Finite Group Databasebeta

← #29606767

Subgroups — #29606767

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×C4×D244C211yesmaximal, characteristic, complemented
2C2×#16839671C211yesmaximal, characteristic
3C2×#16839638C212yesmaximal, complemented
4#21444075C211yesmaximal, characteristic, complemented
5#21444064C211yesmaximal, characteristic, complemented
6#21444061C212yesmaximal, complemented
7#21444059C211yesmaximal, characteristic, complemented
8#21444058C212yesmaximal, complemented
9#21444046C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C61×#388C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C22⋊D61C2212yes—
14C23×C4×D61C2212yes—
15C2×C4×D244—24no—
16C2×C4×D244—28no—
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23#16839671C418yescomplemented
24#16839638—28no—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C61×#388—24no—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C24×D61C2312yes—
41C22×D244—24no—
42C22×D244—24no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244C2×C414yes—
46C22×C22⋊D61—24no—
47C22×C22⋊D61—24no—
48C22×C22⋊D61—42no—
49C22×C22⋊D61—42no—
50C22×C22⋊D61—42no—
51C22×C22⋊D61—42no—
52C22×C22⋊D61C2×C418yescomplemented
53C23×Dic61C2312yes—
54C23×Dic61C2312yes—
55C23×Dic61C2312yes—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—42no—
59C22×C4×D61—42no—
60C22×C4×D61—42no—
61C22×C4×D61—42no—
62C22×C4×D61D418yescomplemented
63C4×D244—232no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61—42no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—42no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198—42no—
80C2×#11758198C2×C418yescomplemented
81#14519684—24no—
82#14519684—22no—
83#14519684—24no—
84#14519684—42no—
85#14519684—42no—
86#14519684—42no—
87#14519684C2×C414yescomplemented
88C25×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
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—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—42no—
103C2×C22⋊C4×C61C2×C414yescomplemented
104C2×C42×C61—24no—
105C2×C42×C61D414yescomplemented
106#95×C61—22no—
107#95×C61—22no—
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—22no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61C22×C412yes—
119C24×C61C2411yescharacteristic
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61C22×C414yes—
133C23×D61C2×D414yes—
134C23×D61#4114yes—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D414yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61#4112yes—
165C2×C22⋊D61—216no—
166C2×C22⋊D61—48no—
167C2×C22⋊D61—48no—
168C2×C22⋊D61—48no—
169C2×C22⋊D61—48no—
170C2×C22⋊D61—48no—
171C2×C22⋊D61—48no—
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×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61C22×C414yes—
192C22×Dic61C2×D414yes—
193C2×D244—28no—
194C2×D244—216no—
195C2×D244—28no—
196C2×D244—216no—
197C2×D244—28no—
198C2×C4×D61—216no—
199C2×C4×D61—48no—
200C2×C4×D61—48no—
201C2×C4×D61—48no—
202C2×C4×D61—48no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C4⋊C4×C61—44no—
206C22⋊C4×C61—28no—
207C22⋊C4×C61—44no—
208C22⋊C4×C61—44no—
209C42×C61—28no—
210C22⋊Dic61—48no—
211#11758198—216no—
212#11758198—48no—
213#11758198—48no—
214#11758198—48no—
215C4⋊Dic61—28no—
216C23×C61—22no—
217C23×C61—24no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—22no—
221C23×C61—41no—
222C23×C61—42no—
223C23×C61—41no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—41no—
227C23×C61—42no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—41no—
237C23×C61—42no—
238C23×C61—41no—
239C23×C61C23×C411yescharacteristic
240C23×C61C22×D412yes—
241C23×C61C22×D411yescharacteristic
242C23×C61C2×#4112yes—
243C23×C61C2×#4111yescharacteristic
244C23×C61H(5,𝔽2)11yescharacteristic
245C23×C61H(5,𝔽2)12yes—
246C23×C61H(5,𝔽2)12yes—
247C23×C61H(5,𝔽2)11yescharacteristic
248C23×C61H(5,𝔽2)11yescharacteristic
249C23×C612−1+411yescharacteristic
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—24no—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—24no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61C4×D418yes—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61C4×D414yes—
314C2×C4×C61#12014yes—
315C22⋊D61—432no—
316C2×Dic61—24no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337D244—232no—
338C4×D61—432no—
339#14299—611nomaximal, Sylow
340C22×C61—44no—
341C22×C61—42no—
342C22×C61—44no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—82no—
348C22×C61—81no—
349C22×C61—82no—
350C22×C61—81no—
351C22×C61C2×C4×D412yes—
352C22×C61C2×C4×D411yescharacteristic
353C22×C61#51812yes—
354C22×C61#51811yescharacteristic
355C22×C61#52011yescharacteristic
356C22×C61C2×#12011yescharacteristic
357C22×C61#52511yescharacteristic
358C22×C61#52512yes—
359C22×C61#53412yes—
360C22×C61#53412yes—
361C22×C61#53511yescharacteristic
362C22×C61#53511yescharacteristic
363C22×C61#53512yes—
364C22×C61#53511yescharacteristic
365C22×C61#53711yescharacteristic
366C22×C61#53712yes—
367C22×C61#53812yes—
368C22×C61#53812yes—
369C22×C61#53812yes—
370C22×C61#53912yes—
371C22×C61#54012yes—
372C22×C61#54011yescharacteristic
373C22×C61#54211yescharacteristic
374C2×D61—28no—
375C2×D61—28no—
376C2×D61—28no—
377C2×D61—44no—
378C2×D61—44no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61—44no—
388C2×D61—44no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61—81no—
394C4×C61—81no—
395Dic61—44no—
396Dic61—44no—
397Dic61—82no—
398C22×C4×D4—611no—
399C2×#392—611no—
400C2×#388D6111yescharacteristic, complemented
401C2×#386—612no—
402#1442—611no—
403#1439—612no—
404#1439—611no—
405#1438—611no—
406#1438—612no—
407#1434—611no—
408C22⋊#95—612no—
409C2×C61—82no—
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—48no—
422C23×D4—612no—
423C23×D4—611no—
424C24×C4—612no—
425C2×C4×D4—1228no—
426C2×C4×D4—1224no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C22⋊C4—612no—
430C22×C22⋊C4—612no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4—612no—
433C22×C22⋊C4—612no—
434C22×C22⋊C4C2×D6111yescharacteristic
435C22×C22⋊C4C2×D6111yescharacteristic
436C22×C22⋊C4C2×D6111yescharacteristic
437C22×C42C2×D6111yescharacteristic
438#392—618no—
439#388—24no—
440#386—1228no—
441C2×#95—611no—
442C2×#95—612no—
443C2×#95—611no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95C2×D6111yescharacteristic
449C2×#95C2×D6111yescharacteristic
450C61#1429911yescharacteristic, complemented, Sylow
451C25—612no—
452C25C22×D6111yescharacteristic
453C22×D4—618no—
454C22×D4—614no—
455C22×D4—1224no—
456C22×D4—1224no—
457C22×D4—1224no—
458C22×D4—1224no—
459C22×D4—1222no—
460C22×D4—1222no—
461C22×D4—2442no—
462C22×D4—2442no—
463C22×D4—2442no—
464C22×D4—2442no—
465C23×C4—612no—
466C23×C4—612no—
467C23×C4—618no—
468C23×C4—612no—
469C23×C4—1224no—
470C23×C4—1224no—
471C23×C4—2442no—
472C23×C4—2442no—
473C23×C4—2442no—
474C23×C4—2442no—
475C23×C4C22×D6111yescharacteristic
476C23×C4C22×D6111yescharacteristic
477C23×C4C22×D6111yescharacteristic
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6111yescharacteristic
480C23×C4C22×D6111yescharacteristic
481C4×D4—12232no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—1222no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—618no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—2442no—
500C2×C22⋊C4—2442no—
501C2×C22⋊C4—2442no—
502C2×C22⋊C4—2442no—
503C2×C22⋊C4—2442no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4C4×D6114yescomplemented
508C2×C42—24no—
509C2×C42C22⋊D6114yescomplemented
510#95—22no—
511#95—22no—
512#95—614no—
513#95—1224no—
514#95—1222no—
515#95—1224no—
516#95—2442no—
517#95—2442no—
518#95—2442no—
519C24—22no—
520C24—21no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—614no—
530C24—614no—
531C24—614no—
532C24—1222no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24C2×C4×D6112yes—
545C24C23×D6111yescharacteristic
546C2×D4—12216no—
547C2×D4—1228no—
548C2×D4—1228no—
549C2×D4—12216no—
550C2×D4—12216no—
551C2×D4—1228no—
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—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—614no—
582C22×C4—614no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—12216no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—2448no—
604C22×C4—2448no—
605C22×C4—2448no—
606C22×C4—2448no—
607C22×C4—2448no—
608C22×C4—2448no—
609C22×C4C2×C4×D6112yes—
610C22×C4C2×C4×D6112yes—
611C22×C4#1175822212yes—
612C22×C4D4×D6114yes—
613C22×C4C2×C22⋊D6112yes—
614C22×C4C2×C22⋊D6112yes—
615C22×C4C2×C22⋊D6112yes—
616C4⋊C4—44no—
617C4⋊C4—1228no—
618C22⋊C4—28no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—12216no—
622C22⋊C4—2448no—
623C22⋊C4—2448no—
624C22⋊C4—2448no—
625C22⋊C4—2448no—
626C42—28no—
627C23—24no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—618no—
651C23—1224no—
652C23—1224no—
653C23—1224no—
654C23—1224no—
655C23—1224no—
656C23—1224no—
657C23—1224no—
658C23—1224no—
659C23—1224no—
660C23—1224no—
661C23—1224no—
662C23—1224no—
663C23—1224no—
664C23—1224no—
665C23—1224no—
666C23—1224no—
667C23—1224no—
668C23—1224no—
669C23—2442no—
670C23—2442no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23—2442no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23C22×C4×D6111yescharacteristic
686C23C2×D4×D6112yes—
687C23C22×C22⋊D6111yescharacteristic
688C23#41×D6112yes—
689C23C2×#1175822211yescharacteristic
690C23#1451982212yes—
691C23#1451982312yes—
692C23#1451982311yescharacteristic
693C23#1451982311yescharacteristic
694C23#1451982311yescharacteristic
695C23#1451982411yescharacteristic
696D4—12232no—
697D4—24432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—24432no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4C4×C22⋊D6114yes—
749C2×C4#1451974514yes—
750C22—44no—
751C22—42no—
752C22—44no—
753C22—42no—
754C22—42no—
755C22—81no—
756C22—81no—
757C22—82no—
758C22—81no—
759C22—82no—
760C22—81no—
761C22—1228no—
762C22—1228no—
763C22—1228no—
764C22—2444no—
765C22—2444no—
766C22—2444no—
767C22—2444no—
768C22—2444no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22—2444no—
773C22—2444no—
774C22—2444no—
775C22—2444no—
776C22C4×D4×D6112yes—
777C22C2×C4×C22⋊D6111yescharacteristic
778C22#1684023412yes—
779C22#1684023611yescharacteristic
780C22#1684024211yescharacteristic
781C22C2×#1451974511yescharacteristic
782C22#1684026911yescharacteristic
783C22#1684027112yes—
784C22#1684032312yes—
785C22#1684032312yes—
786C22#1684032611yescharacteristic
787C22#1684032611yescharacteristic
788C22#1684032812yes—
789C22#1684032911yescharacteristic
790C22#1684034011yescharacteristic
791C22#1684034112yes—
792C22#1684034612yes—
793C22#1684034612yes—
794C22#1684035112yes—
795C22#1684035312yes—
796C22#1684036312yes—
797C22#1684036711yescharacteristic
798C22#1684038311yescharacteristic
799C4—24no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—4882no—
806C4—2444no—
807C4—2444no—
808C2—82no—
809C2—2448no—
810C2C4×#1451974511yescharacteristic
811C2#2144848112yes—
812C2#2144851211yescharacteristic
813C2#2144852312yes—
814C2#2144854111yescharacteristic
815C2#2145153511yescharacteristic
816C2#2145154411yescharacteristic
817C2#2145166612yes—
818C2#2145167211yescharacteristic
819C2#2145171012yes—
820C2#2145171611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC2×#388D61
hypocenterC61#14299
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4×D244C2semidirect
3. C2×#16839638C2semidirect
4. #21444075C2semidirect
5. #21444064C2semidirect
6. #21444061C2semidirect
7. #21444059C2semidirect
8. #21444058C2semidirect
9. #21444046C2semidirect
10. #21444040C2semidirect
11. C2×C61×#388C2semidirect
23. #16839671C4semidirect
52. C22×C22⋊D61C2×C4semidirect
62. C22×C4×D61D4semidirect
80. C2×#11758198C2×C4semidirect
87. #14519684C2×C4semidirect
103. C2×C22⋊C4×C61C2×C4semidirect
105. C2×C42×C61D4semidirect
400. C2×#388D61semidirect
450. C61#14299semidirect
507. C2×C22⋊C4C4×D61semidirect
509. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C2×#168396712
C2×#168396382
#214440752
#214440642
#214440612
#214440592
#214440582
#214440462
#214440402
C2×C61×#3882
#1429961