Finite Group Databasebeta

← #29610772

Subgroups — #29610772

Order 15616.

1586 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×#16839680C211yesmaximal, characteristic
2C2×#16839654C211yesmaximal, characteristic, complemented
3C2×#16839652C211yesmaximal, characteristic, complemented
4#21444076C211yesmaximal, characteristic, complemented
5#21444070C211yesmaximal, characteristic, complemented
6#21444065C211yesmaximal, characteristic, complemented
7#21444063C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444061C211yesmaximal, characteristic, complemented
12#21444059C211yesmaximal, characteristic
13#21444059C211yesmaximal, characteristic
14#21444047C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
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
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839680C418yescomplemented
35#16839654—24no—
36#16839652—24no—
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—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—41no—
71C2×C4⋊Dic61—41no—
72C2×#11758196—22no—
73C2×#11758196—41no—
74C2×#11758196—41no—
75C2×#11758196—41no—
76C2×#11758196—41no—
77C2×#11758196—41no—
78C2×#11758196—41no—
79C2×#11758196—41no—
80C2×#11758196C2×C414yes—
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—41no—
90C2×#11758198—41no—
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×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198C2×C414yes—
114C2×#11758198C2×C414yes—
115C2×#11758198C2×C414yes—
116C2×#11758198C2×C414yes—
117C2×C4×Dic61—41no—
118C2×C4×Dic61—41no—
119C2×C4×Dic61D414yescomplemented
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#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×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×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×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×Dic61C22×C412yes—
264C22×Dic61C22×C412yes—
265C22×Dic61C2×D412yes—
266C22×Dic61C2×D412yes—
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—
276#11758198—28no—
277#11758198—28no—
278#11758198—44no—
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—
288C4⋊Dic61—44no—
289#11758196—44no—
290#11758196—44no—
291#11758196—44no—
292C4×Dic61—44no—
293C23×C61C23×C411yescharacteristic
294C23×C61C22×D411yescharacteristic
295C23×C61C2×#4111yescharacteristic
296C23×C61H(5,𝔽2)11yescharacteristic
297C23×C61H(5,𝔽2)11yescharacteristic
298C23×C61H(5,𝔽2)11yescharacteristic
299C23×C61H(5,𝔽2)11yescharacteristic
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×C612−1+411yescharacteristic
306C23×C612−1+411yescharacteristic
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—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
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×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—41no—
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×Dic61C4×D414yes—
469D244—416no—
470#14632—611nomaximal, Sylow
471C22×C61C2×C4×D411yescharacteristic
472C22×C61#51811yescharacteristic
473C22×C61#51811yescharacteristic
474C22×C61#51811yescharacteristic
475C22×C61#52011yescharacteristic
476C22×C61#52011yescharacteristic
477C22×C61#52011yescharacteristic
478C22×C61#53411yescharacteristic
479C22×C61#53511yescharacteristic
480C22×C61#53511yescharacteristic
481C22×C61#53711yescharacteristic
482C22×C61#53711yescharacteristic
483C22×C61#53711yescharacteristic
484C22×C61#53811yescharacteristic
485C22×C61#53911yescharacteristic
486C22×C61#54011yescharacteristic
487C22×C61#54011yescharacteristic
488C22×C61#54211yescharacteristic
489C22×C61#54211yescharacteristic
490C22×C61#56011yescharacteristic
491C22×C61#56011yescharacteristic
492C22×C61#56011yescharacteristic
493C22×C61#56011yescharacteristic
494C22×C61#56011yescharacteristic
495C22×C61H(3,𝔽4)11yescharacteristic
496C22×C61H(3,𝔽4)11yescharacteristic
497C22×C61#56211yescharacteristic
498C22×C61#56211yescharacteristic
499C22×C61#56211yescharacteristic
500C22×C61#56211yescharacteristic
501C22×C61#56211yescharacteristic
502C22×C61#56211yescharacteristic
503C22×C61#56311yescharacteristic
504C22×C61#56311yescharacteristic
505C22×C61#56311yescharacteristic
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—42no—
537C4×C61—42no—
538C4×C61—42no—
539C4×C61—42no—
540C4×C61—81no—
541C4×C61—81no—
542C4×C61—81no—
543Dic61—24no—
544Dic61—42no—
545Dic61—42no—
546Dic61—81no—
547Dic61—81no—
548Dic61—81no—
549C2×#394—611no—
550C2×#388—611no—
551C2×#388—611no—
552#1442—611no—
553#1442D6111yescharacteristic, complemented
554#1441—611no—
555#1439—611no—
556#1439—611no—
557#1439—611no—
558#1439—611no—
559#1439—611no—
560#1439—611no—
561#1438—611no—
562#1438—611no—
563C4⋊#95—611no—
564C2×C61#232411yescharacteristic
565C2×C61#232411yescharacteristic
566C2×C61#232511yescharacteristic
567C2×C61#237511yescharacteristic
568C2×C61#237611yescharacteristic
569C2×C61#237611yescharacteristic
570C2×C61#237911yescharacteristic
571C2×C61#281311yescharacteristic
572C2×C61#281311yescharacteristic
573C2×C61#281911yescharacteristic
574C2×C61#282311yescharacteristic
575C2×C61#282811yescharacteristic
576C2×C61#283211yescharacteristic
577C2×C61#283711yescharacteristic
578C2×C61#283711yescharacteristic
579D61—82no—
580D61—82no—
581C23×D4—611no—
582C22×C4⋊C4—611no—
583C22×C4⋊C4—611no—
584C22×C4⋊C4—611no—
585C22×C4⋊C4—611no—
586C22×C4⋊C4C2×D6111yescharacteristic
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×C22⋊C4—611no—
598C22×C22⋊C4—611no—
599C22×C42—611no—
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×#95C2×D6111yescharacteristic
614C2×#95C2×D6111yescharacteristic
615C2×#95C2×D6111yescharacteristic
616C2×#95C2×D6111yescharacteristic
617C2×#95C2×D6111yescharacteristic
618C2×#95C2×D6111yescharacteristic
619C61#1463211yescharacteristic, 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—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—614no—
646C2×C4⋊C4—1222no—
647C2×C4⋊C4—1222no—
648C2×C4⋊C4—2441no—
649C2×C4⋊C4—2441no—
650C2×C4⋊C4—2441no—
651C2×C4⋊C4—2441no—
652C2×C4⋊C4—2441no—
653C2×C4⋊C4—2441no—
654C2×C4⋊C4—2441no—
655C2×C4⋊C4—2441no—
656C2×C4⋊C4—2441no—
657C2×C22⋊C4—614no—
658C2×C22⋊C4—614no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—614no—
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—2441no—
670C2×C22⋊C4—2441no—
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×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—614no—
694C2×C42—2441no—
695C2×C42—2441no—
696#95—22no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
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#95C4×D6114yes—
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—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—612no—
796C22×C4—612no—
797C22×C4—612no—
798C22×C4—612no—
799C22×C4—612no—
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×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4C2×C4×D6112yes—
838C22×C4C2×C4×D6112yes—
839C22×C4C2×C4×D6112yes—
840C22×C4D4×D6112yes—
841C4⋊C4—44no—
842C4⋊C4—2444no—
843C4⋊C4—2444no—
844C4⋊C4—2444no—
845C4⋊C4—2444no—
846C22⋊C4—1228no—
847C22⋊C4—1228no—
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—
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
930C23C2×D4×D6111yescharacteristic
931C23#41×D6111yescharacteristic
932C23#1451982211yescharacteristic
933C23#1451982211yescharacteristic
934C23#1451982211yescharacteristic
935C23#1451982311yescharacteristic
936C23#1451982311yescharacteristic
937C23#1451982311yescharacteristic
938C23#1451982311yescharacteristic
939C23#1451982311yescharacteristic
940C23#1451982311yescharacteristic
941C23#1451982411yescharacteristic
942C23#1451982511yescharacteristic
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—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
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—614no—
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—2441no—
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×C4—2441no—
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—
1066C22C4×D4×D6111yescharacteristic
1067C22#1684023411yescharacteristic
1068C22#1684023411yescharacteristic
1069C22#1684023611yescharacteristic
1070C22#1684024211yescharacteristic
1071C22#1684024311yescharacteristic
1072C22#1684024411yescharacteristic
1073C22#1684032311yescharacteristic
1074C22#1684032711yescharacteristic
1075C22#1684033011yescharacteristic
1076C22#1684033911yescharacteristic
1077C22#1684034211yescharacteristic
1078C22#1684034211yescharacteristic
1079C22#1684035111yescharacteristic
1080C22#1684036011yescharacteristic
1081C22#1684036411yescharacteristic
1082C22#1684036411yescharacteristic
1083C22#1684037811yescharacteristic
1084C22#1684038211yescharacteristic
1085C22#1684050011yescharacteristic
1086C22#1684050011yescharacteristic
1087C22#1684050211yescharacteristic
1088C22#1684050311yescharacteristic
1089C22#1684050311yescharacteristic
1090C22#1684050411yescharacteristic
1091C22#1684050411yescharacteristic
1092C22#1684050611yescharacteristic
1093C22#1684050811yescharacteristic
1094C22#1684050811yescharacteristic
1095C22#1684050911yescharacteristic
1096C22#1684051011yescharacteristic
1097C22#1684051011yescharacteristic
1098C22#1684051111yescharacteristic
1099C22#1684051611yescharacteristic
1100C22#1684051611yescharacteristic
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—1224no—
1109C4—4881no—
1110C4—4881no—
1111C4—4881no—
1112C4—2442no—
1113C4—2442no—
1114C2—4882no—
1115C2—4882no—
1116C2#2144850711yescharacteristic
1117C2#2144851111yescharacteristic
1118C2#2144851811yescharacteristic
1119C2#2144895911yescharacteristic
1120C2#2144896411yescharacteristic
1121C2#2144896611yescharacteristic
1122C2#2144899011yescharacteristic
1123C2#2145382411yescharacteristic
1124C2#2145382711yescharacteristic
1125C2#2145386711yescharacteristic
1126C2#2145389411yescharacteristic
1127C2#2145394011yescharacteristic
1128C2#2145398811yescharacteristic
1129C2#2145403011yescharacteristic
1130C2#2145404011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1442D61
hypocenterC61#14632
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#16839654C2semidirect
3. C2×#16839652C2semidirect
4. #21444076C2semidirect
5. #21444070C2semidirect
6. #21444065C2semidirect
7. #21444063C2semidirect
8. #21444063C2semidirect
9. #21444063C2semidirect
10. #21444063C2semidirect
11. #21444061C2semidirect
14. #21444047C2semidirect
15. C61×#1442C2semidirect
34. #16839680C4semidirect
119. C2×C4×Dic61D4semidirect
553. #1442D61semidirect
619. C61#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#168396802
C2×#168396542
C2×#168396522
#214440762
#214440702
#214440652
#214440632
#214440612
#214440592
#214440472
C61×#14422
#1463261