Finite Group Databasebeta

← #29601892

Subgroups — #29601892

Order 15616.

3902 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C211yesmaximal, characteristic
2C22×C22⋊C4×D61C211yesmaximal, characteristic
3C2×#16839624C212yesmaximal, complemented
4C2×#16839617C211yesmaximal, characteristic
5#21444068C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444066C211yesmaximal, characteristic, complemented
8#21444040C212yesmaximal, complemented
9#21444040C212yesmaximal, complemented
10#21444040C212yesmaximal, complemented
11C61×#1440C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C23×C4×D61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C2×C22⋊C4×D61—28no—
25C2×C22⋊C4×D61—24no—
26C2×C22⋊C4×D61—24no—
27C2×C22⋊C4×D61—24no—
28C2×C22⋊C4×D61C418yescomplemented
29#16839624—28no—
30#16839617—24no—
31C2×#14519684C2212yescomplemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C2×#14519684C2212yescomplemented
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C2×#95×C61C2212yescomplemented
41C2×#95×C61C2212yescomplemented
42C24×D61—24no—
43C24×D61—24no—
44C24×D61—24no—
45C24×D61—24no—
46C24×D61—42no—
47C24×D61—42no—
48C24×D61C2×C414yes—
49C24×D61D414yes—
50C24×D61D414yes—
51C24×D61C2311yescharacteristic
52C24×D61C2311yescharacteristic
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2312yes—
57C22×C4×D61—24no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—24no—
63C22×C4×D61—24no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—42no—
69C22×C4×D61—42no—
70C22×C4×D61—42no—
71C22×C4×D61—42no—
72C22×C4×D61C2×C414yescomplemented
73C22×C4×D61C2×C414yescomplemented
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—24no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—42no—
80C2×C22⋊Dic61C2×C414yescomplemented
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198C2×C414yes—
94C2×#11758198C2×C414yes—
95C2×#11758198D418yes—
96C22⋊C4×D61—232no—
97C22⋊C4×D61—232no—
98#14519684—24no—
99#14519684—24no—
100#14519684—24no—
101#14519684—42no—
102#14519684—42no—
103#14519684—42no—
104C25×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2312yes—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—42no—
115C2×C22⋊C4×C61C2×C414yescomplemented
116#95×C61—24no—
117#95×C61—42no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61C22×C412yes—
125C24×C61C2×D412yes—
126C24×C61C2×D412yes—
127C24×C61C2411yescharacteristic
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—28no—
137C23×D61—28no—
138C23×D61—216no—
139C23×D61—28no—
140C23×D61—216no—
141C23×D61—216no—
142C23×D61—216no—
143C23×D61—28no—
144C23×D61—48no—
145C23×D61—48no—
146C23×D61—44no—
147C23×D61—44no—
148C23×D61—48no—
149C23×D61—48no—
150C23×D61—48no—
151C23×D61—48no—
152C23×D61—48no—
153C23×D61—48no—
154C23×D61—48no—
155C23×D61—48no—
156C23×D61C22⋊C4116yes—
157C23×D61C22×C412yes—
158C23×D61C22×C412yes—
159C23×D61C2×D412yes—
160C23×D61C2×D412yes—
161C23×D61C2×D412yes—
162C23×D61C2×D412yes—
163C23×D61C2×D414yes—
164C23×D61#4114yes—
165C23×D61#4114yes—
166C23×D61#4114yes—
167C22×C4×C61—22no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C22×C412yes—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C2×D414yes—
191C22×Dic61—22no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61C22×C412yes—
213C22×Dic61C22×C412yes—
214C22×Dic61C2×D414yes—
215C2×C4×D61—216no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61—216no—
219C2×C4×D61—48no—
220C2×C4×D61—48no—
221C2×C4×D61—48no—
222C2×C4×D61—48no—
223C2×C4×D61—48no—
224C2×C4×D61—48no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61—48no—
228C2×C4×D61—44no—
229C2×C4×D61—48no—
230C2×C4×D61—48no—
231C2×C4×D61—44no—
232C22⋊C4×C61—28no—
233C22⋊C4×C61—28no—
234C22⋊C4×C61—44no—
235C22⋊Dic61—28no—
236C22⋊Dic61—28no—
237C22⋊Dic61—44no—
238#11758198—28no—
239#11758198—28no—
240#11758198—216no—
241#11758198—48no—
242#11758198—48no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—24no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—24no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61C2×C22⋊C414yes—
264C23×C61C23×C411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61C22×D411yescharacteristic
267C23×C61C22×D412yes—
268C23×C61C2×#4112yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4112yes—
271C23×C61H(5,𝔽2)12yes—
272C23×C61H(5,𝔽2)12yes—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—22no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—22no—
283C22×D61—24no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—24no—
290C22×D61—24no—
291C22×D61—24no—
292C22×D61—24no—
293C22×D61—24no—
294C22×D61—24no—
295C22×D61—24no—
296C22×D61—24no—
297C22×D61—24no—
298C22×D61—24no—
299C22×D61—24no—
300C22×D61—24no—
301C22×D61—24no—
302C22×D61—24no—
303C22×D61—24no—
304C22×D61—24no—
305C22×D61—232no—
306C22×D61—232no—
307C22×D61—416no—
308C22×D61—432no—
309C22×D61—432no—
310C22×D61—432no—
311C22×D61—432no—
312C22×D61—432no—
313C22×D61—432no—
314C22×D61C2×C22⋊C414yes—
315C22×D61C2×C22⋊C414yes—
316C22×D61#11714yes—
317C22×D61#11714yes—
318C22×D61C4×D418yes—
319C22×D61#12014yes—
320C22×D61#12118yes—
321C22×D61#12318yes—
322C22×D61#12318yes—
323C22×D61#12314yes—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—24no—
327C2×C4×C61—24no—
328C2×C4×C61—24no—
329C2×C4×C61—24no—
330C2×C4×C61—24no—
331C2×C4×C61—41no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—41no—
335C2×C4×C61—42no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—42no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—24no—
353C2×Dic61—24no—
354C2×Dic61—24no—
355C2×Dic61—41no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—41no—
359C2×Dic61—42no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C4×D61—416no—
373C4×D61—432no—
374C4×D61—416no—
375#13869—611nomaximal, Sylow
376C22×C61—24no—
377C22×C61—24no—
378C22×C61—24no—
379C22×C61—44no—
380C22×C61—44no—
381C22×C61—44no—
382C22×C61—44no—
383C22×C61—44no—
384C22×C61—44no—
385C22×C61C22×C22⋊C411yescharacteristic
386C22×C61C2×#11711yescharacteristic
387C22×C61C2×#11711yescharacteristic
388C22×C61C2×C4×D412yes—
389C22×C61#51812yes—
390C22×C61C2×#12011yescharacteristic
391C22×C61C2×#12112yes—
392C22×C61C2×#12312yes—
393C22×C61C2×#12312yes—
394C22×C61C2×#12311yescharacteristic
395C22×C61#53412yes—
396C22×C61#53411yescharacteristic
397C22×C61#53411yescharacteristic
398C22×C61#54612yes—
399C22×C61#54612yes—
400C22×C61#54612yes—
401C22×C61#54612yes—
402C22×C61#55112yes—
403C22×C61#55112yes—
404C22×C61#55112yes—
405C22×C61#55112yes—
406C2×D61—24no—
407C2×D61—24no—
408C2×D61—28no—
409C2×D61—28no—
410C2×D61—28no—
411C2×D61—28no—
412C2×D61—28no—
413C2×D61—28no—
414C2×D61—28no—
415C2×D61—28no—
416C2×D61—28no—
417C2×D61—28no—
418C2×D61—28no—
419C2×D61—28no—
420C2×D61—24no—
421C2×D61—24no—
422C2×D61—464no—
423C2×D61#38118yescomplemented
424C2×D61#38618yes—
425C4×C61—42no—
426C4×C61—44no—
427C4×C61—42no—
428C4×C61—82no—
429Dic61—42no—
430Dic61—44no—
431Dic61—42no—
432Dic61—82no—
433C23×C22⋊C4—611no—
434C23×C22⋊C4—611no—
435C2×#381—612no—
436C2×#379—611no—
437#1440—611no—
438#1440—611no—
439#1440—611no—
440#1440D6111yescharacteristic, complemented
441C22⋊#95—612no—
442C22⋊#95—612no—
443C22⋊#95—612no—
444C2×C61—44no—
445C2×C61C2×#38111yescharacteristic
446C2×C61C2×#38611yescharacteristic
447C2×C61#230811yescharacteristic
448C2×C61#234212yes—
449C2×C61#234212yes—
450C2×C61#240512yes—
451C2×C61#241212yes—
452C2×C61#241212yes—
453C2×C61#248312yes—
454D61—28no—
455D61—28no—
456C26—611no—
457C24×C4—611no—
458C24×C4—611no—
459C24×C4—612no—
460C22×C22⋊C4—611no—
461C22×C22⋊C4—611no—
462C22×C22⋊C4—611no—
463C22×C22⋊C4—612no—
464C22×C22⋊C4—618no—
465C22×C22⋊C4—611no—
466C22×C22⋊C4—612no—
467C22×C22⋊C4—612no—
468C22×C22⋊C4—611no—
469C22×C22⋊C4—1228no—
470C22×C22⋊C4—1224no—
471C22×C22⋊C4—1224no—
472C22×C22⋊C4—1224no—
473C22×C22⋊C4C2×D6111yescharacteristic
474C22×C22⋊C4C2×D6111yescharacteristic
475C22×C22⋊C4C2×D6111yescharacteristic
476#381—1228no—
477#379—1224no—
478C2×#95—612no—
479C2×#95—612no—
480C2×#95—612no—
481C2×#95—612no—
482C2×#95—612no—
483C2×#95—612no—
484C2×#95C2×D6112yescomplemented
485C2×#95C2×D6112yescomplemented
486C61#1386911yescharacteristic, complemented, Sylow
487C25—611no—
488C25—611no—
489C25—614no—
490C25—614no—
491C25—614no—
492C25—1224no—
493C25—1224no—
494C25—1224no—
495C25—1224no—
496C25—2442no—
497C25—2442no—
498C25C22×D6111yescharacteristic
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—612no—
502C23×C4—614no—
503C23×C4—614no—
504C23×C4—612no—
505C23×C4—1224no—
506C23×C4—1222no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4—1222no—
510C23×C4—1224no—
511C23×C4—1224no—
512C23×C4—1224no—
513C23×C4—1224no—
514C23×C4—1224no—
515C23×C4—1224no—
516C23×C4—2442no—
517C23×C4—2442no—
518C23×C4—2442no—
519C23×C4—2442no—
520C23×C4C22×D6112yes—
521C23×C4C22×D6111yescharacteristic
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6112yes—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—614no—
532C2×C22⋊C4—614no—
533C2×C22⋊C4—618no—
534C2×C22⋊C4—12232no—
535C2×C22⋊C4—12232no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—1222no—
541C2×C22⋊C4—1224no—
542C2×C22⋊C4—1224no—
543C2×C22⋊C4—1222no—
544C2×C22⋊C4—1222no—
545C2×C22⋊C4—1222no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4—1224no—
548C2×C22⋊C4—1224no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—1224no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4C4×D6114yescomplemented
555#95—24no—
556#95—42no—
557#95—1224no—
558#95—1224no—
559#95—1224no—
560#95—2442no—
561#95—2442no—
562#95—2442no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—612no—
570C24—612no—
571C24—614no—
572C24—612no—
573C24—612no—
574C24—612no—
575C24—612no—
576C24—614no—
577C24—614no—
578C24—614no—
579C24—6116no—
580C24—1228no—
581C24—1228no—
582C24—1228no—
583C24—12216no—
584C24—12216no—
585C24—12216no—
586C24—12216no—
587C24—1228no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1222no—
592C24—1222no—
593C24—1222no—
594C24—1222no—
595C24—1222no—
596C24—2448no—
597C24—2448no—
598C24—2444no—
599C24—2444no—
600C24—2448no—
601C24—2448no—
602C24—2448no—
603C24—2448no—
604C24—2448no—
605C24—2448no—
606C24—2448no—
607C24—2448no—
608C24C2×C4×D6112yes—
609C24D4×D6112yes—
610C24D4×D6112yes—
611C24C23×D6111yescharacteristic
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—614no—
636C22×C4—1228no—
637C22×C4—1228no—
638C22×C4—12216no—
639C22×C4—12216no—
640C22×C4—1222no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—2448no—
662C22×C4—2448no—
663C22×C4—2448no—
664C22×C4—2448no—
665C22×C4—2448no—
666C22×C4—2444no—
667C22×C4—2448no—
668C22×C4—2444no—
669C22×C4—2448no—
670C22×C4—2448no—
671C22×C4—2448no—
672C22×C4—2444no—
673C22×C4—2444no—
674C22×C4C2×C4×D6112yes—
675C22×C4C2×C4×D6112yes—
676C22×C4D4×D6114yes—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—44no—
680C22⋊C4—1228no—
681C22⋊C4—1228no—
682C22⋊C4—12216no—
683C22⋊C4—1228no—
684C22⋊C4—1228no—
685C22⋊C4—2448no—
686C22⋊C4—2448no—
687C22⋊C4—2444no—
688C23—22no—
689C23—22no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—614no—
709C23—614no—
710C23—614no—
711C23—614no—
712C23—618no—
713C23—614no—
714C23—618no—
715C23—618no—
716C23—618no—
717C23—614no—
718C23—12232no—
719C23—12232no—
720C23—1222no—
721C23—1222no—
722C23—1224no—
723C23—1224no—
724C23—1224no—
725C23—1222no—
726C23—1224no—
727C23—1224no—
728C23—1224no—
729C23—1222no—
730C23—1224no—
731C23—1224no—
732C23—1222no—
733C23—1222no—
734C23—1222no—
735C23—1222no—
736C23—1224no—
737C23—1224no—
738C23—1224no—
739C23—1224no—
740C23—1224no—
741C23—1224no—
742C23—1224no—
743C23—1224no—
744C23—1224no—
745C23—1224no—
746C23—1224no—
747C23—1224no—
748C23—1224no—
749C23—1224no—
750C23—1224no—
751C23—1224no—
752C23—24416no—
753C23—24432no—
754C23—24432no—
755C23—24432no—
756C23—24432no—
757C23—24432no—
758C23—24432no—
759C23C22⋊C4×D6114yes—
760C23C22×C4×D6111yescharacteristic
761C23C2×D4×D6111yescharacteristic
762C23C2×D4×D6111yescharacteristic
763C23C2×D4×D6112yes—
764C23#41×D6112yes—
765C23#41×D6112yes—
766C23#41×D6112yes—
767C23#1451982212yes—
768C23#1451982312yes—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1224no—
796C2×C4—1224no—
797C2×C4—1224no—
798C2×C4—1224no—
799C2×C4—1224no—
800C2×C4—24416no—
801C2×C4—24432no—
802C2×C4—24416no—
803C2×C4—2442no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2441no—
811C2×C4—2442no—
812C2×C4—2441no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2442no—
819C2×C4—2442no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—618no—
830C22—618no—
831C22—1224no—
832C22—1224no—
833C22—1228no—
834C22—1228no—
835C22—1228no—
836C22—1228no—
837C22—1224no—
838C22—1224no—
839C22—1228no—
840C22—1228no—
841C22—1228no—
842C22—1228no—
843C22—1228no—
844C22—1228no—
845C22—1228no—
846C22—1228no—
847C22—24464no—
848C22C2×C22⋊C4×D6111yescharacteristic
849C22#117×D6111yescharacteristic
850C22#117×D6111yescharacteristic
851C22C4×D4×D6112yes—
852C22#1684023412yes—
853C22#120×D6111yescharacteristic
854C22#121×D6112yes—
855C22#123×D6112yes—
856C22#123×D6112yes—
857C22#123×D6111yescharacteristic
858C22#1684032012yes—
859C22#1684032211yescharacteristic
860C22#1684032311yescharacteristic
861C22#1684040112yes—
862C22#1684040412yes—
863C22#1684040512yes—
864C22#1684040912yes—
865C22#1684043712yes—
866C22#1684043712yes—
867C22#1684044012yes—
868C22#1684044212yes—
869C4—42no—
870C4—44no—
871C4—42no—
872C4—82no—
873C4—4882no—
874C4—2442no—
875C4—2444no—
876C4—2442no—
877C2—44no—
878C2—1228no—
879C2—1228no—
880C2#381×D6111yescharacteristic
881C2#386×D6111yescharacteristic
882C2#2144839311yescharacteristic
883C2#2144866312yes—
884C2#2144866712yes—
885C2#2144914112yes—
886C2#2144920812yes—
887C2#2144921012yes—
888C2#2145009612yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1440C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenter#1440D61
hypocenterC61#13869
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#16839624C2semidirect
5. #21444068C2semidirect
6. #21444066C2semidirect
7. #21444066C2semidirect
8. #21444040C2semidirect
9. #21444040C2semidirect
10. #21444040C2semidirect
11. C61×#1440C2semidirect
28. C2×C22⋊C4×D61C4semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
40. C2×#95×C61C22semidirect
41. C2×#95×C61C22semidirect
72. C22×C4×D61C2×C4semidirect
73. C22×C4×D61C2×C4semidirect
80. C2×C22⋊Dic61C2×C4semidirect
115. C2×C22⋊C4×C61C2×C4semidirect
423. C2×D61#381semidirect
440. #1440D61semidirect
484. C2×#95C2×D61semidirect
485. C2×#95C2×D61semidirect
486. C61#13869semidirect
554. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
C2×#168396242
C2×#168396172
#214440682
#214440662
#214440402
C61×#14402
#1386961