540C22×C4—22no—
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—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—614no—
562C22×C4—614no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—614no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4C2×C4×D6112yes—
590C22×C4C2×C4×D6112yes—
591C22×C4D4×D6114yes—
592C22×C4D4×D6112yes—
593C22×C4D4×D6112yes—
594C4⋊C4—44no—
595C4⋊C4—2444no—
596C4⋊C4—2448no—
597C4⋊C4—2448no—
598C22⋊C4—28no—
599C22⋊C4—48no—
600C22⋊C4—1228no—
601C22⋊C4—1228no—
602C22⋊C4—1228no—
603C22⋊C4—2448no—
604C22⋊C4—2448no—
605C22⋊C4—2448no—
606C42—6116no—
607C42—12216no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—41no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—1222no—
632C23—1224no—
633C23—1224no—
634C23—1222no—
635C23—1222no—
636C23—2442no—
637C23—2441no—
638C23—2441no—
639C23—2442no—
640C23—2441no—
641C23—2442no—
642C23—2441no—
643C23—2442no—
644C23—2441no—
645C23—2442no—
646C23—2441no—
647C23—2442no—
648C23—2441no—
649C23—2441no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23C22×C4×D6111yescharacteristic
655C23C2×D4×D6111yescharacteristic
656C23C2×D4×D6111yescharacteristic
657C23C2×D4×D6112yes—
658C23#41×D6112yes—
659C23#1451982212yes—
660C23#1451982211yescharacteristic
661C23#1451982311yescharacteristic
662C23#1451982412yes—
663C23#1451982411yescharacteristic
664C23#1451982511yescharacteristic
665Q8—24416no—
666D4—24416no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—614no—
691C2×C4—618no—
692C2×C4—618no—
693C2×C4—614no—
694C2×C4—614no—
695C2×C4—614no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1224no—
706C2×C4—1224no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C22⋊C4×D6114yes—
722C22—44no—
723C22—42no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—82no—
728C22—82no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—4882no—
734C22—4882no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—4881no—
739C22—2444no—
740C22—2442no—
741C22—2444no—
742C22—2442no—
743C22—2442no—
744C22C2×C22⋊C4×D6111yescharacteristic
745C22C4×D4×D6112yes—
746C22#1684024112yes—
747C22#1684024211yescharacteristic
748C22#1684024311yescharacteristic
749C22#121×D6112yes—
750C22#124×D6111yescharacteristic
751C22#127×D6111yescharacteristic
752C22#1684032712yes—
753C22#1684032711yescharacteristic
754C22#1684032812yes—
755C22#1684032811yescharacteristic
756C22#1684033412yes—
757C22#1684033411yescharacteristic
758C22#1684033512yes—
759C22#1684033511yescharacteristic
760C22#1684033912yes—
761C22#1684034111yescharacteristic
762C22#1684034211yescharacteristic
763C22#1684037612yes—
764C22#1684037812yes—
765C22#1684038012yes—
766C22#1684038212yes—
767C4—24no—
768C4—44no—
769C4—42no—
770C4—82no—
771C4—618no—
772C4—1224no—
773C4—4882no—
774C4—2444no—
775C4—2442no—
776C2—82no—
777C2—4882no—
778C2#390×D6111yescharacteristic
779C2#2144840611yescharacteristic
780C2#2144840811yescharacteristic
781C2#2144852512yes—
782C2#2144852812yes—
783C2#2145157512yes—
784C2#2145157812yes—
785C2#2145175411yescharacteristic
786C2#2145175711yescharacteristic
787C2#2145192411yescharacteristic
788C2#2145192811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14273
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#16839666C2semidirect
4. C2×#16839631C2semidirect
5. C2×#16839607C2semidirect
6. #21444065C2semidirect
7. #21444064C2semidirect
8. #21444063C2semidirect
9. #21444062C2semidirect
10. #21444061C2semidirect
11. C61×#1439C2semidirect
16. C2×#14519763C4semidirect
212. C4×Dic61C22⋊C4semidirect
392. #1439D61semidirect
436. C61#14273semidirect

Maximal subgroups

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

subgroupindex
C22×#145197632
C2×#168396662
C2×#168396622
C2×#168396312
C2×#168396072
#214440652
#214440642
#214440632
#214440622
#214440612
C61×#14392
#1427361