Finite Group Databasebeta

← #27305655

Subgroups — #27305655

Order 13568.

2666 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810523C211yesmaximal, characteristic
3C2×#16810523C211yesmaximal, characteristic
4C2×C4×#11719919C211yesmaximal, characteristic, complemented
5C2×#16810474C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
7C2×C4×#11719921C211yesmaximal, characteristic, complemented
8#20272952C211yesmaximal, characteristic, complemented
9#20272951C211yesmaximal, characteristic, complemented
10#20272951C211yesmaximal, characteristic, complemented
11#20272943C211yesmaximal, characteristic, complemented
12#20272937C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C53×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C2×#13133177—24no—
20C2×#13133177—24no—
21C2×#13133177C418yescomplemented
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38#16810523C418yescomplemented
39#16810523C418yescomplemented
40C4×#11719919—24no—
41#16810474—24no—
42C22⋊C4×Dic53—24no—
43C4×#11719921—24no—
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C22×C22⋊D53—22no—
62C22×C22⋊D53—22no—
63C22×C22⋊D53—22no—
64C22×C22⋊D53—22no—
65C22×C22⋊D53C2×C414yes—
66C22×C22⋊D53C2×C414yes—
67C22×C22⋊D53C2×C414yes—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—41no—
73C23×Dic53—41no—
74C23×Dic53C2×C414yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C22×C4×D53—22no—
83C22×C4×D53—22no—
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—41no—
87C22×C4×D53—41no—
88C22×C4×D53C2×C414yes—
89#13133177—232no—
90C2×#11719919—22no—
91C2×#11719919—22no—
92C2×#11719919—22no—
93C2×#11719919—22no—
94C2×#11719919C2×C414yes—
95C2×#11719919C2×C414yescomplemented
96C2×#11719919C2×C414yescomplemented
97C2×#11719919D414yes—
98C2×#11719919D414yes—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—41no—
102C2×C22⋊Dic53—41no—
103C2×C22⋊Dic53C2×C414yescomplemented
104C2×C22⋊Dic53C2×C414yescomplemented
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921—41no—
112C2×#11719921—41no—
113C2×#11719921—41no—
114C2×#11719921—41no—
115C2×#11719921C2×C414yes—
116C2×#11719921C2×C414yescomplemented
117C2×#11719921C2×C414yescomplemented
118C2×#11719921C2×C414yescomplemented
119C2×#11719921C2×C414yescomplemented
120C2×C4×Dic53—22no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53—22no—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—22no—
125C2×C4×Dic53—22no—
126C2×C4×Dic53—22no—
127C2×C4×Dic53—22no—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53—22no—
131C2×C4×Dic53—22no—
132C2×C4×Dic53—41no—
133C2×C4×Dic53—41no—
134C2×C4×Dic53—41no—
135C2×C4×Dic53C2×C414yes—
136C2×C4×Dic53C2×C414yescomplemented
137C2×C4×Dic53C2×C414yescomplemented
138#13133124—22no—
139#13133124—22no—
140#13133124—22no—
141#13133124—22no—
142#13133124—22no—
143#13133124—22no—
144#13133124—22no—
145#13133124—41no—
146#13133124D414yescomplemented
147C25×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—41no—
159C2×C22⋊C4×C53—41no—
160C2×C22⋊C4×C53C2×C414yes—
161C2×C22⋊C4×C53C2×C414yescomplemented
162C2×C22⋊C4×C53C2×C414yescomplemented
163C2×C42×C53—22no—
164C2×C42×C53—22no—
165C2×C42×C53—41no—
166#95×C53—22no—
167#95×C53—22no—
168#95×C53—41no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53C22×C412yes—
182C24×C53C22×C412yes—
183C24×C53C22×C412yes—
184C24×C53C2411yescharacteristic
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—21no—
195C23×D53—21no—
196C23×D53—21no—
197C23×D53C22×C412yes—
198C23×D53C22×C412yes—
199C23×D53C22×C412yes—
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×C53C22×C412yes—
233C22×C4×C53C22×C412yes—
234C22×C4×C53C22×C412yes—
235C22×C4×C53C22×C412yes—
236C22×C4×C53C22×C412yes—
237C22×C4×C53C22×C412yes—
238C22×C4×C53C2×D412yes—
239C22×C4×C53C2×D412yes—
240C22×C4×C53C2×D412yes—
241C22×C4×C53#4112yes—
242C2×C22⋊D53—28no—
243C2×C22⋊D53—28no—
244C2×C22⋊D53—28no—
245C2×C22⋊D53—28no—
246C2×C22⋊D53—28no—
247C2×C22⋊D53—28no—
248C2×C22⋊D53C42116yescomplemented
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×Dic53—28no—
280C22×Dic53—28no—
281C22×Dic53—44no—
282C22×Dic53—44no—
283C22×Dic53—44no—
284C22×Dic53—44no—
285C22×Dic53—44no—
286C22×Dic53C22×C412yes—
287C22×Dic53C22×C412yes—
288C22×Dic53C22×C412yes—
289C22×Dic53C22×C412yes—
290C22×Dic53C22×C412yes—
291C22×Dic53C22×C412yes—
292C22×Dic53C22×C412yes—
293C22×Dic53C22×C412yes—
294C22×Dic53C22×C412yes—
295C22×Dic53C2×D412yes—
296C22×Dic53C2×D412yes—
297C22×Dic53C2×D412yes—
298C22×Dic53C2×D412yes—
299C22×Dic53C2×D412yes—
300C22×Dic53C2×D412yes—
301C22×Dic53#4112yes—
302C22×Dic53#4112yes—
303C22×Dic53#4112yes—
304C22×Dic53#4112yes—
305C2×C4×D53—28no—
306C2×C4×D53—28no—
307C2×C4×D53—44no—
308C2×C4×D53—44no—
309C2×C4×D53—44no—
310C2×C4×D53—44no—
311C2×C4×D53—44no—
312C22⋊C4×C53—28no—
313C22⋊C4×C53—28no—
314C22⋊C4×C53—44no—
315C42×C53—44no—
316C22⋊Dic53—28no—
317C22⋊Dic53—44no—
318#11719921—28no—
319#11719921—28no—
320#11719921—28no—
321#11719921—44no—
322#11719921—44no—
323#11719919—28no—
324#11719919—28no—
325#11719919C22⋊C4116yescomplemented
326C4×Dic53—28no—
327C4×Dic53—28no—
328C4×Dic53—28no—
329C4×Dic53—44no—
330C4×Dic53—44no—
331C4×Dic53—44no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53C2×C4214yes—
367C23×C53C23×C411yescharacteristic
368C23×C53C23×C411yescharacteristic
369C23×C53C23×C411yescharacteristic
370C23×C53C22×D411yescharacteristic
371C23×C53C22×D411yescharacteristic
372C23×C53C22×D411yescharacteristic
373C23×C53C2×#4111yescharacteristic
374C23×C53C2×#4111yescharacteristic
375C23×C53C2×#4111yescharacteristic
376C23×C53C2×#4111yescharacteristic
377C23×C53C2×#4111yescharacteristic
378C23×C53H(5,𝔽2)11yescharacteristic
379C23×C53H(5,𝔽2)11yescharacteristic
380C23×C53H(5,𝔽2)11yescharacteristic
381C23×C532−1+411yescharacteristic
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—41no—
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×D53C2×C4214yes—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
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—41no—
442C2×C4×C53—41no—
443C2×C4×C53—41no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53C2×C22⋊C414yes—
458C2×C4×C53C4×D414yescomplemented
459C22⋊D53—232no—
460C2×Dic53—22no—
461C2×Dic53—22no—
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—22no—
468C2×Dic53—22no—
469C2×Dic53—22no—
470C2×Dic53—22no—
471C2×Dic53—22no—
472C2×Dic53—22no—
473C2×Dic53—22no—
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—416no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53—41no—
495C2×Dic53—41no—
496C2×Dic53—41no—
497C2×Dic53—41no—
498C2×Dic53—41no—
499C2×Dic53—41no—
500C2×Dic53C2×C4214yes—
501C2×Dic53C2×C22⋊C414yes—
502C2×Dic53C2×C22⋊C414yes—
503C2×Dic53#11714yes—
504C2×Dic53C4×D414yes—
505C2×Dic53C4×D414yes—
506C2×Dic53C4×D414yes—
507C2×Dic53C4×D414yes—
508C2×Dic53C4×D414yes—
509C2×Dic53C4×D414yescomplemented
510C4×D53—416no—
511#13820—531nomaximal, Sylow
512C22×C53—24no—
513C22×C53—24no—
514C22×C53—24no—
515C22×C53—42no—
516C22×C53—42no—
517C22×C53—42no—
518C22×C53—42no—
519C22×C53—42no—
520C22×C53—42no—
521C22×C53—42no—
522C22×C53—42no—
523C22×C53—42no—
524C22×C53—42no—
525C22×C53—42no—
526C22×C53—42no—
527C22×C53C22×C4211yescharacteristic
528C22×C53C22×C22⋊C411yescharacteristic
529C22×C53C2×#11711yescharacteristic
530C22×C53C2×C4×D411yescharacteristic
531C22×C53C2×C4×D411yescharacteristic
532C22×C53C2×C4×D411yescharacteristic
533C22×C53C2×C4×D411yescharacteristic
534C22×C53C2×C4×D411yescharacteristic
535C22×C53C2×C4×D411yescharacteristic
536C22×C53C2×C4×D411yescharacteristic
537C22×C53C4×#4111yescharacteristic
538C22×C53C4×#4111yescharacteristic
539C22×C53C4×#4111yescharacteristic
540C22×C53#51811yescharacteristic
541C22×C53#51811yescharacteristic
542C22×C53#51811yescharacteristic
543C22×C53#52011yescharacteristic
544C22×C53#52011yescharacteristic
545C22×C53#52011yescharacteristic
546C22×C53D4211yescharacteristic
547C22×C53D4211yescharacteristic
548C22×C53#54611yescharacteristic
549C22×C53#54611yescharacteristic
550C22×C53#54711yescharacteristic
551C22×C53#54811yescharacteristic
552C22×C53#54811yescharacteristic
553C22×C53#55011yescharacteristic
554C22×C53#55011yescharacteristic
555C22×C53#55011yescharacteristic
556C22×C53#55311yescharacteristic
557C22×C53#55311yescharacteristic
558C22×C53#55511yescharacteristic
559C22×C53#55611yescharacteristic
560C22×C53#55911yescharacteristic
561C22×C53#55911yescharacteristic
562C2×D53—24no—
563C2×D53—24no—
564C2×D53—24no—
565C2×D53—42no—
566C2×D53—42no—
567C2×D53—42no—
568C2×D53—42no—
569C2×D53—42no—
570C2×D53—42no—
571C2×D53—42no—
572C2×D53—42no—
573C2×D53—42no—
574C2×D53—42no—
575C2×D53—42no—
576C2×D53—42no—
577C4×C53—24no—
578C4×C53—24no—
579C4×C53—42no—
580C4×C53—42no—
581C4×C53—42no—
582C4×C53—42no—
583Dic53—24no—
584Dic53—24no—
585Dic53—24no—
586Dic53—42no—
587Dic53—42no—
588Dic53—42no—
589Dic53C4×C22⋊C418yescomplemented
590C22×C4×D4—531no—
591C2×#390—531no—
592C2×#390—531no—
593C2×C4×C4⋊C4—531no—
594C2×C4×C4⋊C4—531no—
595C2×C4×C22⋊C4—531no—
596C2×C4×C22⋊C4—531no—
597#1437—531no—
598#1437—531no—
599#1437—531no—
600#1437D5311yescharacteristic, complemented
601C4⋊#95—531no—
602C22⋊#95—531no—
603C22⋊#95—531no—
604C4×#95—531no—
605C2×C53—44no—
606C2×C53C2×C4×C22⋊C411yescharacteristic
607C2×C53C42×D411yescharacteristic
608C2×C53#227511yescharacteristic
609C2×C53D4×C22⋊C411yescharacteristic
610C2×C53#234111yescharacteristic
611C2×C53#235411yescharacteristic
612C2×C53#235711yescharacteristic
613C2×C53#236111yescharacteristic
614C2×C53#236111yescharacteristic
615C2×C53#236311yescharacteristic
616C2×C53#236311yescharacteristic
617C2×C53#236611yescharacteristic
618C2×C53#236611yescharacteristic
619C2×C53#236711yescharacteristic
620C2×C53#236711yescharacteristic
621D53—44no—
622C23×D4—531no—
623C24×C4—531no—
624C24×C4—531no—
625C2×C4×D4—538no—
626C2×C4×D4—1064no—
627C2×C4×D4—1064no—
628C22×C4⋊C4—531no—
629C22×C4⋊C4—531no—
630C22×C4⋊C4—531no—
631C22×C22⋊C4—531no—
632C22×C22⋊C4—531no—
633C22×C22⋊C4—531no—
634C22×C22⋊C4—531no—
635C22×C22⋊C4—531no—
636C22×C22⋊C4—531no—
637C22×C22⋊C4—531no—
638C22×C22⋊C4C2×D5311yescharacteristic
639C22×C22⋊C4C2×D5311yescharacteristic
640C22×C22⋊C4C2×D5311yescharacteristic
641C22×C42—531no—
642C22×C42—531no—
643C22×C42—531no—
644C22×C42—531no—
645C22×C42—531no—
646C22×C42—531no—
647C22×C42C2×D5311yescharacteristic
648#390—538no—
649#390—538no—
650C4×C4⋊C4—1064no—
651C4×C4⋊C4—1064no—
652C4×C22⋊C4—1064no—
653C4×C22⋊C4—1064no—
654C2×#95—531no—
655C2×#95—531no—
656C2×#95—531no—
657C2×#95—531no—
658C2×#95—531no—
659C2×#95—531no—
660C2×#95—531no—
661C2×#95—531no—
662C2×#95—531no—
663C2×#95C2×D5311yescharacteristic
664C2×#95C2×D5311yescharacteristic
665C2×#95C2×D5311yescharacteristic
666C53#1382011yescharacteristic, complemented, Sylow
667C25—531no—
668C25C22×D5311yescharacteristic
669C22×D4—534no—
670C22×D4—534no—
671C22×D4—534no—
672C22×D4—1062no—
673C22×D4—1062no—
674C22×D4—1062no—
675C22×D4—1062no—
676C23×C4—531no—
677C23×C4—531no—
678C23×C4—531no—
679C23×C4—531no—
680C23×C4—531no—
681C23×C4—531no—
682C23×C4—531no—
683C23×C4—534no—
684C23×C4—534no—
685C23×C4—1062no—
686C23×C4—1062no—
687C23×C4—1062no—
688C23×C4—1062no—
689C23×C4—1062no—
690C23×C4—1062no—
691C23×C4—1062no—
692C23×C4—1062no—
693C23×C4—2121no—
694C23×C4—2121no—
695C23×C4—2121no—
696C23×C4—2121no—
697C23×C4C22×D5311yescharacteristic
698C23×C4C22×D5311yescharacteristic
699C23×C4C22×D5311yescharacteristic
700C23×C4C22×D5311yescharacteristic
701C23×C4C22×D5311yescharacteristic
702C23×C4C22×D5311yescharacteristic
703C4×D4—10632no—
704C2×C4⋊C4—534no—
705C2×C4⋊C4—534no—
706C2×C4⋊C4—534no—
707C2×C4⋊C4—534no—
708C2×C4⋊C4—534no—
709C2×C4⋊C4—1062no—
710C2×C4⋊C4—1062no—
711C2×C4⋊C4—1062no—
712C2×C4⋊C4—1062no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—534no—
720C2×C22⋊C4—534no—
721C2×C22⋊C4—534no—
722C2×C22⋊C4—534no—
723C2×C22⋊C4—534no—
724C2×C22⋊C4—534no—
725C2×C22⋊C4—534no—
726C2×C22⋊C4—1062no—
727C2×C22⋊C4—1062no—
728C2×C22⋊C4—1062no—
729C2×C22⋊C4—1062no—
730C2×C22⋊C4—1062no—
731C2×C22⋊C4—1062no—
732C2×C22⋊C4—1062no—
733C2×C22⋊C4—1062no—
734C2×C22⋊C4—2121no—
735C2×C22⋊C4—2121no—
736C2×C22⋊C4—2121no—
737C2×C22⋊C4—2121no—
738C2×C22⋊C4—2121no—
739C2×C22⋊C4—2121no—
740C2×C22⋊C4C4×D5314yes—
741C2×C22⋊C4C4×D5314yescomplemented
742C2×C22⋊C4C4×D5314yescomplemented
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—41no—
746C2×C42—534no—
747C2×C42—534no—
748C2×C42—534no—
749C2×C42—1062no—
750C2×C42—1062no—
751C2×C42—1062no—
752C2×C42—1062no—
753C2×C42—1062no—
754C2×C42—1062no—
755C2×C42—1062no—
756C2×C42—1062no—
757C2×C42—1062no—
758C2×C42—1062no—
759C2×C42—1062no—
760C2×C42—1062no—
761C2×C42—2121no—
762C2×C42—2121no—
763C2×C42—2121no—
764#95—22no—
765#95—22no—
766#95—41no—
767#95—534no—
768#95—1062no—
769#95—1062no—
770#95—1062no—
771#95—1062no—
772#95—1062no—
773#95—1062no—
774#95—1062no—
775#95—2121no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—532no—
789C24—532no—
790C24—532no—
791C24—1061no—
792C24—1061no—
793C24—1061no—
794C24—1061no—
795C24—1061no—
796C24—1061no—
797C24—1061no—
798C24—1061no—
799C24—1061no—
800C24—1061no—
801C24—1061no—
802C24—1061no—
803C24C2×C4×D5312yes—
804C24C2×C4×D5312yes—
805C24C2×C4×D5312yes—
806C24C23×D5311yescharacteristic
807C2×D4—5316no—
808C2×D4—1068no—
809C2×D4—1068no—
810C2×D4—1068no—
811C2×D4—1068no—
812C2×D4—1068no—
813C2×D4—1068no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
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—532no—
847C22×C4—532no—
848C22×C4—532no—
849C22×C4—532no—
850C22×C4—532no—
851C22×C4—532no—
852C22×C4—532no—
853C22×C4—532no—
854C22×C4—532no—
855C22×C4—532no—
856C22×C4—532no—
857C22×C4—532no—
858C22×C4—532no—
859C22×C4—532no—
860C22×C4—532no—
861C22×C4—532no—
862C22×C4—532no—
863C22×C4—532no—
864C22×C4—532no—
865C22×C4—1068no—
866C22×C4—1068no—
867C22×C4—1068no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—1061no—
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—1068no—
899C22×C4—2124no—
900C22×C4—2124no—
901C22×C4—2124no—
902C22×C4—2124no—
903C22×C4—2124no—
904C22×C4—2124no—
905C22×C4—2124no—
906C22×C4—2124no—
907C22×C4—2124no—
908C22×C4—2124no—
909C22×C4C2×C4×D5312yes—
910C22×C4C2×C4×D5312yes—
911C22×C4C2×C4×D5312yes—
912C22×C4C2×C4×D5312yes—
913C22×C4C2×C4×D5312yes—
914C22×C4C2×C4×D5312yes—
915C22×C4D4×D5312yes—
916C22×C4D4×D5312yes—
917C22×C4D4×D5312yes—
918C22×C4#1171994712yes—
919C4⋊C4—5316no—
920C4⋊C4—1068no—
921C4⋊C4—1068no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—44no—
925C22⋊C4—1068no—
926C22⋊C4—1068no—
927C22⋊C4—1068no—
928C22⋊C4—1068no—
929C22⋊C4—2124no—
930C22⋊C4—2124no—
931C22⋊C4—2124no—
932C42—44no—
933C42—1068no—
934C42—1068no—
935C42—1068no—
936C42—2124no—
937C42—2124no—
938C42—2124no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—534no—
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—2121no—
993C23—2121no—
994C23—2121no—
995C23—2121no—
996C23—2121no—
997C23—2121no—
998C23—2121no—
999C23—2121no—
1000C23—2121no—
1001C23—2121no—
1002C23—2121no—
1003C23—2121no—
1004C23—2121no—
1005C23—2121no—
1006C23—2121no—
1007C23—2121no—
1008C23C42×D5314yes—
1009C23C22×C4×D5311yescharacteristic
1010C23C22×C4×D5311yescharacteristic
1011C23C22×C4×D5311yescharacteristic
1012C23C2×D4×D5311yescharacteristic
1013C23C2×D4×D5311yescharacteristic
1014C23C2×D4×D5311yescharacteristic
1015C23#41×D5311yescharacteristic
1016C23#41×D5311yescharacteristic
1017C23#41×D5311yescharacteristic
1018C23#41×D5311yescharacteristic
1019C23C2×#1171994711yescharacteristic
1020C23#1313326211yescharacteristic
1021C23#1313326211yescharacteristic
1022C23#1313326311yescharacteristic
1023C23#1313326411yescharacteristic
1024D4—10632no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—534no—
1066C2×C4—534no—
1067C2×C4—534no—
1068C2×C4—534no—
1069C2×C4—534no—
1070C2×C4—534no—
1071C2×C4—534no—
1072C2×C4—534no—
1073C2×C4—534no—
1074C2×C4—534no—
1075C2×C4—1062no—
1076C2×C4—1062no—
1077C2×C4—1062no—
1078C2×C4—1062no—
1079C2×C4—1062no—
1080C2×C4—1062no—
1081C2×C4—1062no—
1082C2×C4—1062no—
1083C2×C4—1062no—
1084C2×C4—1062no—
1085C2×C4—1062no—
1086C2×C4—1062no—
1087C2×C4—1062no—
1088C2×C4—1062no—
1089C2×C4—1062no—
1090C2×C4—1062no—
1091C2×C4—1062no—
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—21216no—
1103C2×C4—21216no—
1104C2×C4—2121no—
1105C2×C4—2121no—
1106C2×C4—2121no—
1107C2×C4—2121no—
1108C2×C4—2121no—
1109C2×C4—2121no—
1110C2×C4—2121no—
1111C2×C4—2121no—
1112C2×C4—2121no—
1113C2×C4—2121no—
1114C2×C4—2121no—
1115C2×C4—2121no—
1116C2×C4C22⋊C4×D5314yes—
1117C2×C4#1313317714yescomplemented
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—1064no—
1134C22—1064no—
1135C22—1064no—
1136C22—2122no—
1137C22—2122no—
1138C22—2122no—
1139C22—2122no—
1140C22—2122no—
1141C22—2122no—
1142C22—2122no—
1143C22—2122no—
1144C22—2122no—
1145C22—2122no—
1146C22—2122no—
1147C22—2122no—
1148C22C2×C42×D5311yescharacteristic
1149C22C2×C22⋊C4×D5311yescharacteristic
1150C22#117×D5311yescharacteristic
1151C22C4×D4×D5311yescharacteristic
1152C22C4×D4×D5311yescharacteristic
1153C22C4×D4×D5311yescharacteristic
1154C22C4×D4×D5311yescharacteristic
1155C22C4×D4×D5311yescharacteristic
1156C22C4×D4×D5311yescharacteristic
1157C22C2×#1313317711yescharacteristic
1158C22C4×#1171994711yescharacteristic
1159C22C4×#1171994711yescharacteristic
1160C22#1681109111yescharacteristic
1161C22#1681109511yescharacteristic
1162C22#1681109511yescharacteristic
1163C22#1681109611yescharacteristic
1164C22#1681110211yescharacteristic
1165C22#1681110211yescharacteristic
1166C22#1681110311yescharacteristic
1167C22#1681125511yescharacteristic
1168C22#1681125711yescharacteristic
1169C22#1681126211yescharacteristic
1170C22#1681126511yescharacteristic
1171C22#1681127111yescharacteristic
1172C22#1681127911yescharacteristic
1173C22#1681128111yescharacteristic
1174C22#1681129111yescharacteristic
1175C22#1681129111yescharacteristic
1176C22#1681129311yescharacteristic
1177C22#1681131611yescharacteristic
1178C22#1681132411yescharacteristic
1179C22#1681133511yescharacteristic
1180C22#1681134011yescharacteristic
1181C22#1681135511yescharacteristic
1182C22#1681135711yescharacteristic
1183C4—24no—
1184C4—24no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—538no—
1190C4—1064no—
1191C4—1064no—
1192C4—1064no—
1193C4—2122no—
1194C4—2122no—
1195C4—2122no—
1196C2—44no—
1197C2—2124no—
1198C2C4×C22⋊C4×D5311yescharacteristic
1199C2C4×#1313317711yescharacteristic
1200C2#2027707411yescharacteristic
1201C2#2027753311yescharacteristic
1202C2#2027755411yescharacteristic
1203C2#2027766111yescharacteristic
1204C2#2027768511yescharacteristic
1205C2#2027772611yescharacteristic
1206C2#2027772811yescharacteristic
1207C2#2027774811yescharacteristic
1208C2#2027775011yescharacteristic
1209C2#2027777611yescharacteristic
1210C2#2027777811yescharacteristic
1211C2#2027778111yescharacteristic
1212C2#2027778911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×#1437C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1437D53
hypocenterC53#13820
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C4×#11719919C2semidirect
5. C2×#16810474C2semidirect
6. C2×C22⋊C4×Dic53C2semidirect
7. C2×C4×#11719921C2semidirect
8. #20272952C2semidirect
9. #20272951C2semidirect
10. #20272951C2semidirect
11. #20272943C2semidirect
12. #20272937C2semidirect
13. #20272936C2semidirect
14. #95×Dic53C2semidirect
15. C53×#1437C2semidirect
21. C2×#13133177C4semidirect
38. #16810523C4semidirect
39. #16810523C4semidirect
95. C2×#11719919C2×C4semidirect
96. C2×#11719919C2×C4semidirect
103. C2×C22⋊Dic53C2×C4semidirect
104. C2×C22⋊Dic53C2×C4semidirect
116. C2×#11719921C2×C4semidirect
117. C2×#11719921C2×C4semidirect
118. C2×#11719921C2×C4semidirect
119. C2×#11719921C2×C4semidirect
136. C2×C4×Dic53C2×C4semidirect
137. C2×C4×Dic53C2×C4semidirect
146. #13133124D4semidirect
161. C2×C22⋊C4×C53C2×C4semidirect
162. C2×C22⋊C4×C53C2×C4semidirect
248. C2×C22⋊D53C42semidirect
325. #11719919C22⋊C4semidirect
458. C2×C4×C53C4×D4semidirect
509. C2×Dic53C4×D4semidirect
589. Dic53C4×C22⋊C4semidirect
600. #1437D53semidirect
666. C53#13820semidirect
741. C2×C22⋊C4C4×D53semidirect
742. C2×C22⋊C4C4×D53semidirect
1117. C2×C4#13133177semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105232
C2×C4×#117199192
C2×#168104742
C2×C22⋊C4×Dic532
C2×C4×#117199212
#202729522
#202729512
#202729432
#202729372
#202729362
#95×Dic532
C53×#14372
#1382053