Finite Group Databasebeta

← #29601419

Subgroups — #29601419

Order 15616.

2398 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519735C211yesmaximal, characteristic
2C2×#16839624C211yesmaximal, characteristic
3C2×C4×#11758198C211yesmaximal, characteristic
4C2×#16839609C211yesmaximal, characteristic
5C2×#95×D61C211yesmaximal, characteristic
6#21444053C211yesmaximal, characteristic, complemented
7#21444053C211yesmaximal, characteristic, complemented
8#21444051C211yesmaximal, characteristic, complemented
9#21444045C211yesmaximal, characteristic, complemented
10#21444043C211yesmaximal, characteristic, complemented
11#21444040C211yesmaximal, characteristic
12#21444040C211yesmaximal, characteristic
13C4×#14519684C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519735—24no—
20C2×#14519735—24no—
21C2×#14519735C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839624C418yescomplemented
33C4×#11758198—24no—
34#16839609—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
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50#95×D61C418yescomplemented
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61C2×C414yes—
83C22×C4×D61C2×C414yes—
84C22×C4×D61C2×C414yes—
85C22×C4×D61C2×C414yes—
86C22×C4×D61C2×C414yes—
87#14519735—232no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61C2×C414yescomplemented
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198C2×C414yes—
98C2×#11758198C2×C414yes—
99C2×#11758198C2×C414yes—
100C2×#11758198C2×C414yes—
101C2×#11758198D414yes—
102C2×#11758198D414yes—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—41no—
114C2×C4×Dic61—41no—
115C2×C4×Dic61—41no—
116C2×C4×Dic61C2×C414yescomplemented
117C2×C4×Dic61C2×C414yescomplemented
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684C2×C414yes—
128#14519684C2×C414yes—
129#14519684C2×C414yes—
130#14519684C2×C414yescomplemented
131#14519684C2×C414yescomplemented
132#14519684C2×C414yescomplemented
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61C2×C414yescomplemented
143C2×C42×C61—22no—
144C2×C42×C61—22no—
145C2×C42×C61—41no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—41no—
149#95×C61C2×C414yes—
150#95×C61C2×C414yescomplemented
151C24×C61C2411yescharacteristic
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×D61C22×C412yes—
161C23×D61C22×C412yes—
162C23×D61C22×C412yes—
163C23×D61C2×D412yes—
164C23×D61C2×D412yes—
165C23×D61#4112yes—
166C23×D61#4112yes—
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×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×C61C22×C412yes—
204C22×C4×C61C22×C412yes—
205C22×C4×C61C22×C412yes—
206C22×C4×C61C22×C412yes—
207C22×C4×C61C22×C412yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C22×C412yes—
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61#4112yes—
215C22×C4×C61#4112yes—
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×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×Dic61C22×C412yes—
253C22×Dic61C22×C412yes—
254C22×Dic61C22×C412yes—
255C22×Dic61C22×C412yes—
256C22×Dic61C22×C412yes—
257C22×Dic61C22×C412yes—
258C22×Dic61C22×C412yes—
259C22×Dic61C22×C412yes—
260C22×Dic61C22×C412yes—
261C22×Dic61C2×D412yes—
262C22×Dic61C2×D412yes—
263C22×Dic61#4112yes—
264C22×Dic61#4112yes—
265C2×C4×D61—28no—
266C2×C4×D61—28no—
267C2×C4×D61—28no—
268C2×C4×D61—28no—
269C2×C4×D61—28no—
270C2×C4×D61—28no—
271C2×C4×D61—28no—
272C2×C4×D61—28no—
273C2×C4×D61—28no—
274C2×C4×D61—28no—
275C2×C4×D61—44no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
278C2×C4×D61—44no—
279C2×C4×D61—44no—
280C2×C4×D61—44no—
281C2×C4×D61—44no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61C42116yescomplemented
286C4⋊C4×C61—28no—
287C42×C61—44no—
288#11758198—28no—
289#11758198—28no—
290#11758198—28no—
291#11758198C22⋊C4116yes—
292C4⋊Dic61—28no—
293C4×Dic61—28no—
294C4×Dic61—28no—
295C4×Dic61—44no—
296C4×Dic61—44no—
297C4×Dic61—44no—
298C23×C61C23×C411yescharacteristic
299C23×C61C23×C411yescharacteristic
300C23×C61C23×C411yescharacteristic
301C23×C61C22×D411yescharacteristic
302C23×C61C22×D411yescharacteristic
303C23×C61C2×#4111yescharacteristic
304C23×C61C2×#4111yescharacteristic
305C23×C61C2×#4111yescharacteristic
306C23×C61C2×#4111yescharacteristic
307C23×C61C2×#4111yescharacteristic
308C23×C61C2×#4111yescharacteristic
309C23×C61H(5,𝔽2)11yescharacteristic
310C23×C61H(5,𝔽2)11yescharacteristic
311C23×C612−1+411yescharacteristic
312C23×C612−1+411yescharacteristic
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—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61C2×C4214yes—
342C22×D61C2×C22⋊C414yes—
343C22×D61#11714yes—
344C22×D61C4×D414yes—
345C22×D61C4×D414yes—
346C22×D61C4×D414yes—
347C22×D61C4×D414yes—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61C2×C4214yes—
395C2×C4×C61C2×C22⋊C414yes—
396C2×C4×C61#11714yescomplemented
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61C2×C4214yes—
444C2×Dic61C2×C22⋊C414yes—
445C2×Dic61#11714yescomplemented
446C4×D61—232no—
447C4×D61—416no—
448C4×D61—416no—
449#13799—611nomaximal, Sylow
450C22×C61C22×C4211yescharacteristic
451C22×C61C22×C22⋊C411yescharacteristic
452C22×C61C2×#11711yescharacteristic
453C22×C61C2×#11711yescharacteristic
454C22×C61C2×#11711yescharacteristic
455C22×C61C2×C4×D411yescharacteristic
456C22×C61C2×C4×D411yescharacteristic
457C22×C61C2×C4×D411yescharacteristic
458C22×C61C2×C4×D411yescharacteristic
459C22×C61C4×#4111yescharacteristic
460C22×C61C4×#4111yescharacteristic
461C22×C61C4×#4111yescharacteristic
462C22×C61C4×#4111yescharacteristic
463C22×C61#51811yescharacteristic
464C22×C61#51911yescharacteristic
465C22×C61#52011yescharacteristic
466C22×C61#52011yescharacteristic
467C22×C61#52011yescharacteristic
468C22×C61#52011yescharacteristic
469C22×C61#54611yescharacteristic
470C22×C61#54611yescharacteristic
471C22×C61#54611yescharacteristic
472C22×C61#54611yescharacteristic
473C22×C61#54711yescharacteristic
474C22×C61#54711yescharacteristic
475C22×C61#54711yescharacteristic
476C22×C61#54711yescharacteristic
477C22×C61#55111yescharacteristic
478C22×C61#55111yescharacteristic
479C22×C61#55111yescharacteristic
480C22×C61#55111yescharacteristic
481C22×C61#55211yescharacteristic
482C22×C61#55211yescharacteristic
483C22×C61#55211yescharacteristic
484C22×C61#55211yescharacteristic
485C2×D61—24no—
486C2×D61—24no—
487C2×D61—24no—
488C2×D61—24no—
489C2×D61—24no—
490C2×D61—24no—
491C2×D61—24no—
492C2×D61—24no—
493C2×D61—24no—
494C2×D61—24no—
495C2×D61—24no—
496C2×D61—24no—
497C2×D61—24no—
498C2×D61—24no—
499C2×D61C4×C22⋊C418yes—
500C4×C61—24no—
501C4×C61—24no—
502C4×C61—24no—
503C4×C61—42no—
504C4×C61—42no—
505C4×C61—42no—
506C4×C61—42no—
507Dic61—24no—
508Dic61—24no—
509Dic61—24no—
510Dic61—42no—
511Dic61—42no—
512Dic61—42no—
513Dic61—42no—
514C22×#117—611no—
515C2×#381—611no—
516C2×C4×C22⋊C4—611no—
517C2×C4×C22⋊C4—611no—
518C22×#95—611no—
519#1436—611no—
520#1436—611no—
521#1436—611no—
522#1436D6111yescharacteristic, complemented
523#1434—611no—
524#1434—611no—
525C22⋊#95—611no—
526C22⋊#95—611no—
527C4×#95—611no—
528C4×#95—611no—
529C2×C61C2×C4×C22⋊C411yescharacteristic
530C2×C61C4×#11711yescharacteristic
531C2×C61#227411yescharacteristic
532C2×C61#233911yescharacteristic
533C2×C61#233911yescharacteristic
534C2×C61#234211yescharacteristic
535C2×C61#234211yescharacteristic
536C2×C61#234311yescharacteristic
537C2×C61#234311yescharacteristic
538C2×C61#234411yescharacteristic
539C2×C61#234411yescharacteristic
540C2×C61#235911yescharacteristic
541C2×C61#235911yescharacteristic
542C2×C61#235911yescharacteristic
543C2×C61#235911yescharacteristic
544D61—28no—
545C24×C4—611no—
546C24×C4—611no—
547C24×C4—611no—
548C2×#117—618no—
549C2×#117—1224no—
550C2×#117—1224no—
551C22×C4⋊C4—611no—
552C22×C4⋊C4C2×D6111yescharacteristic
553C22×C22⋊C4—611no—
554C22×C22⋊C4—611no—
555C22×C22⋊C4—611no—
556C22×C22⋊C4—611no—
557C22×C42—611no—
558C22×C42—611no—
559C22×C42—611no—
560C22×C42—611no—
561C22×C42—611no—
562C22×C42C2×D6111yescharacteristic
563#381—618no—
564C4×C22⋊C4—1224no—
565C4×C22⋊C4—1224no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C2×#95—611no—
572C2×#95—618no—
573C2×#95—611no—
574C2×#95—611no—
575C2×#95—611no—
576C2×#95—611no—
577C2×#95—611no—
578C2×#95—611no—
579C2×#95—611no—
580C2×#95—611no—
581C2×#95—611no—
582C2×#95C2×D6111yescharacteristic
583C2×#95C2×D6111yescharacteristic
584C2×#95C2×D6111yescharacteristic
585C2×#95C2×D6111yescharacteristic
586C2×#95C2×D6111yescharacteristic
587C61#1379911yescharacteristic, complemented, Sylow
588C25—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—614no—
593C23×C4—614no—
594C23×C4—614no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—614no—
600C23×C4—614no—
601C23×C4—1222no—
602C23×C4—1222no—
603C23×C4—1222no—
604C23×C4—1222no—
605C23×C4—1222no—
606C23×C4—1222no—
607C23×C4—1222no—
608C23×C4—1222no—
609C23×C4—1222no—
610C23×C4—1222no—
611C23×C4—1222no—
612C23×C4—1222no—
613C23×C4—2441no—
614C23×C4—2441no—
615C23×C4—2441no—
616C23×C4—2441no—
617C23×C4C22×D6111yescharacteristic
618C23×C4C22×D6111yescharacteristic
619C23×C4C22×D6111yescharacteristic
620C23×C4C22×D6111yescharacteristic
621C23×C4C22×D6111yescharacteristic
622C23×C4C22×D6111yescharacteristic
623C23×C4C22×D6111yescharacteristic
624#117—12232no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—614no—
628C2×C4⋊C4—1222no—
629C2×C4⋊C4—1222no—
630C2×C4⋊C4C4×D6114yescomplemented
631C2×C22⋊C4—614no—
632C2×C22⋊C4—614no—
633C2×C22⋊C4—614no—
634C2×C22⋊C4—614no—
635C2×C22⋊C4—614no—
636C2×C22⋊C4—614no—
637C2×C22⋊C4—1222no—
638C2×C22⋊C4—1222no—
639C2×C22⋊C4—1222no—
640C2×C22⋊C4—1222no—
641C2×C22⋊C4—1222no—
642C2×C22⋊C4—1222no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—41no—
646C2×C42—614no—
647C2×C42—614no—
648C2×C42—1222no—
649C2×C42—1222no—
650C2×C42—1222no—
651C2×C42—1222no—
652C2×C42—1222no—
653C2×C42—1222no—
654C2×C42—1222no—
655C2×C42—1222no—
656C2×C42—1222no—
657C2×C42—1222no—
658C2×C42—2441no—
659C2×C42—2441no—
660C2×C42—2441no—
661#95—22no—
662#95—22no—
663#95—41no—
664#95—614no—
665#95—614no—
666#95—614no—
667#95—614no—
668#95—614no—
669#95—614no—
670#95—1222no—
671#95—1222no—
672#95—1222no—
673#95—1222no—
674#95—1222no—
675#95—1222no—
676#95—2441no—
677#95—2441no—
678#95—2441no—
679#95C4×D6114yes—
680#95C4×D6114yescomplemented
681C24—612no—
682C24—612no—
683C24—612no—
684C24—612no—
685C24—612no—
686C24—612no—
687C24—612no—
688C24—1221no—
689C24—1221no—
690C24—1221no—
691C24—1221no—
692C24—1221no—
693C24—1221no—
694C24—1221no—
695C24—1221no—
696C24C23×D6111yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—612no—
734C22×C4—612no—
735C22×C4—612no—
736C22×C4—612no—
737C22×C4—612no—
738C22×C4—612no—
739C22×C4—612no—
740C22×C4—612no—
741C22×C4—612no—
742C22×C4—6116no—
743C22×C4—612no—
744C22×C4—612no—
745C22×C4—612no—
746C22×C4—612no—
747C22×C4—1228no—
748C22×C4—1228no—
749C22×C4—1228no—
750C22×C4—1228no—
751C22×C4—1228no—
752C22×C4—1228no—
753C22×C4—1228no—
754C22×C4—1228no—
755C22×C4—1228no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1228no—
793C22×C4—2444no—
794C22×C4—2444no—
795C22×C4—2444no—
796C22×C4—2444no—
797C22×C4—2444no—
798C22×C4—2444no—
799C22×C4—2444no—
800C22×C4—2444no—
801C22×C4—2444no—
802C22×C4—2444no—
803C22×C4C2×C4×D6112yes—
804C22×C4C2×C4×D6112yes—
805C22×C4C2×C4×D6112yes—
806C22×C4C2×C4×D6112yes—
807C22×C4C2×C4×D6112yes—
808C22×C4C2×C4×D6112yes—
809C22×C4C2×C4×D6112yes—
810C22×C4C2×C4×D6112yes—
811C22×C4C2×C4×D6112yes—
812C22×C4D4×D6112yes—
813C22×C4D4×D6112yes—
814C22×C4#1175822412yes—
815C22×C4#1175822612yes—
816C4⋊C4—28no—
817C4⋊C4—1228no—
818C22⋊C4—6116no—
819C22⋊C4—1228no—
820C22⋊C4—1228no—
821C22⋊C4—1228no—
822C42—44no—
823C42—1228no—
824C42—1228no—
825C42—2444no—
826C42—2444no—
827C42—2444no—
828C23—614no—
829C23—614no—
830C23—614no—
831C23—614no—
832C23—614no—
833C23—614no—
834C23—614no—
835C23—1222no—
836C23—1222no—
837C23—1222no—
838C23—1222no—
839C23—1222no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1222no—
847C23—1222no—
848C23—1222no—
849C23—1222no—
850C23—1222no—
851C23—1222no—
852C23—1222no—
853C23—1222no—
854C23—1222no—
855C23—1222no—
856C23—1222no—
857C23—1222no—
858C23—1222no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23C22×C4×D6111yescharacteristic
864C23C22×C4×D6111yescharacteristic
865C23C22×C4×D6111yescharacteristic
866C23C2×D4×D6111yescharacteristic
867C23C2×D4×D6111yescharacteristic
868C23#41×D6111yescharacteristic
869C23#41×D6111yescharacteristic
870C23#41×D6111yescharacteristic
871C23#41×D6111yescharacteristic
872C23C2×#1175822411yescharacteristic
873C23C2×#1175822611yescharacteristic
874C23#1451982211yescharacteristic
875C23#1451982311yescharacteristic
876C23#1451982411yescharacteristic
877C23#1451982511yescharacteristic
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—614no—
925C2×C4—614no—
926C2×C4—614no—
927C2×C4—12232no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—24416no—
959C2×C4—24416no—
960C2×C4—2441no—
961C2×C4—2441no—
962C2×C4—2441no—
963C2×C4—2441no—
964C2×C4—2441no—
965C2×C4—2441no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2441no—
969C2×C4—2441no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4C42×D6114yes—
977C2×C4C22⋊C4×D6114yes—
978C2×C4#1451973514yescomplemented
979C22—618no—
980C22—1224no—
981C22—1224no—
982C22—1224no—
983C22—1224no—
984C22—1224no—
985C22—1224no—
986C22—1224no—
987C22—1224no—
988C22—1224no—
989C22—1224no—
990C22—1224no—
991C22—1224no—
992C22—1224no—
993C22—1224no—
994C22C2×C42×D6111yescharacteristic
995C22C2×C22⋊C4×D6111yescharacteristic
996C22#117×D6111yescharacteristic
997C22#117×D6111yescharacteristic
998C22C2×#1451973511yescharacteristic
999C22C4×D4×D6111yescharacteristic
1000C22C4×D4×D6111yescharacteristic
1001C22C4×D4×D6111yescharacteristic
1002C22C4×D4×D6111yescharacteristic
1003C22C4×#1175822411yescharacteristic
1004C22C4×#1175822411yescharacteristic
1005C22C4×#1175822611yescharacteristic
1006C22C4×#1175822611yescharacteristic
1007C22#1684023411yescharacteristic
1008C22#1684023811yescharacteristic
1009C22#1684024111yescharacteristic
1010C22#1684024211yescharacteristic
1011C22#1684024311yescharacteristic
1012C22#1684024411yescharacteristic
1013C22#1684039911yescharacteristic
1014C22#1684040111yescharacteristic
1015C22#1684040311yescharacteristic
1016C22#1684040511yescharacteristic
1017C22#1684041011yescharacteristic
1018C22#1684041211yescharacteristic
1019C22#1684041411yescharacteristic
1020C22#1684041511yescharacteristic
1021C22#1684043511yescharacteristic
1022C22#1684043711yescharacteristic
1023C22#1684043911yescharacteristic
1024C22#1684044011yescharacteristic
1025C22#1684044411yescharacteristic
1026C22#1684044611yescharacteristic
1027C22#1684044811yescharacteristic
1028C22#1684045011yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—24no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—1224no—
1037C4—1224no—
1038C4—1224no—
1039C4—2442no—
1040C4—2442no—
1041C4—2442no—
1042C4—2442no—
1043C2—1228no—
1044C2C4×C22⋊C4×D6111yescharacteristic
1045C2C4×#1451973511yescharacteristic
1046C2#2144817311yescharacteristic
1047C2#2144864511yescharacteristic
1048C2#2144864811yescharacteristic
1049C2#2144866611yescharacteristic
1050C2#2144866711yescharacteristic
1051C2#2144867411yescharacteristic
1052C2#2144867811yescharacteristic
1053C2#2144868511yescharacteristic
1054C2#2144868711yescharacteristic
1055C2#2144880611yescharacteristic
1056C2#2144881011yescharacteristic
1057C2#2144881411yescharacteristic
1058C2#2144881811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1436D61
hypocenterC61#13799
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #21444053C2semidirect
7. #21444053C2semidirect
8. #21444051C2semidirect
9. #21444045C2semidirect
10. #21444043C2semidirect
13. C4×#14519684C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1436C2semidirect
21. C2×#14519735C4semidirect
32. #16839624C4semidirect
50. #95×D61C4semidirect
90. C2×C4⋊Dic61C2×C4semidirect
116. C2×C4×Dic61C2×C4semidirect
117. C2×C4×Dic61C2×C4semidirect
130. #14519684C2×C4semidirect
131. #14519684C2×C4semidirect
132. #14519684C2×C4semidirect
142. C2×C4⋊C4×C61C2×C4semidirect
150. #95×C61C2×C4semidirect
285. C2×C4×D61C42semidirect
396. C2×C4×C61#117semidirect
445. C2×Dic61#117semidirect
522. #1436D61semidirect
587. C61#13799semidirect
630. C2×C4⋊C4C4×D61semidirect
680. #95C4×D61semidirect
978. C2×C4#14519735semidirect

Maximal subgroups

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

subgroupindex
C22×#145197352
C2×#168396242
C2×C4×#117581982
C2×#168396092
C2×#95×D612
#214440532
#214440512
#214440452
#214440432
#214440402
C4×#145196842
#95×Dic612
C61×#14362
#1379961