Finite Group Databasebeta

← #27306969

Subgroups — #27306969

Order 13568.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1230 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×#16810495C211yesmaximal, characteristic, complemented
8C2×#16810494C211yesmaximal, characteristic, complemented
9C2×#16810492C211yesmaximal, characteristic, complemented
10#20272961C211yesmaximal, characteristic, complemented
11#20272959C211yesmaximal, characteristic, complemented
12#20272958C211yesmaximal, characteristic, complemented
13#20272943C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, 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×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40#16810523—24no—
41#16810523C418yescomplemented
42#16810520—24no—
43#16810498—24no—
44#16810497—24no—
45#16810495—24no—
46#16810494—24no—
47#16810492—24no—
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C22×C22⋊C4×C53C2211yescharacteristic
58C22×C22⋊C4×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
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×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—22no—
73C23×Dic53—22no—
74C23×Dic53—22no—
75C23×Dic53—41no—
76C23×Dic53—41no—
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—22no—
87C22×C4×D53—22no—
88C22×C4×D53—22no—
89C22×C4×D53—41no—
90C22×C4×D53—41no—
91#13133177—232no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—22no—
94C2×C4⋊Dic53—22no—
95C2×C4⋊Dic53—22no—
96C2×C4⋊Dic53—22no—
97C2×C4⋊Dic53—41no—
98C2×#11719919—22no—
99C2×#11719919—22no—
100C2×#11719919—22no—
101C2×#11719919—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×#11719919—41no—
114C2×#11719919C2×C414yescomplemented
115C2×#11719919D414yes—
116C2×C22⋊Dic53—22no—
117C2×C22⋊Dic53—22no—
118C2×C22⋊Dic53—22no—
119C2×C22⋊Dic53—22no—
120C2×C22⋊Dic53—41no—
121C2×C22⋊Dic53C2×C414yescomplemented
122C2×#11719921—22no—
123C2×#11719921—22no—
124C2×#11719921—22no—
125C2×#11719921—22no—
126C2×#11719921—22no—
127C2×#11719921—22no—
128C2×#11719921—22no—
129C2×#11719921—22no—
130C2×#11719921—22no—
131C2×#11719921—22no—
132C2×#11719921—22no—
133C2×#11719921—41no—
134C2×#11719921—41no—
135C2×#11719921C2×C414yescomplemented
136C2×#11719921C2×C414yescomplemented
137C2×C4×Dic53—22no—
138C2×C4×Dic53—22no—
139C2×C4×Dic53—22no—
140C2×C4×Dic53—22no—
141C2×C4×Dic53—22no—
142C2×C4×Dic53—22no—
143C2×C4×Dic53—22no—
144C2×C4×Dic53C2×C414yescomplemented
145C2×C4×Dic53D414yes—
146#13133124—22no—
147#13133124—22no—
148#13133124—22no—
149#13133124—22no—
150#13133124—22no—
151#13133124D414yescomplemented
152#13133124D414yescomplemented
153C25×C53C2311yescharacteristic
154C23×C4×C53C2311yescharacteristic
155C23×C4×C53C2311yescharacteristic
156C23×C4×C53C2311yescharacteristic
157C23×C4×C53C2311yescharacteristic
158C23×C4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C2×C4⋊C4×C53—22no—
161C2×C4⋊C4×C53—22no—
162C2×C4⋊C4×C53—41no—
163C2×C22⋊C4×C53—22no—
164C2×C22⋊C4×C53—22no—
165C2×C22⋊C4×C53—22no—
166C2×C22⋊C4×C53—22no—
167C2×C22⋊C4×C53—22no—
168C2×C22⋊C4×C53—22no—
169C2×C22⋊C4×C53—22no—
170C2×C22⋊C4×C53—41no—
171C2×C22⋊C4×C53C2×C414yescomplemented
172#95×C53—22no—
173#95×C53—22no—
174#95×C53—22no—
175C24×C53—21no—
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×C53C22×C412yes—
188C24×C53C2×D412yes—
189C24×C53C2×Q812yes—
190C24×C53C2411yescharacteristic
191C23×D53—21no—
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×D53—21no—
201C23×D53—21no—
202C23×D53—21no—
203C23×D53C22×C412yes—
204C23×D53C2×D412yes—
205C23×D53C2×Q812yes—
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×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C22×C412yes—
243C22×C4×C53C2×D412yes—
244C22×C4×C53C2×D412yes—
245C22×C4×C53C2×D412yes—
246C22×C4×C53C2×D412yes—
247C22×C4×C53#4112yes—
248C2×C22⋊D53—28no—
249C2×C22⋊D53—28no—
250C2×C22⋊D53—28no—
251C2×C22⋊D53—28no—
252C2×C22⋊D53—28no—
253C2×C22⋊D53—28no—
254C2×C22⋊D53C4⋊C4116yescomplemented
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—28no—
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—44no—
290C22×Dic53—44no—
291C22×Dic53—44no—
292C22×Dic53—44no—
293C22×Dic53—44no—
294C22×Dic53—44no—
295C22×Dic53C22×C412yes—
296C22×Dic53C22×C412yes—
297C22×Dic53C22×C412yes—
298C22×Dic53C2×D412yes—
299C22×Dic53C2×D412yes—
300C22×Dic53C2×D412yes—
301C22×Dic53C2×D412yes—
302C22×Dic53C2×D412yes—
303C22×Dic53C2×D412yes—
304C22×Dic53C2×D412yes—
305C22×Dic53C2×D412yes—
306C22×Dic53C2×D412yes—
307C22×Dic53C2×Q812yes—
308C22×Dic53#4112yes—
309C22×Dic53#4112yes—
310C22×Dic53#4112yes—
311C2×C4×D53—28no—
312C2×C4×D53—44no—
313C2×C4×D53—44no—
314C2×C4×D53—44no—
315C2×C4×D53—44no—
316C2×C4×D53—44no—
317C2×C4×D53—44no—
318C4⋊C4×C53—44no—
319C22⋊C4×C53—28no—
320C22⋊C4×C53—28no—
321C22⋊C4×C53—44no—
322C22⋊Dic53—28no—
323C22⋊Dic53—44no—
324#11719921—28no—
325#11719921—28no—
326#11719921—28no—
327#11719921—44no—
328#11719921—44no—
329C4⋊Dic53—44no—
330C4⋊Dic53—44no—
331#11719919—28no—
332#11719919—28no—
333#11719919—44no—
334#11719919—44no—
335#11719919—44no—
336#11719919—44no—
337C4×Dic53—28no—
338C4×Dic53—28no—
339C4×Dic53—44no—
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—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
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×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53C2×C4⋊C414yes—
375C23×C53C23×C411yescharacteristic
376C23×C53C22×D411yescharacteristic
377C23×C53C22×D411yescharacteristic
378C23×C53C22×D411yescharacteristic
379C23×C53C22×D411yescharacteristic
380C23×C53C22×D411yescharacteristic
381C23×C53C22×Q811yescharacteristic
382C23×C53C2×#4111yescharacteristic
383C23×C53C2×#4111yescharacteristic
384C23×C53C2×#4111yescharacteristic
385C23×C53C2×#4111yescharacteristic
386C23×C53H(5,𝔽2)11yescharacteristic
387C23×C53H(5,𝔽2)11yescharacteristic
388C23×C532−1+411yescharacteristic
389C23×C532−1+411yescharacteristic
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—22no—
402C22×D53—22no—
403C22×D53—22no—
404C22×D53—22no—
405C22×D53—22no—
406C22×D53—22no—
407C22×D53—22no—
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×D53—41no—
418C22×D53—41no—
419C22×D53—41no—
420C22×D53—41no—
421C22×D53—41no—
422C22×D53—41no—
423C22×D53—41no—
424C22×D53C2×C4⋊C414yes—
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—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×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×C53C4×D414yescomplemented
467C22⋊D53—232no—
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—22no—
488C2×Dic53—22no—
489C2×Dic53—416no—
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×Dic53—41no—
503C2×Dic53—41no—
504C2×Dic53—41no—
505C2×Dic53—41no—
506C2×Dic53—41no—
507C2×Dic53—41no—
508C2×Dic53—41no—
509C2×Dic53C2×C4⋊C414yes—
510C2×Dic53C4×D414yes—
511C2×Dic53C4×D414yes—
512C2×Dic53C4×D414yescomplemented
513C2×Dic53#12014yes—
514C2×Dic53C22⋊Q814yes—
515C2×Dic53C22⋊Q814yes—
516C2×Dic53#12314yes—
517C2×Dic53#12714yes—
518C4×D53—416no—
519#13977—531nomaximal, Sylow
520C22×C53—24no—
521C22×C53—24no—
522C22×C53—24no—
523C22×C53—42no—
524C22×C53—42no—
525C22×C53—42no—
526C22×C53—42no—
527C22×C53—42no—
528C22×C53—42no—
529C22×C53—42no—
530C22×C53—42no—
531C22×C53—42no—
532C22×C53—42no—
533C22×C53—42no—
534C22×C53—42no—
535C22×C53C22×C4⋊C411yescharacteristic
536C22×C53C2×C4×D411yescharacteristic
537C22×C53C2×C4×D411yescharacteristic
538C22×C53C2×C4×D411yescharacteristic
539C22×C53C2×C4×D411yescharacteristic
540C22×C53#52011yescharacteristic
541C22×C53#52011yescharacteristic
542C22×C53C2×#12011yescharacteristic
543C22×C53C2×C22⋊Q811yescharacteristic
544C22×C53C2×C22⋊Q811yescharacteristic
545C22×C53C2×#12311yescharacteristic
546C22×C53C2×#12711yescharacteristic
547C22×C53#53211yescharacteristic
548C22×C53#53211yescharacteristic
549C22×C53#53211yescharacteristic
550C22×C53#53511yescharacteristic
551C22×C53#53611yescharacteristic
552C22×C53#54211yescharacteristic
553C22×C53#54211yescharacteristic
554C22×C53D4211yescharacteristic
555C22×C53D4211yescharacteristic
556C22×C53D4211yescharacteristic
557C22×C53D4211yescharacteristic
558C22×C53#54711yescharacteristic
559C22×C53#54711yescharacteristic
560C22×C53#54711yescharacteristic
561C22×C53#54711yescharacteristic
562C22×C53#54811yescharacteristic
563C22×C53#54811yescharacteristic
564C22×C53D4×Q811yescharacteristic
565C22×C53D4×Q811yescharacteristic
566C22×C53#55311yescharacteristic
567C22×C53#55311yescharacteristic
568C22×C53#55411yescharacteristic
569C22×C53#55411yescharacteristic
570C2×D53—24no—
571C2×D53—24no—
572C2×D53—24no—
573C2×D53—42no—
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—
585C4×C53—24no—
586C4×C53—42no—
587C4×C53—42no—
588C4×C53—42no—
589C4×C53—42no—
590C4×C53—81no—
591Dic53—24no—
592Dic53—24no—
593Dic53—42no—
594Dic53—42no—
595Dic53—42no—
596Dic53—81no—
597Dic53#38518yescomplemented
598C22×C4×D4—531no—
599C2×#390—531no—
600C2×#390—531no—
601C2×#389—531no—
602C2×#385—531no—
603C2×#385—531no—
604C2×#385—531no—
605C2×#385—531no—
606C2×#384—531no—
607#1439—531no—
608#1439—531no—
609#1439—531no—
610#1439D5311yescharacteristic, complemented
611C4⋊#95—531no—
612C4×#95—531no—
613C2×C53—44no—
614C2×C53C2×#38511yescharacteristic
615C2×C53C4×#12711yescharacteristic
616C2×C53#232611yescharacteristic
617C2×C53D4×C4⋊C411yescharacteristic
618C2×C53D4×C4⋊C411yescharacteristic
619C2×C53#236111yescharacteristic
620C2×C53#236111yescharacteristic
621C2×C53#242211yescharacteristic
622C2×C53#242211yescharacteristic
623C2×C53#243211yescharacteristic
624C2×C53#243311yescharacteristic
625C2×C53#245211yescharacteristic
626C2×C53#245211yescharacteristic
627C2×C53#254211yescharacteristic
628C2×C53#256611yescharacteristic
629D53—44no—
630C23×D4—531no—
631C24×C4—531no—
632C24×C4—531no—
633C2×C4×D4—1064no—
634C2×C4×D4—1064no—
635C2×C4×D4—1064no—
636C22×C4⋊C4—531no—
637C22×C4⋊C4—531no—
638C22×C4⋊C4—531no—
639C22×C4⋊C4—531no—
640C22×C4⋊C4—531no—
641C22×C4⋊C4—531no—
642C22×C4⋊C4—531no—
643C22×C4⋊C4—531no—
644C22×C4⋊C4C2×D5311yescharacteristic
645C22×C22⋊C4—531no—
646C22×C22⋊C4—531no—
647C22×C22⋊C4—531no—
648C22×C22⋊C4—531no—
649C22×C22⋊C4—531no—
650C22×C22⋊C4—531no—
651C22×C22⋊C4—531no—
652C22×C22⋊C4C2×D5311yescharacteristic
653C22×C22⋊C4C2×D5311yescharacteristic
654C22×C22⋊C4C2×D5311yescharacteristic
655C22×C42—531no—
656C22×C42—531no—
657C22×C42—531no—
658#390—538no—
659#390—1064no—
660#389—1064no—
661#385—1064no—
662#385—1064no—
663#385—1064no—
664#385—1064no—
665#384—1064no—
666C2×#95—531no—
667C2×#95—531no—
668C2×#95—531no—
669C2×#95—531no—
670C2×#95—531no—
671C2×#95—531no—
672C2×#95—531no—
673C2×#95C2×D5311yescharacteristic
674C2×#95C2×D5311yescharacteristic
675C2×#95C2×D5311yescharacteristic
676C53#1397711yescharacteristic, complemented, Sylow
677C25—531no—
678C25C22×D5311yescharacteristic
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—531no—
693C23×C4—1062no—
694C23×C4—1062no—
695C23×C4—1062no—
696C23×C4—1062no—
697C23×C4—1062no—
698C23×C4—1062no—
699C23×C4—1062no—
700C23×C4—1062no—
701C23×C4—1062no—
702C23×C4—1062no—
703C23×C4—2121no—
704C23×C4—2121no—
705C23×C4—2121no—
706C23×C4—2121no—
707C23×C4C22×D5311yescharacteristic
708C23×C4C22×D5311yescharacteristic
709C23×C4C22×D5311yescharacteristic
710C23×C4C22×D5311yescharacteristic
711C23×C4C22×D5311yescharacteristic
712C23×C4C22×D5311yescharacteristic
713C4×D4—10632no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—41no—
717C2×C4⋊C4—534no—
718C2×C4⋊C4—534no—
719C2×C4⋊C4—1062no—
720C2×C4⋊C4—1062no—
721C2×C4⋊C4—1062no—
722C2×C4⋊C4—1062no—
723C2×C4⋊C4—1062no—
724C2×C4⋊C4—1062no—
725C2×C4⋊C4—1062no—
726C2×C4⋊C4—1062no—
727C2×C4⋊C4—1062no—
728C2×C4⋊C4—1062no—
729C2×C4⋊C4—1062no—
730C2×C4⋊C4—1062no—
731C2×C4⋊C4—1062no—
732C2×C4⋊C4—1062no—
733C2×C4⋊C4—1062no—
734C2×C4⋊C4—1062no—
735C2×C4⋊C4—1062no—
736C2×C4⋊C4—1062no—
737C2×C4⋊C4—1062no—
738C2×C4⋊C4—2121no—
739C2×C4⋊C4—2121no—
740C2×C4⋊C4—2121no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—534no—
750C2×C22⋊C4—534no—
751C2×C22⋊C4—534no—
752C2×C22⋊C4—1062no—
753C2×C22⋊C4—1062no—
754C2×C22⋊C4—1062no—
755C2×C22⋊C4—1062no—
756C2×C22⋊C4—1062no—
757C2×C22⋊C4—1062no—
758C2×C22⋊C4—1062no—
759C2×C22⋊C4—1062no—
760C2×C22⋊C4—1062no—
761C2×C22⋊C4—1062no—
762C2×C22⋊C4—1062no—
763C2×C22⋊C4—1062no—
764C2×C22⋊C4—1062no—
765C2×C22⋊C4—1062no—
766C2×C22⋊C4—1062no—
767C2×C22⋊C4—2121no—
768C2×C22⋊C4—2121no—
769C2×C22⋊C4—2121no—
770C2×C22⋊C4C4×D5314yescomplemented
771C2×C42—534no—
772C2×C42—534no—
773C2×C42—1062no—
774C2×C42—1062no—
775C2×C42—1062no—
776C2×C42—1062no—
777C2×C42—1062no—
778C2×C42—1062no—
779C2×C42—1062no—
780#95—22no—
781#95—22no—
782#95—22no—
783#95—534no—
784#95—534no—
785#95—1062no—
786#95—1062no—
787#95—1062no—
788#95—1062no—
789#95—1062no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—532no—
803C24—532no—
804C24—532no—
805C24—1061no—
806C24—1061no—
807C24—1061no—
808C24—1061no—
809C24—1061no—
810C24—1061no—
811C24—1061no—
812C24—1061no—
813C24—1061no—
814C24—1061no—
815C24—1061no—
816C24—1061no—
817C24C2×C4×D5312yes—
818C24D4×D5312yes—
819C24Q8×D5312yes—
820C24C23×D5311yescharacteristic
821C2×D4—5316no—
822C2×D4—1068no—
823C2×D4—1068no—
824C2×D4—1068no—
825C2×D4—1068no—
826C2×D4—1068no—
827C2×D4—1068no—
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—21no—
861C22×C4—21no—
862C22×C4—21no—
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—532no—
873C22×C4—532no—
874C22×C4—532no—
875C22×C4—532no—
876C22×C4—532no—
877C22×C4—532no—
878C22×C4—532no—
879C22×C4—1068no—
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—1068no—
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—1061no—
909C22×C4—1061no—
910C22×C4—1061no—
911C22×C4—1061no—
912C22×C4—1061no—
913C22×C4—1061no—
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×C4C2×C4×D5312yes—
927C22×C4C2×C4×D5312yes—
928C22×C4D4×D5312yes—
929C22×C4D4×D5312yes—
930C22×C4D4×D5312yes—
931C22×C4D4×D5312yes—
932C22×C4#1171994712yes—
933C4⋊C4—44no—
934C4⋊C4—1068no—
935C4⋊C4—1068no—
936C4⋊C4—2124no—
937C4⋊C4—2124no—
938C4⋊C4—2124no—
939C4⋊C4—2124no—
940C4⋊C4—2124no—
941C4⋊C4—2124no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—1068no—
946C22⋊C4—1068no—
947C22⋊C4—1068no—
948C22⋊C4—1068no—
949C22⋊C4—2124no—
950C22⋊C4—2124no—
951C22⋊C4—2124no—
952C42—1068no—
953C42—1068no—
954C42—2124no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—534no—
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—2121no—
1009C23—2121no—
1010C23—2121no—
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—
1024C23C4⋊C4×D5314yes—
1025C23C22×C4×D5311yescharacteristic
1026C23C2×D4×D5311yescharacteristic
1027C23C2×D4×D5311yescharacteristic
1028C23C2×D4×D5311yescharacteristic
1029C23C2×D4×D5311yescharacteristic
1030C23C2×D4×D5311yescharacteristic
1031C23C2×Q8×D5311yescharacteristic
1032C23#41×D5311yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23C2×#1171994711yescharacteristic
1036C23#1313326211yescharacteristic
1037C23#1313326311yescharacteristic
1038C23#1313326411yescharacteristic
1039C23#1313326411yescharacteristic
1040D4—10632no—
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—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—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
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—534no—
1083C2×C4—534no—
1084C2×C4—534no—
1085C2×C4—534no—
1086C2×C4—534no—
1087C2×C4—534no—
1088C2×C4—534no—
1089C2×C4—534no—
1090C2×C4—534no—
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—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—21216no—
1113C2×C4—21216no—
1114C2×C4—2121no—
1115C2×C4—2121no—
1116C2×C4—2121no—
1117C2×C4—2121no—
1118C2×C4—2121no—
1119C2×C4—2121no—
1120C2×C4—2121no—
1121C2×C4—2121no—
1122C2×C4—2121no—
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#1313317714yescomplemented
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—1064no—
1150C22—1064no—
1151C22—1064no—
1152C22—2122no—
1153C22—2122no—
1154C22—2122no—
1155C22—2122no—
1156C22—2122no—
1157C22—2122no—
1158C22—2122no—
1159C22—2122no—
1160C22—2122no—
1161C22—2122no—
1162C22—2122no—
1163C22—2122no—
1164C22C2×C4⋊C4×D5311yescharacteristic
1165C22C4×D4×D5311yescharacteristic
1166C22C4×D4×D5311yescharacteristic
1167C22C4×D4×D5311yescharacteristic
1168C22C2×#1313317711yescharacteristic
1169C22#1681110211yescharacteristic
1170C22#1681110311yescharacteristic
1171C22#120×D5311yescharacteristic
1172C22C22⋊Q8×D5311yescharacteristic
1173C22C22⋊Q8×D5311yescharacteristic
1174C22#123×D5311yescharacteristic
1175C22#127×D5311yescharacteristic
1176C22#1681116811yescharacteristic
1177C22#1681116811yescharacteristic
1178C22#1681117211yescharacteristic
1179C22#1681118911yescharacteristic
1180C22#1681119511yescharacteristic
1181C22#1681123711yescharacteristic
1182C22#1681123911yescharacteristic
1183C22#1681125511yescharacteristic
1184C22#1681125511yescharacteristic
1185C22#1681125711yescharacteristic
1186C22#1681125711yescharacteristic
1187C22#1681127111yescharacteristic
1188C22#1681127111yescharacteristic
1189C22#1681127111yescharacteristic
1190C22#1681127311yescharacteristic
1191C22#1681127911yescharacteristic
1192C22#1681128111yescharacteristic
1193C22#1681128611yescharacteristic
1194C22#1681128611yescharacteristic
1195C22#1681131611yescharacteristic
1196C22#1681132411yescharacteristic
1197C22#1681132711yescharacteristic
1198C22#1681133111yescharacteristic
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—81no—
1205C4—538no—
1206C4—1064no—
1207C4—1064no—
1208C4—4241no—
1209C4—2122no—
1210C4—2122no—
1211C4—2122no—
1212C2—44no—
1213C2—2124no—
1214C2#385×D5311yescharacteristic
1215C2#2027727911yescharacteristic
1216C2#2027742411yescharacteristic
1217C2#2027761111yescharacteristic
1218C2#2027761311yescharacteristic
1219C2#2027772611yescharacteristic
1220C2#2027772811yescharacteristic
1221C2#2027822211yescharacteristic
1222C2#2027822411yescharacteristic
1223C2#2027833811yescharacteristic
1224C2#2027834711yescharacteristic
1225C2#2027855811yescharacteristic
1226C2#2027856011yescharacteristic
1227C2#2027966311yescharacteristic
1228C2#2027991011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1439C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1439D53
hypocenterC53#13977
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×#16810495C2semidirect
8. C2×#16810494C2semidirect
9. C2×#16810492C2semidirect
10. #20272961C2semidirect
11. #20272959C2semidirect
12. #20272958C2semidirect
13. #20272943C2semidirect
14. #95×Dic53C2semidirect
15. C53×#1439C2semidirect
41. #16810523C4semidirect
114. C2×#11719919C2×C4semidirect
121. C2×C22⋊Dic53C2×C4semidirect
135. C2×#11719921C2×C4semidirect
136. C2×#11719921C2×C4semidirect
144. C2×C4×Dic53C2×C4semidirect
151. #13133124D4semidirect
152. #13133124D4semidirect
171. C2×C22⋊C4×C53C2×C4semidirect
254. C2×C22⋊D53C4⋊C4semidirect
466. C2×C4×C53C4×D4semidirect
512. C2×Dic53C4×D4semidirect
597. Dic53#385semidirect
610. #1439D53semidirect
676. C53#13977semidirect
770. C2×C22⋊C4C4×D53semidirect
1133. 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×#168104952
C2×#168104942
C2×#168104922
#202729612
#202729592
#202729582
#202729432
#95×Dic532
C53×#14392
#1397753