Finite Group Databasebeta

← #29645383

Subgroups — #29645383

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444085C211yesmaximal, characteristic, complemented
2#21444083C211yesmaximal, characteristic, complemented
3#21444081C211yesmaximal, characteristic, complemented
4#21444080C211yesmaximal, characteristic, complemented
5#21444079C211yesmaximal, characteristic, complemented
6#21444077C211yesmaximal, characteristic, complemented
7#21444074C211yesmaximal, characteristic, complemented
8#21444073C211yesmaximal, characteristic, complemented
9#21444066C211yesmaximal, characteristic
10#21444066C211yesmaximal, characteristic
11#21444064C211yesmaximal, characteristic
12#21444062C211yesmaximal, characteristic
13#21444062C211yesmaximal, characteristic
14#21444062C211yesmaximal, characteristic
15C61×#1440C211yesmaximal, characteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C22×C22⋊C4×C61C2211yescharacteristic
45C22×C22⋊C4×C61C2211yescharacteristic
46C22×C22⋊C4×C61C2211yescharacteristic
47C2×#95×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C2×C4⋊Dic61—41no—
60C2×C4⋊Dic61—41no—
61C2×C4⋊Dic61—41no—
62C2×#11758196—22no—
63C2×#11758196—22no—
64C2×#11758196—41no—
65C2×#11758196—41no—
66C2×#11758196—41no—
67C2×#11758196—41no—
68C2×#11758196—41no—
69C2×#11758196—41no—
70C2×#11758196—41no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—41no—
77C2×C22⋊Dic61—41no—
78C2×C22⋊Dic61—41no—
79C2×C22⋊Dic61—41no—
80C2×C22⋊Dic61—41no—
81C2×C22⋊Dic61—41no—
82C2×C22⋊Dic61—41no—
83#14519684—22no—
84#14519684—22no—
85#14519684—22no—
86#14519684—22no—
87#14519684—22no—
88#14519684—41no—
89#14519684—41no—
90#14519684—41no—
91#14519684—41no—
92#14519684—41no—
93#14519684—41no—
94#14519684—41no—
95#14519684—41no—
96#14519684—41no—
97#14519684—41no—
98#14519684—41no—
99#14519684—41no—
100#14519684—41no—
101#14519684—41no—
102#14519684—41no—
103C25×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—41no—
113C2×C22⋊C4×C61—41no—
114C2×C22⋊C4×C61—41no—
115C2×C22⋊C4×C61—41no—
116C2×C22⋊C4×C61—41no—
117C2×C22⋊C4×C61—41no—
118C2×C22⋊C4×C61—41no—
119#95×C61—22no—
120#95×C61—41no—
121#95×C61—41no—
122#95×C61—41no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—21no—
126C24×C61—21no—
127C24×C61—21no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C24×C61#4112yes—
138C24×C61C2411yescharacteristic
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61#4112yes—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
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#4112yes—
235C22×Dic61#4112yes—
236C22×Dic61#4112yes—
237C22⋊C4×C61—44no—
238C22⋊C4×C61—44no—
239C22⋊C4×C61—44no—
240C22⋊Dic61—44no—
241C22⋊Dic61—44no—
242C22⋊Dic61—44no—
243C22⋊Dic61—44no—
244C4⋊Dic61—44no—
245#11758196—44no—
246#11758196—44no—
247#11758196—44no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61C2×#4111yescharacteristic
284C23×C61C2×#4111yescharacteristic
285C23×C61C2×#4111yescharacteristic
286C23×C61C2×#4111yescharacteristic
287C23×C61C2×#4111yescharacteristic
288C23×C61H(5,𝔽2)11yescharacteristic
289C23×C61H(5,𝔽2)11yescharacteristic
290C23×C61H(5,𝔽2)11yescharacteristic
291C23×C61H(5,𝔽2)11yescharacteristic
292C23×C61H(5,𝔽2)11yescharacteristic
293C23×C61H(5,𝔽2)11yescharacteristic
294C23×C61H(5,𝔽2)11yescharacteristic
295C23×C612−1+411yescharacteristic
296C23×C612−1+411yescharacteristic
297C23×C612−1+411yescharacteristic
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396#17290—611nomaximal, Sylow
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61#53811yescharacteristic
413C22×C61#53811yescharacteristic
414C22×C61#53811yescharacteristic
415C22×C61#53811yescharacteristic
416C22×C61#53811yescharacteristic
417C22×C61#53911yescharacteristic
418C22×C61#53911yescharacteristic
419C22×C61#53911yescharacteristic
420C22×C61#53911yescharacteristic
421C22×C61#54011yescharacteristic
422C22×C61#54211yescharacteristic
423C22×C61#54211yescharacteristic
424C22×C61#54211yescharacteristic
425C22×C61#54211yescharacteristic
426C22×C61#54211yescharacteristic
427C22×C61#55111yescharacteristic
428C22×C61#55111yescharacteristic
429C22×C61#55211yescharacteristic
430C22×C61#55211yescharacteristic
431C22×C61#55211yescharacteristic
432C22×C61#55311yescharacteristic
433C22×C61#55311yescharacteristic
434C22×C61#55311yescharacteristic
435C22×C61#55511yescharacteristic
436C22×C61#55911yescharacteristic
437C22×C61#56011yescharacteristic
438C22×C61#56011yescharacteristic
439C22×C61#56011yescharacteristic
440C22×C61#56011yescharacteristic
441C22×C61#56211yescharacteristic
442C22×C61#56211yescharacteristic
443C22×C61#56211yescharacteristic
444C22×C61#56311yescharacteristic
445C22×C61#56311yescharacteristic
446C22×C61#56311yescharacteristic
447C4×C61—42no—
448C4×C61—81no—
449C4×C61—81no—
450C4×C61—81no—
451C4×C61—81no—
452C4×C61—81no—
453Dic61—42no—
454Dic61—42no—
455Dic61—42no—
456Dic61—81no—
457Dic61—81no—
458Dic61—81no—
459Dic61—81no—
460Dic61—81no—
461#1445—611no—
462#1444—611no—
463#1443—611no—
464#1443—611no—
465#1443—611no—
466#1442—611no—
467#1442—611no—
468#1441—611no—
469#1440—611no—
470#1440—611no—
471#1440D6111yescharacteristic
472#1439—611no—
473#1439—611no—
474#1439—611no—
475#1439—611no—
476C2×C61—82no—
477C2×C61#273711yescharacteristic
478C2×C61#274111yescharacteristic
479C2×C61#276411yescharacteristic
480C2×C61#276511yescharacteristic
481C2×C61#277111yescharacteristic
482C2×C61#277911yescharacteristic
483C2×C61#278111yescharacteristic
484C2×C61#279511yescharacteristic
485C2×C61#279611yescharacteristic
486C2×C61#279711yescharacteristic
487C2×C61#282511yescharacteristic
488C2×C61#282711yescharacteristic
489C2×C61#283011yescharacteristic
490C2×C61#283711yescharacteristic
491C2×C61#283811yescharacteristic
492C22×C4⋊C4—611no—
493C22×C4⋊C4—611no—
494C22×C4⋊C4—611no—
495C22×C4⋊C4—611no—
496C22×C22⋊C4—611no—
497C22×C22⋊C4—611no—
498C22×C22⋊C4—611no—
499C22×C22⋊C4—611no—
500C22×C22⋊C4C2×D6111yescharacteristic
501C22×C22⋊C4C2×D6111yescharacteristic
502C22×C22⋊C4C2×D6111yescharacteristic
503C2×#95—611no—
504C2×#95—611no—
505C2×#95—611no—
506C2×#95—611no—
507C2×#95—611no—
508C2×#95—611no—
509C2×#95—611no—
510C2×#95—611no—
511C2×#95—611no—
512C2×#95—611no—
513C2×#95—611no—
514C2×#95—611no—
515C2×#95—611no—
516C2×#95—611no—
517C2×#95—611no—
518C2×#95—611no—
519C2×#95—611no—
520C2×#95—611no—
521C2×#95—611no—
522C2×#95—611no—
523C2×#95C2×D6111yescharacteristic
524C2×#95C2×D6111yescharacteristic
525C2×#95C2×D6111yescharacteristic
526C2×#95C2×D6111yescharacteristic
527C61#1729011yescharacteristic, complemented, Sylow
528C25C22×D6111yescharacteristic
529C23×C4—611no—
530C23×C4—611no—
531C23×C4—611no—
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—611no—
537C23×C4C22×D6111yescharacteristic
538C23×C4C22×D6111yescharacteristic
539C23×C4C22×D6111yescharacteristic
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542C23×C4C22×D6111yescharacteristic
543C2×C4⋊C4—1222no—
544C2×C4⋊C4—1222no—
545C2×C4⋊C4—2441no—
546C2×C4⋊C4—2441no—
547C2×C4⋊C4—2441no—
548C2×C4⋊C4—2441no—
549C2×C4⋊C4—2441no—
550C2×C4⋊C4—2441no—
551C2×C4⋊C4—2441no—
552C2×C4⋊C4—2441no—
553C2×C4⋊C4—2441no—
554C2×C4⋊C4—2441no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—1222no—
565C2×C22⋊C4—1222no—
566C2×C22⋊C4—1222no—
567C2×C22⋊C4—1222no—
568C2×C22⋊C4—1222no—
569C2×C22⋊C4—2441no—
570C2×C22⋊C4—2441no—
571C2×C22⋊C4—2441no—
572C2×C22⋊C4—2441no—
573C2×C22⋊C4—2441no—
574C2×C22⋊C4—2441no—
575C2×C22⋊C4—2441no—
576#95—22no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—1222no—
581#95—1222no—
582#95—1222no—
583#95—1222no—
584#95—1222no—
585#95—2441no—
586#95—2441no—
587#95—2441no—
588#95—2441no—
589#95—2441no—
590#95—2441no—
591#95—2441no—
592#95—2441no—
593#95—2441no—
594#95—2441no—
595#95—2441no—
596#95—2441no—
597#95—2441no—
598#95—2441no—
599#95—2441no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24#1175822212yes—
615C24C23×D6111yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4#1175822412yes—
714C4⋊C4—2444no—
715C4⋊C4—2444no—
716C4⋊C4—2444no—
717C4⋊C4—2444no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—2444no—
722C22⋊C4—2444no—
723C22⋊C4—2444no—
724C22⋊C4—2444no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23#41×D6111yescharacteristic
761C23#41×D6111yescharacteristic
762C23#41×D6111yescharacteristic
763C23C2×#1175822411yescharacteristic
764C23C2×#1175822211yescharacteristic
765C23#1451982211yescharacteristic
766C23#1451982211yescharacteristic
767C23#1451982211yescharacteristic
768C23#1451982211yescharacteristic
769C23#1451982211yescharacteristic
770C23#1451982311yescharacteristic
771C23#1451982311yescharacteristic
772C23#1451982411yescharacteristic
773C23#1451982411yescharacteristic
774C23#1451982411yescharacteristic
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22#1684034511yescharacteristic
889C22#1684034511yescharacteristic
890C22#1684034611yescharacteristic
891C22#1684034711yescharacteristic
892C22#1684035011yescharacteristic
893C22#1684035311yescharacteristic
894C22#1684035511yescharacteristic
895C22#1684035511yescharacteristic
896C22#1684035511yescharacteristic
897C22#1684036211yescharacteristic
898C22#1684037611yescharacteristic
899C22#1684037611yescharacteristic
900C22#1684037811yescharacteristic
901C22#1684037911yescharacteristic
902C22#1684038111yescharacteristic
903C22#1684043511yescharacteristic
904C22#1684043711yescharacteristic
905C22#1684044511yescharacteristic
906C22#1684044511yescharacteristic
907C22#1684045211yescharacteristic
908C22#1684045511yescharacteristic
909C22#1684045711yescharacteristic
910C22#1684046111yescharacteristic
911C22#1684047611yescharacteristic
912C22#1684049611yescharacteristic
913C22#1684050011yescharacteristic
914C22#1684050011yescharacteristic
915C22#1684050111yescharacteristic
916C22#1684050211yescharacteristic
917C22#1684050711yescharacteristic
918C22#1684050711yescharacteristic
919C22#1684050911yescharacteristic
920C22#1684051411yescharacteristic
921C22#1684051511yescharacteristic
922C22#1684051511yescharacteristic
923C4—42no—
924C4—81no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—81no—
929C4—4881no—
930C4—4881no—
931C4—4881no—
932C4—4881no—
933C4—4881no—
934C4—2442no—
935C4—2442no—
936C4—2442no—
937C2—82no—
938C2#2145287311yescharacteristic
939C2#2145293511yescharacteristic
940C2#2145324411yescharacteristic
941C2#2145324811yescharacteristic
942C2#2145333411yescharacteristic
943C2#2145344911yescharacteristic
944C2#2145348511yescharacteristic
945C2#2145365011yescharacteristic
946C2#2145366611yescharacteristic
947C2#2145368211yescharacteristic
948C2#2145390511yescharacteristic
949C2#2145392411yescharacteristic
950C2#2145396511yescharacteristic
951C2#2145403611yescharacteristic
952C2#2145405111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC61×#1440C2
prime radicalC25×C61C23
hypercenter#1440D61
hypocenterC61#17290
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
1. #21444085C2semidirect
2. #21444083C2semidirect
3. #21444081C2semidirect
4. #21444080C2semidirect
5. #21444079C2semidirect
6. #21444077C2semidirect
7. #21444074C2semidirect
8. #21444073C2semidirect
527. C61#17290semidirect

Maximal subgroups

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

subgroupindex
#214440852
#214440832
#214440812
#214440802
#214440792
#214440772
#214440742
#214440732
#214440662
#214440642
#214440622
C61×#14402
#1729061