Finite Group Databasebeta

← #29610867

Subgroups — #29610867

Order 15616.

1226 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839690C211yesmaximal, characteristic
2#21444083C211yesmaximal, characteristic, complemented
3#21444080C211yesmaximal, characteristic, complemented
4#21444079C211yesmaximal, characteristic, complemented
5#21444078C211yesmaximal, characteristic, complemented
6#21444070C211yesmaximal, characteristic, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic
9#21444064C211yesmaximal, characteristic
10#21444062C211yesmaximal, characteristic
11#21444062C211yesmaximal, characteristic
12#21444056C211yesmaximal, characteristic
13#21444053C211yesmaximal, characteristic, complemented
14#21444050C211yesmaximal, characteristic, complemented
15C61×#1439C211yesmaximal, characteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25#16839690C418yescomplemented
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
44C2×#14519684C2211yescharacteristic
45C22×C4⋊C4×C61C2211yescharacteristic
46C22×C22⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C2×C4⋊Dic61—22no—
61C2×C4⋊Dic61—41no—
62C2×C4⋊Dic61—41no—
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×#11758196C2×C414yes—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—41no—
74C2×C22⋊Dic61—41no—
75C2×C22⋊Dic61—41no—
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⋊Dic61C2×C414yes—
83C2×C22⋊Dic61C2×C414yes—
84C2×C4×Dic61—41no—
85C2×C4×Dic61—41no—
86C2×C4×Dic61—41no—
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—
103#14519684C2×C414yes—
104#14519684C2×C414yes—
105#14519684C2×C414yes—
106C25×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61—41no—
114C2×C4⋊C4×C61—41no—
115C2×C4⋊C4×C61—41no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—41no—
118C2×C22⋊C4×C61—41no—
119C2×C22⋊C4×C61—41no—
120C2×C22⋊C4×C61—41no—
121C2×C22⋊C4×C61—41no—
122C2×C22⋊C4×C61—41no—
123C2×C22⋊C4×C61—41no—
124C2×C22⋊C4×C61C2×C414yes—
125#95×C61—22no—
126#95×C61—41no—
127#95×C61—41no—
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—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61C22×C412yes—
143C24×C61C2411yescharacteristic
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—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61C22×C412yes—
184C22×C4×C61C22×C412yes—
185C22×C4×C61#4112yes—
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—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61C22×C412yes—
238C22×Dic61C22×C412yes—
239C22×Dic61C22×C412yes—
240C22×Dic61C22×C412yes—
241C22×Dic61#4112yes—
242C4⋊C4×C61—44no—
243C22⋊C4×C61—44no—
244C22⋊C4×C61—44no—
245C22⋊C4×C61—44no—
246C22⋊Dic61—44no—
247C22⋊Dic61—44no—
248C22⋊Dic61—44no—
249C22⋊Dic61—44no—
250C4⋊Dic61—44no—
251#11758196—44no—
252#11758196—44no—
253#11758196—44no—
254C4×Dic61—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
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×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61C23×C411yescharacteristic
291C23×C61C2×#4111yescharacteristic
292C23×C61C2×#4111yescharacteristic
293C23×C61H(5,𝔽2)11yescharacteristic
294C23×C61H(5,𝔽2)11yescharacteristic
295C23×C61H(5,𝔽2)11yescharacteristic
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×C612−1+411yescharacteristic
302C23×C612−1+411yescharacteristic
303C23×C612−1+411yescharacteristic
304C23×C612−1+411yescharacteristic
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
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×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
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—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403#14642—611nomaximal, Sylow
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61—81no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61C4×#4111yescharacteristic
420C22×C61#51811yescharacteristic
421C22×C61#51811yescharacteristic
422C22×C61#52011yescharacteristic
423C22×C61#52011yescharacteristic
424C22×C61#52011yescharacteristic
425C22×C61#52011yescharacteristic
426C22×C61#53811yescharacteristic
427C22×C61#53811yescharacteristic
428C22×C61#53811yescharacteristic
429C22×C61#53811yescharacteristic
430C22×C61#53911yescharacteristic
431C22×C61#53911yescharacteristic
432C22×C61#54011yescharacteristic
433C22×C61#54111yescharacteristic
434C22×C61#54211yescharacteristic
435C22×C61#54211yescharacteristic
436C22×C61#54211yescharacteristic
437C22×C61#54211yescharacteristic
438C22×C61#56011yescharacteristic
439C22×C61#56011yescharacteristic
440C22×C61#56011yescharacteristic
441C22×C61#56011yescharacteristic
442C22×C61#56011yescharacteristic
443C22×C61#56211yescharacteristic
444C22×C61#56211yescharacteristic
445C22×C61#56211yescharacteristic
446C22×C61#56211yescharacteristic
447C22×C61#56211yescharacteristic
448C22×C61#56211yescharacteristic
449C22×C61#56311yescharacteristic
450C22×C61#56311yescharacteristic
451C22×C61#56311yescharacteristic
452C22×C61#56311yescharacteristic
453C22×C61#56311yescharacteristic
454C4×C61—42no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61—81no—
458C4×C61—81no—
459C4×C61—81no—
460Dic61—42no—
461Dic61—42no—
462Dic61—42no—
463Dic61—42no—
464Dic61—42no—
465Dic61—81no—
466Dic61—81no—
467Dic61—81no—
468C2×#397—611no—
469#1444—611no—
470#1443—611no—
471#1443—611no—
472#1442—611no—
473#1441—611no—
474#1441—611no—
475#1440—611no—
476#1439—611no—
477#1439—611no—
478#1439—611no—
479#1439D6111yescharacteristic
480#1437—611no—
481#1436—611no—
482#1436—611no—
483C2×C61—82no—
484C2×C61#233411yescharacteristic
485C2×C61#233511yescharacteristic
486C2×C61#233711yescharacteristic
487C2×C61#237611yescharacteristic
488C2×C61#237611yescharacteristic
489C2×C61#237711yescharacteristic
490C2×C61#238311yescharacteristic
491C2×C61#282511yescharacteristic
492C2×C61#282711yescharacteristic
493C2×C61#282911yescharacteristic
494C2×C61#283011yescharacteristic
495C2×C61#283111yescharacteristic
496C2×C61#283111yescharacteristic
497C2×C61#283711yescharacteristic
498C2×C61#283811yescharacteristic
499C22×C4⋊C4—611no—
500C22×C4⋊C4—611no—
501C22×C4⋊C4—611no—
502C22×C4⋊C4—611no—
503C22×C4⋊C4C2×D6111yescharacteristic
504C22×C22⋊C4—611no—
505C22×C22⋊C4—611no—
506C22×C22⋊C4—611no—
507C22×C22⋊C4—611no—
508C22×C22⋊C4C2×D6111yescharacteristic
509C22×C22⋊C4C2×D6111yescharacteristic
510C22×C22⋊C4C2×D6111yescharacteristic
511C22×C42—611no—
512#397—618no—
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×#95—611no—
524C2×#95—611no—
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95—611no—
530C2×#95—611no—
531C2×#95—611no—
532C2×#95C2×D6111yescharacteristic
533C2×#95C2×D6111yescharacteristic
534C2×#95C2×D6111yescharacteristic
535C61#1464211yescharacteristic, complemented, Sylow
536C25C22×D6111yescharacteristic
537C23×C4—611no—
538C23×C4—611no—
539C23×C4—611no—
540C23×C4—611no—
541C23×C4—611no—
542C23×C4—611no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4C22×D6111yescharacteristic
546C23×C4C22×D6111yescharacteristic
547C23×C4C22×D6111yescharacteristic
548C23×C4C22×D6111yescharacteristic
549C23×C4C22×D6111yescharacteristic
550C23×C4C22×D6111yescharacteristic
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—2441no—
558C2×C4⋊C4—2441no—
559C2×C4⋊C4—2441no—
560C2×C4⋊C4—2441no—
561C2×C4⋊C4—2441no—
562C2×C4⋊C4—2441no—
563C2×C4⋊C4—2441no—
564C2×C4⋊C4—2441no—
565C2×C4⋊C4—2441no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—614no—
575C2×C22⋊C4—614no—
576C2×C22⋊C4—1222no—
577C2×C22⋊C4—2441no—
578C2×C22⋊C4—2441no—
579C2×C22⋊C4—2441no—
580C2×C22⋊C4—2441no—
581C2×C22⋊C4—2441no—
582C2×C22⋊C4—2441no—
583C2×C22⋊C4—2441no—
584C2×C22⋊C4—2441no—
585C2×C22⋊C4—2441no—
586C2×C22⋊C4C4×D6114yes—
587C2×C42—2441no—
588C2×C42—2441no—
589C2×C42—2441no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—614no—
594#95—614no—
595#95—614no—
596#95—1222no—
597#95—2441no—
598#95—2441no—
599#95—2441no—
600#95—2441no—
601#95—2441no—
602#95—2441no—
603#95—2441no—
604#95—2441no—
605#95—2441no—
606#95—2441no—
607#95—2441no—
608#95—2441no—
609#95—2441no—
610#95—2441no—
611#95—2441no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C2×C4×D6112yes—
627C24C23×D6111yescharacteristic
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—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
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—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4C2×C4×D6112yes—
724C22×C4C2×C4×D6112yes—
725C22×C4#1175822412yes—
726C4⋊C4—44no—
727C4⋊C4—2444no—
728C4⋊C4—2444no—
729C4⋊C4—2444no—
730C4⋊C4—2444no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—2444no—
735C22⋊C4—2444no—
736C22⋊C4—2444no—
737C22⋊C4—2444no—
738C42—2444no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
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—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C22×C4×D6111yescharacteristic
775C23#41×D6111yescharacteristic
776C23C2×#1175822411yescharacteristic
777C23#1451982211yescharacteristic
778C23#1451982211yescharacteristic
779C23#1451982211yescharacteristic
780C23#1451982211yescharacteristic
781C23#1451982211yescharacteristic
782C23#1451982211yescharacteristic
783C23#1451982311yescharacteristic
784C23#1451982311yescharacteristic
785C23#1451982411yescharacteristic
786C23#1451982411yescharacteristic
787C23#1451982411yescharacteristic
788C23#1451982511yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
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—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
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—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22C4×#1175822411yescharacteristic
903C22#1684023411yescharacteristic
904C22#1684023511yescharacteristic
905C22#1684024111yescharacteristic
906C22#1684024111yescharacteristic
907C22#1684024211yescharacteristic
908C22#1684024311yescharacteristic
909C22#1684034411yescharacteristic
910C22#1684034611yescharacteristic
911C22#1684034711yescharacteristic
912C22#1684034811yescharacteristic
913C22#1684035611yescharacteristic
914C22#1684035711yescharacteristic
915C22#1684036611yescharacteristic
916C22#1684036911yescharacteristic
917C22#1684037611yescharacteristic
918C22#1684037911yescharacteristic
919C22#1684038211yescharacteristic
920C22#1684038511yescharacteristic
921C22#1684050011yescharacteristic
922C22#1684050011yescharacteristic
923C22#1684050111yescharacteristic
924C22#1684050111yescharacteristic
925C22#1684050211yescharacteristic
926C22#1684050611yescharacteristic
927C22#1684050711yescharacteristic
928C22#1684050711yescharacteristic
929C22#1684050711yescharacteristic
930C22#1684050811yescharacteristic
931C22#1684050911yescharacteristic
932C22#1684051311yescharacteristic
933C22#1684051311yescharacteristic
934C22#1684051311yescharacteristic
935C22#1684051411yescharacteristic
936C22#1684051511yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4—4881no—
944C4—4881no—
945C4—4881no—
946C4—2442no—
947C4—2442no—
948C4—2442no—
949C4—2442no—
950C4—2442no—
951C2—82no—
952C2#2144860111yescharacteristic
953C2#2144860611yescharacteristic
954C2#2144863311yescharacteristic
955C2#2144896111yescharacteristic
956C2#2144896311yescharacteristic
957C2#2144897711yescharacteristic
958C2#2144900711yescharacteristic
959C2#2145390411yescharacteristic
960C2#2145392711yescharacteristic
961C2#2145395111yescharacteristic
962C2#2145396311yescharacteristic
963C2#2145396811yescharacteristic
964C2#2145397611yescharacteristic
965C2#2145403311yescharacteristic
966C2#2145405011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenter#1439D61
hypocenterC61#14642
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #21444083C2semidirect
3. #21444080C2semidirect
4. #21444079C2semidirect
5. #21444078C2semidirect
6. #21444070C2semidirect
7. #21444069C2semidirect
13. #21444053C2semidirect
14. #21444050C2semidirect
25. #16839690C4semidirect
535. C61#14642semidirect

Maximal subgroups

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

subgroupindex
C2×#168396902
#214440832
#214440802
#214440792
#214440782
#214440702
#214440692
#214440662
#214440642
#214440622
#214440562
#214440532
#214440502
C61×#14392
#1464261