Finite Group Databasebeta

← #27305584

Subgroups — #27305584

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133179C211yesmaximal, characteristic
2C2×#16810501C211yesmaximal, characteristic
3C2×#16810501C211yesmaximal, characteristic
4C2×C4×#11719921C211yesmaximal, characteristic, complemented
5C2×C4×#11719921C211yesmaximal, characteristic, complemented
6C2×#16810470C211yesmaximal, characteristic, complemented
7C2×#95×D53C211yesmaximal, characteristic, complemented
8#20272951C211yesmaximal, characteristic, complemented
9#20272951C211yesmaximal, characteristic, complemented
10#20272947C211yesmaximal, characteristic, complemented
11#20272940C211yesmaximal, characteristic, complemented
12#20272936C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C53×#1436C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C2×#13133179—24no—
22C2×#13133179—24no—
23C2×#13133179C418yescomplemented
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36#16810501C418yescomplemented
37#16810501C418yescomplemented
38C4×#11719921—24no—
39C4×#11719921—24no—
40#16810470—24no—
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52#95×D53—24no—
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C24×D53C2311yescharacteristic
62C22×D212—22no—
63C22×D212—22no—
64C22×D212—22no—
65C22×D212—22no—
66C22×D212C2×C414yes—
67C22×D212C2×C414yes—
68C22×D212C2×C414yes—
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C22×C4×D53—22no—
76C22×C4×D53—22no—
77C22×C4×D53—22no—
78C22×C4×D53—22no—
79C22×C4×D53—22no—
80C22×C4×D53—22no—
81C22×C4×D53—22no—
82C22×C4×D53—22no—
83C22×C4×D53—22no—
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—22no—
87C22×C4×D53—22no—
88C22×C4×D53—22no—
89C22×C4×D53—22no—
90C22×C4×D53—22no—
91C22×C4×D53—41no—
92C22×C4×D53—41no—
93C22×C4×D53—41no—
94C22×C4×D53—41no—
95C22×C4×D53—41no—
96C22×C4×D53—41no—
97C22×C4×D53—41no—
98C22×C4×D53—41no—
99C22×C4×D53C2×C414yes—
100C22×C4×D53C2×C414yescomplemented
101C22×C4×D53C2×C414yescomplemented
102C22×C4×D53C2×C414yescomplemented
103#13133179—232no—
104C2×#11719921—22no—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921—22no—
112C2×#11719921—22no—
113C2×#11719921—22no—
114C2×#11719921—41no—
115C2×#11719921—41no—
116C2×#11719921—41no—
117C2×#11719921—41no—
118C2×#11719921C2×C414yes—
119C2×#11719921C2×C414yescomplemented
120C2×#11719921C2×C414yescomplemented
121C2×#11719921C2×C414yescomplemented
122C2×#11719921C2×C414yescomplemented
123C2×#11719921C2×C414yescomplemented
124C2×#11719921C2×C414yescomplemented
125C2×#11719921C2×C414yescomplemented
126C2×#11719921D414yes—
127C2×#11719921D414yes—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53—22no—
131C2×C4×Dic53—22no—
132C2×C4×Dic53—22no—
133C2×C4×Dic53—22no—
134C2×C4×Dic53—22no—
135C2×C4×Dic53—22no—
136C2×C4×Dic53—41no—
137C2×C4×Dic53—41no—
138C2×C4×Dic53—41no—
139C2×C4×Dic53C2×C414yescomplemented
140#13133124—22no—
141#13133124—22no—
142#13133124—22no—
143#13133124—22no—
144#13133124—22no—
145#13133124—22no—
146#13133124—22no—
147#13133124—41no—
148#13133124C2×C414yescomplemented
149#13133124C2×C414yescomplemented
150#13133124D414yescomplemented
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C23×C4×C53C2311yescharacteristic
155C23×C4×C53C2311yescharacteristic
156C23×C4×C53C2311yescharacteristic
157C23×C4×C53C2311yescharacteristic
158C2×C4⋊C4×C53—22no—
159C2×C4⋊C4×C53—22no—
160C2×C4⋊C4×C53C2×C414yescomplemented
161C2×C42×C53—22no—
162C2×C42×C53—22no—
163C2×C42×C53—41no—
164#95×C53—22no—
165#95×C53—22no—
166#95×C53—41no—
167#95×C53C2×C414yescomplemented
168#95×C53C2×C414yescomplemented
169C24×C53C2411yescharacteristic
170C23×D53—21no—
171C23×D53—21no—
172C23×D53—21no—
173C23×D53—21no—
174C23×D53—21no—
175C23×D53—21no—
176C23×D53—21no—
177C23×D53—21no—
178C23×D53—21no—
179C23×D53—21no—
180C23×D53—21no—
181C23×D53—21no—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C23×D53C22×C412yes—
191C23×D53C22×C412yes—
192C23×D53C22×C412yes—
193C23×D53C22×C412yes—
194C23×D53C22×C412yes—
195C23×D53C22×C412yes—
196C23×D53C2×D412yes—
197C23×D53C2×D412yes—
198C23×D53#4112yes—
199C23×D53#4112yes—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53C22×C412yes—
237C22×C4×C53C22×C412yes—
238C22×C4×C53C22×C412yes—
239C22×C4×C53C22×C412yes—
240C22×C4×C53C22×C412yes—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C22×C412yes—
243C22×C4×C53C22×C412yes—
244C22×C4×C53C22×C412yes—
245C22×C4×C53C2×D412yes—
246C22×C4×C53C2×D412yes—
247C22×C4×C53C2×D412yes—
248C22×C4×C53#4112yes—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53C22×C412yes—
280C22×Dic53C22×C412yes—
281C22×Dic53C22×C412yes—
282C22×Dic53C22×C412yes—
283C22×Dic53C22×C412yes—
284C22×Dic53C22×C412yes—
285C22×Dic53C2×D412yes—
286C22×Dic53C2×D412yes—
287C22×Dic53C2×D412yes—
288C22×Dic53C2×D412yes—
289C22×Dic53#4112yes—
290C22×Dic53#4112yes—
291C2×D212—28no—
292C2×D212—28no—
293C2×D212—28no—
294C2×D212—28no—
295C2×D212—28no—
296C2×D212—28no—
297C2×D212C42116yescomplemented
298C2×C4×D53—28no—
299C2×C4×D53—28no—
300C2×C4×D53—28no—
301C2×C4×D53—28no—
302C2×C4×D53—28no—
303C2×C4×D53—28no—
304C2×C4×D53—28no—
305C2×C4×D53—28no—
306C2×C4×D53—44no—
307C2×C4×D53—44no—
308C2×C4×D53—44no—
309C2×C4×D53—44no—
310C2×C4×D53—44no—
311C2×C4×D53—44no—
312C2×C4×D53—44no—
313C2×C4×D53—44no—
314C2×C4×D53—44no—
315C2×C4×D53—44no—
316C2×C4×D53—44no—
317C2×C4×D53—44no—
318C2×C4×D53—44no—
319C2×C4×D53—44no—
320C2×C4×D53—44no—
321C2×C4×D53—44no—
322C2×C4×D53—44no—
323C2×C4×D53—44no—
324C2×C4×D53—44no—
325C2×C4×D53—44no—
326C4⋊C4×C53—28no—
327C42×C53—44no—
328#11719921—28no—
329#11719921—28no—
330#11719921—28no—
331#11719921—28no—
332#11719921—28no—
333#11719921—44no—
334#11719921—44no—
335#11719921C22⋊C4116yescomplemented
336C4×Dic53—28no—
337C4×Dic53—44no—
338C4×Dic53—44no—
339C4×Dic53—44no—
340C23×C53C23×C411yescharacteristic
341C23×C53C23×C411yescharacteristic
342C23×C53C23×C411yescharacteristic
343C23×C53C22×D411yescharacteristic
344C23×C53C22×D411yescharacteristic
345C23×C53C22×D411yescharacteristic
346C23×C53C2×#4111yescharacteristic
347C23×C53C2×#4111yescharacteristic
348C23×C53C2×#4111yescharacteristic
349C23×C53C2×#4111yescharacteristic
350C23×C53C2×#4111yescharacteristic
351C23×C53H(5,𝔽2)11yescharacteristic
352C23×C53H(5,𝔽2)11yescharacteristic
353C23×C53H(5,𝔽2)11yescharacteristic
354C23×C532−1+411yescharacteristic
355C22×D53—22no—
356C22×D53—22no—
357C22×D53—22no—
358C22×D53—22no—
359C22×D53—22no—
360C22×D53—22no—
361C22×D53—22no—
362C22×D53—22no—
363C22×D53—22no—
364C22×D53—22no—
365C22×D53—22no—
366C22×D53—22no—
367C22×D53—22no—
368C22×D53—22no—
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—22no—
373C22×D53—22no—
374C22×D53—22no—
375C22×D53—22no—
376C22×D53—22no—
377C22×D53—22no—
378C22×D53—22no—
379C22×D53—22no—
380C22×D53—22no—
381C22×D53—22no—
382C22×D53—22no—
383C22×D53—22no—
384C22×D53—22no—
385C22×D53—22no—
386C22×D53—22no—
387C22×D53—22no—
388C22×D53—22no—
389C22×D53—22no—
390C22×D53—22no—
391C22×D53—22no—
392C22×D53—22no—
393C22×D53—22no—
394C22×D53—22no—
395C22×D53—22no—
396C22×D53—22no—
397C22×D53—22no—
398C22×D53—22no—
399C22×D53—22no—
400C22×D53—22no—
401C22×D53—41no—
402C22×D53—41no—
403C22×D53—41no—
404C22×D53—41no—
405C22×D53—41no—
406C22×D53—41no—
407C22×D53—41no—
408C22×D53—41no—
409C22×D53—41no—
410C22×D53—41no—
411C22×D53—41no—
412C22×D53—41no—
413C22×D53—41no—
414C22×D53—41no—
415C22×D53—41no—
416C22×D53—41no—
417C22×D53C2×C4214yes—
418C22×D53C2×C4214yes—
419C22×D53C2×C22⋊C414yes—
420C22×D53#11714yes—
421C22×D53C4×D414yes—
422C22×D53C4×D414yes—
423C22×D53C4×D414yes—
424C22×D53C4×D414yes—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—22no—
435C2×C4×C53—22no—
436C2×C4×C53—22no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53—22no—
447C2×C4×C53—22no—
448C2×C4×C53—22no—
449C2×C4×C53—22no—
450C2×C4×C53—22no—
451C2×C4×C53—22no—
452C2×C4×C53—22no—
453C2×C4×C53—22no—
454C2×C4×C53—22no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53—41no—
461C2×C4×C53—41no—
462C2×C4×C53—41no—
463C2×C4×C53—41no—
464C2×C4×C53—41no—
465C2×C4×C53—41no—
466C2×C4×C53—41no—
467C2×C4×C53—41no—
468C2×C4×C53—41no—
469C2×C4×C53—41no—
470C2×C4×C53—41no—
471C2×C4×C53C2×C4214yes—
472C2×C4×C53C2×C22⋊C414yes—
473C2×C4×C53C4×D414yescomplemented
474C2×Dic53—22no—
475C2×Dic53—22no—
476C2×Dic53—22no—
477C2×Dic53—22no—
478C2×Dic53—22no—
479C2×Dic53—22no—
480C2×Dic53—22no—
481C2×Dic53—22no—
482C2×Dic53—22no—
483C2×Dic53—22no—
484C2×Dic53—22no—
485C2×Dic53—22no—
486C2×Dic53—22no—
487C2×Dic53—22no—
488C2×Dic53—22no—
489C2×Dic53—22no—
490C2×Dic53—22no—
491C2×Dic53—22no—
492C2×Dic53—22no—
493C2×Dic53—22no—
494C2×Dic53—22no—
495C2×Dic53—22no—
496C2×Dic53—22no—
497C2×Dic53—22no—
498C2×Dic53—22no—
499C2×Dic53—22no—
500C2×Dic53—22no—
501C2×Dic53—41no—
502C2×Dic53—41no—
503C2×Dic53—41no—
504C2×Dic53—41no—
505C2×Dic53—41no—
506C2×Dic53—41no—
507C2×Dic53—41no—
508C2×Dic53—41no—
509C2×Dic53—41no—
510C2×Dic53—41no—
511C2×Dic53—41no—
512C2×Dic53—41no—
513C2×Dic53C2×C22⋊C414yes—
514C2×Dic53C4×D414yes—
515C2×Dic53C4×D414yescomplemented
516D212—232no—
517C4×D53—416no—
518C4×D53—416no—
519C4×D53—416no—
520C4×D53—416no—
521#13813—531nomaximal, Sylow
522C22×C53C22×C4211yescharacteristic
523C22×C53C22×C22⋊C411yescharacteristic
524C22×C53C2×#11711yescharacteristic
525C22×C53C2×C4×D411yescharacteristic
526C22×C53C2×C4×D411yescharacteristic
527C22×C53C2×C4×D411yescharacteristic
528C22×C53C2×C4×D411yescharacteristic
529C22×C53C2×C4×D411yescharacteristic
530C22×C53C2×C4×D411yescharacteristic
531C22×C53C2×C4×D411yescharacteristic
532C22×C53C4×#4111yescharacteristic
533C22×C53C4×#4111yescharacteristic
534C22×C53C4×#4111yescharacteristic
535C22×C53#51811yescharacteristic
536C22×C53#51811yescharacteristic
537C22×C53#51811yescharacteristic
538C22×C53#52011yescharacteristic
539C22×C53#52011yescharacteristic
540C22×C53#52011yescharacteristic
541C22×C53D4211yescharacteristic
542C22×C53D4211yescharacteristic
543C22×C53#54611yescharacteristic
544C22×C53#54611yescharacteristic
545C22×C53#54611yescharacteristic
546C22×C53#54611yescharacteristic
547C22×C53#54611yescharacteristic
548C22×C53#54711yescharacteristic
549C22×C53#54711yescharacteristic
550C22×C53#54811yescharacteristic
551C22×C53#55111yescharacteristic
552C22×C53#55111yescharacteristic
553C22×C53#55211yescharacteristic
554C22×C53#55311yescharacteristic
555C22×C53#55311yescharacteristic
556C22×C53#55311yescharacteristic
557C2×D53—24no—
558C2×D53—24no—
559C2×D53—24no—
560C2×D53—24no—
561C2×D53—24no—
562C2×D53—24no—
563C2×D53—24no—
564C2×D53—24no—
565C2×D53—24no—
566C2×D53—24no—
567C2×D53—24no—
568C2×D53—24no—
569C2×D53—24no—
570C2×D53—24no—
571C2×D53—24no—
572C2×D53—24no—
573C2×D53—24no—
574C2×D53—42no—
575C2×D53—42no—
576C2×D53—42no—
577C2×D53—42no—
578C2×D53—42no—
579C2×D53—42no—
580C2×D53—42no—
581C2×D53—42no—
582C2×D53—42no—
583C2×D53—42no—
584C2×D53—42no—
585C2×D53—42no—
586C2×D53C4×C22⋊C418yescomplemented
587C4×C53—24no—
588C4×C53—24no—
589C4×C53—24no—
590C4×C53—42no—
591C4×C53—42no—
592C4×C53—42no—
593C4×C53—42no—
594Dic53—24no—
595Dic53—24no—
596Dic53—24no—
597Dic53—42no—
598Dic53—42no—
599Dic53—42no—
600C22×C4×D4—531no—
601C2×#386—531no—
602C2×#386—531no—
603C2×C4×C22⋊C4—531no—
604C2×C4×C22⋊C4—531no—
605C2×C4×C22⋊C4—531no—
606C22×#95—531no—
607#1437—531no—
608#1437—531no—
609#1436—531no—
610#1436D5311yescharacteristic, complemented
611#1434—531no—
612C22⋊#95—531no—
613C22⋊#95—531no—
614C4×#95—531no—
615C2×C53C2×C4×C22⋊C411yescharacteristic
616C2×C53C42×D411yescharacteristic
617C2×C53#227511yescharacteristic
618C2×C53D4×C22⋊C411yescharacteristic
619C2×C53#233911yescharacteristic
620C2×C53#235211yescharacteristic
621C2×C53#235311yescharacteristic
622C2×C53#235811yescharacteristic
623C2×C53#235811yescharacteristic
624C2×C53#235911yescharacteristic
625C2×C53#235911yescharacteristic
626C2×C53#236111yescharacteristic
627C2×C53#236111yescharacteristic
628C2×C53#236411yescharacteristic
629C2×C53#236411yescharacteristic
630D53—28no—
631D53—44no—
632C23×D4—531no—
633C24×C4—531no—
634C24×C4—531no—
635C24×C4—531no—
636C24×C4—531no—
637C2×C4×D4—538no—
638C2×C4×D4—1064no—
639C2×C4×D4—1064no—
640C22×C4⋊C4C2×D5311yescharacteristic
641C22×C22⋊C4—531no—
642C22×C22⋊C4—531no—
643C22×C22⋊C4—531no—
644C22×C22⋊C4—531no—
645C22×C22⋊C4—531no—
646C22×C22⋊C4—531no—
647C22×C22⋊C4—531no—
648C22×C22⋊C4—531no—
649C22×C42—531no—
650C22×C42—531no—
651C22×C42—531no—
652C22×C42—531no—
653C22×C42C2×D5311yescharacteristic
654#386—538no—
655#386—538no—
656C4×C22⋊C4—1064no—
657C4×C22⋊C4—1064no—
658C4×C22⋊C4—1064no—
659C2×#95—531no—
660C2×#95—531no—
661C2×#95—531no—
662C2×#95—531no—
663C2×#95—531no—
664C2×#95—531no—
665C2×#95—531no—
666C2×#95—531no—
667C2×#95—531no—
668C2×#95—531no—
669C2×#95—531no—
670C2×#95—1064no—
671C2×#95C2×D5311yescharacteristic
672C2×#95C2×D5311yescharacteristic
673C2×#95C2×D5311yescharacteristic
674C2×#95C2×D5311yescharacteristic
675C2×#95C2×D5311yescharacteristic
676C53#1381311yescharacteristic, complemented, Sylow
677C25—531no—
678C25—531no—
679C22×D4—534no—
680C22×D4—534no—
681C22×D4—534no—
682C22×D4—1062no—
683C22×D4—1062no—
684C22×D4—1062no—
685C22×D4—1062no—
686C23×C4—531no—
687C23×C4—531no—
688C23×C4—531no—
689C23×C4—531no—
690C23×C4—531no—
691C23×C4—531no—
692C23×C4—534no—
693C23×C4—534no—
694C23×C4—534no—
695C23×C4—534no—
696C23×C4—1062no—
697C23×C4—1062no—
698C23×C4—1062no—
699C23×C4—1062no—
700C23×C4—1062no—
701C23×C4—1062no—
702C23×C4—1062no—
703C23×C4—1062no—
704C23×C4—1062no—
705C23×C4—1062no—
706C23×C4—1062no—
707C23×C4—1062no—
708C23×C4—1062no—
709C23×C4—1062no—
710C23×C4—1062no—
711C23×C4—1062no—
712C23×C4—2121no—
713C23×C4—2121no—
714C23×C4—2121no—
715C23×C4—2121no—
716C23×C4—2121no—
717C23×C4—2121no—
718C23×C4—2121no—
719C23×C4—2121no—
720C23×C4C22×D5311yescharacteristic
721C23×C4C22×D5311yescharacteristic
722C23×C4C22×D5311yescharacteristic
723C23×C4C22×D5311yescharacteristic
724C23×C4C22×D5311yescharacteristic
725C23×C4C22×D5311yescharacteristic
726C23×C4C22×D5311yescharacteristic
727C4×D4—10632no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4C4×D5314yescomplemented
731C2×C22⋊C4—534no—
732C2×C22⋊C4—534no—
733C2×C22⋊C4—534no—
734C2×C22⋊C4—534no—
735C2×C22⋊C4—534no—
736C2×C22⋊C4—534no—
737C2×C22⋊C4—534no—
738C2×C22⋊C4—534no—
739C2×C22⋊C4—534no—
740C2×C22⋊C4—534no—
741C2×C22⋊C4—1062no—
742C2×C22⋊C4—1062no—
743C2×C22⋊C4—1062no—
744C2×C22⋊C4—1062no—
745C2×C22⋊C4—1062no—
746C2×C22⋊C4—1062no—
747C2×C22⋊C4—1062no—
748C2×C22⋊C4—1062no—
749C2×C22⋊C4—1062no—
750C2×C22⋊C4—1062no—
751C2×C22⋊C4—2121no—
752C2×C22⋊C4—2121no—
753C2×C22⋊C4—2121no—
754C2×C22⋊C4—2121no—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—41no—
758C2×C42—534no—
759C2×C42—1062no—
760C2×C42—1062no—
761C2×C42—1062no—
762C2×C42—1062no—
763C2×C42—1062no—
764C2×C42—1062no—
765C2×C42—1062no—
766C2×C42—1062no—
767C2×C42—2121no—
768C2×C42—2121no—
769C2×C42—2121no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—534no—
774#95—534no—
775#95—534no—
776#95—1062no—
777#95—1062no—
778#95—1062no—
779#95—1062no—
780#95—1062no—
781#95—1062no—
782#95—1062no—
783#95—2121no—
784#95C4×D5314yescomplemented
785#95C4×D5314yescomplemented
786C24—532no—
787C24—532no—
788C24—532no—
789C24—532no—
790C24—532no—
791C24—532no—
792C24—532no—
793C24—532no—
794C24—532no—
795C24—532no—
796C24—1061no—
797C24—1061no—
798C24—1061no—
799C24—1061no—
800C24—1061no—
801C24—1061no—
802C24—1061no—
803C24—1061no—
804C24—1061no—
805C24—1061no—
806C24—1061no—
807C24—1061no—
808C24—1061no—
809C24—1061no—
810C24—1061no—
811C24—1061no—
812C24—1061no—
813C24—1061no—
814C24—1061no—
815C24—1061no—
816C24C23×D5311yescharacteristic
817C2×D4—5316no—
818C2×D4—1068no—
819C2×D4—1068no—
820C2×D4—1068no—
821C2×D4—1068no—
822C2×D4—1068no—
823C2×D4—1068no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—532no—
861C22×C4—532no—
862C22×C4—532no—
863C22×C4—532no—
864C22×C4—532no—
865C22×C4—532no—
866C22×C4—532no—
867C22×C4—532no—
868C22×C4—532no—
869C22×C4—532no—
870C22×C4—532no—
871C22×C4—532no—
872C22×C4—1068no—
873C22×C4—1068no—
874C22×C4—1068no—
875C22×C4—1068no—
876C22×C4—1068no—
877C22×C4—1068no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4—1061no—
888C22×C4—1061no—
889C22×C4—1061no—
890C22×C4—1061no—
891C22×C4—1061no—
892C22×C4—1061no—
893C22×C4—1061no—
894C22×C4—1061no—
895C22×C4—1061no—
896C22×C4—1061no—
897C22×C4—1061no—
898C22×C4—1061no—
899C22×C4—1061no—
900C22×C4—1061no—
901C22×C4—1061no—
902C22×C4—1061no—
903C22×C4—1061no—
904C22×C4—1061no—
905C22×C4—1061no—
906C22×C4—1061no—
907C22×C4—1061no—
908C22×C4—1068no—
909C22×C4—1068no—
910C22×C4—2124no—
911C22×C4—2124no—
912C22×C4—2124no—
913C22×C4—2124no—
914C22×C4—2124no—
915C22×C4—2124no—
916C22×C4—2124no—
917C22×C4—2124no—
918C22×C4—2124no—
919C22×C4—2124no—
920C22×C4—2124no—
921C22×C4—2124no—
922C22×C4—2124no—
923C22×C4—2124no—
924C22×C4—2124no—
925C22×C4—2124no—
926C22×C4—2124no—
927C22×C4—2124no—
928C22×C4—2124no—
929C22×C4—2124no—
930C22×C4C2×C4×D5312yes—
931C22×C4C2×C4×D5312yes—
932C22×C4C2×C4×D5312yes—
933C22×C4C2×C4×D5312yes—
934C22×C4C2×C4×D5312yes—
935C22×C4C2×C4×D5312yes—
936C22×C4C2×C4×D5312yes—
937C22×C4C2×C4×D5312yes—
938C22×C4C2×C4×D5312yes—
939C22×C4D4×D5312yes—
940C22×C4D4×D5312yes—
941C22×C4D4×D5312yes—
942C22×C4#1171994912yes—
943C4⋊C4—28no—
944C22⋊C4—5316no—
945C22⋊C4—1068no—
946C22⋊C4—1068no—
947C22⋊C4—1068no—
948C22⋊C4—1068no—
949C22⋊C4—1068no—
950C22⋊C4—2124no—
951C22⋊C4—2124no—
952C42—44no—
953C42—1068no—
954C42—2124no—
955C42—2124no—
956C42—2124no—
957C23—534no—
958C23—534no—
959C23—534no—
960C23—534no—
961C23—534no—
962C23—534no—
963C23—534no—
964C23—534no—
965C23—1062no—
966C23—1062no—
967C23—1062no—
968C23—1062no—
969C23—1062no—
970C23—1062no—
971C23—1062no—
972C23—1062no—
973C23—1062no—
974C23—1062no—
975C23—1062no—
976C23—1062no—
977C23—1062no—
978C23—1062no—
979C23—1062no—
980C23—1062no—
981C23—1062no—
982C23—1062no—
983C23—1062no—
984C23—1062no—
985C23—1062no—
986C23—1062no—
987C23—1062no—
988C23—1062no—
989C23—1062no—
990C23—1062no—
991C23—1062no—
992C23—1062no—
993C23—1062no—
994C23—1062no—
995C23—1062no—
996C23—1062no—
997C23—1062no—
998C23—1062no—
999C23—1062no—
1000C23—1062no—
1001C23—1062no—
1002C23—1062no—
1003C23—1062no—
1004C23—1062no—
1005C23—1062no—
1006C23—1062no—
1007C23—1062no—
1008C23—1062no—
1009C23—1062no—
1010C23—1062no—
1011C23—2121no—
1012C23—2121no—
1013C23—2121no—
1014C23—2121no—
1015C23—2121no—
1016C23—2121no—
1017C23—2121no—
1018C23—2121no—
1019C23—2121no—
1020C23—2121no—
1021C23—2121no—
1022C23—2121no—
1023C23—2121no—
1024C23—2121no—
1025C23—2121no—
1026C23—2121no—
1027C23C22×C4×D5311yescharacteristic
1028C23C22×C4×D5311yescharacteristic
1029C23C22×C4×D5311yescharacteristic
1030C23C2×D4×D5311yescharacteristic
1031C23C2×D4×D5311yescharacteristic
1032C23C2×D4×D5311yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23#41×D5311yescharacteristic
1036C23#41×D5311yescharacteristic
1037C23C2×#1171994911yescharacteristic
1038C23#1313326211yescharacteristic
1039C23#1313326311yescharacteristic
1040C23#1313326311yescharacteristic
1041C23#1313326511yescharacteristic
1042D4—10632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—534no—
1090C2×C4—534no—
1091C2×C4—534no—
1092C2×C4—1062no—
1093C2×C4—1062no—
1094C2×C4—1062no—
1095C2×C4—1062no—
1096C2×C4—1062no—
1097C2×C4—1062no—
1098C2×C4—1062no—
1099C2×C4—1062no—
1100C2×C4—1062no—
1101C2×C4—1062no—
1102C2×C4—1062no—
1103C2×C4—1062no—
1104C2×C4—1062no—
1105C2×C4—1062no—
1106C2×C4—1062no—
1107C2×C4—1062no—
1108C2×C4—1062no—
1109C2×C4—1062no—
1110C2×C4—1062no—
1111C2×C4—1062no—
1112C2×C4—1062no—
1113C2×C4—1062no—
1114C2×C4—1062no—
1115C2×C4—1062no—
1116C2×C4—1062no—
1117C2×C4—1062no—
1118C2×C4—1062no—
1119C2×C4—21216no—
1120C2×C4—21216no—
1121C2×C4—21216no—
1122C2×C4—21216no—
1123C2×C4—2121no—
1124C2×C4—2121no—
1125C2×C4—2121no—
1126C2×C4—2121no—
1127C2×C4—2121no—
1128C2×C4—2121no—
1129C2×C4—2121no—
1130C2×C4—2121no—
1131C2×C4—2121no—
1132C2×C4—2121no—
1133C2×C4—2121no—
1134C2×C4—2121no—
1135C2×C4C42×D5314yes—
1136C2×C4C22⋊C4×D5314yes—
1137C2×C4#1313317914yescomplemented
1138C22—538no—
1139C22—1064no—
1140C22—1064no—
1141C22—1064no—
1142C22—1064no—
1143C22—1064no—
1144C22—1064no—
1145C22—1064no—
1146C22—1064no—
1147C22—1064no—
1148C22—1064no—
1149C22—1064no—
1150C22—1064no—
1151C22—1064no—
1152C22—1064no—
1153C22—1064no—
1154C22—1064no—
1155C22—1064no—
1156C22—2122no—
1157C22—2122no—
1158C22—2122no—
1159C22—2122no—
1160C22—2122no—
1161C22—2122no—
1162C22—2122no—
1163C22—2122no—
1164C22—2122no—
1165C22—2122no—
1166C22—2122no—
1167C22—2122no—
1168C22C2×C42×D5311yescharacteristic
1169C22C2×C22⋊C4×D5311yescharacteristic
1170C22#117×D5311yescharacteristic
1171C22C4×D4×D5311yescharacteristic
1172C22C4×D4×D5311yescharacteristic
1173C22C4×D4×D5311yescharacteristic
1174C22C4×D4×D5311yescharacteristic
1175C22C4×D4×D5311yescharacteristic
1176C22C4×D4×D5311yescharacteristic
1177C22C2×#1313317911yescharacteristic
1178C22#1681109111yescharacteristic
1179C22C4×#1171994911yescharacteristic
1180C22C4×#1171994911yescharacteristic
1181C22#1681109511yescharacteristic
1182C22#1681109511yescharacteristic
1183C22#1681109711yescharacteristic
1184C22#1681110411yescharacteristic
1185C22#1681110511yescharacteristic
1186C22#1681110511yescharacteristic
1187C22#1681125511yescharacteristic
1188C22#1681125711yescharacteristic
1189C22#1681126211yescharacteristic
1190C22#1681126411yescharacteristic
1191C22#1681126511yescharacteristic
1192C22#1681126511yescharacteristic
1193C22#1681126611yescharacteristic
1194C22#1681127511yescharacteristic
1195C22#1681127611yescharacteristic
1196C22#1681128311yescharacteristic
1197C22#1681129811yescharacteristic
1198C22#1681130011yescharacteristic
1199C22#1681130511yescharacteristic
1200C22#1681131811yescharacteristic
1201C22#1681132411yescharacteristic
1202C22#1681132611yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—1064no—
1211C4—1064no—
1212C4—1064no—
1213C4—2122no—
1214C4—2122no—
1215C4—2122no—
1216C2—1068no—
1217C2—2124no—
1218C2C4×C22⋊C4×D5311yescharacteristic
1219C2C4×#1313317911yescharacteristic
1220C2#2027707511yescharacteristic
1221C2#2027753311yescharacteristic
1222C2#2027754411yescharacteristic
1223C2#2027763911yescharacteristic
1224C2#2027765411yescharacteristic
1225C2#2027769111yescharacteristic
1226C2#2027769311yescharacteristic
1227C2#2027770011yescharacteristic
1228C2#2027770211yescharacteristic
1229C2#2027773011yescharacteristic
1230C2#2027773411yescharacteristic
1231C2#2027775911yescharacteristic
1232C2#2027776111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×#1436C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenter#1436D53
hypocenterC53#13813
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4×#11719921C2semidirect
5. C2×C4×#11719921C2semidirect
6. C2×#16810470C2semidirect
7. C2×#95×D53C2semidirect
8. #20272951C2semidirect
9. #20272951C2semidirect
10. #20272947C2semidirect
11. #20272940C2semidirect
12. #20272936C2semidirect
13. #20272936C2semidirect
14. #95×Dic53C2semidirect
15. C53×#1436C2semidirect
23. C2×#13133179C4semidirect
36. #16810501C4semidirect
37. #16810501C4semidirect
100. C22×C4×D53C2×C4semidirect
101. C22×C4×D53C2×C4semidirect
102. C22×C4×D53C2×C4semidirect
119. C2×#11719921C2×C4semidirect
120. C2×#11719921C2×C4semidirect
121. C2×#11719921C2×C4semidirect
122. C2×#11719921C2×C4semidirect
123. C2×#11719921C2×C4semidirect
124. C2×#11719921C2×C4semidirect
125. C2×#11719921C2×C4semidirect
139. C2×C4×Dic53C2×C4semidirect
148. #13133124C2×C4semidirect
149. #13133124C2×C4semidirect
150. #13133124D4semidirect
160. C2×C4⋊C4×C53C2×C4semidirect
167. #95×C53C2×C4semidirect
168. #95×C53C2×C4semidirect
297. C2×D212C42semidirect
335. #11719921C22⋊C4semidirect
473. C2×C4×C53C4×D4semidirect
515. C2×Dic53C4×D4semidirect
586. C2×D53C4×C22⋊C4semidirect
610. #1436D53semidirect
676. C53#13813semidirect
730. C2×C4⋊C4C4×D53semidirect
784. #95C4×D53semidirect
785. #95C4×D53semidirect
1137. C2×C4#13133179semidirect

Maximal subgroups

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

subgroupindex
C22×#131331792
C2×#168105012
C2×C4×#117199212
C2×#168104702
C2×#95×D532
#202729512
#202729472
#202729402
#202729362
#95×Dic532
C53×#14362
#1381353