Finite Group Databasebeta

← #29608256

Subgroups — #29608256

Order 15616.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839654C211yesmaximal, characteristic, complemented
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4#21444080C211yesmaximal, characteristic, complemented
5#21444076C211yesmaximal, characteristic, complemented
6#21444067C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444059C211yesmaximal, characteristic
9#21444055C211yesmaximal, characteristic, complemented
10#21444045C211yesmaximal, characteristic, complemented
11#21444040C211yesmaximal, characteristic, complemented
12#21444040C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1443C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839654—24no—
32#16839640—24no—
33#16839640C418yescomplemented
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#95×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—22no—
59C22×D244—22no—
60C22×D244—41no—
61C22×D244—41no—
62C22×D244C2×C414yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—41no—
73C22×C4×D61—41no—
74C22×C4×D61—41no—
75C22×C4×D61—41no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61C2×C414yescomplemented
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61—41no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
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×#11758198C2×C414yes—
113C2×#11758198C2×C414yes—
114C2×#11758198C2×C414yescomplemented
115C2×#11758198D414yes—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—41no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—41no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684C2×C414yescomplemented
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139#95×C61—22no—
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×D61C22×C412yes—
172C23×D61C22×C412yes—
173C23×D61C2×D412yes—
174C23×D61#4112yes—
175C23×D61#4112yes—
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×C61C22×C412yes—
222C22×C4×C61C22×C412yes—
223C22×C4×C61C22×C412yes—
224C22×C4×C61C2×D412yes—
225C22×C4×C61#4112yes—
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×Dic61C22×C412yes—
265C22×Dic61C22×C412yes—
266C22×Dic61C2×D412yes—
267C22×Dic61#4112yes—
268C2×D244—28no—
269C2×D244—28no—
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—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289#11758198—28no—
290#11758198—44no—
291#11758198—44no—
292#11758198—44no—
293#11758198—44no—
294#11758198—44no—
295#11758198—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299C4⋊Dic61—44no—
300C4×Dic61—44no—
301C23×C61C23×C411yescharacteristic
302C23×C61C22×D411yescharacteristic
303C23×C61C2×#4111yescharacteristic
304C23×C61C2×#4111yescharacteristic
305C23×C61C2×#4111yescharacteristic
306C23×C61C2×#4111yescharacteristic
307C23×C61C2×#4111yescharacteristic
308C23×C61H(5,𝔽2)11yescharacteristic
309C23×C61H(5,𝔽2)11yescharacteristic
310C23×C61H(5,𝔽2)11yescharacteristic
311C23×C61H(5,𝔽2)11yescharacteristic
312C23×C61H(5,𝔽2)11yescharacteristic
313C23×C61H(5,𝔽2)11yescharacteristic
314C23×C61H(5,𝔽2)11yescharacteristic
315C23×C612−1+411yescharacteristic
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—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
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×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61#11714yes—
385C22×D61C4×D414yes—
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—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
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×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
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—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477D244—416no—
478C4×D61—416no—
479C4×D61—416no—
480#14427—611nomaximal, Sylow
481C22×C61C2×#11711yescharacteristic
482C22×C61C2×C4×D411yescharacteristic
483C22×C61C4×#4111yescharacteristic
484C22×C61#51811yescharacteristic
485C22×C61#51811yescharacteristic
486C22×C61#51811yescharacteristic
487C22×C61#52011yescharacteristic
488C22×C61#53411yescharacteristic
489C22×C61#53711yescharacteristic
490C22×C61#53811yescharacteristic
491C22×C61#53811yescharacteristic
492C22×C61#53811yescharacteristic
493C22×C61#53811yescharacteristic
494C22×C61#53911yescharacteristic
495C22×C61#53911yescharacteristic
496C22×C61#53911yescharacteristic
497C22×C61#53911yescharacteristic
498C22×C61#54011yescharacteristic
499C22×C61#54211yescharacteristic
500C22×C61#54611yescharacteristic
501C22×C61#54611yescharacteristic
502C22×C61#54611yescharacteristic
503C22×C61#54611yescharacteristic
504C22×C61#55111yescharacteristic
505C22×C61#55111yescharacteristic
506C22×C61#55111yescharacteristic
507C22×C61#55111yescharacteristic
508C22×C61#55311yescharacteristic
509C22×C61#55311yescharacteristic
510C22×C61#55311yescharacteristic
511C22×C61#55311yescharacteristic
512C22×C61#56011yescharacteristic
513C22×C61#56011yescharacteristic
514C22×C61#56011yescharacteristic
515C22×C61H(3,𝔽4)11yescharacteristic
516C2×D61—24no—
517C2×D61—24no—
518C2×D61—24no—
519C2×D61—24no—
520C2×D61—24no—
521C2×D61—24no—
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—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C4×C61—42no—
547C4×C61—42no—
548C4×C61—42no—
549C4×C61—42no—
550C4×C61—42no—
551C4×C61—81no—
552C4×C61—81no—
553Dic61—42no—
554Dic61—42no—
555Dic61—42no—
556Dic61—42no—
557Dic61—81no—
558Dic61—81no—
559C2×#388—611no—
560C2×#386—611no—
561C2×#386—611no—
562#1443—611no—
563#1443D6111yescharacteristic, complemented
564#1442—611no—
565#1440—611no—
566#1439—611no—
567#1438—611no—
568#1437—611no—
569#1434—611no—
570C22⋊#95—611no—
571C22⋊#95—611no—
572C22⋊#95—611no—
573C22⋊#95—611no—
574C2×C61#231811yescharacteristic
575C2×C61#232511yescharacteristic
576C2×C61#233511yescharacteristic
577C2×C61#234211yescharacteristic
578C2×C61#235311yescharacteristic
579C2×C61#236411yescharacteristic
580C2×C61#237511yescharacteristic
581C2×C61#268411yescharacteristic
582C2×C61#268811yescharacteristic
583C2×C61#269111yescharacteristic
584C2×C61#269311yescharacteristic
585C2×C61#274611yescharacteristic
586C2×C61#274911yescharacteristic
587C2×C61#277811yescharacteristic
588C2×C61#278211yescharacteristic
589D61—44no—
590D61—44no—
591C23×D4—611no—
592C24×C4—611no—
593C24×C4—611no—
594C22×C4⋊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—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C42—611no—
606#388—1224no—
607#386—618no—
608#386—1224no—
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×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95C2×D6111yescharacteristic
623C2×#95C2×D6111yescharacteristic
624C2×#95C2×D6111yescharacteristic
625C2×#95C2×D6111yescharacteristic
626C2×#95C2×D6111yescharacteristic
627C2×#95C2×D6111yescharacteristic
628C2×#95C2×D6111yescharacteristic
629C61#1442711yescharacteristic, complemented, Sylow
630C25—611no—
631C25—611no—
632C22×D4—614no—
633C22×D4—1222no—
634C22×D4—1222no—
635C22×D4—1222no—
636C22×D4—1222no—
637C22×D4—2441no—
638C22×D4—2441no—
639C23×C4—611no—
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C23×C4—614no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—1222no—
647C23×C4—1222no—
648C23×C4—1222no—
649C23×C4—2441no—
650C23×C4—2441no—
651C23×C4—2441no—
652C23×C4—2441no—
653C23×C4—2441no—
654C23×C4—2441no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4—2441no—
659C23×C4C22×D6111yescharacteristic
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C23×C4C22×D6111yescharacteristic
665C23×C4C22×D6111yescharacteristic
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—2441no—
668C2×C4⋊C4—2441no—
669C2×C22⋊C4—614no—
670C2×C22⋊C4—614no—
671C2×C22⋊C4—614no—
672C2×C22⋊C4—614no—
673C2×C22⋊C4—1222no—
674C2×C22⋊C4—1222no—
675C2×C22⋊C4—1222no—
676C2×C22⋊C4—1222no—
677C2×C22⋊C4—1222no—
678C2×C22⋊C4—1222no—
679C2×C22⋊C4—1222no—
680C2×C22⋊C4—1222no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1222no—
683C2×C22⋊C4—1222no—
684C2×C22⋊C4—1222no—
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—
699C2×C42—1222no—
700C2×C42—1222no—
701C2×C42—2441no—
702#95—22no—
703#95—22no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—614no—
709#95—1222no—
710#95—1222no—
711#95—1222no—
712#95—2441no—
713#95—2441no—
714#95—2441no—
715#95—2441no—
716#95—2441no—
717#95—2441no—
718#95—2441no—
719#95—2441no—
720#95—2441no—
721#95C4×D6114yescomplemented
722C24—612no—
723C24—612no—
724C24—612no—
725C24—612no—
726C24—612no—
727C24—612no—
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—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24C23×D6111yescharacteristic
753C2×D4—1228no—
754C2×D4—1228no—
755C2×D4—2444no—
756C2×D4—2444no—
757C2×D4—2444no—
758C2×D4—2444no—
759C2×D4—2444no—
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—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
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—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—2444no—
847C22×C4—2444no—
848C22×C4—2444no—
849C22×C4—2444no—
850C22×C4—2444no—
851C22×C4—2444no—
852C22×C4—2444no—
853C22×C4—2444no—
854C22×C4—2444no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4C2×C4×D6112yes—
861C22×C4C2×C4×D6112yes—
862C22×C4C2×C4×D6112yes—
863C22×C4D4×D6112yes—
864C22×C4#1175822612yes—
865C4⋊C4—2444no—
866C22⋊C4—1228no—
867C22⋊C4—2444no—
868C22⋊C4—2444no—
869C22⋊C4—2444no—
870C22⋊C4—2444no—
871C22⋊C4—2444no—
872C22⋊C4—2444no—
873C22⋊C4—2444no—
874C22⋊C4—2444no—
875C22⋊C4—2444no—
876C42—2444no—
877C23—614no—
878C23—614no—
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—1222no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
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—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23C22×C4×D6111yescharacteristic
948C23C2×D4×D6111yescharacteristic
949C23#41×D6111yescharacteristic
950C23#41×D6111yescharacteristic
951C23#41×D6111yescharacteristic
952C23#41×D6111yescharacteristic
953C23C2×#1175822611yescharacteristic
954C23#1451982211yescharacteristic
955C23#1451982211yescharacteristic
956C23#1451982311yescharacteristic
957C23#1451982311yescharacteristic
958C23#1451982311yescharacteristic
959C23#1451982311yescharacteristic
960C23#1451982311yescharacteristic
961C23#1451982411yescharacteristic
962D4—24416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
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—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—24416no—
1025C2×C4—24416no—
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—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C22—1224no—
1057C22—1224no—
1058C22—1224no—
1059C22—1224no—
1060C22—1224no—
1061C22—1224no—
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—
1076C22—2442no—
1077C22—2442no—
1078C22—2442no—
1079C22—2442no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22#117×D6111yescharacteristic
1087C22C4×D4×D6111yescharacteristic
1088C22C4×#1175822611yescharacteristic
1089C22#1684023411yescharacteristic
1090C22#1684023411yescharacteristic
1091C22#1684023611yescharacteristic
1092C22#1684024211yescharacteristic
1093C22#1684032311yescharacteristic
1094C22#1684034111yescharacteristic
1095C22#1684034611yescharacteristic
1096C22#1684034811yescharacteristic
1097C22#1684035111yescharacteristic
1098C22#1684035111yescharacteristic
1099C22#1684035311yescharacteristic
1100C22#1684035311yescharacteristic
1101C22#1684035311yescharacteristic
1102C22#1684036111yescharacteristic
1103C22#1684036811yescharacteristic
1104C22#1684037811yescharacteristic
1105C22#1684040111yescharacteristic
1106C22#1684040311yescharacteristic
1107C22#1684040411yescharacteristic
1108C22#1684040511yescharacteristic
1109C22#1684043711yescharacteristic
1110C22#1684043711yescharacteristic
1111C22#1684043911yescharacteristic
1112C22#1684044011yescharacteristic
1113C22#1684045711yescharacteristic
1114C22#1684046311yescharacteristic
1115C22#1684046511yescharacteristic
1116C22#1684046511yescharacteristic
1117C22#1684050011yescharacteristic
1118C22#1684050211yescharacteristic
1119C22#1684050311yescharacteristic
1120C22#1684050411yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—81no—
1127C4—81no—
1128C4—4881no—
1129C4—4881no—
1130C4—2442no—
1131C4—2442no—
1132C4—2442no—
1133C4—2442no—
1134C2—2444no—
1135C2—2444no—
1136C2#2144845011yescharacteristic
1137C2#2144852311yescharacteristic
1138C2#2144860811yescharacteristic
1139C2#2144866711yescharacteristic
1140C2#2144875811yescharacteristic
1141C2#2144886511yescharacteristic
1142C2#2144895911yescharacteristic
1143C2#2145220111yescharacteristic
1144C2#2145226211yescharacteristic
1145C2#2145230211yescharacteristic
1146C2#2145233111yescharacteristic
1147C2#2145299611yescharacteristic
1148C2#2145304911yescharacteristic
1149C2#2145343611yescharacteristic
1150C2#2145349811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1443C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1443D61
hypocenterC61#14427
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#16839654C2semidirect
4. #21444080C2semidirect
5. #21444076C2semidirect
6. #21444067C2semidirect
7. #21444065C2semidirect
9. #21444055C2semidirect
10. #21444045C2semidirect
11. #21444040C2semidirect
12. #21444040C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1443C2semidirect
33. #16839640C4semidirect
82. C22×C4×D61C2×C4semidirect
114. C2×#11758198C2×C4semidirect
131. #14519684C2×C4semidirect
145. #95×C61C2×C4semidirect
563. #1443D61semidirect
629. C61#14427semidirect
721. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396542
C2×#168396402
#214440802
#214440762
#214440672
#214440652
#214440592
#214440552
#214440452
#214440402
C61×#14432
#1442761