Finite Group Databasebeta

← #29602732

Subgroups — #29602732

Order 15616.

2590 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal
3C2×#16839621C211yesmaximal, characteristic, complemented
4C2×#95×D61C211yesmaximal, characteristic, complemented
5#21444071C212yesmaximal, complemented
6#21444063C212yesmaximal, complemented
7#21444046C211yesmaximal, characteristic, complemented
8#21444040C212yesmaximal, complemented
9#21444040C211yesmaximal, characteristic, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C61×#1434C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×C4×D244—24no—
17C2×C4×D244—24no—
18C2×C4×D244C418yescomplemented
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26#16839640—28no—
27#16839621—24no—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35#95×D61—24no—
36C22×C42×C61C2211yescharacteristic
37C2×#95×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C2×#95×C61C2211yescharacteristic
41C24×D61C2311yescharacteristic
42C24×D61C2311yescharacteristic
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244C2×C414yes—
48C22×D244D414yes—
49C22×D244Q814yes—
50C23×Dic61C2312yes—
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C22×C4×D61—24no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—42no—
62C22×C4×D61—42no—
63C22×C4×D61—42no—
64C22×C4×D61—42no—
65C22×C4×D61—42no—
66C22×C4×D61—42no—
67C22×C4×D61C2×C414yes—
68C22×C4×D61C2×C414yescomplemented
69C22×C4×D61D414yes—
70C22×C4×D61D414yes—
71C4×D244—232no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61C2×C414yescomplemented
75C2×#11758196—24no—
76C2×#11758196—42no—
77C2×#11758196—42no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—42no—
90C2×#11758198—42no—
91C2×#11758198C2×C414yes—
92C2×#11758198C2×C414yescomplemented
93#14519684—22no—
94#14519684—22no—
95#14519684—24no—
96#14519684—24no—
97#14519684—24no—
98#14519684—42no—
99#14519684—42no—
100C23×C4×C61C2312yes—
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2312yes—
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C2×C42×C61—22no—
106C2×C42×C61—22no—
107C2×C42×C61C2×C414yescomplemented
108#95×C61—22no—
109#95×C61—22no—
110#95×C61—24no—
111#95×C61—24no—
112C24×C61C2411yescharacteristic
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61C22×C412yes—
126C23×D61C22×C412yes—
127C23×D61C2×D412yes—
128C23×D61C2×D412yes—
129C23×D61C2×D412yes—
130C23×D61C2×D412yes—
131C23×D61C2×Q812yes—
132C23×D61C2×Q812yes—
133C23×D61#4112yes—
134C23×D61#4112yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
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—21no—
144C22×C4×C61—21no—
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×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×Q812yes—
165C22×C4×C61#4114yes—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—21no—
171C22×Dic61—21no—
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×Dic61C22×C412yes—
186C22×Dic61C22×C412yes—
187C22×Dic61C2×D412yes—
188C22×Dic61C2×D412yes—
189C22×Dic61#4114yes—
190C2×D244—28no—
191C2×D244—28no—
192C2×D244—28no—
193C2×D244—28no—
194C2×D244—28no—
195C2×D244—28no—
196C2×D244C4⋊C4116yescomplemented
197C2×C4×D61—216no—
198C2×C4×D61—28no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61—44no—
202C2×C4×D61—44no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C2×C4×D61—48no—
207C2×C4×D61—48no—
208C2×C4×D61—48no—
209C2×C4×D61—48no—
210C2×C4×D61—48no—
211C2×C4×D61—48no—
212C2×C4×D61—48no—
213C2×C4×D61C22⋊C4116yescomplemented
214C42×C61—28no—
215#11758198—28no—
216#11758198—28no—
217#11758198—48no—
218#11758198—48no—
219#11758198—48no—
220C4⋊Dic61—28no—
221#11758196—48no—
222C23×C61C23×C411yescharacteristic
223C23×C61C22×D411yescharacteristic
224C23×C61C22×D411yescharacteristic
225C23×C61C22×D411yescharacteristic
226C23×C61C22×Q811yescharacteristic
227C23×C61C2×#4111yescharacteristic
228C23×C61C2×#4111yescharacteristic
229C23×C61C2×#4112yes—
230C23×C61C2×#4112yes—
231C23×C61H(5,𝔽2)12yes—
232C23×C61H(5,𝔽2)12yes—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—24no—
240C22×D61—24no—
241C22×D61—24no—
242C22×D61—24no—
243C22×D61—24no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61C2×C22⋊C414yes—
272C22×D61C2×C4⋊C414yes—
273C22×D61C2×C4⋊C414yes—
274C22×D61#11714yes—
275C22×D61#12114yes—
276C22×D61#12114yes—
277C22×D61C22⋊Q814yes—
278C22×D61C22⋊Q814yes—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
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×C61—42no—
308C2×C4×C61C2×C22⋊C414yes—
309C2×C4×C61C2×C4⋊C414yes—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—42no—
321C2×Dic61—42no—
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×Dic61C2×C22⋊C414yes—
334D244—232no—
335C4×D61—416no—
336C4×D61—416no—
337C4×D61—432no—
338#13960—611nomaximal, Sylow
339C22×C61C22×C22⋊C411yescharacteristic
340C22×C61C22×C4⋊C411yescharacteristic
341C22×C61C2×#11711yescharacteristic
342C22×C61C4×#4111yescharacteristic
343C22×C61C4×#4111yescharacteristic
344C22×C61#51811yescharacteristic
345C22×C61#51811yescharacteristic
346C22×C61C2×#12111yescharacteristic
347C22×C61C2×#12111yescharacteristic
348C22×C61C2×C22⋊Q811yescharacteristic
349C22×C61C2×C22⋊Q811yescharacteristic
350C22×C61#52512yes—
351C22×C61#53212yes—
352C22×C61#53412yes—
353C22×C61#53412yes—
354C22×C61#54612yes—
355C22×C61#54612yes—
356C22×C61#55112yes—
357C22×C61#55112yes—
358C22×C61#55312yes—
359C22×C61#55312yes—
360C22×C61#55412yes—
361C22×C61#55412yes—
362C2×D61—24no—
363C2×D61—28no—
364C2×D61—28no—
365C2×D61—24no—
366C2×D61—24no—
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—28no—
370C2×D61—28no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61—24no—
375C2×D61—42no—
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—42no—
383C2×D61#38018yes—
384C4×C61—24no—
385C4×C61—24no—
386C4×C61—44no—
387C4×C61—42no—
388C4×C61—82no—
389Dic61—24no—
390Dic61—42no—
391Dic61—44no—
392Dic61—82no—
393C22×C4×D4—611no—
394C2×#386—612no—
395C2×#380—611no—
396C22×#95—611no—
397#1441—612no—
398#1439—612no—
399#1434—611no—
400#1434D6111yescharacteristic, complemented
401C22⋊#95—612no—
402C22⋊#95—611no—
403C22⋊#95—611no—
404C2×C61C2×#38011yescharacteristic
405C2×C61#229711yescharacteristic
406C2×C61#230811yescharacteristic
407C2×C61#234911yescharacteristic
408C2×C61#234911yescharacteristic
409C2×C61#235311yescharacteristic
410C2×C61#235311yescharacteristic
411C2×C61#253412yes—
412C2×C61#254312yes—
413C2×C61#256412yes—
414C2×C61#257912yes—
415D61—28no—
416D61—44no—
417C23×D4—611no—
418C24×C4—611no—
419C24×C4—611no—
420C24×C4—612no—
421C2×C4×D4—618no—
422C2×C4×D4—1224no—
423C2×C4×D4—1224no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—612no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—611no—
428C22×C22⋊C4—612no—
429C22×C22⋊C4—612no—
430C22×C22⋊C4—612no—
431C22×C42C2×D6111yescharacteristic
432#386—1228no—
433#380—1224no—
434C2×#95—612no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—612no—
438C2×#95—612no—
439C2×#95—612no—
440C2×#95—612no—
441C2×#95—1224no—
442C2×#95C2×D6112yes—
443C2×#95C2×D6111yescharacteristic
444C2×#95C2×D6111yescharacteristic
445C2×#95C2×D6112yes—
446C61#1396011yescharacteristic, complemented, Sylow
447C25—611no—
448C25—611no—
449C22×D4—614no—
450C22×D4—614no—
451C22×D4—614no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1222no—
456C23×C4—611no—
457C23×C4—614no—
458C23×C4—614no—
459C23×C4—614no—
460C23×C4—611no—
461C23×C4—612no—
462C23×C4—614no—
463C23×C4—612no—
464C23×C4—1224no—
465C23×C4—1224no—
466C23×C4—1224no—
467C23×C4—1224no—
468C23×C4—1224no—
469C23×C4—1222no—
470C23×C4—1222no—
471C23×C4—2442no—
472C23×C4—2442no—
473C23×C4—2442no—
474C23×C4—2442no—
475C23×C4—2442no—
476C23×C4—2442no—
477C23×C4C22×D6112yes—
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6112yes—
480C23×C4C22×D6111yescharacteristic
481C23×C4C22×D6111yescharacteristic
482C4×D4—12232no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1224no—
487C2×C4⋊C4—2442no—
488C2×C4⋊C4—2442no—
489C2×C22⋊C4—614no—
490C2×C22⋊C4—614no—
491C2×C22⋊C4—1222no—
492C2×C22⋊C4—1222no—
493C2×C22⋊C4—1222no—
494C2×C22⋊C4—1222no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—2442no—
503C2×C22⋊C4—2442no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42C4×D6114yescomplemented
507#95—24no—
508#95—22no—
509#95—22no—
510#95—24no—
511#95—1224no—
512#95—1224no—
513#95—1222no—
514#95—1222no—
515#95—1224no—
516#95—2442no—
517#95—2442no—
518C24—612no—
519C24—612no—
520C24—612no—
521C24—612no—
522C24—612no—
523C24—612no—
524C24—612no—
525C24—612no—
526C24—612no—
527C24—612no—
528C24—1222no—
529C24—1222no—
530C24—1222no—
531C24—1222no—
532C24—1221no—
533C24—1221no—
534C24—1222no—
535C24—1221no—
536C24—1221no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24C23×D6111yescharacteristic
541C2×D4—6116no—
542C2×D4—1228no—
543C2×D4—1228no—
544C2×D4—1228no—
545C2×D4—1228no—
546C2×D4—1228no—
547C2×D4—1228no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—6116no—
575C22×C4—612no—
576C22×C4—614no—
577C22×C4—12216no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1228no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—2444no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4—2444no—
602C22×C4—2448no—
603C22×C4—2448no—
604C22×C4—2448no—
605C22×C4—2448no—
606C22×C4—2448no—
607C22×C4—2448no—
608C22×C4—2448no—
609C22×C4—2448no—
610C22×C4—2448no—
611C22×C4—2448no—
612C22×C4C2×C4×D6112yes—
613C22×C4C2×C4×D6112yes—
614C22×C4C2×C4×D6112yes—
615C22×C4#1175822214yes—
616C22×C4D4×D6112yes—
617C22×C4D4×D6112yes—
618C22×C4D4×D6112yes—
619C22×C4Q8×D6112yes—
620C4⋊C4—1228no—
621C4⋊C4—2448no—
622C22⋊C4—1228no—
623C22⋊C4—1228no—
624C22⋊C4—2448no—
625C22⋊C4—2448no—
626C22⋊C4—2448no—
627C42—28no—
628C23—614no—
629C23—614no—
630C23—614no—
631C23—614no—
632C23—614no—
633C23—614no—
634C23—614no—
635C23—614no—
636C23—1224no—
637C23—1224no—
638C23—1224no—
639C23—1224no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1224no—
645C23—1224no—
646C23—1224no—
647C23—1224no—
648C23—1224no—
649C23—1224no—
650C23—1224no—
651C23—1224no—
652C23—1222no—
653C23—1224no—
654C23—1222no—
655C23—1224no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1224no—
665C23—1224no—
666C23—2442no—
667C23—2442no—
668C23—2442no—
669C23—2442no—
670C23—2442no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23C22×C4×D6111yescharacteristic
675C23C2×D4×D6111yescharacteristic
676C23C2×D4×D6111yescharacteristic
677C23C2×D4×D6111yescharacteristic
678C23C2×Q8×D6111yescharacteristic
679C23#41×D6111yescharacteristic
680C23#41×D6112yes—
681C23#41×D6111yescharacteristic
682C23C2×#1175822212yes—
683C23#1451982312yes—
684C23#1451982312yes—
685D4—12232no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—614no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1224no—
719C2×C4—1224no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1224no—
724C2×C4—1224no—
725C2×C4—1224no—
726C2×C4—24416no—
727C2×C4—24416no—
728C2×C4—24432no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
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×C4C22⋊C4×D6114yes—
743C2×C4C4⋊C4×D6114yes—
744C22—618no—
745C22—1224no—
746C22—1224no—
747C22—1228no—
748C22—1224no—
749C22—1224no—
750C22—1224no—
751C22—1228no—
752C22—1224no—
753C22—1228no—
754C22—1228no—
755C22—1224no—
756C22—1224no—
757C22—1224no—
758C22—2444no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22—2444no—
763C22—2442no—
764C22—2444no—
765C22—2444no—
766C22C2×C22⋊C4×D6111yescharacteristic
767C22C2×C4⋊C4×D6111yescharacteristic
768C22#117×D6111yescharacteristic
769C22#1684023011yescharacteristic
770C22C4×#1175822211yescharacteristic
771C22#1684023611yescharacteristic
772C22#1684023611yescharacteristic
773C22#121×D6111yescharacteristic
774C22#121×D6111yescharacteristic
775C22C22⋊Q8×D6111yescharacteristic
776C22C22⋊Q8×D6111yescharacteristic
777C22#1684027112yes—
778C22#1684030912yes—
779C22#1684032312yes—
780C22#1684032312yes—
781C22#1684040512yes—
782C22#1684040812yes—
783C22#1684043612yes—
784C22#1684043712yes—
785C22#1684045612yes—
786C22#1684046312yes—
787C22#1684046812yes—
788C22#1684047212yes—
789C4—24no—
790C4—24no—
791C4—42no—
792C4—44no—
793C4—82no—
794C4—1224no—
795C4—4882no—
796C4—2442no—
797C4—2444no—
798C2—1228no—
799C2—2444no—
800C2#380×D6111yescharacteristic
801C2#2144830511yescharacteristic
802C2#2144839611yescharacteristic
803C2#2144872711yescharacteristic
804C2#2144873011yescharacteristic
805C2#2144875211yescharacteristic
806C2#2144876011yescharacteristic
807C2#2145071312yes—
808C2#2145078412yes—
809C2#2145099812yes—
810C2#2145117012yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#13960
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16839621C2semidirect
4. C2×#95×D61C2semidirect
5. #21444071C2semidirect
6. #21444063C2semidirect
7. #21444046C2semidirect
8. #21444040C2semidirect
9. #21444040C2semidirect
10. #21444040C2semidirect
11. C61×#1434C2semidirect
18. C2×C4×D244C4semidirect
68. C22×C4×D61C2×C4semidirect
74. C2×C4⋊Dic61C2×C4semidirect
92. C2×#11758198C2×C4semidirect
107. C2×C42×C61C2×C4semidirect
196. C2×D244C4⋊C4semidirect
213. C2×C4×D61C22⋊C4semidirect
400. #1434D61semidirect
446. C61#13960semidirect
506. C2×C42C4×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×#168396402
C2×#168396212
C2×#95×D612
#214440712
#214440632
#214440462
#214440402
C61×#14342
#1396061