Finite Group Databasebeta

← #27307452

Subgroups — #27307452

Order 13568.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic, complemented
3C2×#16810499C211yesmaximal, characteristic
4C2×#16810499C211yesmaximal, characteristic
5C2×#16810496C211yesmaximal, characteristic, complemented
6C2×#16810494C211yesmaximal, characteristic, complemented
7#20272979C211yesmaximal, characteristic, complemented
8#20272978C211yesmaximal, characteristic, complemented
9#20272960C211yesmaximal, characteristic, complemented
10#20272958C211yesmaximal, characteristic, complemented
11#20272950C211yesmaximal, characteristic, complemented
12#20272947C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic, complemented
14#20272936C211yesmaximal, characteristic, complemented
15C2×C53×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×C4×C22⋊D53—24no—
21C2×C4×C22⋊D53—24no—
22C2×C4×C22⋊D53—24no—
23C22×C4⋊Dic53C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C2×C4⋊C4×D53—24no—
29C2×C4⋊C4×D53—24no—
30C2×C4⋊C4×D53—24no—
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C22⋊Dic53C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38#16810499—24no—
39#16810499C418yescomplemented
40#16810496—24no—
41#16810494—24no—
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C24×C4×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C22×C22⋊C4×C53C2211yescharacteristic
58C22×C22⋊C4×C53C2211yescharacteristic
59C53×#385—24no—
60C2×#95×C53C2211yescharacteristic
61C2×#95×C53C2211yescharacteristic
62C24×D53C2311yescharacteristic
63C22×C22⋊D53—22no—
64C22×C22⋊D53—22no—
65C22×C22⋊D53—22no—
66C22×C22⋊D53—22no—
67C22×C22⋊D53C2×C414yes—
68C22×C22⋊D53D414yes—
69C22×C22⋊D53Q814yes—
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
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—22no—
92C22×C4×D53—41no—
93C22×C4×D53—41no—
94C22×C4×D53—41no—
95C22×C4×D53—41no—
96C22×C4×D53C2×C414yescomplemented
97C22×C4×D53D414yes—
98C4×C22⋊D53—232no—
99C2×C4⋊Dic53—22no—
100C2×C4⋊Dic53—22no—
101C2×C4⋊Dic53—22no—
102C2×#11719919—22no—
103C2×#11719919—22no—
104C2×#11719919—22no—
105C2×#11719919—22no—
106C2×#11719919—22no—
107C2×#11719919—22no—
108C2×#11719919—22no—
109C2×#11719919—22no—
110C2×#11719919—22no—
111C2×#11719919—22no—
112C2×#11719919—41no—
113C2×#11719919D414yescomplemented
114C4⋊C4×D53—232no—
115C2×C22⋊Dic53—22no—
116C2×C22⋊Dic53—22no—
117C2×C22⋊Dic53—22no—
118C2×C22⋊Dic53—22no—
119C2×C22⋊Dic53—22no—
120C2×C22⋊Dic53—22no—
121C2×C22⋊Dic53—22no—
122C2×C22⋊Dic53—41no—
123C2×C22⋊Dic53C2×C414yescomplemented
124C2×#11719921—22no—
125C2×#11719921—22no—
126C2×#11719921—22no—
127C2×#11719921—22no—
128C2×#11719921—22no—
129C2×#11719921—22no—
130C2×#11719921—22no—
131C2×#11719921C2×C414yescomplemented
132C2×#11719921D414yes—
133C2×C4×Dic53—22no—
134C2×C4×Dic53—22no—
135C2×C4×Dic53—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—22no—
139#13133124—22no—
140#13133124—22no—
141#13133124—22no—
142#13133124—22no—
143#13133124—22no—
144#13133124—41no—
145#13133124—41no—
146#13133124C2×C414yescomplemented
147#13133124C2×C414yescomplemented
148C25×C53C2311yescharacteristic
149C23×C4×C53—22no—
150C23×C4×C53—22no—
151C23×C4×C53—22no—
152C23×C4×C53—22no—
153C23×C4×C53—22no—
154C23×C4×C53—41no—
155C23×C4×C53—41no—
156C23×C4×C53C2311yescharacteristic
157C23×C4×C53C2311yescharacteristic
158C23×C4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C2×C4⋊C4×C53—22no—
163C2×C4⋊C4×C53—22no—
164C2×C4⋊C4×C53—22no—
165C2×C4⋊C4×C53—22no—
166C2×C4⋊C4×C53—41no—
167C2×C4⋊C4×C53D414yescomplemented
168C2×C22⋊C4×C53—22no—
169C2×C22⋊C4×C53—22no—
170C2×C22⋊C4×C53—22no—
171C2×C22⋊C4×C53—22no—
172C2×C22⋊C4×C53—41no—
173C2×C22⋊C4×C53C2×C414yescomplemented
174#95×C53—22no—
175#95×C53—22no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53C22×C412yes—
189C24×C53C2×D412yes—
190C24×C53C2×Q812yes—
191C24×C53C2411yescharacteristic
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—21no—
195C23×D53—21no—
196C23×D53—21no—
197C23×D53—21no—
198C23×D53—21no—
199C23×D53—21no—
200C23×D53C22×C412yes—
201C23×D53C2×D412yes—
202C23×D53C2×D412yes—
203C23×D53C2×D412yes—
204C23×D53C2×Q812yes—
205C23×D53#4112yes—
206C23×D53#4112yes—
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—28no—
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×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—44no—
242C22×C4×C53—44no—
243C22×C4×C53—44no—
244C22×C4×C53—44no—
245C22×C4×C53—44no—
246C22×C4×C53—44no—
247C22×C4×C53C22×C412yes—
248C22×C4×C53C22×C412yes—
249C22×C4×C53C2×D412yes—
250C22×C4×C53C2×D412yes—
251C22×C4×C53C2×D412yes—
252C22×C4×C53C2×D412yes—
253C22×C4×C53C2×D412yes—
254C22×C4×C53C2×D412yes—
255C22×C4×C53#4112yes—
256C2×C22⋊D53—28no—
257C2×C22⋊D53—28no—
258C2×C22⋊D53—28no—
259C2×C22⋊D53—28no—
260C2×C22⋊D53—28no—
261C2×C22⋊D53—28no—
262C2×C22⋊D53C4⋊C4116yescomplemented
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—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—21no—
284C22×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53—21no—
290C22×Dic53—21no—
291C22×Dic53—21no—
292C22×Dic53—21no—
293C22×Dic53—21no—
294C22×Dic53—21no—
295C22×Dic53—21no—
296C22×Dic53—21no—
297C22×Dic53—21no—
298C22×Dic53—21no—
299C22×Dic53—21no—
300C22×Dic53—21no—
301C22×Dic53—21no—
302C22×Dic53C22×C412yes—
303C22×Dic53C22×C412yes—
304C22×Dic53C22×C412yes—
305C22×Dic53C2×D412yes—
306C22×Dic53C2×D412yes—
307C22×Dic53C2×D412yes—
308C22×Dic53C2×D412yes—
309C22×Dic53C2×D412yes—
310C22×Dic53C2×Q812yes—
311C22×Dic53#4112yes—
312C2×C4×D53—28no—
313C2×C4×D53—28no—
314C2×C4×D53—28no—
315C2×C4×D53—28no—
316C2×C4×D53—28no—
317C2×C4×D53—28no—
318C2×C4×D53—28no—
319C2×C4×D53—28no—
320C2×C4×D53—28no—
321C2×C4×D53—28no—
322C2×C4×D53—44no—
323C2×C4×D53—44no—
324C2×C4×D53—44no—
325C2×C4×D53—44no—
326C2×C4×D53—44no—
327C2×C4×D53—44no—
328C2×C4×D53—44no—
329C2×C4×D53—44no—
330C2×C4×D53—44no—
331C2×C4×D53—44no—
332C2×C4×D53—44no—
333C4⋊C4×C53—28no—
334C4⋊C4×C53—44no—
335C22⋊C4×C53—28no—
336C22⋊C4×C53—44no—
337C22⋊Dic53—28no—
338C22⋊Dic53—28no—
339C22⋊Dic53—44no—
340#11719921—28no—
341#11719921—28no—
342#11719921—44no—
343C4⋊Dic53—28no—
344#11719919—28no—
345#11719919—28no—
346#11719919—28no—
347#11719919—44no—
348C4×Dic53—28no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53C2×C4⋊C414yescomplemented
384C23×C53C23×C411yescharacteristic
385C23×C53C22×D411yescharacteristic
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C23×C53C22×D411yescharacteristic
389C23×C53C22×D411yescharacteristic
390C23×C53C22×Q811yescharacteristic
391C23×C53C2×#4111yescharacteristic
392C23×C53C2×#4111yescharacteristic
393C23×C53C2×#4111yescharacteristic
394C23×C53C2×#4111yescharacteristic
395C23×C53H(5,𝔽2)11yescharacteristic
396C23×C53H(5,𝔽2)11yescharacteristic
397C23×C532−1+411yescharacteristic
398C23×C532−1+411yescharacteristic
399C22×D53—22no—
400C22×D53—22no—
401C22×D53—22no—
402C22×D53—22no—
403C22×D53—22no—
404C22×D53—22no—
405C22×D53—22no—
406C22×D53—22no—
407C22×D53—22no—
408C22×D53—22no—
409C22×D53—22no—
410C22×D53—22no—
411C22×D53—22no—
412C22×D53—22no—
413C22×D53—22no—
414C22×D53—22no—
415C22×D53—22no—
416C22×D53—22no—
417C22×D53—22no—
418C22×D53—22no—
419C22×D53—22no—
420C22×D53—22no—
421C22×D53—22no—
422C22×D53—22no—
423C22×D53—22no—
424C22×D53—22no—
425C22×D53—22no—
426C22×D53—22no—
427C22×D53C2×C4⋊C414yes—
428C22×D53C4×D414yes—
429C22×D53C4×D414yes—
430C22×D53#12014yes—
431C22×D53C22⋊Q814yes—
432C22×D53C22⋊Q814yes—
433C22×D53#12314yes—
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—416no—
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×C53—41no—
472C2×C4×C53—41no—
473C2×C4×C53—41no—
474C2×C4×C53—41no—
475C2×C4×C53C4×D414yescomplemented
476C2×C4×C53#12014yes—
477C22⋊D53—232no—
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—22no—
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×Dic53—41no—
514C2×Dic53—41no—
515C2×Dic53—41no—
516C2×Dic53—41no—
517C2×Dic53—41no—
518C2×Dic53—41no—
519C2×Dic53—41no—
520C2×Dic53—41no—
521C2×Dic53—41no—
522C2×Dic53—41no—
523C2×Dic53—41no—
524C2×Dic53—41no—
525C2×Dic53C2×C4⋊C414yescomplemented
526C2×Dic53C4×D414yescomplemented
527C4×D53—232no—
528C4×D53—416no—
529C4×D53—416no—
530#14015—531nomaximal, Sylow
531C22×C53—24no—
532C22×C53—24no—
533C22×C53—24no—
534C22×C53—42no—
535C22×C53—42no—
536C22×C53—42no—
537C22×C53—42no—
538C22×C53—42no—
539C22×C53—42no—
540C22×C53—42no—
541C22×C53—42no—
542C22×C53—42no—
543C22×C53—42no—
544C22×C53—42no—
545C22×C53—42no—
546C22×C53C22×C4⋊C411yescharacteristic
547C22×C53C2×C4×D411yescharacteristic
548C22×C53C2×C4×D411yescharacteristic
549C22×C53C2×C4×D411yescharacteristic
550C22×C53C2×C4×D411yescharacteristic
551C22×C53#52011yescharacteristic
552C22×C53#52011yescharacteristic
553C22×C53C2×#12011yescharacteristic
554C22×C53C2×#12011yescharacteristic
555C22×C53C2×C22⋊Q811yescharacteristic
556C22×C53C2×C22⋊Q811yescharacteristic
557C22×C53C2×#12311yescharacteristic
558C22×C53#52511yescharacteristic
559C22×C53#52511yescharacteristic
560C22×C53#52511yescharacteristic
561C22×C53#53411yescharacteristic
562C22×C53#53611yescharacteristic
563C22×C53#53911yescharacteristic
564C22×C53#53911yescharacteristic
565C22×C53D4211yescharacteristic
566C22×C53D4211yescharacteristic
567C22×C53D4211yescharacteristic
568C22×C53D4211yescharacteristic
569C22×C53#54711yescharacteristic
570C22×C53#54711yescharacteristic
571C22×C53#54711yescharacteristic
572C22×C53#54711yescharacteristic
573C22×C53#54811yescharacteristic
574C22×C53#54811yescharacteristic
575C22×C53D4×Q811yescharacteristic
576C22×C53D4×Q811yescharacteristic
577C22×C53#55311yescharacteristic
578C22×C53#55311yescharacteristic
579C22×C53#55411yescharacteristic
580C22×C53#55411yescharacteristic
581C2×D53—24no—
582C2×D53—24no—
583C2×D53—24no—
584C2×D53—24no—
585C2×D53—24no—
586C2×D53—24no—
587C2×D53—24no—
588C2×D53—24no—
589C2×D53—24no—
590C2×D53—24no—
591C2×D53—24no—
592C2×D53—24no—
593C2×D53—24no—
594C2×D53—24no—
595C2×D53#38518yescomplemented
596C4×C53—24no—
597C4×C53—24no—
598C4×C53—42no—
599C4×C53—42no—
600C4×C53—42no—
601C4×C53—81no—
602Dic53—24no—
603Dic53—24no—
604Dic53—42no—
605Dic53—42no—
606Dic53—42no—
607Dic53—42no—
608Dic53—81no—
609C22×C4×D4—531no—
610C23×C4⋊C4—531no—
611C2×#386—531no—
612C2×#386—531no—
613C2×#385—531no—
614C2×#385—531no—
615C2×#385D5311yescharacteristic, complemented
616#1444—531no—
617#1444—531no—
618#1439—531no—
619#1439—531no—
620#1436—531no—
621#1436—531no—
622C22⋊#95—531no—
623C22⋊#95—531no—
624C2×C53—44no—
625C2×C53C2×#38511yescharacteristic
626C2×C53C4×#12011yescharacteristic
627C2×C53#232211yescharacteristic
628C2×C53D4×C4⋊C411yescharacteristic
629C2×C53D4×C4⋊C411yescharacteristic
630C2×C53#236111yescharacteristic
631C2×C53#236111yescharacteristic
632C2×C53#240311yescharacteristic
633C2×C53#240611yescharacteristic
634C2×C53#240911yescharacteristic
635C2×C53#244311yescharacteristic
636C2×C53#244311yescharacteristic
637C2×C53#244911yescharacteristic
638C2×C53#244911yescharacteristic
639C2×C53#257911yescharacteristic
640D53—28no—
641C23×D4—531no—
642C24×C4—531no—
643C24×C4—531no—
644C24×C4—531no—
645C24×C4C2×D5311yescharacteristic
646C2×C4×D4—1064no—
647C2×C4×D4—1064no—
648C2×C4×D4—1064no—
649C22×C4⋊C4—531no—
650C22×C4⋊C4—531no—
651C22×C4⋊C4—531no—
652C22×C4⋊C4—531no—
653C22×C4⋊C4—531no—
654C22×C4⋊C4—1064no—
655C22×C4⋊C4—1064no—
656C22×C4⋊C4—1064no—
657C22×C4⋊C4C2×D5311yescharacteristic
658C22×C4⋊C4C2×D5311yescharacteristic
659C22×C22⋊C4—531no—
660C22×C22⋊C4—531no—
661C22×C22⋊C4—531no—
662C22×C22⋊C4—531no—
663C22×C22⋊C4—531no—
664C22×C22⋊C4—531no—
665C22×C22⋊C4C2×D5311yescharacteristic
666C22×C22⋊C4C2×D5311yescharacteristic
667C22×C42—531no—
668#386—538no—
669#386—1064no—
670#385—24no—
671#385—1064no—
672#385—1064no—
673C2×#95—531no—
674C2×#95—531no—
675C2×#95—531no—
676C2×#95—531no—
677C2×#95—531no—
678C2×#95—531no—
679C2×#95—531no—
680C2×#95—531no—
681C2×#95—531no—
682C2×#95—531no—
683C2×#95—531no—
684C2×#95—531no—
685C2×#95C2×D5311yescharacteristic
686C2×#95C2×D5311yescharacteristic
687C53#1401511yescharacteristic, complemented, Sylow
688C25—531no—
689C25C22×D5311yescharacteristic
690C22×D4—534no—
691C22×D4—534no—
692C22×D4—534no—
693C22×D4—1062no—
694C22×D4—1062no—
695C22×D4—1062no—
696C22×D4—1062no—
697C23×C4—22no—
698C23×C4—22no—
699C23×C4—22no—
700C23×C4—22no—
701C23×C4—22no—
702C23×C4—41no—
703C23×C4—41no—
704C23×C4—531no—
705C23×C4—531no—
706C23×C4—531no—
707C23×C4—531no—
708C23×C4—531no—
709C23×C4—531no—
710C23×C4—534no—
711C23×C4—534no—
712C23×C4—531no—
713C23×C4—1062no—
714C23×C4—1062no—
715C23×C4—1062no—
716C23×C4—1062no—
717C23×C4—1062no—
718C23×C4—1062no—
719C23×C4—1062no—
720C23×C4—1062no—
721C23×C4—1062no—
722C23×C4—1062no—
723C23×C4—1062no—
724C23×C4—1062no—
725C23×C4—1062no—
726C23×C4—1062no—
727C23×C4—1062no—
728C23×C4—2121no—
729C23×C4—2121no—
730C23×C4—2121no—
731C23×C4—2121no—
732C23×C4C22×D5311yescharacteristic
733C23×C4C22×D5311yescharacteristic
734C23×C4C22×D5311yescharacteristic
735C23×C4C22×D5311yescharacteristic
736C23×C4C22×D5311yescharacteristic
737C23×C4C22×D5311yescharacteristic
738C4×D4—10632no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4—22no—
742C2×C4⋊C4—22no—
743C2×C4⋊C4—41no—
744C2×C4⋊C4—534no—
745C2×C4⋊C4—10632no—
746C2×C4⋊C4—1062no—
747C2×C4⋊C4—1062no—
748C2×C4⋊C4—1062no—
749C2×C4⋊C4—1062no—
750C2×C4⋊C4—1062no—
751C2×C4⋊C4—1062no—
752C2×C4⋊C4—1062no—
753C2×C4⋊C4—1062no—
754C2×C4⋊C4—1062no—
755C2×C4⋊C4—1062no—
756C2×C4⋊C4—1062no—
757C2×C4⋊C4—1062no—
758C2×C4⋊C4—1062no—
759C2×C4⋊C4—2121no—
760C2×C4⋊C4C22⋊D5314yescomplemented
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—534no—
767C2×C22⋊C4—534no—
768C2×C22⋊C4—534no—
769C2×C22⋊C4—1062no—
770C2×C22⋊C4—1062no—
771C2×C22⋊C4—1062no—
772C2×C22⋊C4—1062no—
773C2×C22⋊C4—1062no—
774C2×C22⋊C4—1062no—
775C2×C22⋊C4—1062no—
776C2×C22⋊C4—1062no—
777C2×C22⋊C4—1062no—
778C2×C22⋊C4—1062no—
779C2×C22⋊C4—1062no—
780C2×C22⋊C4—1062no—
781C2×C22⋊C4—1062no—
782C2×C22⋊C4—1062no—
783C2×C22⋊C4—2121no—
784C2×C22⋊C4C4×D5314yescomplemented
785C2×C42—1062no—
786C2×C42—1062no—
787C2×C42—1062no—
788#95—22no—
789#95—22no—
790#95—534no—
791#95—534no—
792#95—1062no—
793#95—1062no—
794#95—1062no—
795#95—1062no—
796#95—1062no—
797#95—1062no—
798#95—1062no—
799#95—1062no—
800#95—2121no—
801#95—2121no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—532no—
815C24—532no—
816C24—532no—
817C24—532no—
818C24—532no—
819C24—532no—
820C24—532no—
821C24—1061no—
822C24—1061no—
823C24—1061no—
824C24—1061no—
825C24—1061no—
826C24—1061no—
827C24—1061no—
828C24—1061no—
829C24C2×C4×D5312yes—
830C24D4×D5312yes—
831C24Q8×D5312yes—
832C24C23×D5311yescharacteristic
833C2×D4—5316no—
834C2×D4—1068no—
835C2×D4—1068no—
836C2×D4—1068no—
837C2×D4—1068no—
838C2×D4—1068no—
839C2×D4—1068no—
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—28no—
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—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—532no—
881C22×C4—532no—
882C22×C4—532no—
883C22×C4—532no—
884C22×C4—532no—
885C22×C4—532no—
886C22×C4—532no—
887C22×C4—532no—
888C22×C4—532no—
889C22×C4—532no—
890C22×C4—1068no—
891C22×C4—1068no—
892C22×C4—1068no—
893C22×C4—1068no—
894C22×C4—1068no—
895C22×C4—1068no—
896C22×C4—1068no—
897C22×C4—1068no—
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—1068no—
907C22×C4—1061no—
908C22×C4—1061no—
909C22×C4—1061no—
910C22×C4—1061no—
911C22×C4—1061no—
912C22×C4—1061no—
913C22×C4—1061no—
914C22×C4—1061no—
915C22×C4—1061no—
916C22×C4—1061no—
917C22×C4—1061no—
918C22×C4—1061no—
919C22×C4—1061no—
920C22×C4—1061no—
921C22×C4—1061no—
922C22×C4—1061no—
923C22×C4—1061no—
924C22×C4—1061no—
925C22×C4—1061no—
926C22×C4—1061no—
927C22×C4—1061no—
928C22×C4—1061no—
929C22×C4—1061no—
930C22×C4—1061no—
931C22×C4—1068no—
932C22×C4—1061no—
933C22×C4—1061no—
934C22×C4—1061no—
935C22×C4—1061no—
936C22×C4—1061no—
937C22×C4—1061no—
938C22×C4—1061no—
939C22×C4—2124no—
940C22×C4—2124no—
941C22×C4—2124no—
942C22×C4—2124no—
943C22×C4—2124no—
944C22×C4—2124no—
945C22×C4—2124no—
946C22×C4—2124no—
947C22×C4—2124no—
948C22×C4—2124no—
949C22×C4—2124no—
950C22×C4C2×C4×D5312yes—
951C22×C4C2×C4×D5312yes—
952C22×C4#1171994512yes—
953C22×C4D4×D5312yes—
954C22×C4D4×D5312yes—
955C22×C4D4×D5312yes—
956C22×C4C2×C22⋊D5312yes—
957C22×C4C2×C22⋊D5312yes—
958C22×C4C2×C22⋊D5312yes—
959C4⋊C4—28no—
960C4⋊C4—44no—
961C4⋊C4—1068no—
962C4⋊C4—1068no—
963C4⋊C4—1068no—
964C4⋊C4—1068no—
965C4⋊C4—2124no—
966C22⋊C4—28no—
967C22⋊C4—44no—
968C22⋊C4—1068no—
969C22⋊C4—1068no—
970C22⋊C4—1068no—
971C22⋊C4—1068no—
972C22⋊C4—2124no—
973C22⋊C4—2124no—
974C42—1068no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—534no—
1010C23—534no—
1011C23—534no—
1012C23—534no—
1013C23—534no—
1014C23—534no—
1015C23—534no—
1016C23—1062no—
1017C23—1062no—
1018C23—1062no—
1019C23—1062no—
1020C23—1062no—
1021C23—1062no—
1022C23—1062no—
1023C23—1062no—
1024C23—1062no—
1025C23—1062no—
1026C23—1062no—
1027C23—1062no—
1028C23—1062no—
1029C23—1062no—
1030C23—1062no—
1031C23—1062no—
1032C23—1062no—
1033C23—1062no—
1034C23—1062no—
1035C23—1062no—
1036C23—1062no—
1037C23—1062no—
1038C23—1062no—
1039C23—1062no—
1040C23—1062no—
1041C23—1062no—
1042C23—1062no—
1043C23—1062no—
1044C23C4⋊C4×D5314yescomplemented
1045C23C22×C4×D5311yescharacteristic
1046C23C2×D4×D5311yescharacteristic
1047C23C2×D4×D5311yescharacteristic
1048C23C2×D4×D5311yescharacteristic
1049C23C2×D4×D5311yescharacteristic
1050C23C22×C22⋊D5311yescharacteristic
1051C23C2×Q8×D5311yescharacteristic
1052C23#41×D5311yescharacteristic
1053C23#41×D5311yescharacteristic
1054C23#41×D5311yescharacteristic
1055C23C2×#1171994511yescharacteristic
1056C23#1313326211yescharacteristic
1057C23#1313326211yescharacteristic
1058C23#1313326411yescharacteristic
1059C23#1313326511yescharacteristic
1060D4—10632no—
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—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—416no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—534no—
1103C2×C4—534no—
1104C2×C4—10632no—
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—1062no—
1120C2×C4—1062no—
1121C2×C4—1062no—
1122C2×C4—1062no—
1123C2×C4—1062no—
1124C2×C4—1062no—
1125C2×C4—1062no—
1126C2×C4—1062no—
1127C2×C4—1062no—
1128C2×C4—1062no—
1129C2×C4—21216no—
1130C2×C4—21216no—
1131C2×C4—2121no—
1132C2×C4—2121no—
1133C2×C4—2121no—
1134C2×C4—2121no—
1135C2×C4—2121no—
1136C2×C4—2121no—
1137C2×C4—2121no—
1138C2×C4—2121no—
1139C2×C4—2121no—
1140C2×C4—2121no—
1141C2×C4—2121no—
1142C2×C4—2121no—
1143C2×C4—2121no—
1144C2×C4—2121no—
1145C2×C4—2121no—
1146C2×C4—2121no—
1147C2×C4—2121no—
1148C2×C4—2121no—
1149C2×C4—2121no—
1150C2×C4—2121no—
1151C2×C4—2121no—
1152C2×C4—2121no—
1153C2×C4—2121no—
1154C2×C4C4×C22⋊D5314yescomplemented
1155C2×C4#1313318514yes—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—538no—
1172C22—1064no—
1173C22—1064no—
1174C22—1064no—
1175C22—1064no—
1176C22—1064no—
1177C22—1064no—
1178C22—1064no—
1179C22—1064no—
1180C22—1064no—
1181C22—1064no—
1182C22—1064no—
1183C22—1064no—
1184C22—1064no—
1185C22—1064no—
1186C22C2×C4⋊C4×D5311yescharacteristic
1187C22C4×D4×D5311yescharacteristic
1188C22C4×D4×D5311yescharacteristic
1189C22C4×D4×D5311yescharacteristic
1190C22C2×C4×C22⋊D5311yescharacteristic
1191C22#1681110211yescharacteristic
1192C22#1681110411yescharacteristic
1193C22#120×D5311yescharacteristic
1194C22C2×#1313318511yescharacteristic
1195C22C22⋊Q8×D5311yescharacteristic
1196C22C22⋊Q8×D5311yescharacteristic
1197C22#123×D5311yescharacteristic
1198C22#1681113011yescharacteristic
1199C22#1681113211yescharacteristic
1200C22#1681113211yescharacteristic
1201C22#1681118311yescharacteristic
1202C22#1681119611yescharacteristic
1203C22#1681121611yescharacteristic
1204C22#1681121911yescharacteristic
1205C22#1681125511yescharacteristic
1206C22#1681125511yescharacteristic
1207C22D4×C22⋊D5311yescharacteristic
1208C22D4×C22⋊D5311yescharacteristic
1209C22#1681127111yescharacteristic
1210C22#1681127411yescharacteristic
1211C22#1681127511yescharacteristic
1212C22#1681127811yescharacteristic
1213C22#1681128011yescharacteristic
1214C22#1681128311yescharacteristic
1215C22#1681128611yescharacteristic
1216C22Q8×C22⋊D5311yescharacteristic
1217C22#1681131811yescharacteristic
1218C22#1681132311yescharacteristic
1219C22#1681132711yescharacteristic
1220C22#1681132811yescharacteristic
1221C4—24no—
1222C4—24no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—81no—
1227C4—1064no—
1228C4—1064no—
1229C4—4241no—
1230C4—2122no—
1231C4—2122no—
1232C4—2122no—
1233C4—2122no—
1234C2—44no—
1235C2—1068no—
1236C2#385×D5311yescharacteristic
1237C2C4×#1313318511yescharacteristic
1238C2#2027738211yescharacteristic
1239C2#2027761311yescharacteristic
1240C2C4⋊C4×C22⋊D5311yescharacteristic
1241C2#2027772711yescharacteristic
1242C2#2027773411yescharacteristic
1243C2#2027802611yescharacteristic
1244C2#2027804811yescharacteristic
1245C2#2027807611yescharacteristic
1246C2#2027844711yescharacteristic
1247C2#2027844911yescharacteristic
1248C2#2027852111yescharacteristic
1249C2#2027852311yescharacteristic
1250C2#2028006011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53#14015
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D53C2semidirect
5. C2×#16810496C2semidirect
6. C2×#16810494C2semidirect
7. #20272979C2semidirect
8. #20272978C2semidirect
9. #20272960C2semidirect
10. #20272958C2semidirect
11. #20272950C2semidirect
12. #20272947C2semidirect
13. #20272936C2semidirect
14. #20272936C2semidirect
15. C2×C53×#385C2semidirect
39. #16810499C4semidirect
96. C22×C4×D53C2×C4semidirect
113. C2×#11719919D4semidirect
123. C2×C22⋊Dic53C2×C4semidirect
131. C2×#11719921C2×C4semidirect
146. #13133124C2×C4semidirect
147. #13133124C2×C4semidirect
167. C2×C4⋊C4×C53D4semidirect
173. C2×C22⋊C4×C53C2×C4semidirect
262. C2×C22⋊D53C4⋊C4semidirect
383. C23×C53C2×C4⋊C4semidirect
475. C2×C4×C53C4×D4semidirect
525. C2×Dic53C2×C4⋊C4semidirect
526. C2×Dic53C4×D4semidirect
595. C2×D53#385semidirect
615. C2×#385D53semidirect
687. C53#14015semidirect
760. C2×C4⋊C4C22⋊D53semidirect
784. C2×C22⋊C4C4×D53semidirect
1044. C23C4⋊C4×D53semidirect
1154. C2×C4C4×C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C22×C4⋊C4×D532
C2×#168104992
C2×#168104962
C2×#168104942
#202729792
#202729782
#202729602
#202729582
#202729502
#202729472
#202729362
C2×C53×#3852
#1401553