Finite Group Databasebeta

← #29608129

Subgroups — #29608129

Order 15616.

1766 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×#16839654C211yesmaximal, characteristic, complemented
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839619C211yesmaximal, characteristic, complemented
4#21444080C211yesmaximal, characteristic, complemented
5#21444067C211yesmaximal, characteristic, complemented
6#21444061C211yesmaximal, characteristic, complemented
7#21444059C211yesmaximal, characteristic
8#21444059C211yesmaximal, characteristic
9#21444055C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444045C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839654—24no—
33#16839640C418yescomplemented
34#16839619—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—22no—
70C22×C4×D61—22no—
71C22×C4×D61—41no—
72C22×C4×D61—41no—
73C22×C4×D61—41no—
74C22×C4×D61—41no—
75C22×C4×D61C2×C414yes—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61D414yescomplemented
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—22no—
92C2×#11758198—22no—
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×#11758198C2×C414yes—
110C2×#11758198C2×C414yes—
111C2×#11758198C2×C414yes—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—41no—
115C2×C4×Dic61—41no—
116C2×C4×Dic61—41no—
117C2×C4×Dic61—41no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684C2×C414yes—
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×C414yes—
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×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×C61C22×C412yes—
221C22×C4×C61C22×C412yes—
222C22×C4×C61C22×C412yes—
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×Dic61C2×D412yes—
266C22×Dic61C2×D412yes—
267C22×Dic61#4112yes—
268C2×D244—28no—
269C2×D244—44no—
270C2×D244—44no—
271C2×D244—44no—
272C2×D244—44no—
273C2×D244—44no—
274C2×D244—44no—
275C2×C4×D61—28no—
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—
295C4×Dic61—44no—
296C4×Dic61—44no—
297C23×C61C23×C411yescharacteristic
298C23×C61C22×D411yescharacteristic
299C23×C61C2×#4111yescharacteristic
300C23×C61C2×#4111yescharacteristic
301C23×C61C2×#4111yescharacteristic
302C23×C61C2×#4111yescharacteristic
303C23×C61C2×#4111yescharacteristic
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×C61H(5,𝔽2)11yescharacteristic
310C23×C61H(5,𝔽2)11yescharacteristic
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×D61#11714yes—
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—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×C61C4×D414yes—
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—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
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#14415—611nomaximal, Sylow
476C22×C61C2×#11711yescharacteristic
477C22×C61C2×C4×D411yescharacteristic
478C22×C61C4×#4111yescharacteristic
479C22×C61#51811yescharacteristic
480C22×C61#51811yescharacteristic
481C22×C61#51811yescharacteristic
482C22×C61#52011yescharacteristic
483C22×C61#53411yescharacteristic
484C22×C61#53511yescharacteristic
485C22×C61#53811yescharacteristic
486C22×C61#53811yescharacteristic
487C22×C61#53811yescharacteristic
488C22×C61#53811yescharacteristic
489C22×C61#53811yescharacteristic
490C22×C61#53811yescharacteristic
491C22×C61#53811yescharacteristic
492C22×C61#53911yescharacteristic
493C22×C61#54011yescharacteristic
494C22×C61#54211yescharacteristic
495C22×C61#54611yescharacteristic
496C22×C61#54611yescharacteristic
497C22×C61#54811yescharacteristic
498C22×C61#55011yescharacteristic
499C22×C61#55111yescharacteristic
500C22×C61#55111yescharacteristic
501C22×C61#55211yescharacteristic
502C22×C61#55311yescharacteristic
503C22×C61#55311yescharacteristic
504C22×C61#55311yescharacteristic
505C22×C61#55311yescharacteristic
506C22×C61#55511yescharacteristic
507C22×C61#56011yescharacteristic
508C22×C61#56011yescharacteristic
509C22×C61#56211yescharacteristic
510C22×C61#56211yescharacteristic
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—24no—
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—42no—
552Dic61—42no—
553Dic61—81no—
554C2×#388—611no—
555C2×#386—611no—
556C2×#380—611no—
557#1443—611no—
558#1442D6111yescharacteristic, complemented
559#1440—611no—
560#1439—611no—
561#1438—611no—
562#1438—611no—
563#1437—611no—
564#1437—611no—
565#1437—611no—
566#1436—611no—
567#1434—611no—
568C22⋊#95—611no—
569C2×C61#231211yescharacteristic
570C2×C61#232111yescharacteristic
571C2×C61#233511yescharacteristic
572C2×C61#235211yescharacteristic
573C2×C61#235311yescharacteristic
574C2×C61#236311yescharacteristic
575C2×C61#237711yescharacteristic
576C2×C61#268811yescharacteristic
577C2×C61#269611yescharacteristic
578C2×C61#271411yescharacteristic
579C2×C61#273011yescharacteristic
580C2×C61#275611yescharacteristic
581C2×C61#277811yescharacteristic
582C2×C61#277911yescharacteristic
583C2×C61#278111yescharacteristic
584D61—44no—
585D61—82no—
586C23×D4—611no—
587C24×C4—611no—
588C22×C4⋊C4—611no—
589C22×C4⋊C4C2×D6111yescharacteristic
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×C22⋊C4—611no—
598C22×C22⋊C4—611no—
599C22×C22⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C42—611no—
602C22×C42—611no—
603#388—1224no—
604#386—618no—
605#380—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#1441511yescharacteristic, 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—611no—
638C23×C4—611no—
639C23×C4—614no—
640C23×C4—611no—
641C23×C4—1222no—
642C23×C4—1222no—
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—2441no—
659C2×C4⋊C4—2441no—
660C2×C22⋊C4—614no—
661C2×C22⋊C4—614no—
662C2×C22⋊C4—614no—
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—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×C42—1222no—
694C2×C42—1222no—
695C2×C42—2441no—
696C2×C42—2441no—
697C2×C42—2441no—
698C2×C42—2441no—
699#95—22no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—614no—
705#95—1222no—
706#95—1222no—
707#95—1222no—
708#95—1222no—
709#95—1222no—
710#95—2441no—
711#95—2441no—
712#95—2441no—
713#95—2441no—
714#95—2441no—
715#95—2441no—
716#95C4×D6114yes—
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—612no—
799C22×C4—612no—
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—1228no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—2444no—
842C22×C4—2444no—
843C22×C4—2444no—
844C22×C4—2444no—
845C22×C4—2444no—
846C22×C4—2444no—
847C22×C4C2×C4×D6112yes—
848C22×C4C2×C4×D6112yes—
849C22×C4C2×C4×D6112yes—
850C22×C4D4×D6112yes—
851C22×C4#1175822612yes—
852C22×C4#1175822612yes—
853C4⋊C4—44no—
854C4⋊C4—2444no—
855C22⋊C4—1228no—
856C22⋊C4—2444no—
857C22⋊C4—2444no—
858C22⋊C4—2444no—
859C22⋊C4—2444no—
860C22⋊C4—2444no—
861C22⋊C4—2444no—
862C22⋊C4—2444no—
863C22⋊C4—2444no—
864C22⋊C4—2444no—
865C22⋊C4—2444no—
866C42—2444no—
867C42—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#41×D6111yescharacteristic
942C23#41×D6111yescharacteristic
943C23C2×#1175822611yescharacteristic
944C23C2×#1175822611yescharacteristic
945C23#1451982211yescharacteristic
946C23#1451982211yescharacteristic
947C23#1451982211yescharacteristic
948C23#1451982311yescharacteristic
949C23#1451982311yescharacteristic
950C23#1451982311yescharacteristic
951C23#1451982311yescharacteristic
952C23#1451982411yescharacteristic
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—22no—
967C2×C4—22no—
968C2×C4—22no—
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—1222no—
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—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—24416no—
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#1451973914yes—
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—
1076C22#117×D6111yescharacteristic
1077C22C2×#1451973911yescharacteristic
1078C22C4×#1175822611yescharacteristic
1079C22#1684023411yescharacteristic
1080C22#1684023411yescharacteristic
1081C22#1684023411yescharacteristic
1082C22#1684024211yescharacteristic
1083C22#1684032311yescharacteristic
1084C22#1684032711yescharacteristic
1085C22#1684034411yescharacteristic
1086C22#1684034611yescharacteristic
1087C22#1684034811yescharacteristic
1088C22#1684034811yescharacteristic
1089C22#1684035111yescharacteristic
1090C22#1684035211yescharacteristic
1091C22#1684035211yescharacteristic
1092C22#1684036111yescharacteristic
1093C22#1684036811yescharacteristic
1094C22#1684037811yescharacteristic
1095C22#1684040311yescharacteristic
1096C22#1684040511yescharacteristic
1097C22#1684042011yescharacteristic
1098C22#1684043011yescharacteristic
1099C22#1684043711yescharacteristic
1100C22#1684043911yescharacteristic
1101C22#1684045011yescharacteristic
1102C22#1684045711yescharacteristic
1103C22#1684046511yescharacteristic
1104C22#1684046511yescharacteristic
1105C22#1684046511yescharacteristic
1106C22#1684047811yescharacteristic
1107C22#1684050011yescharacteristic
1108C22#1684050311yescharacteristic
1109C22#1684050611yescharacteristic
1110C22#1684050911yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—4881no—
1119C4—2442no—
1120C4—2442no—
1121C4—2442no—
1122C4—2442no—
1123C4—2442no—
1124C2—4882no—
1125C2—2444no—
1126C2#2144841311yescharacteristic
1127C2#2144847611yescharacteristic
1128C2#2144860811yescharacteristic
1129C2#2144874511yescharacteristic
1130C2#2144875811yescharacteristic
1131C2#2144885611yescharacteristic
1132C2#2144897211yescharacteristic
1133C2#2145226211yescharacteristic
1134C2#2145237611yescharacteristic
1135C2#2145262011yescharacteristic
1136C2#2145282111yescharacteristic
1137C2#2145314711yescharacteristic
1138C2#2145344311yescharacteristic
1139C2#2145345811yescharacteristic
1140C2#2145348811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1442D61
hypocenterC61#14415
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#16839654C2semidirect
3. C2×#16839619C2semidirect
4. #21444080C2semidirect
5. #21444067C2semidirect
6. #21444061C2semidirect
9. #21444055C2semidirect
10. #21444055C2semidirect
11. #21444055C2semidirect
12. #21444053C2semidirect
13. #21444045C2semidirect
14. #21444040C2semidirect
15. C61×#1442C2semidirect
33. #16839640C4semidirect
78. C2×C4⋊Dic61D4semidirect
558. #1442D61semidirect
624. C61#14415semidirect

Maximal subgroups

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

subgroupindex
C2×#168396542
C2×#168396402
C2×#168396192
#214440802
#214440672
#214440612
#214440592
#214440552
#214440532
#214440452
#214440402
C61×#14422
#1441561