Finite Group Databasebeta

← #29610000

Subgroups — #29610000

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839679C211yesmaximal, characteristic
2C2×#16839654C211yesmaximal, characteristic, complemented
3C2×#16839651C211yesmaximal, characteristic, complemented
4#21444079C211yesmaximal, characteristic, complemented
5#21444065C211yesmaximal, characteristic, complemented
6#21444063C211yesmaximal, characteristic, complemented
7#21444059C211yesmaximal, characteristic
8#21444059C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444057C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444054C211yesmaximal, characteristic, complemented
14#21444048C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839679C418yescomplemented
34#16839654—24no—
35#16839651—24no—
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
48C22×C42×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C24×D61C2311yescharacteristic
55C24×D61C2311yescharacteristic
56C22×D244—41no—
57C22×D244—41no—
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
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61—41no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196—41no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—41no—
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×#11758198C2×C414yes—
108C2×#11758198C2×C414yes—
109C2×#11758198C2×C414yes—
110C2×#11758198C2×C414yes—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—41no—
115C2×C4×Dic61—41no—
116C2×C4×Dic61—41no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684C2×C414yes—
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61—41no—
136C2×C4⋊C4×C61—41no—
137C2×C4⋊C4×C61C2×C414yes—
138C2×C42×C61—41no—
139C2×C42×C61—41no—
140C2×C42×C61—41no—
141#95×C61—22no—
142#95×C61—41no—
143#95×C61—41no—
144#95×C61—41no—
145#95×C61D414yescomplemented
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×D61—21no—
174C23×D61—21no—
175C23×D61C22×C412yes—
176C23×D61C22×C412yes—
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×C61C22×C412yes—
219C22×C4×C61C22×C412yes—
220C22×C4×C61C22×C412yes—
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D412yes—
223C22×C4×C61C2×D412yes—
224C22×C4×C61#4112yes—
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×Dic61C22×C412yes—
264C22×Dic61C22×C412yes—
265C22×Dic61#4112yes—
266C22×Dic61#4112yes—
267C22×Dic61#4112yes—
268C2×D244—44no—
269C2×D244—44no—
270C2×D244—44no—
271C2×D244—44no—
272C2×D244—44no—
273C2×D244—44no—
274C2×D244—44no—
275C4⋊C4×C61—44no—
276C42×C61—44no—
277#11758198—28no—
278#11758198—28no—
279#11758198—44no—
280#11758198—44no—
281#11758198—44no—
282#11758198—44no—
283#11758198—44no—
284#11758198—44no—
285#11758198—44no—
286#11758198—44no—
287#11758198—44no—
288#11758198—44no—
289C4⋊Dic61—44no—
290#11758196—44no—
291C4×Dic61—44no—
292C4×Dic61—44no—
293C23×C61C23×C411yescharacteristic
294C23×C61C22×D411yescharacteristic
295C23×C61C2×#4111yescharacteristic
296C23×C61C2×#4111yescharacteristic
297C23×C61C2×#4111yescharacteristic
298C23×C61C2×#4111yescharacteristic
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×C612−1+411yescharacteristic
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
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—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
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—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
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—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
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×C61C4×D414yes—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
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—22no—
441C2×Dic61—22no—
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—
469D244—416no—
470#14566—611nomaximal, Sylow
471C22×C61C2×C4×D411yescharacteristic
472C22×C61C4×#4111yescharacteristic
473C22×C61C4×#4111yescharacteristic
474C22×C61#51811yescharacteristic
475C22×C61#51811yescharacteristic
476C22×C61#51811yescharacteristic
477C22×C61#52011yescharacteristic
478C22×C61#53511yescharacteristic
479C22×C61#53711yescharacteristic
480C22×C61#53811yescharacteristic
481C22×C61#53811yescharacteristic
482C22×C61#53811yescharacteristic
483C22×C61#53911yescharacteristic
484C22×C61#54011yescharacteristic
485C22×C61#54011yescharacteristic
486C22×C61#54211yescharacteristic
487C22×C61#54211yescharacteristic
488C22×C61#54211yescharacteristic
489C22×C61#54211yescharacteristic
490C22×C61#54611yescharacteristic
491C22×C61#54611yescharacteristic
492C22×C61#54611yescharacteristic
493C22×C61#55011yescharacteristic
494C22×C61#55111yescharacteristic
495C22×C61#55311yescharacteristic
496C22×C61#55311yescharacteristic
497C22×C61#55311yescharacteristic
498C22×C61#55311yescharacteristic
499C22×C61#55311yescharacteristic
500C22×C61#55511yescharacteristic
501C22×C61#55911yescharacteristic
502C22×C61#56011yescharacteristic
503C22×C61#56011yescharacteristic
504C22×C61#56011yescharacteristic
505C22×C61H(3,𝔽4)11yescharacteristic
506C2×D61—42no—
507C2×D61—42no—
508C2×D61—42no—
509C2×D61—42no—
510C2×D61—42no—
511C2×D61—42no—
512C2×D61—42no—
513C2×D61—42no—
514C2×D61—42no—
515C2×D61—42no—
516C2×D61—42no—
517C2×D61—42no—
518C2×D61—42no—
519C2×D61—42no—
520C2×D61—81no—
521C2×D61—81no—
522C2×D61—81no—
523C2×D61—81no—
524C2×D61—81no—
525C2×D61—81no—
526C2×D61—81no—
527C2×D61—81no—
528C2×D61—81no—
529C2×D61—81no—
530C2×D61—81no—
531C2×D61—81no—
532C2×D61—81no—
533C2×D61—81no—
534C2×D61—81no—
535C2×D61—81no—
536C4×C61—24no—
537C4×C61—42no—
538C4×C61—42no—
539C4×C61—42no—
540C4×C61—42no—
541C4×C61—42no—
542C4×C61—81no—
543Dic61—42no—
544Dic61—42no—
545Dic61—42no—
546Dic61—42no—
547Dic61—42no—
548Dic61—81no—
549C2×#394—611no—
550C2×#388—611no—
551C2×#388—611no—
552#1443—611no—
553#1439—611no—
554#1439—611no—
555#1438—611no—
556#1438—611no—
557#1437—611no—
558#1437—611no—
559#1437—611no—
560#1437—611no—
561#1436—611no—
562#1436D6111yescharacteristic, complemented
563C4⋊#95—611no—
564C2×C61#232411yescharacteristic
565C2×C61#233511yescharacteristic
566C2×C61#233711yescharacteristic
567C2×C61#236311yescharacteristic
568C2×C61#236411yescharacteristic
569C2×C61#237411yescharacteristic
570C2×C61#237511yescharacteristic
571C2×C61#270311yescharacteristic
572C2×C61#270511yescharacteristic
573C2×C61#271211yescharacteristic
574C2×C61#271411yescharacteristic
575C2×C61#275311yescharacteristic
576C2×C61#279511yescharacteristic
577C2×C61#280111yescharacteristic
578C2×C61#280311yescharacteristic
579D61—82no—
580D61—82no—
581C23×D4—611no—
582C22×C4⋊C4—611no—
583C22×C4⋊C4—611no—
584C22×C4⋊C4C2×D6111yescharacteristic
585C22×C22⋊C4—611no—
586C22×C22⋊C4—611no—
587C22×C22⋊C4—611no—
588C22×C22⋊C4—611no—
589C22×C22⋊C4—611no—
590C22×C22⋊C4—611no—
591C22×C22⋊C4—611no—
592C22×C22⋊C4—611no—
593C22×C22⋊C4—611no—
594C22×C22⋊C4—611no—
595C22×C22⋊C4—611no—
596C22×C22⋊C4—611no—
597C22×C42—611no—
598C22×C42—611no—
599C22×C42C2×D6111yescharacteristic
600#394—618no—
601#388—1224no—
602#388—1224no—
603C2×#95—611no—
604C2×#95—611no—
605C2×#95—611no—
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×#95C2×D6111yescharacteristic
615C2×#95C2×D6111yescharacteristic
616C2×#95C2×D6111yescharacteristic
617C2×#95C2×D6111yescharacteristic
618C2×#95C2×D6111yescharacteristic
619C61#1456611yescharacteristic, complemented, Sylow
620C25—611no—
621C25—611no—
622C22×D4—614no—
623C22×D4—2441no—
624C22×D4—2441no—
625C22×D4—2441no—
626C22×D4—2441no—
627C22×D4—2441no—
628C22×D4—2441no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4C22×D6111yescharacteristic
636C23×C4C22×D6111yescharacteristic
637C23×C4C22×D6111yescharacteristic
638C23×C4C22×D6111yescharacteristic
639C23×C4C22×D6111yescharacteristic
640C23×C4C22×D6111yescharacteristic
641C23×C4C22×D6111yescharacteristic
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—1222no—
645C2×C4⋊C4—1222no—
646C2×C4⋊C4—1222no—
647C2×C4⋊C4—1222no—
648C2×C4⋊C4—2441no—
649C2×C4⋊C4—2441no—
650C2×C4⋊C4C4×D6114yes—
651C2×C22⋊C4—614no—
652C2×C22⋊C4—614no—
653C2×C22⋊C4—614no—
654C2×C22⋊C4—614no—
655C2×C22⋊C4—1222no—
656C2×C22⋊C4—1222no—
657C2×C22⋊C4—1222no—
658C2×C22⋊C4—1222no—
659C2×C22⋊C4—1222no—
660C2×C22⋊C4—1222no—
661C2×C22⋊C4—1222no—
662C2×C22⋊C4—1222no—
663C2×C22⋊C4—1222no—
664C2×C22⋊C4—1222no—
665C2×C22⋊C4—1222no—
666C2×C22⋊C4—1222no—
667C2×C22⋊C4—1222no—
668C2×C22⋊C4—1222no—
669C2×C22⋊C4—1222no—
670C2×C22⋊C4—1222no—
671C2×C22⋊C4—2441no—
672C2×C22⋊C4—2441no—
673C2×C22⋊C4—2441no—
674C2×C22⋊C4—2441no—
675C2×C22⋊C4—2441no—
676C2×C22⋊C4—2441no—
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×C42—41no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—1222no—
691C2×C42—1222no—
692C2×C42—1222no—
693C2×C42—2441no—
694C2×C42—2441no—
695C2×C42—2441no—
696#95—22no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—614no—
701#95—1222no—
702#95—1222no—
703#95—1222no—
704#95—2441no—
705#95—2441no—
706#95—2441no—
707#95—2441no—
708#95—2441no—
709#95—2441no—
710#95—2441no—
711#95D24414yescomplemented
712C24—612no—
713C24—612no—
714C24—1221no—
715C24—1221no—
716C24—1221no—
717C24—1221no—
718C24—1221no—
719C24—1221no—
720C24—1221no—
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—
742C24C23×D6111yescharacteristic
743C2×D4—2444no—
744C2×D4—2444no—
745C2×D4—2444no—
746C2×D4—2444no—
747C2×D4—2444no—
748C2×D4—2444no—
749C2×D4—2444no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
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—612no—
792C22×C4—612no—
793C22×C4—612no—
794C22×C4—612no—
795C22×C4—612no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
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×C4C2×C4×D6112yes—
834C22×C4C2×C4×D6112yes—
835C22×C4C2×C4×D6112yes—
836C22×C4C2×D24412yes—
837C22×C4C2×D24412yes—
838C22×C4C2×D24412yes—
839C22×C4#1175822212yes—
840C22×C4#1175822612yes—
841C4⋊C4—44no—
842C4⋊C4—2444no—
843C4⋊C4—2444no—
844C22⋊C4—1228no—
845C22⋊C4—1228no—
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—
856C42—44no—
857C42—2444no—
858C42—2444no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23—1222no—
864C23—1222no—
865C23—1222no—
866C23—1222no—
867C23—1222no—
868C23—1222no—
869C23—1222no—
870C23—1222no—
871C23—1222no—
872C23—1222no—
873C23—2441no—
874C23—2441no—
875C23—2441no—
876C23—2441no—
877C23—2441no—
878C23—2441no—
879C23—2441no—
880C23—2441no—
881C23—2441no—
882C23—2441no—
883C23—2441no—
884C23—2441no—
885C23—2441no—
886C23—2441no—
887C23—2441no—
888C23—2441no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23—2441no—
893C23—2441no—
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—
929C23C22×C4×D6111yescharacteristic
930C23C22×D24411yescharacteristic
931C23#41×D6111yescharacteristic
932C23#41×D6111yescharacteristic
933C23#41×D6111yescharacteristic
934C23C2×#1175822211yescharacteristic
935C23C2×#1175822611yescharacteristic
936C23#1451982211yescharacteristic
937C23#1451982211yescharacteristic
938C23#1451982211yescharacteristic
939C23#1451982211yescharacteristic
940C23#1451982311yescharacteristic
941C23#1451982311yescharacteristic
942C23#1451982311yescharacteristic
943C23#1451982511yescharacteristic
944D4—24416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
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—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1222no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2441no—
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×C4C4×D24414yes—
1036C22—4881no—
1037C22—4881no—
1038C22—4881no—
1039C22—4881no—
1040C22—4881no—
1041C22—4881no—
1042C22—4881no—
1043C22—4881no—
1044C22—4881no—
1045C22—4881no—
1046C22—4881no—
1047C22—4881no—
1048C22—4881no—
1049C22—4881no—
1050C22—4881no—
1051C22—4881no—
1052C22—2442no—
1053C22—2442no—
1054C22—2442no—
1055C22—2442no—
1056C22—2442no—
1057C22—2442no—
1058C22—2442no—
1059C22—2442no—
1060C22—2442no—
1061C22—2442no—
1062C22—2442no—
1063C22—2442no—
1064C22—2442no—
1065C22—2442no—
1066C22C2×C4×D24411yescharacteristic
1067C22#1684023011yescharacteristic
1068C22C4×#1175822611yescharacteristic
1069C22#1684023411yescharacteristic
1070C22#1684023411yescharacteristic
1071C22#1684023511yescharacteristic
1072C22#1684024411yescharacteristic
1073C22#1684033111yescharacteristic
1074C22#1684034311yescharacteristic
1075C22#1684034611yescharacteristic
1076C22#1684035111yescharacteristic
1077C22#1684035211yescharacteristic
1078C22#1684036011yescharacteristic
1079C22#1684036311yescharacteristic
1080C22#1684036411yescharacteristic
1081C22#1684038211yescharacteristic
1082C22#1684038211yescharacteristic
1083C22#1684038411yescharacteristic
1084C22#1684038611yescharacteristic
1085C22#1684040711yescharacteristic
1086C22#1684040711yescharacteristic
1087C22#1684040711yescharacteristic
1088C22#1684043411yescharacteristic
1089C22#1684043911yescharacteristic
1090C22#1684046011yescharacteristic
1091C22#1684046111yescharacteristic
1092C22#1684046111yescharacteristic
1093C22#1684046311yescharacteristic
1094C22#1684046511yescharacteristic
1095C22#1684047511yescharacteristic
1096C22#1684049611yescharacteristic
1097C22#1684050011yescharacteristic
1098C22#1684050011yescharacteristic
1099C22#1684050211yescharacteristic
1100C22#1684050511yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—81no—
1108C4—4881no—
1109C4—2442no—
1110C4—2442no—
1111C4—2442no—
1112C4—2442no—
1113C4—2442no—
1114C2—4882no—
1115C2—4882no—
1116C2#2144851311yescharacteristic
1117C2#2144861511yescharacteristic
1118C2#2144863111yescharacteristic
1119C2#2144885911yescharacteristic
1120C2#2144886911yescharacteristic
1121C2#2144895111yescharacteristic
1122C2#2144895711yescharacteristic
1123C2#2145246011yescharacteristic
1124C2#2145249011yescharacteristic
1125C2#2145258711yescharacteristic
1126C2#2145261311yescharacteristic
1127C2#2145309711yescharacteristic
1128C2#2145364711yescharacteristic
1129C2#2145372411yescharacteristic
1130C2#2145374711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#14566
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#16839654C2semidirect
3. C2×#16839651C2semidirect
4. #21444079C2semidirect
5. #21444065C2semidirect
6. #21444063C2semidirect
9. #21444057C2semidirect
10. #21444057C2semidirect
11. #21444055C2semidirect
12. #21444055C2semidirect
13. #21444054C2semidirect
14. #21444048C2semidirect
15. C61×#1436C2semidirect
33. #16839679C4semidirect
145. #95×C61D4semidirect
562. #1436D61semidirect
619. C61#14566semidirect
711. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396792
C2×#168396542
C2×#168396512
#214440792
#214440652
#214440632
#214440592
#214440572
#214440552
#214440542
#214440482
C61×#14362
#1456661