Finite Group Databasebeta

← #29606766

Subgroups — #29606766

Order 15616.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic61C211yesmaximal, characteristic, complemented
2C2×#16839670C211yesmaximal, characteristic
3C2×#16839651C211yesmaximal, characteristic, complemented
4C2×#16839639C212yesmaximal, complemented
5#21444075C211yesmaximal, characteristic, complemented
6#21444065C211yesmaximal, characteristic, complemented
7#21444062C212yesmaximal, complemented
8#21444058C212yesmaximal, complemented
9#21444044C211yesmaximal, characteristic, complemented
10#21444041C212yesmaximal, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2212yes—
13C24×Dic61C2212yes—
14C2×D4×Dic61—24no—
15C2×D4×Dic61—28no—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25#16839670C418yescomplemented
26#16839651—24no—
27#16839639—28no—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C23×D4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2212yes—
37C22×C22⋊C4×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—24no—
42C22×C22⋊D61—24no—
43C22×C22⋊D61—42no—
44C22×C22⋊D61—42no—
45C22×C22⋊D61—42no—
46C22×C22⋊D61—42no—
47C22×C22⋊D61C2×C418yescomplemented
48C23×Dic61—24no—
49C23×Dic61—24no—
50C23×Dic61—42no—
51C23×Dic61—42no—
52C23×Dic61—42no—
53C23×Dic61—42no—
54C23×Dic61D418yescomplemented
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60D4×Dic61—232no—
61C2×C4⋊Dic61—22no—
62C2×C4⋊Dic61—24no—
63C2×#11758196—22no—
64C2×#11758196—42no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—24no—
68C2×C22⋊Dic61—42no—
69C2×C22⋊Dic61—42no—
70C2×C22⋊Dic61C2×C418yescomplemented
71C2×#11758198—22no—
72C2×#11758198—22no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198—42no—
80C2×#11758198C2×C414yescomplemented
81C2×C4×Dic61—24no—
82C2×C4×Dic61D414yescomplemented
83#14519684—24no—
84#14519684—24no—
85#14519684—22no—
86#14519684—42no—
87#14519684—42no—
88#14519684—42no—
89#14519684C2×C414yescomplemented
90C25×C61C2312yes—
91C22×D4×C61—24no—
92C22×D4×C61—24no—
93C22×D4×C61—22no—
94C22×D4×C61—22no—
95C22×D4×C61C2×C414yes—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2312yes—
99C23×C4×C61C2311yescharacteristic
100C2×C22⋊C4×C61—24no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—42no—
103C2×C22⋊C4×C61—42no—
104C2×C22⋊C4×C61—42no—
105C2×C22⋊C4×C61—42no—
106#95×C61—22no—
107#95×C61—22no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61C22×C414yes—
121C24×C61C2×D414yes—
122C24×C61#4114yes—
123C24×C61C2411yescharacteristic
124C23×D61—22no—
125C23×D61—21no—
126C23×D61—22no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61C22×C412yes—
135C2×D4×C61—28no—
136C2×D4×C61—216no—
137C2×D4×C61—28no—
138C2×D4×C61—216no—
139C2×D4×C61—28no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61#4112yes—
162C2×C22⋊D61—216no—
163C2×C22⋊D61—48no—
164C2×C22⋊D61—48no—
165C2×C22⋊D61—48no—
166C2×C22⋊D61—48no—
167C2×C22⋊D61—48no—
168C2×C22⋊D61—48no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—21no—
192C22×Dic61—216no—
193C22×Dic61—48no—
194C22×Dic61—48no—
195C22×Dic61—48no—
196C22×Dic61—48no—
197C22×Dic61—48no—
198C22×Dic61—48no—
199C22×Dic61C22×C414yes—
200C22×Dic61C22×C412yes—
201C22×Dic61C2×D414yes—
202C22×Dic61C2×D412yes—
203C22×Dic61C2×D412yes—
204C22×Dic61C2×D414yes—
205C22⋊C4×C61—48no—
206C22⋊C4×C61—48no—
207C22⋊Dic61—216no—
208C22⋊Dic61—48no—
209#11758198—28no—
210#11758198—48no—
211#11758198—44no—
212#11758198—44no—
213C4⋊Dic61—28no—
214#11758196—44no—
215C4×Dic61—28no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—24no—
232C23×C61—24no—
233C23×C61—24no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61C4×D418yes—
251C23×C61C23×C411yescharacteristic
252C23×C61C22×D412yes—
253C23×C61C22×D411yescharacteristic
254C23×C61C2×#4112yes—
255C23×C61C2×#4111yescharacteristic
256C23×C61H(5,𝔽2)11yescharacteristic
257C23×C61H(5,𝔽2)12yes—
258C23×C61H(5,𝔽2)11yescharacteristic
259C23×C61H(5,𝔽2)12yes—
260C23×C61H(5,𝔽2)11yescharacteristic
261C23×C612−1+411yescharacteristic
262C22×D61—22no—
263C22×D61—24no—
264C22×D61—22no—
265C22×D61—24no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—42no—
269C22×D61—41no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—41no—
283C22×D61—42no—
284C22×D61—41no—
285D4×C61—232no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61C4×D414yes—
308C22⋊D61—432no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—24no—
317C2×Dic61—24no—
318C2×Dic61—22no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—432no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61#12014yes—
339#14299—611nomaximal, Sylow
340C22×C61—28no—
341C22×C61—28no—
342C22×C61—28no—
343C22×C61—44no—
344C22×C61—44no—
345C22×C61—44no—
346C22×C61—44no—
347C22×C61—44no—
348C22×C61—44no—
349C22×C61—44no—
350C22×C61—44no—
351C22×C61—44no—
352C22×C61—44no—
353C22×C61—44no—
354C22×C61—44no—
355C22×C61C2×C4×D412yes—
356C22×C61C2×C4×D411yescharacteristic
357C22×C61#51811yescharacteristic
358C22×C61#51812yes—
359C22×C61#52011yescharacteristic
360C22×C61C2×#12011yescharacteristic
361C22×C61#52512yes—
362C22×C61#52511yescharacteristic
363C22×C61#53412yes—
364C22×C61#53412yes—
365C22×C61#53511yescharacteristic
366C22×C61#53512yes—
367C22×C61#53511yescharacteristic
368C22×C61#53511yescharacteristic
369C22×C61#53712yes—
370C22×C61#53711yescharacteristic
371C22×C61#53812yes—
372C22×C61#53812yes—
373C22×C61#53812yes—
374C22×C61#53912yes—
375C22×C61#54012yes—
376C22×C61#54011yescharacteristic
377C22×C61#54211yescharacteristic
378C2×D61—44no—
379C2×D61—42no—
380C2×D61—44no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—82no—
386C2×D61—81no—
387C2×D61—82no—
388C2×D61—81no—
389C4×C61—24no—
390C4×C61—81no—
391C4×C61—81no—
392C4×C61—82no—
393Dic61—24no—
394Dic61—44no—
395Dic61—42no—
396Dic61—44no—
397Dic61—42no—
398C22×C4×D4—611no—
399C2×#392—611no—
400C2×#388—611no—
401C2×#386—612no—
402#1442—611no—
403#1439—611no—
404#1439—612no—
405#1438—612no—
406#1438D6111yescharacteristic, complemented
407#1434—611no—
408C22⋊#95—612no—
409C2×C61—48no—
410C2×C61C4×#12011yescharacteristic
411C2×C61#232112yes—
412C2×C61#232411yescharacteristic
413C2×C61#232512yes—
414C2×C61#232811yescharacteristic
415C2×C61#261311yescharacteristic
416C2×C61#261511yescharacteristic
417C2×C61#263012yes—
418C2×C61#263111yescharacteristic
419C2×C61#263512yes—
420C2×C61#263611yescharacteristic
421D61—82no—
422C23×D4—612no—
423C23×D4C2×D6111yescharacteristic
424C24×C4—612no—
425C2×C4×D4—1224no—
426C2×C4×D4—1228no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C22⋊C4—611no—
430C22×C22⋊C4—612no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4—611no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—612no—
435C22×C22⋊C4C2×D6112yes—
436C22×C22⋊C4C2×D6112yes—
437C22×C42—611no—
438#392—618no—
439#388—1224no—
440#386—1228no—
441C2×#95—611no—
442C2×#95—611no—
443C2×#95—612no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95C2×D6111yescharacteristic
449C2×#95C2×D6111yescharacteristic
450C61#1429911yescharacteristic, complemented, Sylow
451C25—611no—
452C25C22×D6112yes—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—618no—
458C22×D4—1224no—
459C22×D4—1224no—
460C22×D4—2442no—
461C22×D4—2442no—
462C22×D4—2442no—
463C22×D4—2442no—
464C22×D4C4×D6114yes—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—612no—
469C23×C4—612no—
470C23×C4—618no—
471C23×C4—1224no—
472C23×C4—1224no—
473C23×C4—2442no—
474C23×C4—2442no—
475C23×C4—2442no—
476C23×C4—2442no—
477C23×C4C22×D6111yescharacteristic
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6112yes—
480C23×C4C22×D6111yescharacteristic
481C4×D4—12232no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—2442no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—618no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4—1222no—
503C2×C22⋊C4—2442no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4—2442no—
508C2×C42—614no—
509C2×C42—1224no—
510#95—22no—
511#95—22no—
512#95—614no—
513#95—1224no—
514#95—1224no—
515#95—1222no—
516#95—2442no—
517#95—2442no—
518#95—2442no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—612no—
532C24—1221no—
533C24—1222no—
534C24—1221no—
535C24—1222no—
536C24—1221no—
537C24—1222no—
538C24—1221no—
539C24—1222no—
540C24—1221no—
541C24—1221no—
542C24C2×C4×D6114yes—
543C24D4×D6114yes—
544C24#1175822414yes—
545C24C23×D6111yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—28no—
551C2×D4—12216no—
552C2×D4—2448no—
553C2×D4—2448no—
554C2×D4—2448no—
555C2×D4—2448no—
556C2×D4—2448no—
557C2×D4—2448no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—612no—
578C22×C4—614no—
579C22×C4—614no—
580C22×C4—612no—
581C22×C4—614no—
582C22×C4—612no—
583C22×C4—12216no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1221no—
607C22×C4—2448no—
608C22×C4—2448no—
609C22×C4—2448no—
610C22×C4—2448no—
611C22×C4—2448no—
612C22×C4—2448no—
613C22×C4C2×C4×D6112yes—
614C22×C4D4×D6112yes—
615C22×C4#1175822412yes—
616C4⋊C4—1228no—
617C4⋊C4—2444no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—12216no—
621C22⋊C4—1228no—
622C22⋊C4—2444no—
623C22⋊C4—2448no—
624C22⋊C4—2444no—
625C22⋊C4—2448no—
626C42—1228no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—1222no—
662C23—1224no—
663C23—1222no—
664C23—1224no—
665C23—1222no—
666C23—2441no—
667C23—2442no—
668C23—2441no—
669C23—2442no—
670C23—2442no—
671C23—2441no—
672C23—2442no—
673C23—2441no—
674C23—2441no—
675C23—2442no—
676C23—2441no—
677C23—2442no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2441no—
683C23—2441no—
684C23#1451973718yes—
685C23C22×C4×D6111yescharacteristic
686C23C2×D4×D6112yes—
687C23C2×D4×D6111yescharacteristic
688C23C2×#1175822412yes—
689C23C2×#1175822411yescharacteristic
690C23#1451982212yes—
691C23#1451982211yescharacteristic
692C23#1451982211yescharacteristic
693C23#1451982312yes—
694C23#1451982311yescharacteristic
695C23#1451982411yescharacteristic
696D4—232no—
697D4—24432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—614no—
720C2×C4—1224no—
721C2×C4—1224no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1224no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1222no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—24432no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2441no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2441no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4#1451973714yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—4881no—
766C22—4881no—
767C22—4882no—
768C22—4881no—
769C22—4882no—
770C22—4881no—
771C22—2444no—
772C22—2442no—
773C22—2444no—
774C22—2442no—
775C22—2442no—
776C22C2×#1451973712yes—
777C22C2×#1451973711yescharacteristic
778C22#1684023411yescharacteristic
779C22#1684023412yes—
780C22#1684024111yescharacteristic
781C22#120×D6111yescharacteristic
782C22#1684026812yes—
783C22#1684026811yescharacteristic
784C22#1684032012yes—
785C22#1684032312yes—
786C22#1684032511yescharacteristic
787C22#1684032712yes—
788C22#1684032811yescharacteristic
789C22#1684033011yescharacteristic
790C22#1684033912yes—
791C22#1684034111yescharacteristic
792C22#1684034712yes—
793C22#1684034912yes—
794C22#1684034912yes—
795C22#1684035612yes—
796C22#1684036512yes—
797C22#1684036611yescharacteristic
798C22#1684038111yescharacteristic
799C4—24no—
800C4—81no—
801C4—81no—
802C4—82no—
803C4—1224no—
804C4—2444no—
805C4—2442no—
806C4—2444no—
807C4—2442no—
808C2—48no—
809C2—4882no—
810C2#2144831811yescharacteristic
811C2#2144848212yes—
812C2#2144851511yescharacteristic
813C2#2144852012yes—
814C2#2144854311yescharacteristic
815C2#2145153211yescharacteristic
816C2#2145154211yescharacteristic
817C2#2145165712yes—
818C2#2145167011yescharacteristic
819C2#2145170212yes—
820C2#2145171511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenter#1438D61
hypocenterC61#14299
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic61C2semidirect
3. C2×#16839651C2semidirect
4. C2×#16839639C2semidirect
5. #21444075C2semidirect
6. #21444065C2semidirect
7. #21444062C2semidirect
8. #21444058C2semidirect
9. #21444044C2semidirect
10. #21444041C2semidirect
11. C61×#1438C2semidirect
25. #16839670C4semidirect
47. C22×C22⋊D61C2×C4semidirect
54. C23×Dic61D4semidirect
70. C2×C22⋊Dic61C2×C4semidirect
80. C2×#11758198C2×C4semidirect
82. C2×C4×Dic61D4semidirect
89. #14519684C2×C4semidirect
406. #1438D61semidirect
450. C61#14299semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic612
C2×#168396702
C2×#168396512
C2×#168396392
#214440752
#214440652
#214440622
#214440582
#214440442
#214440412
C61×#14382
#1429961