Finite Group Databasebeta

← #27307482

Subgroups — #27307482

Order 13568.

2474 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×#16810520C211yesmaximal, characteristic, complemented
5C2×#16810498C211yesmaximal, characteristic, complemented
6C2×#16810497C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
8#20272961C211yesmaximal, characteristic, complemented
9#20272958C211yesmaximal, characteristic, complemented
10#20272957C211yesmaximal, characteristic, complemented
11#20272943C211yesmaximal, characteristic, complemented
12#20272943C211yesmaximal, characteristic, complemented
13#20272937C211yesmaximal, characteristic, complemented
14#20272936C211yesmaximal, characteristic, complemented
15C53×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C2×#13133177—24no—
20C2×#13133177—24no—
21C2×#13133177—24no—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38#16810523—24no—
39#16810523C418yescomplemented
40#16810520—24no—
41#16810498—24no—
42#16810497—24no—
43C4⋊C4×Dic53—24no—
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×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⋊D53D414yes—
67C22×C22⋊D53Q814yes—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—22no—
73C23×Dic53—41no—
74C23×Dic53—41no—
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—22no—
87C22×C4×D53—41no—
88C22×C4×D53—41no—
89#13133177—232no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—22no—
94C2×C4⋊Dic53—41no—
95C2×C4⋊Dic53D414yescomplemented
96C2×#11719919—22no—
97C2×#11719919—22no—
98C2×#11719919—22no—
99C2×#11719919—22no—
100C2×#11719919—22no—
101C2×#11719919—22no—
102C2×#11719919—22no—
103C2×#11719919—22no—
104C2×#11719919—22no—
105C2×#11719919—41no—
106C2×#11719919C2×C414yescomplemented
107C2×#11719919D414yes—
108C2×C22⋊Dic53—22no—
109C2×C22⋊Dic53—22no—
110C2×C22⋊Dic53—41no—
111C2×C22⋊Dic53—41no—
112C2×C22⋊Dic53—41no—
113C2×C22⋊Dic53C2×C414yescomplemented
114C2×#11719921—22no—
115C2×#11719921—22no—
116C2×#11719921—22no—
117C2×#11719921—22no—
118C2×#11719921—22no—
119C2×#11719921—22no—
120C2×#11719921—22no—
121C2×#11719921—22no—
122C2×#11719921—22no—
123C2×#11719921—41no—
124C2×#11719921—41no—
125C2×#11719921—41no—
126C2×#11719921—41no—
127C2×#11719921C2×C414yescomplemented
128C2×#11719921C2×C414yescomplemented
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×Dic53C2×C414yescomplemented
137C2×C4×Dic53D414yes—
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#13133124—41no—
147C25×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C2×C4⋊C4×C53—22no—
155C2×C4⋊C4×C53—22no—
156C2×C4⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—22no—
159C2×C22⋊C4×C53—22no—
160C2×C22⋊C4×C53—22no—
161C2×C22⋊C4×C53—22no—
162C2×C22⋊C4×C53—22no—
163C2×C22⋊C4×C53—22no—
164C2×C22⋊C4×C53—41no—
165C2×C22⋊C4×C53C2×C414yescomplemented
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×C53C2×D412yes—
183C24×C53C2×Q812yes—
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×D53C2×D412yes—
199C23×D53C2×Q812yes—
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×C53C22×C412yes—
236C22×C4×C53C22×C412yes—
237C22×C4×C53C2×D412yes—
238C22×C4×C53C2×D412yes—
239C22×C4×C53C2×D412yes—
240C22×C4×C53#4112yes—
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⋊D53C4⋊C4116yescomplemented
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—28no—
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—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—21no—
284C22×Dic53—21no—
285C22×Dic53—44no—
286C22×Dic53—44no—
287C22×Dic53—44no—
288C22×Dic53—44no—
289C22×Dic53—44no—
290C22×Dic53—44no—
291C22×Dic53C22×C412yes—
292C22×Dic53C22×C412yes—
293C22×Dic53C22×C412yes—
294C22×Dic53C2×D412yes—
295C22×Dic53C2×D412yes—
296C22×Dic53C2×D412yes—
297C22×Dic53C2×D412yes—
298C22×Dic53C2×D412yes—
299C22×Dic53C2×D412yes—
300C22×Dic53C2×D412yes—
301C22×Dic53C2×Q812yes—
302C22×Dic53#4112yes—
303C22×Dic53#4112yes—
304C22×Dic53#4112yes—
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—
312C4⋊C4×C53—28no—
313C22⋊C4×C53—28no—
314C22⋊C4×C53—28no—
315C22⋊C4×C53—44no—
316C22⋊Dic53—44no—
317C22⋊Dic53—44no—
318#11719921—28no—
319#11719921—28no—
320#11719921—44no—
321#11719921—44no—
322#11719921—44no—
323C4⋊Dic53—28no—
324C4⋊Dic53—44no—
325#11719919—28no—
326#11719919—28no—
327#11719919—44no—
328#11719919—44no—
329C4×Dic53—28no—
330C4×Dic53—28no—
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×C4⋊C414yes—
367C23×C53C23×C411yescharacteristic
368C23×C53C22×D411yescharacteristic
369C23×C53C22×D411yescharacteristic
370C23×C53C22×D411yescharacteristic
371C23×C53C22×D411yescharacteristic
372C23×C53C22×Q811yescharacteristic
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×C4⋊C414yes—
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—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—41no—
440C2×C4×C53—41no—
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×C53—41no—
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—416no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
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×Dic53—41no—
501C2×Dic53—41no—
502C2×Dic53C2×C4⋊C414yes—
503C2×Dic53C4×D414yes—
504C2×Dic53C4×D414yes—
505C2×Dic53#12014yes—
506C2×Dic53#12114yes—
507C2×Dic53C22⋊Q814yes—
508C2×Dic53C22⋊Q814yes—
509C2×Dic53#12314yes—
510C4×D53—416no—
511#14018—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×C4⋊C411yescharacteristic
528C22×C53C2×C4×D411yescharacteristic
529C22×C53C2×C4×D411yescharacteristic
530C22×C53C2×C4×D411yescharacteristic
531C22×C53C4×#4111yescharacteristic
532C22×C53#51811yescharacteristic
533C22×C53#52011yescharacteristic
534C22×C53C2×#12011yescharacteristic
535C22×C53C2×#12111yescharacteristic
536C22×C53C2×C22⋊Q811yescharacteristic
537C22×C53C2×C22⋊Q811yescharacteristic
538C22×C53C2×#12311yescharacteristic
539C22×C53#52511yescharacteristic
540C22×C53#52911yescharacteristic
541C22×C53#53211yescharacteristic
542C22×C53#53511yescharacteristic
543C22×C53#53711yescharacteristic
544C22×C53#54011yescharacteristic
545C22×C53#54211yescharacteristic
546C22×C53D4211yescharacteristic
547C22×C53D4211yescharacteristic
548C22×C53#54611yescharacteristic
549C22×C53#54611yescharacteristic
550C22×C53#54611yescharacteristic
551C22×C53#54711yescharacteristic
552C22×C53#54811yescharacteristic
553C22×C53D4×Q811yescharacteristic
554C22×C53#55011yescharacteristic
555C22×C53#55011yescharacteristic
556C22×C53#55411yescharacteristic
557C22×C53#55411yescharacteristic
558C22×C53#55411yescharacteristic
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—42no—
579C4×C53—42no—
580C4×C53—42no—
581C4×C53—42no—
582C4×C53—81no—
583Dic53—24no—
584Dic53—42no—
585Dic53—42no—
586Dic53—42no—
587Dic53—42no—
588Dic53—81no—
589Dic53#38518yescomplemented
590C22×C4×D4—531no—
591C2×#390—531no—
592C2×#390—531no—
593C2×#389—531no—
594C2×#385—531no—
595C2×#385—531no—
596C2×C4×C4⋊C4—531no—
597#1439—531no—
598#1439—531no—
599#1439—531no—
600#1439D5311yescharacteristic, complemented
601C4⋊#95—531no—
602C4⋊#95—531no—
603C22⋊#95—531no—
604C22⋊#95—531no—
605C2×C53—44no—
606C2×C53C2×#38511yescharacteristic
607C2×C53C4×#12111yescharacteristic
608C2×C53#232411yescharacteristic
609C2×C53D4×C4⋊C411yescharacteristic
610C2×C53#234911yescharacteristic
611C2×C53#236611yescharacteristic
612C2×C53#236711yescharacteristic
613C2×C53#240711yescharacteristic
614C2×C53#240811yescharacteristic
615C2×C53#244511yescharacteristic
616C2×C53#244711yescharacteristic
617C2×C53#245211yescharacteristic
618C2×C53#245411yescharacteristic
619C2×C53#253811yescharacteristic
620C2×C53#258011yescharacteristic
621D53—44no—
622C23×D4—531no—
623C24×C4—531no—
624C24×C4—531no—
625C2×C4×D4—1064no—
626C2×C4×D4—1064no—
627C2×C4×D4—1064no—
628C22×C4⋊C4—531no—
629C22×C4⋊C4—531no—
630C22×C4⋊C4—531no—
631C22×C4⋊C4—531no—
632C22×C4⋊C4—531no—
633C22×C4⋊C4—531no—
634C22×C4⋊C4C2×D5311yescharacteristic
635C22×C22⋊C4—531no—
636C22×C22⋊C4—531no—
637C22×C22⋊C4—531no—
638C22×C22⋊C4—531no—
639C22×C22⋊C4—531no—
640C22×C22⋊C4—531no—
641C22×C22⋊C4—531no—
642C22×C22⋊C4C2×D5311yescharacteristic
643C22×C22⋊C4C2×D5311yescharacteristic
644C22×C22⋊C4C2×D5311yescharacteristic
645C22×C42—531no—
646C22×C42—531no—
647C22×C42—531no—
648#390—538no—
649#390—1064no—
650#389—1064no—
651#385—1064no—
652#385—1064no—
653C4×C4⋊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#1401811yescharacteristic, 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—1062no—
684C23×C4—1062no—
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—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—534no—
708C2×C4⋊C4—534no—
709C2×C4⋊C4—534no—
710C2×C4⋊C4—1062no—
711C2×C4⋊C4—1062no—
712C2×C4⋊C4—1062no—
713C2×C4⋊C4—1062no—
714C2×C4⋊C4—1062no—
715C2×C4⋊C4—1062no—
716C2×C4⋊C4—1062no—
717C2×C4⋊C4—1062no—
718C2×C4⋊C4—1062no—
719C2×C4⋊C4—1062no—
720C2×C4⋊C4—1062no—
721C2×C4⋊C4—1062no—
722C2×C4⋊C4—1062no—
723C2×C4⋊C4—2121no—
724C2×C4⋊C4—2121no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—534no—
734C2×C22⋊C4—534no—
735C2×C22⋊C4—534no—
736C2×C22⋊C4—1062no—
737C2×C22⋊C4—1062no—
738C2×C22⋊C4—1062no—
739C2×C22⋊C4—1062no—
740C2×C22⋊C4—1062no—
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—2121no—
748C2×C22⋊C4—2121no—
749C2×C22⋊C4—2121no—
750C2×C22⋊C4—2121no—
751C2×C22⋊C4—2121no—
752C2×C22⋊C4—2121no—
753C2×C22⋊C4—2121no—
754C2×C22⋊C4C4×D5314yescomplemented
755C2×C42—534no—
756C2×C42—534no—
757C2×C42—1062no—
758C2×C42—1062no—
759C2×C42—1062no—
760C2×C42—1062no—
761C2×C42—1062no—
762C2×C42—1062no—
763C2×C42—1062no—
764#95—22no—
765#95—22no—
766#95—41no—
767#95—1062no—
768#95—1062no—
769#95—1062no—
770#95—1062no—
771#95—1062no—
772#95—1062no—
773#95—2121no—
774#95—2121no—
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—
804C24D4×D5312yes—
805C24Q8×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—21no—
847C22×C4—21no—
848C22×C4—21no—
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—1068no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1068no—
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—1061no—
899C22×C4—1061no—
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×C4—2124no—
910C22×C4—2124no—
911C22×C4—2124no—
912C22×C4C2×C4×D5312yes—
913C22×C4C2×C4×D5312yes—
914C22×C4D4×D5312yes—
915C22×C4D4×D5312yes—
916C22×C4D4×D5312yes—
917C22×C4#1171994712yes—
918C22×C4#1171994712yes—
919C4⋊C4—28no—
920C4⋊C4—1068no—
921C4⋊C4—1068no—
922C4⋊C4—1068no—
923C4⋊C4—2124no—
924C4⋊C4—2124no—
925C4⋊C4—2124no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—44no—
929C22⋊C4—1068no—
930C22⋊C4—1068no—
931C22⋊C4—2124no—
932C22⋊C4—2124no—
933C22⋊C4—2124no—
934C22⋊C4—2124no—
935C22⋊C4—2124no—
936C42—1068no—
937C42—1068no—
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—
1008C23C4⋊C4×D5314yes—
1009C23C22×C4×D5311yescharacteristic
1010C23C2×D4×D5311yescharacteristic
1011C23C2×D4×D5311yescharacteristic
1012C23C2×D4×D5311yescharacteristic
1013C23C2×D4×D5311yescharacteristic
1014C23C2×Q8×D5311yescharacteristic
1015C23#41×D5311yescharacteristic
1016C23#41×D5311yescharacteristic
1017C23#41×D5311yescharacteristic
1018C23C2×#1171994711yescharacteristic
1019C23C2×#1171994711yescharacteristic
1020C23#1313326211yescharacteristic
1021C23#1313326311yescharacteristic
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—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
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—41no—
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—1062no—
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—21216no—
1093C2×C4—21216no—
1094C2×C4—2121no—
1095C2×C4—2121no—
1096C2×C4—2121no—
1097C2×C4—2121no—
1098C2×C4—2121no—
1099C2×C4—2121no—
1100C2×C4—2121no—
1101C2×C4—2121no—
1102C2×C4—2121no—
1103C2×C4—2121no—
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×C4—2121no—
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×C4⋊C4×D5311yescharacteristic
1149C22C4×D4×D5311yescharacteristic
1150C22C4×D4×D5311yescharacteristic
1151C22C2×#1313317711yescharacteristic
1152C22C4×#1171994711yescharacteristic
1153C22#1681109511yescharacteristic
1154C22#1681110311yescharacteristic
1155C22#120×D5311yescharacteristic
1156C22#121×D5311yescharacteristic
1157C22C22⋊Q8×D5311yescharacteristic
1158C22C22⋊Q8×D5311yescharacteristic
1159C22#123×D5311yescharacteristic
1160C22#1681112911yescharacteristic
1161C22#1681115011yescharacteristic
1162C22#1681116811yescharacteristic
1163C22#1681119111yescharacteristic
1164C22#1681120011yescharacteristic
1165C22#1681122511yescharacteristic
1166C22#1681123911yescharacteristic
1167C22#1681125711yescharacteristic
1168C22#1681125711yescharacteristic
1169C22#1681126011yescharacteristic
1170C22#1681126511yescharacteristic
1171C22#1681126511yescharacteristic
1172C22#1681127311yescharacteristic
1173C22#1681127911yescharacteristic
1174C22#1681128611yescharacteristic
1175C22#1681129111yescharacteristic
1176C22#1681129311yescharacteristic
1177C22#1681132711yescharacteristic
1178C22#1681133111yescharacteristic
1179C22#1681133111yescharacteristic
1180C22#1681134011yescharacteristic
1181C22#1681135511yescharacteristic
1182C22#1681135511yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—538no—
1190C4—1064no—
1191C4—4241no—
1192C4—2122no—
1193C4—2122no—
1194C4—2122no—
1195C4—2122no—
1196C2—44no—
1197C2—2124no—
1198C2#385×D5311yescharacteristic
1199C2#2027722511yescharacteristic
1200C2#2027740311yescharacteristic
1201C2#2027761111yescharacteristic
1202C2#2027762111yescharacteristic
1203C2#2027777611yescharacteristic
1204C2#2027778911yescharacteristic
1205C2#2027805311yescharacteristic
1206C2#2027806611yescharacteristic
1207C2#2027847311yescharacteristic
1208C2#2027849711yescharacteristic
1209C2#2027855811yescharacteristic
1210C2#2027858211yescharacteristic
1211C2#2027963211yescharacteristic
1212C2#2028006811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1439C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1439D53
hypocenterC53#14018
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#16810520C2semidirect
5. C2×#16810498C2semidirect
6. C2×#16810497C2semidirect
7. C2×C4⋊C4×Dic53C2semidirect
8. #20272961C2semidirect
9. #20272958C2semidirect
10. #20272957C2semidirect
11. #20272943C2semidirect
12. #20272943C2semidirect
13. #20272937C2semidirect
14. #20272936C2semidirect
15. C53×#1439C2semidirect
39. #16810523C4semidirect
95. C2×C4⋊Dic53D4semidirect
106. C2×#11719919C2×C4semidirect
113. C2×C22⋊Dic53C2×C4semidirect
127. C2×#11719921C2×C4semidirect
128. C2×#11719921C2×C4semidirect
136. C2×C4×Dic53C2×C4semidirect
165. C2×C22⋊C4×C53C2×C4semidirect
248. C2×C22⋊D53C4⋊C4semidirect
458. C2×C4×C53C4×D4semidirect
589. Dic53#385semidirect
600. #1439D53semidirect
666. C53#14018semidirect
754. 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×#168105202
C2×#168104982
C2×#168104972
C2×C4⋊C4×Dic532
#202729612
#202729582
#202729572
#202729432
#202729372
#202729362
C53×#14392
#1401853