Finite Group Databasebeta

← #29610013

Subgroups — #29610013

Order 15616.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839670C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic, complemented
3C2×#16839652C211yesmaximal, characteristic, complemented
4C2×#16839650C211yesmaximal, characteristic, complemented
5#21444066C211yesmaximal, characteristic, complemented
6#21444060C211yesmaximal, characteristic, complemented
7#21444058C211yesmaximal, characteristic, complemented
8#21444058C211yesmaximal, characteristic, complemented
9#21444058C211yesmaximal, characteristic, complemented
10#21444057C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444056C211yesmaximal, characteristic, complemented
13#21444052C211yesmaximal, characteristic, complemented
14#21444051C211yesmaximal, characteristic, complemented
15C2×C61×#390C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839670C418yescomplemented
33#16839662—24no—
34#16839652—24no—
35#16839650—24no—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C23×D4×C61C2211yescharacteristic
49C22×C4⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C61×#390—24no—
56C24×D61C2311yescharacteristic
57C22×C22⋊D61—22no—
58C22×C22⋊D61—22no—
59C22×C22⋊D61—41no—
60C22×C22⋊D61—41no—
61C22×C22⋊D61—41no—
62C22×C22⋊D61—41no—
63C22×C22⋊D61—41no—
64C22×C22⋊D61—41no—
65C22×C22⋊D61—41no—
66C22×C22⋊D61—41no—
67C22×C22⋊D61—41no—
68C22×C22⋊D61—41no—
69C22×C22⋊D61C2×C414yes—
70C22×C22⋊D61C2×C414yes—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C2×#11758196—41no—
79C2×#11758196—41no—
80C2×#11758196D414yescomplemented
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—41no—
88C2×C22⋊Dic61—41no—
89C2×C22⋊Dic61—41no—
90C2×C22⋊Dic61—41no—
91C2×C22⋊Dic61—41no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61—41no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61C2×C414yes—
98C2×C22⋊Dic61C2×C414yes—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198C2×C414yes—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—41no—
118C2×C4×Dic61—41no—
119C2×C4×Dic61—41no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684C2×C414yes—
132C25×C61C2311yescharacteristic
133C25×C61C2311yescharacteristic
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—41no—
137C22×D4×C61—41no—
138C22×D4×C61—41no—
139C22×D4×C61—41no—
140C22×D4×C61C2×C414yes—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61—41no—
147C2×C4⋊C4×C61—41no—
148C2×C4⋊C4×C61D414yescomplemented
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—41no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61—41no—
160C2×C22⋊C4×C61—41no—
161C2×C42×C61—22no—
162C2×C42×C61—41no—
163C2×C42×C61—41no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61C22×C412yes—
193C24×C61C22×C412yes—
194C24×C61C2411yescharacteristic
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61C22×C412yes—
210C2×D4×C61—28no—
211C2×D4×C61—44no—
212C2×D4×C61—44no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—44no—
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×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61C22×C412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×D412yes—
249C22×C4×C61C2×D412yes—
250C22×C4×C61#4112yes—
251C22×C4×C61#4112yes—
252C2×C22⋊D61—28no—
253C2×C22⋊D61—44no—
254C2×C22⋊D61—44no—
255C2×C22⋊D61—44no—
256C2×C22⋊D61—44no—
257C2×C22⋊D61—44no—
258C2×C22⋊D61—44no—
259C2×C22⋊D61—44no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61—44no—
262C2×C22⋊D61—44no—
263C2×C22⋊D61—44no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61—44no—
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×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61C22×C412yes—
309C22×Dic61C22×C412yes—
310C22×Dic61C22×C412yes—
311C22×Dic61C2×D412yes—
312C22×Dic61C2×D412yes—
313C22×Dic61#4112yes—
314C22×Dic61#4112yes—
315C4⋊C4×C61—44no—
316C22⋊C4×C61—44no—
317C22⋊C4×C61—44no—
318C22⋊C4×C61—44no—
319C22⋊C4×C61—44no—
320C42×C61—44no—
321C22⋊Dic61—28no—
322C22⋊Dic61—44no—
323C22⋊Dic61—44no—
324C22⋊Dic61—44no—
325C22⋊Dic61—44no—
326C22⋊Dic61—44no—
327#11758198—28no—
328#11758198—44no—
329#11758198—44no—
330#11758198—44no—
331#11758198—44no—
332#11758196—44no—
333C4×Dic61—44no—
334C4×Dic61—44no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61C23×C411yescharacteristic
406C23×C61C22×D411yescharacteristic
407C23×C61C22×D411yescharacteristic
408C23×C61C2×#4111yescharacteristic
409C23×C61C2×#4111yescharacteristic
410C23×C61C2×#4111yescharacteristic
411C23×C61C2×#4111yescharacteristic
412C23×C61H(5,𝔽2)11yescharacteristic
413C23×C61H(5,𝔽2)11yescharacteristic
414C23×C61H(5,𝔽2)11yescharacteristic
415C23×C61H(5,𝔽2)11yescharacteristic
416C23×C61H(5,𝔽2)11yescharacteristic
417C23×C61H(5,𝔽2)11yescharacteristic
418C23×C61H(5,𝔽2)11yescharacteristic
419C23×C61H(5,𝔽2)11yescharacteristic
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×D61—41no—
428C22×D61—41no—
429C22×D61—41no—
430C22×D61—41no—
431C22×D61—41no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—41no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455D4×C61—416no—
456C2×C4×C61—22no—
457C2×C4×C61—22no—
458C2×C4×C61—22no—
459C2×C4×C61—22no—
460C2×C4×C61—22no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61—41no—
481C2×C4×C61—41no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61C4×D414yes—
491C22⋊D61—416no—
492C22⋊D61—416no—
493C2×Dic61—22no—
494C2×Dic61—22no—
495C2×Dic61—22no—
496C2×Dic61—22no—
497C2×Dic61—22no—
498C2×Dic61—22no—
499C2×Dic61—22no—
500C2×Dic61—22no—
501C2×Dic61—22no—
502C2×Dic61—22no—
503C2×Dic61—22no—
504C2×Dic61—22no—
505C2×Dic61—22no—
506C2×Dic61—22no—
507C2×Dic61—22no—
508C2×Dic61—22no—
509C2×Dic61—22no—
510C2×Dic61—22no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61—41no—
519C2×Dic61—41no—
520C2×Dic61—41no—
521C2×Dic61—41no—
522C2×Dic61—41no—
523C2×Dic61—41no—
524C2×Dic61—41no—
525C2×Dic61—41no—
526C2×Dic61—41no—
527C2×Dic61—41no—
528C2×Dic61—41no—
529C2×Dic61—41no—
530C2×Dic61—41no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
540C2×Dic61—41no—
541C2×Dic61C4×D414yes—
542#14567—611nomaximal, Sylow
543C22×C61—42no—
544C22×C61—42no—
545C22×C61—42no—
546C22×C61—42no—
547C22×C61—42no—
548C22×C61—42no—
549C22×C61—42no—
550C22×C61—42no—
551C22×C61—42no—
552C22×C61—42no—
553C22×C61—42no—
554C22×C61—42no—
555C22×C61—42no—
556C22×C61—42no—
557C22×C61—81no—
558C22×C61—81no—
559C22×C61—81no—
560C22×C61—81no—
561C22×C61—81no—
562C22×C61—81no—
563C22×C61—81no—
564C22×C61—81no—
565C22×C61—81no—
566C22×C61—81no—
567C22×C61—81no—
568C22×C61—81no—
569C22×C61—81no—
570C22×C61—81no—
571C22×C61—81no—
572C22×C61—81no—
573C22×C61C2×C4×D411yescharacteristic
574C22×C61C2×C4×D411yescharacteristic
575C22×C61C4×#4111yescharacteristic
576C22×C61#51811yescharacteristic
577C22×C61#51811yescharacteristic
578C22×C61#51811yescharacteristic
579C22×C61#51811yescharacteristic
580C22×C61#53411yescharacteristic
581C22×C61#53411yescharacteristic
582C22×C61#53511yescharacteristic
583C22×C61#53511yescharacteristic
584C22×C61#53811yescharacteristic
585C22×C61#53811yescharacteristic
586C22×C61#53811yescharacteristic
587C22×C61#53811yescharacteristic
588C22×C61#53811yescharacteristic
589C22×C61#53811yescharacteristic
590C22×C61#54011yescharacteristic
591C22×C61#54011yescharacteristic
592C22×C61D4211yescharacteristic
593C22×C61#54611yescharacteristic
594C22×C61#54611yescharacteristic
595C22×C61#55011yescharacteristic
596C22×C61#55011yescharacteristic
597C22×C61#55011yescharacteristic
598C22×C61#55011yescharacteristic
599C22×C61#55311yescharacteristic
600C22×C61#55311yescharacteristic
601C22×C61#55511yescharacteristic
602C22×C61#55511yescharacteristic
603C22×C61#55911yescharacteristic
604C22×C61#56011yescharacteristic
605C22×C61#56011yescharacteristic
606C22×C61#56011yescharacteristic
607C22×C61H(3,𝔽4)11yescharacteristic
608C2×D61—42no—
609C2×D61—42no—
610C2×D61—42no—
611C2×D61—42no—
612C2×D61—42no—
613C2×D61—42no—
614C2×D61—42no—
615C2×D61—81no—
616C2×D61—81no—
617C2×D61—81no—
618C2×D61—81no—
619C2×D61—81no—
620C2×D61—81no—
621C2×D61—81no—
622C2×D61—81no—
623C4×C61—24no—
624C4×C61—42no—
625C4×C61—42no—
626C4×C61—42no—
627C4×C61—42no—
628Dic61—24no—
629Dic61—42no—
630Dic61—42no—
631Dic61—42no—
632Dic61—42no—
633Dic61—81no—
634Dic61—81no—
635C2×#392—611no—
636C2×#390—611no—
637C2×#390D6111yescharacteristic, complemented
638C2×#388—611no—
639C2×#388—611no—
640#1440—611no—
641#1438—611no—
642#1438—611no—
643#1438—611no—
644#1438—611no—
645#1437—611no—
646#1437—611no—
647#1437—611no—
648#1436—611no—
649#1436—611no—
650C2×C61—82no—
651C2×C61—82no—
652C2×C61#232111yescharacteristic
653C2×C61#232111yescharacteristic
654C2×C61#233311yescharacteristic
655C2×C61#236311yescharacteristic
656C2×C61#236311yescharacteristic
657C2×C61#236611yescharacteristic
658C2×C61#237511yescharacteristic
659C2×C61#267311yescharacteristic
660C2×C61#267311yescharacteristic
661C2×C61#271411yescharacteristic
662C2×C61#271411yescharacteristic
663C2×C61#273311yescharacteristic
664C2×C61#273311yescharacteristic
665C2×C61#280311yescharacteristic
666C2×C61#280311yescharacteristic
667D61—82no—
668C23×D4—611no—
669C23×D4—611no—
670C23×D4C2×D6111yescharacteristic
671C22×C4⋊C4—611no—
672C22×C4⋊C4C2×D6111yescharacteristic
673C22×C22⋊C4—611no—
674C22×C22⋊C4—611no—
675C22×C22⋊C4—611no—
676C22×C22⋊C4—611no—
677C22×C22⋊C4—611no—
678C22×C22⋊C4—611no—
679C22×C22⋊C4—611no—
680C22×C22⋊C4—611no—
681C22×C22⋊C4—611no—
682C22×C22⋊C4—611no—
683C22×C22⋊C4—611no—
684C22×C22⋊C4C2×D6111yescharacteristic
685C22×C22⋊C4C2×D6111yescharacteristic
686C22×C22⋊C4C2×D6111yescharacteristic
687C22×C22⋊C4C2×D6111yescharacteristic
688C22×C42—611no—
689C22×C42—611no—
690C22×C42C2×D6111yescharacteristic
691#392—618no—
692#390—24no—
693#390—1224no—
694#388—1224no—
695#388—1224no—
696C2×#95—611no—
697C2×#95—611no—
698C2×#95—611no—
699C2×#95—611no—
700C2×#95—611no—
701C2×#95—611no—
702C2×#95—611no—
703C2×#95—611no—
704C2×#95—611no—
705C2×#95—611no—
706C2×#95—611no—
707C2×#95—611no—
708C61#1456711yescharacteristic, complemented, Sylow
709C25—611no—
710C25C22×D6111yescharacteristic
711C25C22×D6111yescharacteristic
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—614no—
719C22×D4—614no—
720C22×D4—1222no—
721C22×D4—1222no—
722C22×D4—2441no—
723C22×D4—2441no—
724C22×D4—2441no—
725C22×D4—2441no—
726C22×D4—2441no—
727C22×D4—2441no—
728C22×D4—2441no—
729C22×D4—2441no—
730C22×D4—2441no—
731C22×D4—2441no—
732C22×D4C4×D6114yes—
733C23×C4—611no—
734C23×C4—611no—
735C23×C4—611no—
736C23×C4—611no—
737C23×C4—611no—
738C23×C4—611no—
739C23×C4—611no—
740C23×C4C22×D6111yescharacteristic
741C23×C4C22×D6111yescharacteristic
742C23×C4C22×D6111yescharacteristic
743C23×C4C22×D6111yescharacteristic
744C23×C4C22×D6111yescharacteristic
745C2×C4⋊C4—41no—
746C2×C4⋊C4—41no—
747C2×C4⋊C4—614no—
748C2×C4⋊C4—2441no—
749C2×C4⋊C4—2441no—
750C2×C4⋊C4C22⋊D6114yescomplemented
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—41no—
760C2×C22⋊C4—41no—
761C2×C22⋊C4—41no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—614no—
764C2×C22⋊C4—614no—
765C2×C22⋊C4—614no—
766C2×C22⋊C4—1222no—
767C2×C22⋊C4—1222no—
768C2×C22⋊C4—1222no—
769C2×C22⋊C4—1222no—
770C2×C22⋊C4—1222no—
771C2×C22⋊C4—1222no—
772C2×C22⋊C4—1222no—
773C2×C22⋊C4—1222no—
774C2×C22⋊C4—1222no—
775C2×C22⋊C4—1222no—
776C2×C22⋊C4—1222no—
777C2×C22⋊C4—1222no—
778C2×C22⋊C4—1222no—
779C2×C22⋊C4—1222no—
780C2×C22⋊C4—2441no—
781C2×C22⋊C4—2441no—
782C2×C22⋊C4—2441no—
783C2×C22⋊C4—2441no—
784C2×C22⋊C4—2441no—
785C2×C22⋊C4—2441no—
786C2×C22⋊C4—2441no—
787C2×C22⋊C4—2441no—
788C2×C22⋊C4—2441no—
789C2×C22⋊C4—2441no—
790C2×C22⋊C4—2441no—
791C2×C22⋊C4—2441no—
792C2×C22⋊C4—2441no—
793C2×C22⋊C4—2441no—
794C2×C22⋊C4—2441no—
795C2×C22⋊C4—2441no—
796C2×C42—22no—
797C2×C42—41no—
798C2×C42—41no—
799C2×C42—1222no—
800C2×C42—1222no—
801C2×C42—1222no—
802C2×C42—2441no—
803C2×C42—2441no—
804C2×C42—2441no—
805#95—614no—
806#95—1222no—
807#95—1222no—
808#95—1222no—
809#95—1222no—
810#95—1222no—
811#95—1222no—
812#95—2441no—
813#95—2441no—
814#95—2441no—
815#95—2441no—
816#95—2441no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—612no—
846C24—1221no—
847C24—1221no—
848C24—1221no—
849C24—1221no—
850C24—1221no—
851C24—1221no—
852C24—1221no—
853C24—1221no—
854C24—1221no—
855C24—1221no—
856C24—1221no—
857C24—1221no—
858C24—1221no—
859C24—1221no—
860C24C2×C4×D6112yes—
861C24C2×C4×D6112yes—
862C24C23×D6111yescharacteristic
863C2×D4—28no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—1228no—
871C2×D4—2444no—
872C2×D4—2444no—
873C2×D4—2444no—
874C2×D4—2444no—
875C2×D4—2444no—
876C2×D4—2444no—
877C2×D4—2444no—
878C2×D4—2444no—
879C2×D4—2444no—
880C2×D4—2444no—
881C2×D4—2444no—
882C2×D4—2444no—
883C2×D4—2444no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—612no—
913C22×C4—612no—
914C22×C4—612no—
915C22×C4—612no—
916C22×C4—612no—
917C22×C4—612no—
918C22×C4—612no—
919C22×C4—1221no—
920C22×C4—1221no—
921C22×C4—1221no—
922C22×C4—1221no—
923C22×C4—1221no—
924C22×C4—1221no—
925C22×C4—1221no—
926C22×C4—1221no—
927C22×C4—1221no—
928C22×C4—1221no—
929C22×C4—1221no—
930C22×C4—1221no—
931C22×C4—1221no—
932C22×C4—1221no—
933C22×C4—1221no—
934C22×C4—1221no—
935C22×C4—1221no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—1221no—
941C22×C4—1221no—
942C22×C4—1221no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4C2×C4×D6112yes—
962C22×C4#1175822212yes—
963C22×C4D4×D6112yes—
964C22×C4#1175822412yes—
965C22×C4C2×C22⋊D6112yes—
966C22×C4C2×C22⋊D6112yes—
967C22×C4C2×C22⋊D6112yes—
968C4⋊C4—44no—
969C4⋊C4—2444no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—1228no—
975C22⋊C4—1228no—
976C22⋊C4—2444no—
977C22⋊C4—2444no—
978C22⋊C4—2444no—
979C22⋊C4—2444no—
980C22⋊C4—2444no—
981C22⋊C4—2444no—
982C22⋊C4—2444no—
983C22⋊C4—2444no—
984C22⋊C4—2444no—
985C42—44no—
986C42—2444no—
987C42—2444no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—1222no—
1059C23—1222no—
1060C23—1222no—
1061C23—1222no—
1062C23—1222no—
1063C23—1222no—
1064C23—1222no—
1065C23—2441no—
1066C23—2441no—
1067C23—2441no—
1068C23—2441no—
1069C23—2441no—
1070C23—2441no—
1071C23—2441no—
1072C23—2441no—
1073C23—2441no—
1074C23—2441no—
1075C23—2441no—
1076C23—2441no—
1077C23—2441no—
1078C23—2441no—
1079C23—2441no—
1080C23—2441no—
1081C23—2441no—
1082C23—2441no—
1083C23—2441no—
1084C23—2441no—
1085C23—2441no—
1086C23—2441no—
1087C23—2441no—
1088C23—2441no—
1089C23—2441no—
1090C23—2441no—
1091C23—2441no—
1092C23—2441no—
1093C23C22×C4×D6111yescharacteristic
1094C23C2×D4×D6111yescharacteristic
1095C23C22×C22⋊D6111yescharacteristic
1096C23#41×D6111yescharacteristic
1097C23#41×D6111yescharacteristic
1098C23C2×#1175822411yescharacteristic
1099C23C2×#1175822211yescharacteristic
1100C23#1451982211yescharacteristic
1101C23#1451982211yescharacteristic
1102C23#1451982211yescharacteristic
1103C23#1451982211yescharacteristic
1104C23#1451982211yescharacteristic
1105C23#1451982211yescharacteristic
1106C23#1451982311yescharacteristic
1107C23#1451982311yescharacteristic
1108D4—416no—
1109D4—24416no—
1110D4—24416no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—614no—
1146C2×C4—1222no—
1147C2×C4—1222no—
1148C2×C4—1222no—
1149C2×C4—1222no—
1150C2×C4—1222no—
1151C2×C4—1222no—
1152C2×C4—1222no—
1153C2×C4—1222no—
1154C2×C4—1222no—
1155C2×C4—1222no—
1156C2×C4—1222no—
1157C2×C4—1222no—
1158C2×C4—1222no—
1159C2×C4—1222no—
1160C2×C4—1222no—
1161C2×C4—1222no—
1162C2×C4—1222no—
1163C2×C4—1222no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4—2441no—
1167C2×C4—2441no—
1168C2×C4—2441no—
1169C2×C4—2441no—
1170C2×C4—2441no—
1171C2×C4—2441no—
1172C2×C4—2441no—
1173C2×C4—2441no—
1174C2×C4—2441no—
1175C2×C4—2441no—
1176C2×C4—2441no—
1177C2×C4—2441no—
1178C2×C4—2441no—
1179C2×C4—2441no—
1180C2×C4—2441no—
1181C2×C4—2441no—
1182C2×C4—2441no—
1183C2×C4—2441no—
1184C2×C4—2441no—
1185C2×C4—2441no—
1186C2×C4—2441no—
1187C2×C4—2441no—
1188C2×C4—2441no—
1189C2×C4—2441no—
1190C2×C4—2441no—
1191C2×C4—2441no—
1192C2×C4—2441no—
1193C2×C4—2441no—
1194C2×C4C4×C22⋊D6114yes—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—4881no—
1226C22—4881no—
1227C22—4881no—
1228C22—4881no—
1229C22—4881no—
1230C22—4881no—
1231C22—4881no—
1232C22—4881no—
1233C22—2442no—
1234C22—2442no—
1235C22—2442no—
1236C22—2442no—
1237C22—2442no—
1238C22—2442no—
1239C22—2442no—
1240C22C4×D4×D6111yescharacteristic
1241C22C2×C4×C22⋊D6111yescharacteristic
1242C22C4×#1175822411yescharacteristic
1243C22#1684023411yescharacteristic
1244C22#1684023411yescharacteristic
1245C22#1684023511yescharacteristic
1246C22#1684023511yescharacteristic
1247C22#1684032011yescharacteristic
1248C22#1684032111yescharacteristic
1249C22#1684032511yescharacteristic
1250C22#1684032911yescharacteristic
1251C22#1684034411yescharacteristic
1252C22#1684034611yescharacteristic
1253C22#1684034611yescharacteristic
1254C22#1684034911yescharacteristic
1255C22#1684035011yescharacteristic
1256C22#1684035011yescharacteristic
1257C22#1684036211yescharacteristic
1258C22#1684036611yescharacteristic
1259C22D4×C22⋊D6111yescharacteristic
1260C22#1684040111yescharacteristic
1261C22#1684040611yescharacteristic
1262C22#1684043111yescharacteristic
1263C22#1684043111yescharacteristic
1264C22#1684043211yescharacteristic
1265C22#1684043311yescharacteristic
1266C22#1684045511yescharacteristic
1267C22#1684046211yescharacteristic
1268C22#1684047411yescharacteristic
1269C22#1684047711yescharacteristic
1270C22#1684049511yescharacteristic
1271C22#1684049911yescharacteristic
1272C22#1684050011yescharacteristic
1273C22#1684050011yescharacteristic
1274C22#1684050411yescharacteristic
1275C4—24no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—1224no—
1281C4—4881no—
1282C4—4881no—
1283C4—2442no—
1284C4—2442no—
1285C4—2442no—
1286C4—2442no—
1287C2—82no—
1288C2—82no—
1289C2—4882no—
1290C2#2144847711yescharacteristic
1291C2#2144847811yescharacteristic
1292C2#2144857811yescharacteristic
1293C2#2144885311yescharacteristic
1294C2#2144885411yescharacteristic
1295C2#2144888111yescharacteristic
1296C2#2144895611yescharacteristic
1297C2#2145207911yescharacteristic
1298C2#2145208011yescharacteristic
1299C2#2145260911yescharacteristic
1300C2#2145261211yescharacteristic
1301C2#2145284311yescharacteristic
1302C2#2145284411yescharacteristic
1303C2#2145374811yescharacteristic
1304C2#2145375311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#390C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC2×#390D61
hypocenterC61#14567
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#16839662C2semidirect
3. C2×#16839652C2semidirect
4. C2×#16839650C2semidirect
5. #21444066C2semidirect
6. #21444060C2semidirect
7. #21444058C2semidirect
8. #21444058C2semidirect
9. #21444058C2semidirect
10. #21444057C2semidirect
11. #21444056C2semidirect
12. #21444056C2semidirect
13. #21444052C2semidirect
14. #21444051C2semidirect
15. C2×C61×#390C2semidirect
32. #16839670C4semidirect
80. C2×#11758196D4semidirect
148. C2×C4⋊C4×C61D4semidirect
637. C2×#390D61semidirect
708. C61#14567semidirect
750. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396702
C2×#168396622
C2×#168396522
C2×#168396502
#214440662
#214440602
#214440582
#214440572
#214440562
#214440522
#214440512
C2×C61×#3902
#1456761