Finite Group Databasebeta

← #29602878

Subgroups — #29602878

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839636C211yesmaximal, characteristic, complemented
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×#16839619C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444084C211yesmaximal, characteristic, complemented
9#21444075C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444061C211yesmaximal, characteristic, complemented
12#21444052C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×C4×D244—24no—
22C2×C4×D244—24no—
23C2×C4×D244—24no—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36#16839640—24no—
37#16839640C418yescomplemented
38#16839636—24no—
39#16839636—24no—
40#16839619—24no—
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52#95×D61—24no—
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244C2×C414yes—
67C22×D244D414yes—
68C22×D244Q814yes—
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—41no—
94C22×C4×D61—41no—
95C22×C4×D61—41no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61—41no—
100C22×C4×D61—41no—
101C22×C4×D61C2×C414yescomplemented
102C22×C4×D61D414yes—
103C4×D244—232no—
104C2×C4⋊Dic61—22no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—22no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—22no—
109C2×C4⋊Dic61—22no—
110C2×C4⋊Dic61—41no—
111C2×C4⋊Dic61—41no—
112C2×C4⋊Dic61—41no—
113C2×#11758196—22no—
114C2×#11758196—22no—
115C2×#11758196—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198—41no—
136C2×#11758198C2×C414yescomplemented
137C2×#11758198C2×C414yescomplemented
138C2×#11758198C2×C414yescomplemented
139C2×#11758198D414yes—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—41no—
150#14519684C2×C414yescomplemented
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C2×C4⋊C4×C61—22no—
159C2×C4⋊C4×C61—22no—
160C2×C4⋊C4×C61—41no—
161C2×C42×C61—22no—
162C2×C42×C61—22no—
163C2×C42×C61—22no—
164#95×C61—22no—
165#95×C61—22no—
166#95×C61—41no—
167#95×C61C2×C414yescomplemented
168#95×C61D414yescomplemented
169C24×C61C2411yescharacteristic
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61C22×C412yes—
191C23×D61C22×C412yes—
192C23×D61C2×D412yes—
193C23×D61C2×D412yes—
194C23×D61C2×D412yes—
195C23×D61C2×D412yes—
196C23×D61C2×Q812yes—
197C23×D61C2×Q812yes—
198C23×D61#4112yes—
199C23×D61#4112yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61C22×C412yes—
238C22×C4×C61C22×C412yes—
239C22×C4×C61C22×C412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×Q812yes—
247C22×C4×C61#4112yes—
248C22×C4×C61#4112yes—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61C22×C412yes—
287C22×Dic61C22×C412yes—
288C22×Dic61C2×D412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61#4112yes—
291C2×D244—28no—
292C2×D244—28no—
293C2×D244—28no—
294C2×D244—28no—
295C2×D244—28no—
296C2×D244—28no—
297C2×D244C4⋊C4116yescomplemented
298C2×C4×D61—28no—
299C2×C4×D61—28no—
300C2×C4×D61—28no—
301C2×C4×D61—28no—
302C2×C4×D61—28no—
303C2×C4×D61—28no—
304C2×C4×D61—44no—
305C2×C4×D61—44no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×C4×D61—44no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C2×C4×D61—44no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C2×C4×D61—44no—
319C2×C4×D61—44no—
320C2×C4×D61—44no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C4⋊C4×C61—44no—
327C42×C61—28no—
328#11758198—28no—
329#11758198—28no—
330#11758198—28no—
331#11758198—28no—
332#11758198—44no—
333#11758198—44no—
334#11758198—44no—
335#11758198—44no—
336C4⋊Dic61—28no—
337C4⋊Dic61—44no—
338C4⋊Dic61—44no—
339#11758196—44no—
340C23×C61C23×C411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C22×D411yescharacteristic
344C23×C61C22×D411yescharacteristic
345C23×C61C22×Q811yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61C2×#4111yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61C2×#4111yescharacteristic
350C23×C61C2×#4111yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C61H(5,𝔽2)11yescharacteristic
353C23×C61H(5,𝔽2)11yescharacteristic
354C23×C612−1+411yescharacteristic
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61C2×C4⋊C414yes—
418C22×D61C2×C4⋊C414yes—
419C22×D61C4×D414yes—
420C22×D61C4×D414yes—
421C22×D61#12014yes—
422C22×D61C22⋊Q814yes—
423C22×D61C22⋊Q814yes—
424C22×D61#12314yes—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
449C2×C4×C61—22no—
450C2×C4×C61—22no—
451C2×C4×C61—22no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61C2×C4⋊C414yes—
472C2×C4×C61C4×D414yescomplemented
473C2×C4×C61#12114yes—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516D244—232no—
517C4×D61—416no—
518C4×D61—416no—
519C4×D61—416no—
520C4×D61—416no—
521#13975—611nomaximal, Sylow
522C22×C61C22×C4⋊C411yescharacteristic
523C22×C61C2×C4×D411yescharacteristic
524C22×C61C2×C4×D411yescharacteristic
525C22×C61C2×C4×D411yescharacteristic
526C22×C61C4×#4111yescharacteristic
527C22×C61#51811yescharacteristic
528C22×C61#52011yescharacteristic
529C22×C61C2×#12011yescharacteristic
530C22×C61C2×#12111yescharacteristic
531C22×C61C2×C22⋊Q811yescharacteristic
532C22×C61C2×C22⋊Q811yescharacteristic
533C22×C61C2×#12311yescharacteristic
534C22×C61#52511yescharacteristic
535C22×C61#52911yescharacteristic
536C22×C61#53211yescharacteristic
537C22×C61#53411yescharacteristic
538C22×C61#53711yescharacteristic
539C22×C61#53811yescharacteristic
540C22×C61#53911yescharacteristic
541C22×C61D4211yescharacteristic
542C22×C61D4211yescharacteristic
543C22×C61#54611yescharacteristic
544C22×C61#54611yescharacteristic
545C22×C61#54611yescharacteristic
546C22×C61#54611yescharacteristic
547C22×C61#54611yescharacteristic
548C22×C61#54711yescharacteristic
549C22×C61#54711yescharacteristic
550C22×C61D4×Q811yescharacteristic
551C22×C61#55111yescharacteristic
552C22×C61#55111yescharacteristic
553C22×C61#55211yescharacteristic
554C22×C61#55411yescharacteristic
555C22×C61#55411yescharacteristic
556C22×C61#55411yescharacteristic
557C2×D61—24no—
558C2×D61—24no—
559C2×D61—24no—
560C2×D61—24no—
561C2×D61—24no—
562C2×D61—24no—
563C2×D61—24no—
564C2×D61—24no—
565C2×D61—24no—
566C2×D61—24no—
567C2×D61—24no—
568C2×D61—24no—
569C2×D61—24no—
570C2×D61—24no—
571C2×D61—24no—
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—42no—
586C2×D61#38518yescomplemented
587C4×C61—24no—
588C4×C61—24no—
589C4×C61—24no—
590C4×C61—42no—
591C4×C61—42no—
592C4×C61—42no—
593C4×C61—81no—
594Dic61—42no—
595Dic61—42no—
596Dic61—42no—
597Dic61—42no—
598Dic61—42no—
599Dic61—81no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386—611no—
603C2×#385—611no—
604C2×#385—611no—
605C2×#380—611no—
606C22×#95—611no—
607#1444—611no—
608#1442—611no—
609#1439—611no—
610#1439—611no—
611#1436—611no—
612#1436D6111yescharacteristic, complemented
613C22⋊#95—611no—
614C22⋊#95—611no—
615C2×C61C2×#38511yescharacteristic
616C2×C61C4×#12111yescharacteristic
617C2×C61#232511yescharacteristic
618C2×C61D4×C4⋊C411yescharacteristic
619C2×C61#234911yescharacteristic
620C2×C61#235811yescharacteristic
621C2×C61#235911yescharacteristic
622C2×C61#241011yescharacteristic
623C2×C61#241711yescharacteristic
624C2×C61#241811yescharacteristic
625C2×C61#241911yescharacteristic
626C2×C61#243011yescharacteristic
627C2×C61#244911yescharacteristic
628C2×C61#245011yescharacteristic
629C2×C61#256411yescharacteristic
630D61—28no—
631D61—44no—
632C23×D4—611no—
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4—611no—
637C2×C4×D4—1224no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4—611no—
644C22×C4⋊C4C2×D6111yescharacteristic
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4—611no—
651C22×C22⋊C4—611no—
652C22×C22⋊C4—611no—
653C22×C42C2×D6111yescharacteristic
654#386—618no—
655#386—1224no—
656#385—1224no—
657#385—1224no—
658#380—1224no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—1224no—
671C2×#95C2×D6111yescharacteristic
672C2×#95C2×D6111yescharacteristic
673C2×#95C2×D6111yescharacteristic
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1397511yescharacteristic, complemented, Sylow
677C25—611no—
678C25—611no—
679C22×D4—614no—
680C22×D4—614no—
681C22×D4—614no—
682C22×D4—1222no—
683C22×D4—1222no—
684C22×D4—1222no—
685C22×D4—1222no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—611no—
689C23×C4—611no—
690C23×C4—611no—
691C23×C4—614no—
692C23×C4—614no—
693C23×C4—611no—
694C23×C4—1222no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—1222no—
710C23×C4—1222no—
711C23×C4—1222no—
712C23×C4—2441no—
713C23×C4—2441no—
714C23×C4—2441no—
715C23×C4—2441no—
716C23×C4—2441no—
717C23×C4—2441no—
718C23×C4—2441no—
719C23×C4—2441no—
720C23×C4C22×D6111yescharacteristic
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—41no—
731C2×C4⋊C4—1222no—
732C2×C4⋊C4—1222no—
733C2×C4⋊C4—1222no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1222no—
738C2×C4⋊C4—1222no—
739C2×C4⋊C4—1222no—
740C2×C4⋊C4—2441no—
741C2×C4⋊C4—2441no—
742C2×C4⋊C4—2441no—
743C2×C22⋊C4—614no—
744C2×C22⋊C4—614no—
745C2×C22⋊C4—614no—
746C2×C22⋊C4—614no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—1222no—
750C2×C22⋊C4—1222no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—1222no—
763C2×C22⋊C4—2441no—
764C2×C22⋊C4—2441no—
765C2×C22⋊C4—2441no—
766C2×C22⋊C4—2441no—
767C2×C42—22no—
768C2×C42—22no—
769C2×C42—22no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—614no—
774#95—1222no—
775#95—1222no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—2441no—
784#95C4×D6114yescomplemented
785#95D24414yescomplemented
786C24—612no—
787C24—612no—
788C24—612no—
789C24—612no—
790C24—612no—
791C24—612no—
792C24—612no—
793C24—612no—
794C24—612no—
795C24—612no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24—1221no—
804C24—1221no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24—1221no—
810C24—1221no—
811C24—1221no—
812C24—1221no—
813C24—1221no—
814C24—1221no—
815C24—1221no—
816C24C23×D6111yescharacteristic
817C2×D4—6116no—
818C2×D4—1228no—
819C2×D4—1228no—
820C2×D4—1228no—
821C2×D4—1228no—
822C2×D4—1228no—
823C2×D4—1228no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—612no—
862C22×C4—612no—
863C22×C4—612no—
864C22×C4—612no—
865C22×C4—612no—
866C22×C4—1228no—
867C22×C4—1228no—
868C22×C4—1228no—
869C22×C4—1228no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1228no—
901C22×C4—1228no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—2444no—
910C22×C4—2444no—
911C22×C4—2444no—
912C22×C4—2444no—
913C22×C4—2444no—
914C22×C4—2444no—
915C22×C4—2444no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4—2444no—
926C22×C4—2444no—
927C22×C4—2444no—
928C22×C4—2444no—
929C22×C4—2444no—
930C22×C4—2444no—
931C22×C4C2×C4×D6112yes—
932C22×C4C2×C4×D6112yes—
933C22×C4C2×C4×D6112yes—
934C22×C4C2×D24412yes—
935C22×C4C2×D24412yes—
936C22×C4C2×D24412yes—
937C22×C4#1175822212yes—
938C22×C4D4×D6112yes—
939C22×C4D4×D6112yes—
940C22×C4D4×D6112yes—
941C22×C4Q8×D6112yes—
942C22×C4#1175822612yes—
943C4⋊C4—44no—
944C4⋊C4—1228no—
945C4⋊C4—2444no—
946C4⋊C4—2444no—
947C4⋊C4—2444no—
948C22⋊C4—1228no—
949C22⋊C4—1228no—
950C22⋊C4—1228no—
951C22⋊C4—1228no—
952C22⋊C4—2444no—
953C22⋊C4—2444no—
954C22⋊C4—2444no—
955C22⋊C4—2444no—
956C42—28no—
957C23—614no—
958C23—614no—
959C23—614no—
960C23—614no—
961C23—614no—
962C23—614no—
963C23—614no—
964C23—614no—
965C23—1222no—
966C23—1222no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1222no—
980C23—1222no—
981C23—1222no—
982C23—1222no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—1222no—
1005C23—1222no—
1006C23—1222no—
1007C23—1222no—
1008C23—1222no—
1009C23—1222no—
1010C23—1222no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23—2441no—
1017C23—2441no—
1018C23—2441no—
1019C23—2441no—
1020C23—2441no—
1021C23—2441no—
1022C23—2441no—
1023C23—2441no—
1024C23—2441no—
1025C23—2441no—
1026C23—2441no—
1027C23C22×C4×D6111yescharacteristic
1028C23C2×D4×D6111yescharacteristic
1029C23C2×D4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C22×D24411yescharacteristic
1032C23C2×Q8×D6111yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23#41×D6111yescharacteristic
1036C23C2×#1175822211yescharacteristic
1037C23C2×#1175822611yescharacteristic
1038C23#1451982211yescharacteristic
1039C23#1451982311yescharacteristic
1040C23#1451982311yescharacteristic
1041C23#1451982411yescharacteristic
1042D4—12232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—24416no—
1105C2×C4—24416no—
1106C2×C4—24416no—
1107C2×C4—24416no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4—2441no—
1131C2×C4—2441no—
1132C2×C4—2441no—
1133C2×C4—2441no—
1134C2×C4—2441no—
1135C2×C4C4⋊C4×D6114yes—
1136C2×C4C4×D24414yescomplemented
1137C2×C4#1451975214yes—
1138C22—618no—
1139C22—1224no—
1140C22—1224no—
1141C22—1224no—
1142C22—1224no—
1143C22—1224no—
1144C22—1224no—
1145C22—1224no—
1146C22—1224no—
1147C22—1224no—
1148C22—1224no—
1149C22—1224no—
1150C22—1224no—
1151C22—1224no—
1152C22—1224no—
1153C22—1224no—
1154C22—1224no—
1155C22—1224no—
1156C22—2442no—
1157C22—2442no—
1158C22—2442no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22—2442no—
1168C22C2×C4⋊C4×D6111yescharacteristic
1169C22C4×D4×D6111yescharacteristic
1170C22C4×D4×D6111yescharacteristic
1171C22C2×C4×D24411yescharacteristic
1172C22C4×#1175822611yescharacteristic
1173C22#1684023411yescharacteristic
1174C22#1684024211yescharacteristic
1175C22#120×D6111yescharacteristic
1176C22C2×#1451975211yescharacteristic
1177C22C22⋊Q8×D6111yescharacteristic
1178C22C22⋊Q8×D6111yescharacteristic
1179C22#123×D6111yescharacteristic
1180C22#1684027411yescharacteristic
1181C22#1684029911yescharacteristic
1182C22#1684030911yescharacteristic
1183C22#1684032311yescharacteristic
1184C22#1684034111yescharacteristic
1185C22#1684034611yescharacteristic
1186C22#1684035311yescharacteristic
1187C22D4×D24411yescharacteristic
1188C22D4×D24411yescharacteristic
1189C22#1684040211yescharacteristic
1190C22#1684040311yescharacteristic
1191C22#1684040311yescharacteristic
1192C22#1684040711yescharacteristic
1193C22#1684040911yescharacteristic
1194C22#1684041011yescharacteristic
1195C22#1684041711yescharacteristic
1196C22Q8×D24411yescharacteristic
1197C22#1684043611yescharacteristic
1198C22#1684043711yescharacteristic
1199C22#1684045011yescharacteristic
1200C22#1684046811yescharacteristic
1201C22#1684047211yescharacteristic
1202C22#1684047311yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—81no—
1210C4—4881no—
1211C4—2442no—
1212C4—2442no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—1228no—
1217C2—2444no—
1218C2#385×D6111yescharacteristic
1219C2C4×#1451975211yescharacteristic
1220C2#2144852311yescharacteristic
1221C2C4⋊C4×D24411yescharacteristic
1222C2#2144872811yescharacteristic
1223C2#2144880111yescharacteristic
1224C2#2144881811yescharacteristic
1225C2#2144919111yescharacteristic
1226C2#2144926811yescharacteristic
1227C2#2144928611yescharacteristic
1228C2#2144930311yescharacteristic
1229C2#2144942611yescharacteristic
1230C2#2144963311yescharacteristic
1231C2#2144964011yescharacteristic
1232C2#2145099811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#13975
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#16839636C2semidirect
5. C2×#16839636C2semidirect
6. C2×#16839619C2semidirect
7. C2×#95×D61C2semidirect
8. #21444084C2semidirect
9. #21444075C2semidirect
10. #21444065C2semidirect
11. #21444061C2semidirect
12. #21444052C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1436C2semidirect
37. #16839640C4semidirect
101. C22×C4×D61C2×C4semidirect
136. C2×#11758198C2×C4semidirect
137. C2×#11758198C2×C4semidirect
138. C2×#11758198C2×C4semidirect
150. #14519684C2×C4semidirect
167. #95×C61C2×C4semidirect
168. #95×C61D4semidirect
297. C2×D244C4⋊C4semidirect
472. C2×C4×C61C4×D4semidirect
586. C2×D61#385semidirect
612. #1436D61semidirect
676. C61#13975semidirect
784. #95C4×D61semidirect
785. #95D244semidirect
1136. C2×C4C4×D244semidirect

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×#168396362
C2×#168396192
C2×#95×D612
#214440842
#214440752
#214440652
#214440612
#214440522
#214440402
C61×#14362
#1397561