Finite Group Databasebeta

← #29610669

Subgroups — #29610669

Order 15616.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839680C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839633C211yesmaximal, characteristic, complemented
4#21444085C211yesmaximal, characteristic, complemented
5#21444076C211yesmaximal, characteristic, complemented
6#21444070C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444063C211yesmaximal, characteristic, complemented
12#21444061C211yesmaximal, characteristic, complemented
13#21444059C211yesmaximal, characteristic
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32#16839680C418yescomplemented
33#16839640—24no—
34#16839633—24no—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C22×C4⋊C4×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C24×D61C2311yescharacteristic
55C24×D61C2311yescharacteristic
56C22×D244—22no—
57C22×D244—22no—
58C22×D244—41no—
59C22×D244—41no—
60C22×D244—41no—
61C22×D244—41no—
62C22×D244C2×C414yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C22×C4×D61—41no—
70C22×C4×D61—41no—
71C22×C4×D61—41no—
72C22×C4×D61—41no—
73C22×C4×D61—41no—
74C22×C4×D61—41no—
75C22×C4×D61D414yes—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61—41no—
79C2×#11758196—22no—
80C2×#11758196—41no—
81C2×#11758196—41no—
82C2×#11758196—41no—
83C2×#11758196—41no—
84C2×#11758196C2×C414yescomplemented
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—41no—
93C2×#11758198—41no—
94C2×#11758198—41no—
95C2×#11758198—41no—
96C2×#11758198—41no—
97C2×#11758198—41no—
98C2×#11758198—41no—
99C2×#11758198—41no—
100C2×#11758198—41no—
101C2×#11758198—41no—
102C2×#11758198—41no—
103C2×#11758198—41no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198C2×C414yes—
115C2×#11758198C2×C414yes—
116C2×#11758198C2×C414yescomplemented
117C2×#11758198C2×C414yescomplemented
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—41no—
122#14519684—41no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—22no—
138C2×C4⋊C4×C61—41no—
139C2×C4⋊C4×C61—41no—
140#95×C61—22no—
141#95×C61—41no—
142#95×C61—41no—
143#95×C61—41no—
144#95×C61—41no—
145#95×C61C2×C414yescomplemented
146C24×C61C2411yescharacteristic
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61C22×C412yes—
174C23×D61C22×C412yes—
175C23×D61C2×D412yes—
176C23×D61#4112yes—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
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×C61C22×C412yes—
223C22×C4×C61C22×C412yes—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C2×D412yes—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
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×Dic61C22×C412yes—
266C22×Dic61C22×C412yes—
267C22×Dic61C2×D412yes—
268C2×D244—28no—
269C2×D244—44no—
270C2×D244—44no—
271C2×D244—44no—
272C2×D244—44no—
273C2×D244—44no—
274C2×D244—44no—
275C2×C4×D61—44no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
278C2×C4×D61—44no—
279C2×C4×D61—44no—
280C2×C4×D61—44no—
281C2×C4×D61—44no—
282C4⋊C4×C61—44no—
283#11758198—28no—
284#11758198—44no—
285#11758198—44no—
286#11758198—44no—
287#11758198—44no—
288#11758198—44no—
289#11758198—44no—
290#11758198—44no—
291#11758198—44no—
292#11758198—44no—
293#11758198—44no—
294C4⋊Dic61—44no—
295#11758196—44no—
296#11758196—44no—
297C23×C61C23×C411yescharacteristic
298C23×C61C22×D411yescharacteristic
299C23×C61C2×#4111yescharacteristic
300C23×C61H(5,𝔽2)11yescharacteristic
301C23×C61H(5,𝔽2)11yescharacteristic
302C23×C61H(5,𝔽2)11yescharacteristic
303C23×C61H(5,𝔽2)11yescharacteristic
304C23×C61H(5,𝔽2)11yescharacteristic
305C23×C61H(5,𝔽2)11yescharacteristic
306C23×C61H(5,𝔽2)11yescharacteristic
307C23×C61H(5,𝔽2)11yescharacteristic
308C23×C61H(5,𝔽2)11yescharacteristic
309C23×C612−1+411yescharacteristic
310C23×C612−1+411yescharacteristic
311C23×C612−1+411yescharacteristic
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61C4×D414yes—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473D244—416no—
474C4×D61—416no—
475#14622—611nomaximal, Sylow
476C22×C61C2×C4×D411yescharacteristic
477C22×C61#51811yescharacteristic
478C22×C61#51811yescharacteristic
479C22×C61#51811yescharacteristic
480C22×C61#52011yescharacteristic
481C22×C61#52011yescharacteristic
482C22×C61#52011yescharacteristic
483C22×C61#53411yescharacteristic
484C22×C61#53411yescharacteristic
485C22×C61#53411yescharacteristic
486C22×C61#53511yescharacteristic
487C22×C61#53611yescharacteristic
488C22×C61#53711yescharacteristic
489C22×C61#53811yescharacteristic
490C22×C61#53811yescharacteristic
491C22×C61#53811yescharacteristic
492C22×C61#53911yescharacteristic
493C22×C61#53911yescharacteristic
494C22×C61#53911yescharacteristic
495C22×C61#56011yescharacteristic
496C22×C61#56011yescharacteristic
497C22×C61#56011yescharacteristic
498C22×C61#56011yescharacteristic
499C22×C61#56011yescharacteristic
500C22×C61H(3,𝔽4)11yescharacteristic
501C22×C61#56211yescharacteristic
502C22×C61#56211yescharacteristic
503C22×C61#56211yescharacteristic
504C22×C61#56211yescharacteristic
505C22×C61#56211yescharacteristic
506C22×C61#56211yescharacteristic
507C22×C61#56211yescharacteristic
508C22×C61#56211yescharacteristic
509C22×C61#56311yescharacteristic
510C22×C61#56311yescharacteristic
511C2×D61—24no—
512C2×D61—24no—
513C2×D61—24no—
514C2×D61—42no—
515C2×D61—42no—
516C2×D61—42no—
517C2×D61—42no—
518C2×D61—42no—
519C2×D61—42no—
520C2×D61—42no—
521C2×D61—42no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—81no—
534C2×D61—81no—
535C2×D61—81no—
536C2×D61—81no—
537C2×D61—81no—
538C2×D61—81no—
539C2×D61—81no—
540C2×D61—81no—
541C4×C61—42no—
542C4×C61—42no—
543C4×C61—42no—
544C4×C61—42no—
545C4×C61—81no—
546C4×C61—81no—
547C4×C61—81no—
548Dic61—42no—
549Dic61—42no—
550Dic61—42no—
551Dic61—81no—
552Dic61—81no—
553Dic61—81no—
554C2×#394—611no—
555C2×#386—611no—
556C2×#385—611no—
557#1445—611no—
558#1442—611no—
559#1442D6111yescharacteristic, complemented
560#1441—611no—
561#1440—611no—
562#1440—611no—
563#1439—611no—
564#1439—611no—
565#1439—611no—
566#1439—611no—
567#1438—611no—
568C22⋊#95—611no—
569C2×C61#232111yescharacteristic
570C2×C61#232211yescharacteristic
571C2×C61#232511yescharacteristic
572C2×C61#237611yescharacteristic
573C2×C61#237711yescharacteristic
574C2×C61#237711yescharacteristic
575C2×C61#237911yescharacteristic
576C2×C61#281211yescharacteristic
577C2×C61#281311yescharacteristic
578C2×C61#281411yescharacteristic
579C2×C61#281611yescharacteristic
580C2×C61#282411yescharacteristic
581C2×C61#282611yescharacteristic
582C2×C61#282711yescharacteristic
583C2×C61#282711yescharacteristic
584D61—44no—
585D61—82no—
586C23×D4—611no—
587C24×C4—611no—
588C22×C4⋊C4—611no—
589C22×C4⋊C4—611no—
590C22×C4⋊C4—611no—
591C22×C4⋊C4C2×D6111yescharacteristic
592C22×C22⋊C4—611no—
593C22×C22⋊C4—611no—
594C22×C22⋊C4—611no—
595C22×C22⋊C4—611no—
596C22×C22⋊C4—611no—
597C22×C22⋊C4—611no—
598C22×C22⋊C4—611no—
599C22×C22⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603#394—618no—
604#386—1224no—
605#385—1224no—
606C2×#95—611no—
607C2×#95—611no—
608C2×#95—611no—
609C2×#95—611no—
610C2×#95—611no—
611C2×#95—611no—
612C2×#95—611no—
613C2×#95—611no—
614C2×#95—611no—
615C2×#95—611no—
616C2×#95—611no—
617C2×#95—611no—
618C2×#95C2×D6111yescharacteristic
619C2×#95C2×D6111yescharacteristic
620C2×#95C2×D6111yescharacteristic
621C2×#95C2×D6111yescharacteristic
622C2×#95C2×D6111yescharacteristic
623C2×#95C2×D6111yescharacteristic
624C61#1462211yescharacteristic, complemented, Sylow
625C25—611no—
626C25—611no—
627C22×D4—614no—
628C22×D4—1222no—
629C22×D4—1222no—
630C22×D4—2441no—
631C22×D4—2441no—
632C22×D4—2441no—
633C22×D4—2441no—
634C23×C4—611no—
635C23×C4—611no—
636C23×C4—611no—
637C23×C4—614no—
638C23×C4—611no—
639C23×C4—611no—
640C23×C4—611no—
641C23×C4—2441no—
642C23×C4—2441no—
643C23×C4—2441no—
644C23×C4—2441no—
645C23×C4—2441no—
646C23×C4—2441no—
647C23×C4C22×D6111yescharacteristic
648C23×C4C22×D6111yescharacteristic
649C23×C4C22×D6111yescharacteristic
650C23×C4C22×D6111yescharacteristic
651C23×C4C22×D6111yescharacteristic
652C23×C4C22×D6111yescharacteristic
653C23×C4C22×D6111yescharacteristic
654C2×C4⋊C4—22no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—614no—
658C2×C4⋊C4—1222no—
659C2×C4⋊C4—2441no—
660C2×C4⋊C4—2441no—
661C2×C4⋊C4—2441no—
662C2×C4⋊C4—2441no—
663C2×C4⋊C4—2441no—
664C2×C4⋊C4—2441no—
665C2×C4⋊C4—2441no—
666C2×C22⋊C4—614no—
667C2×C22⋊C4—614no—
668C2×C22⋊C4—614no—
669C2×C22⋊C4—614no—
670C2×C22⋊C4—1222no—
671C2×C22⋊C4—1222no—
672C2×C22⋊C4—1222no—
673C2×C22⋊C4—1222no—
674C2×C22⋊C4—1222no—
675C2×C22⋊C4—1222no—
676C2×C22⋊C4—1222no—
677C2×C22⋊C4—2441no—
678C2×C22⋊C4—2441no—
679C2×C22⋊C4—2441no—
680C2×C22⋊C4—2441no—
681C2×C22⋊C4—2441no—
682C2×C22⋊C4—2441no—
683C2×C22⋊C4—2441no—
684C2×C22⋊C4—2441no—
685C2×C22⋊C4—2441no—
686C2×C22⋊C4—2441no—
687C2×C22⋊C4—2441no—
688C2×C22⋊C4—2441no—
689C2×C22⋊C4—2441no—
690C2×C22⋊C4—2441no—
691C2×C22⋊C4—2441no—
692C2×C22⋊C4—2441no—
693C2×C22⋊C4—2441no—
694C2×C22⋊C4—2441no—
695C2×C22⋊C4—2441no—
696C2×C22⋊C4—2441no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699#95—22no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—1222no—
705#95—1222no—
706#95—1222no—
707#95—2441no—
708#95—2441no—
709#95—2441no—
710#95—2441no—
711#95—2441no—
712#95—2441no—
713#95—2441no—
714#95—2441no—
715#95—2441no—
716#95C4×D6114yescomplemented
717C24—612no—
718C24—612no—
719C24—612no—
720C24—612no—
721C24—1221no—
722C24—1221no—
723C24—1221no—
724C24—1221no—
725C24—1221no—
726C24—1221no—
727C24—1221no—
728C24—1221no—
729C24—1221no—
730C24—1221no—
731C24—1221no—
732C24—1221no—
733C24—1221no—
734C24—1221no—
735C24—1221no—
736C24—1221no—
737C24—1221no—
738C24—1221no—
739C24—1221no—
740C24—1221no—
741C24—1221no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24C23×D6111yescharacteristic
748C2×D4—1228no—
749C2×D4—2444no—
750C2×D4—2444no—
751C2×D4—2444no—
752C2×D4—2444no—
753C2×D4—2444no—
754C2×D4—2444no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—612no—
801C22×C4—612no—
802C22×C4—612no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—2444no—
843C22×C4—2444no—
844C22×C4—2444no—
845C22×C4—2444no—
846C22×C4—2444no—
847C22×C4—2444no—
848C22×C4—2444no—
849C22×C4C2×C4×D6112yes—
850C22×C4C2×C4×D6112yes—
851C22×C4C2×C4×D6112yes—
852C22×C4D4×D6112yes—
853C4⋊C4—44no—
854C4⋊C4—2444no—
855C4⋊C4—2444no—
856C4⋊C4—2444no—
857C22⋊C4—1228no—
858C22⋊C4—2444no—
859C22⋊C4—2444no—
860C22⋊C4—2444no—
861C22⋊C4—2444no—
862C22⋊C4—2444no—
863C22⋊C4—2444no—
864C22⋊C4—2444no—
865C22⋊C4—2444no—
866C22⋊C4—2444no—
867C22⋊C4—2444no—
868C23—614no—
869C23—1222no—
870C23—1222no—
871C23—1222no—
872C23—1222no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—1222no—
885C23—1222no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—1222no—
891C23—1222no—
892C23—1222no—
893C23—1222no—
894C23—2441no—
895C23—2441no—
896C23—2441no—
897C23—2441no—
898C23—2441no—
899C23—2441no—
900C23—2441no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23—2441no—
905C23—2441no—
906C23—2441no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23—2441no—
911C23—2441no—
912C23—2441no—
913C23—2441no—
914C23—2441no—
915C23—2441no—
916C23—2441no—
917C23—2441no—
918C23—2441no—
919C23—2441no—
920C23—2441no—
921C23—2441no—
922C23—2441no—
923C23—2441no—
924C23—2441no—
925C23—2441no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23C22×C4×D6111yescharacteristic
939C23C2×D4×D6111yescharacteristic
940C23#41×D6111yescharacteristic
941C23#1451982211yescharacteristic
942C23#1451982211yescharacteristic
943C23#1451982211yescharacteristic
944C23#1451982311yescharacteristic
945C23#1451982311yescharacteristic
946C23#1451982311yescharacteristic
947C23#1451982311yescharacteristic
948C23#1451982311yescharacteristic
949C23#1451982311yescharacteristic
950C23#1451982411yescharacteristic
951C23#1451982511yescharacteristic
952C23#1451982511yescharacteristic
953D4—24416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—24416no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2441no—
1018C2×C4—2441no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4—2441no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C22—1224no—
1047C22—1224no—
1048C22—1224no—
1049C22—4881no—
1050C22—4881no—
1051C22—4881no—
1052C22—4881no—
1053C22—4881no—
1054C22—4881no—
1055C22—4881no—
1056C22—4881no—
1057C22—2442no—
1058C22—2442no—
1059C22—2442no—
1060C22—2442no—
1061C22—2442no—
1062C22—2442no—
1063C22—2442no—
1064C22—2442no—
1065C22—2442no—
1066C22—2442no—
1067C22—2442no—
1068C22—2442no—
1069C22—2442no—
1070C22—2442no—
1071C22—2442no—
1072C22—2442no—
1073C22—2442no—
1074C22—2442no—
1075C22—2442no—
1076C22C4×D4×D6111yescharacteristic
1077C22#1684023411yescharacteristic
1078C22#1684023411yescharacteristic
1079C22#1684023611yescharacteristic
1080C22#1684024211yescharacteristic
1081C22#1684024311yescharacteristic
1082C22#1684024411yescharacteristic
1083C22#1684032011yescharacteristic
1084C22#1684032211yescharacteristic
1085C22#1684032311yescharacteristic
1086C22#1684033011yescharacteristic
1087C22#1684033511yescharacteristic
1088C22#1684034211yescharacteristic
1089C22#1684034811yescharacteristic
1090C22#1684034811yescharacteristic
1091C22#1684035111yescharacteristic
1092C22#1684035311yescharacteristic
1093C22#1684035811yescharacteristic
1094C22#1684036011yescharacteristic
1095C22#1684050011yescharacteristic
1096C22#1684050011yescharacteristic
1097C22#1684050211yescharacteristic
1098C22#1684050311yescharacteristic
1099C22#1684050311yescharacteristic
1100C22#1684050411yescharacteristic
1101C22#1684050611yescharacteristic
1102C22#1684050611yescharacteristic
1103C22#1684050811yescharacteristic
1104C22#1684050811yescharacteristic
1105C22#1684050911yescharacteristic
1106C22#1684051011yescharacteristic
1107C22#1684051011yescharacteristic
1108C22#1684051011yescharacteristic
1109C22#1684051111yescharacteristic
1110C22#1684051611yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—4881no—
1119C4—4881no—
1120C4—4881no—
1121C4—2442no—
1122C4—2442no—
1123C4—2442no—
1124C2—4882no—
1125C2—2444no—
1126C2#2144847211yescharacteristic
1127C2#2144849211yescharacteristic
1128C2#2144851611yescharacteristic
1129C2#2144896411yescharacteristic
1130C2#2144897211yescharacteristic
1131C2#2144897411yescharacteristic
1132C2#2144899011yescharacteristic
1133C2#2145381511yescharacteristic
1134C2#2145382411yescharacteristic
1135C2#2145383911yescharacteristic
1136C2#2145384511yescharacteristic
1137C2#2145390011yescharacteristic
1138C2#2145391111yescharacteristic
1139C2#2145392611yescharacteristic
1140C2#2145393411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1442D61
hypocenterC61#14622
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
3. C2×#16839633C2semidirect
4. #21444085C2semidirect
5. #21444076C2semidirect
6. #21444070C2semidirect
7. #21444067C2semidirect
8. #21444067C2semidirect
9. #21444065C2semidirect
10. #21444065C2semidirect
11. #21444063C2semidirect
12. #21444061C2semidirect
14. #21444040C2semidirect
15. C61×#1442C2semidirect
32. #16839680C4semidirect
84. C2×#11758196C2×C4semidirect
116. C2×#11758198C2×C4semidirect
117. C2×#11758198C2×C4semidirect
145. #95×C61C2×C4semidirect
559. #1442D61semidirect
624. C61#14622semidirect
716. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396802
C2×#168396402
C2×#168396332
#214440852
#214440762
#214440702
#214440672
#214440652
#214440632
#214440612
#214440592
#214440402
C61×#14422
#1462261