Finite Group Databasebeta

← #29607181

Subgroups — #29607181

Order 15616.

3390 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C211yesmaximal, characteristic
2C2×#16839621C211yesmaximal, characteristic, complemented
3C2×#16839619C211yesmaximal, characteristic, complemented
4C2×#16839617C212yesmaximal
5#21444065C211yesmaximal, characteristic, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444063C212yesmaximal, complemented
8#21444062C212yesmaximal, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×C4⋊Dic61C2211yescharacteristic, complemented
16C22×#11758196C2212yescomplemented
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C2×C22⋊C4×D61—24no—
26C2×C22⋊C4×D61—24no—
27C2×C22⋊C4×D61C418yescomplemented
28#16839621—24no—
29#16839619—24no—
30#16839617—28no—
31C2×#14519684C2211yescharacteristic, complemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C22×C4⋊C4×C61C2211yescharacteristic, complemented
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2212yes—
39C2×#95×C61C2211yescharacteristic, complemented
40C2×#95×C61C2212yescomplemented
41C24×D61—22no—
42C24×D61—22no—
43C24×D61—22no—
44C24×D61—22no—
45C24×D61—42no—
46C24×D61—42no—
47C24×D61—42no—
48C24×D61—42no—
49C24×D61C2×C414yes—
50C24×D61D414yes—
51C24×D61Q814yes—
52C24×D61C2311yescharacteristic
53C24×D61C2311yescharacteristic
54C23×Dic61C2312yes—
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—42no—
61C22×C4×D61—42no—
62C22×C4×D61—42no—
63C22×C4×D61—42no—
64C22×C4×D61C2×C414yes—
65C22×C4×D61C2×C414yes—
66C22×C4×D61D414yes—
67C22×C4×D61D414yes—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—42no—
70C2×#11758196—24no—
71C2×#11758196—42no—
72C2×#11758196—42no—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—24no—
76C2×C22⋊Dic61—42no—
77C2×C22⋊Dic61—42no—
78C2×C22⋊Dic61C2×C414yes—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×#11758198—42no—
92C2×#11758198—42no—
93C2×#11758198—42no—
94C2×#11758198—42no—
95C2×#11758198C2×C414yes—
96C2×#11758198C2×C414yes—
97C22⋊C4×D61—232no—
98#14519684—22no—
99#14519684—24no—
100#14519684—42no—
101#14519684—42no—
102#14519684—42no—
103C25×C61C2311yescharacteristic
104C23×C4×C61C2312yes—
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—42no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—42no—
114C2×C22⋊C4×C61—42no—
115C2×C22⋊C4×C61C2×C414yes—
116#95×C61—22no—
117#95×C61—42no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—21no—
121C24×C61—21no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61C22×C412yes—
127C24×C61C2×D412yes—
128C24×C61C2×Q812yes—
129C24×C61C2411yescharacteristic
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—21no—
137C23×D61—21no—
138C23×D61—22no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61—28no—
143C23×D61—28no—
144C23×D61—28no—
145C23×D61—28no—
146C23×D61—28no—
147C23×D61—28no—
148C23×D61—48no—
149C23×D61—48no—
150C23×D61—48no—
151C23×D61—48no—
152C23×D61—48no—
153C23×D61—48no—
154C23×D61—48no—
155C23×D61—44no—
156C23×D61—44no—
157C23×D61—44no—
158C23×D61—48no—
159C23×D61—44no—
160C23×D61—48no—
161C23×D61—48no—
162C23×D61—48no—
163C23×D61—48no—
164C23×D61C4⋊C4116yescomplemented
165C23×D61C22×C412yes—
166C23×D61C22×C412yes—
167C23×D61C2×D412yes—
168C23×D61C2×D412yes—
169C23×D61C2×D412yes—
170C23×D61C2×D412yes—
171C23×D61C2×Q812yes—
172C23×D61C2×Q812yes—
173C23×D61#4112yes—
174C23×D61#4112yes—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
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×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D412yes—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—21no—
202C22×Dic61—21no—
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×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61C22×C412yes—
220C22×Dic61C22×C412yes—
221C22×Dic61C2×D412yes—
222C22×Dic61C2×D412yes—
223C2×C4×D61—28no—
224C2×C4×D61—48no—
225C2×C4×D61—48no—
226C2×C4×D61—48no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61—48no—
231C2×C4×D61—44no—
232C2×C4×D61C22⋊C4116yescomplemented
233C4⋊C4×C61—44no—
234C22⋊C4×C61—28no—
235C22⋊C4×C61—48no—
236C22⋊Dic61—28no—
237C22⋊Dic61—48no—
238#11758198—28no—
239#11758198—28no—
240#11758198—48no—
241#11758198—48no—
242#11758198—48no—
243#11758198—48no—
244C4⋊Dic61—44no—
245#11758196—48no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—24no—
255C23×C61—24no—
256C23×C61—24no—
257C23×C61—24no—
258C23×C61—42no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—42no—
263C23×C61—41no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C2×C4⋊C414yes—
269C23×C61C23×C411yescharacteristic
270C23×C61C22×D411yescharacteristic
271C23×C61C22×D411yescharacteristic
272C23×C61C22×D411yescharacteristic
273C23×C61C22×Q811yescharacteristic
274C23×C61C2×#4111yescharacteristic
275C23×C61C2×#4111yescharacteristic
276C23×C61H(5,𝔽2)12yes—
277C23×C61H(5,𝔽2)12yes—
278C23×C61H(5,𝔽2)12yes—
279C23×C61H(5,𝔽2)12yes—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—24no—
286C22×D61—24no—
287C22×D61—22no—
288C22×D61—24no—
289C22×D61—22no—
290C22×D61—24no—
291C22×D61—24no—
292C22×D61—24no—
293C22×D61—24no—
294C22×D61—24no—
295C22×D61—24no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—24no—
299C22×D61—24no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—24no—
305C22×D61—24no—
306C22×D61—24no—
307C22×D61—24no—
308C22×D61—232no—
309C22×D61—432no—
310C22×D61—416no—
311C22×D61—416no—
312C22×D61—432no—
313C22×D61—416no—
314C22×D61—416no—
315C22×D61—432no—
316C22×D61—416no—
317C22×D61—416no—
318C22×D61—432no—
319C22×D61—42no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—42no—
324C22×D61—41no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61C2×C22⋊C414yes—
330C22×D61C2×C4⋊C414yes—
331C22×D61C2×C4⋊C414yes—
332C22×D61#11714yes—
333C22×D61#12114yes—
334C22×D61#12114yes—
335C22×D61C22⋊Q814yes—
336C22×D61C22⋊Q814yes—
337C2×C4×C61—24no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—24no—
341C2×C4×C61—22no—
342C2×C4×C61—24no—
343C2×C4×C61—41no—
344C2×C4×C61—42no—
345C2×C4×C61—41no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61C2×C22⋊C414yes—
361C2×Dic61—24no—
362C2×Dic61—24no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—24no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61—41no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—42no—
378C2×Dic61—42no—
379C2×Dic61—42no—
380C2×Dic61—42no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61—42no—
384C2×Dic61C2×C22⋊C414yes—
385C4×D61—416no—
386C4×D61—416no—
387#14338—611nomaximal, Sylow
388C22×C61—28no—
389C22×C61—24no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—44no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—44no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—44no—
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61C22×C4⋊C411yescharacteristic
401C22×C61C2×#11711yescharacteristic
402C22×C61#51812yes—
403C22×C61#51812yes—
404C22×C61C2×#12111yescharacteristic
405C22×C61C2×#12111yescharacteristic
406C22×C61C2×C22⋊Q811yescharacteristic
407C22×C61C2×C22⋊Q811yescharacteristic
408C22×C61#53412yes—
409C22×C61#53411yescharacteristic
410C22×C61#53412yes—
411C22×C61#53411yescharacteristic
412C22×C61#53412yes—
413C22×C61#53511yescharacteristic
414C22×C61#53512yes—
415C22×C61#53511yescharacteristic
416C22×C61#53812yes—
417C22×C61#53812yes—
418C22×C61#53812yes—
419C22×C61#53812yes—
420C22×C61#54312yes—
421C22×C61#54312yes—
422C2×D61—24no—
423C2×D61—24no—
424C2×D61—28no—
425C2×D61—28no—
426C2×D61—24no—
427C2×D61—24no—
428C2×D61—28no—
429C2×D61—24no—
430C2×D61—24no—
431C2×D61—28no—
432C2×D61—28no—
433C2×D61—24no—
434C2×D61—464no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—44no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—44no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—44no—
444C2×D61#38018yes—
445C4×C61—24no—
446C4×C61—42no—
447C4×C61—82no—
448C4×C61—82no—
449Dic61—24no—
450Dic61—42no—
451Dic61—82no—
452Dic61—82no—
453C23×C22⋊C4—611no—
454C2×#380—611no—
455C2×#380—611no—
456C2×#379—612no—
457#1439—612no—
458#1439—611no—
459#1439—611no—
460#1439—612no—
461#1439—611no—
462#1439D6111yescharacteristic, complemented
463C22⋊#95—612no—
464C2×C61—44no—
465C2×C61C2×#38011yescharacteristic
466C2×C61#230811yescharacteristic
467C2×C61#230911yescharacteristic
468C2×C61#231212yes—
469C2×C61#231512yes—
470C2×C61#261711yescharacteristic
471C2×C61#261711yescharacteristic
472C2×C61#261712yes—
473C2×C61#262611yescharacteristic
474C2×C61#262611yescharacteristic
475C2×C61#262612yes—
476D61—28no—
477D61—44no—
478C26—611no—
479C24×C4—611no—
480C24×C4—611no—
481C22×C4⋊C4—612no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4C2×D6111yescharacteristic, complemented
484C22×C22⋊C4—611no—
485C22×C22⋊C4—611no—
486C22×C22⋊C4—611no—
487C22×C22⋊C4—618no—
488C22×C22⋊C4—612no—
489C22×C22⋊C4—612no—
490C22×C22⋊C4—612no—
491C22×C22⋊C4—612no—
492C22×C22⋊C4—612no—
493C22×C22⋊C4—1224no—
494C22×C22⋊C4—1224no—
495C22×C22⋊C4C2×D6111yescharacteristic
496C22×C22⋊C4C2×D6112yes—
497#380—1224no—
498#380—1224no—
499#379—1228no—
500C2×#95—612no—
501C2×#95—611no—
502C2×#95—612no—
503C2×#95—612no—
504C2×#95—612no—
505C2×#95C2×D6111yescharacteristic, complemented
506C2×#95C2×D6112yescomplemented
507C61#1433811yescharacteristic, complemented, Sylow
508C25—611no—
509C25—611no—
510C25—614no—
511C25—614no—
512C25—614no—
513C25—1222no—
514C25—1222no—
515C25—1222no—
516C25—1222no—
517C25—2442no—
518C25—2442no—
519C25—2442no—
520C25—2442no—
521C25C22×D6111yescharacteristic
522C23×C4—611no—
523C23×C4—614no—
524C23×C4—614no—
525C23×C4—614no—
526C23×C4—611no—
527C23×C4—614no—
528C23×C4—612no—
529C23×C4—612no—
530C23×C4—1222no—
531C23×C4—1222no—
532C23×C4—2442no—
533C23×C4—2442no—
534C23×C4—2442no—
535C23×C4—2442no—
536C23×C4C22×D6112yes—
537C23×C4C22×D6112yes—
538C23×C4C22×D6111yescharacteristic
539C23×C4C22×D6111yescharacteristic
540C2×C4⋊C4—22no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—1224no—
543C2×C4⋊C4—1222no—
544C2×C4⋊C4—2442no—
545C2×C4⋊C4—2442no—
546C2×C4⋊C4—2442no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—614no—
553C2×C22⋊C4—614no—
554C2×C22⋊C4—614no—
555C2×C22⋊C4—12232no—
556C2×C22⋊C4—1222no—
557C2×C22⋊C4—1222no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1222no—
560C2×C22⋊C4—1222no—
561C2×C22⋊C4—1222no—
562C2×C22⋊C4—1224no—
563C2×C22⋊C4—1224no—
564C2×C22⋊C4—1224no—
565C2×C22⋊C4—1224no—
566C2×C22⋊C4—1224no—
567C2×C22⋊C4—1224no—
568C2×C22⋊C4—1224no—
569C2×C22⋊C4—1224no—
570C2×C22⋊C4—1224no—
571C2×C22⋊C4—2442no—
572C2×C22⋊C4—2442no—
573C2×C22⋊C4—2442no—
574C2×C22⋊C4—2442no—
575C2×C22⋊C4—2442no—
576C2×C22⋊C4—2442no—
577C2×C22⋊C4C4×D6114yes—
578#95—22no—
579#95—42no—
580#95—1224no—
581#95—1222no—
582#95—2442no—
583#95—2442no—
584#95—2442no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—612no—
594C24—612no—
595C24—612no—
596C24—612no—
597C24—612no—
598C24—612no—
599C24—612no—
600C24—612no—
601C24—612no—
602C24—612no—
603C24—6116no—
604C24—1228no—
605C24—1228no—
606C24—1228no—
607C24—1228no—
608C24—1228no—
609C24—1228no—
610C24—1222no—
611C24—1222no—
612C24—1222no—
613C24—1222no—
614C24—1221no—
615C24—1221no—
616C24—1221no—
617C24—1221no—
618C24—1222no—
619C24—1222no—
620C24—1222no—
621C24—1222no—
622C24—2448no—
623C24—2448no—
624C24—2448no—
625C24—2448no—
626C24—2448no—
627C24—2448no—
628C24—2448no—
629C24—2444no—
630C24—2444no—
631C24—2444no—
632C24—2448no—
633C24—2444no—
634C24—2448no—
635C24—2448no—
636C24—2448no—
637C24—2448no—
638C24C2×C4×D6112yes—
639C24D4×D6112yes—
640C24Q8×D6112yes—
641C24C23×D6111yescharacteristic
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—6116no—
666C22×C4—612no—
667C22×C4—1228no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1222no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—2448no—
689C22×C4—2448no—
690C22×C4—2444no—
691C22×C4—2444no—
692C22×C4—2448no—
693C22×C4—2444no—
694C22×C4—2448no—
695C22×C4—2444no—
696C22×C4C2×C4×D6112yes—
697C22×C4C2×C4×D6112yes—
698C22×C4D4×D6112yes—
699C22×C4D4×D6112yes—
700C4⋊C4—44no—
701C4⋊C4—2444no—
702C4⋊C4—2448no—
703C22⋊C4—28no—
704C22⋊C4—48no—
705C22⋊C4—1228no—
706C22⋊C4—1228no—
707C22⋊C4—1228no—
708C22⋊C4—2448no—
709C22⋊C4—2448no—
710C22⋊C4—2448no—
711C22⋊C4—2448no—
712C22⋊C4—2448no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—41no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—614no—
736C23—614no—
737C23—614no—
738C23—614no—
739C23—614no—
740C23—614no—
741C23—614no—
742C23—614no—
743C23—12232no—
744C23—1224no—
745C23—1224no—
746C23—1224no—
747C23—1222no—
748C23—1224no—
749C23—1222no—
750C23—1224no—
751C23—1222no—
752C23—1224no—
753C23—1222no—
754C23—1224no—
755C23—1224no—
756C23—1224no—
757C23—1224no—
758C23—1224no—
759C23—1224no—
760C23—1222no—
761C23—1222no—
762C23—1224no—
763C23—1224no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—1222no—
768C23—1224no—
769C23—1224no—
770C23—1224no—
771C23—1224no—
772C23—24432no—
773C23—24416no—
774C23—24416no—
775C23—24432no—
776C23—24416no—
777C23—24416no—
778C23—24432no—
779C23—24416no—
780C23—24416no—
781C23—24432no—
782C23—2442no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2442no—
787C23—2441no—
788C23—2442no—
789C23—2442no—
790C23—2442no—
791C23—2442no—
792C23C4⋊C4×D6114yes—
793C23C22×C4×D6111yescharacteristic
794C23C2×D4×D6111yescharacteristic
795C23C2×D4×D6111yescharacteristic
796C23C2×D4×D6111yescharacteristic
797C23C2×Q8×D6111yescharacteristic
798C23#41×D6111yescharacteristic
799C23#41×D6111yescharacteristic
800C23#1451982212yes—
801C23#1451982212yes—
802C23#1451982312yes—
803C23#1451982312yes—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—614no—
828C2×C4—1224no—
829C2×C4—1224no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1224no—
834C2×C4—24416no—
835C2×C4—24416no—
836C2×C4—2442no—
837C2×C4—2442no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4—2442no—
849C2×C4—2442no—
850C2×C4—2441no—
851C2×C4—2442no—
852C2×C4—2441no—
853C2×C4C22⋊C4×D6114yes—
854C22—28no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—44no—
859C22—42no—
860C22—42no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—618no—
866C22—1224no—
867C22—1224no—
868C22—1228no—
869C22—1224no—
870C22—1224no—
871C22—1228no—
872C22—1224no—
873C22—1224no—
874C22—1228no—
875C22—1228no—
876C22—1228no—
877C22—1224no—
878C22—24464no—
879C22—2442no—
880C22—2442no—
881C22—2444no—
882C22—2442no—
883C22—2442no—
884C22—2444no—
885C22—2442no—
886C22—2442no—
887C22—2444no—
888C22C2×C22⋊C4×D6111yescharacteristic
889C22C2×C4⋊C4×D6111yescharacteristic
890C22#117×D6111yescharacteristic
891C22#1684023412yes—
892C22#1684023412yes—
893C22#121×D6111yescharacteristic
894C22#121×D6111yescharacteristic
895C22C22⋊Q8×D6111yescharacteristic
896C22C22⋊Q8×D6111yescharacteristic
897C22#1684032012yes—
898C22#1684032212yes—
899C22#1684032211yescharacteristic
900C22#1684032312yes—
901C22#1684032311yescharacteristic
902C22#1684032511yescharacteristic
903C22#1684032812yes—
904C22#1684033011yescharacteristic
905C22#1684034412yes—
906C22#1684034612yes—
907C22#1684034812yes—
908C22#1684035112yes—
909C22#1684038712yes—
910C22#1684038712yes—
911C4—24no—
912C4—42no—
913C4—82no—
914C4—82no—
915C4—1224no—
916C4—4882no—
917C4—4882no—
918C4—2442no—
919C2—44no—
920C2—1228no—
921C2—2444no—
922C2#380×D6111yescharacteristic
923C2#2144839311yescharacteristic
924C2#2144839811yescharacteristic
925C2#2144841312yes—
926C2#2144843012yes—
927C2#2145155211yescharacteristic
928C2#2145155411yescharacteristic
929C2#2145155812yes—
930C2#2145162311yescharacteristic
931C2#2145162511yescharacteristic
932C2#2145162912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenter#1439D61
hypocenterC61#14338
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#16839621C2semidirect
3. C2×#16839619C2semidirect
5. #21444065C2semidirect
6. #21444064C2semidirect
7. #21444063C2semidirect
8. #21444062C2semidirect
9. #21444061C2semidirect
10. #21444040C2semidirect
11. C61×#1439C2semidirect
15. C22×C4⋊Dic61C22semidirect
16. C22×#11758196C22semidirect
27. C2×C22⋊C4×D61C4semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
36. C22×C4⋊C4×C61C22semidirect
39. C2×#95×C61C22semidirect
40. C2×#95×C61C22semidirect
164. C23×D61C4⋊C4semidirect
232. C2×C4×D61C22⋊C4semidirect
462. #1439D61semidirect
483. C22×C4⋊C4C2×D61semidirect
505. C2×#95C2×D61semidirect
506. C2×#95C2×D61semidirect
507. C61#14338semidirect

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×#168396212
C2×#168396192
C2×#168396172
#214440652
#214440642
#214440632
#214440622
#214440612
#214440402
C61×#14392
#1433861