Finite Group Databasebeta

← #27315510

Subgroups — #27315510

Order 13568.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic
3C2×#16810544C211yesmaximal, characteristic, complemented
4C2×#16810543C211yesmaximal, characteristic, complemented
5C2×#16810497C211yesmaximal, characteristic
6C2×#16810494C211yesmaximal, characteristic
7#20272979C211yesmaximal, characteristic, complemented
8#20272978C211yesmaximal, characteristic, complemented
9#20272978C211yesmaximal, characteristic, complemented
10#20272967C211yesmaximal, characteristic, complemented
11#20272966C211yesmaximal, characteristic, complemented
12#20272936C211yesmaximal, characteristic
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×#1444C211yesmaximal, characteristic, complemented
16C23×Dic106C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133195—24no—
21C2×#13133195—24no—
22C2×#13133195—24no—
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C2×C4⋊C4×D53—24no—
32C2×C4⋊C4×D53—24no—
33C2×C4⋊C4×D53—24no—
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38#16810544—24no—
39#16810543—24no—
40#16810497—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
54C22×C4⋊C4×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C2×#95×C53C2211yescharacteristic
61C24×D53C2311yescharacteristic
62C22×Dic106—22no—
63C22×Dic106—22no—
64C22×Dic106—22no—
65C22×Dic106—22no—
66C22×Dic106—22no—
67C22×Dic106—41no—
68C22×Dic106—41no—
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C22×C4×D53—22no—
77C22×C4×D53—22no—
78C22×C4×D53—22no—
79C22×C4×D53—22no—
80C22×C4×D53—22no—
81C22×C4×D53—22no—
82C22×C4×D53—22no—
83C22×C4×D53—22no—
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—22no—
87C22×C4×D53—22no—
88C22×C4×D53—22no—
89C22×C4×D53—22no—
90C22×C4×D53—22no—
91C22×C4×D53—41no—
92C22×C4×D53—41no—
93C22×C4×D53—41no—
94C22×C4×D53—41no—
95C22×C4×D53D414yes—
96C22×C4×D53Q814yescomplemented
97#13133195—232no—
98C2×C4⋊Dic53—22no—
99C2×C4⋊Dic53—22no—
100C2×C4⋊Dic53—22no—
101C2×C4⋊Dic53—22no—
102C2×C4⋊Dic53—41no—
103C2×C4⋊Dic53D414yes—
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—22no—
113C2×#11719919—22no—
114C2×#11719919—22no—
115C2×#11719919—22no—
116C2×#11719919—22no—
117C2×#11719919—22no—
118C2×#11719919—22no—
119C2×#11719919—41no—
120C2×#11719919—41no—
121C2×#11719919D414yes—
122C4⋊C4×D53—232no—
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×#11719921D414yes—
132C2×#11719921D414yes—
133C2×#11719921Q814yescomplemented
134C2×#11719921Q814yescomplemented
135#13133124—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—22no—
145#13133124—22no—
146#13133124—41no—
147C23×C4×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×C4⋊C4×C53—22no—
158C2×C4⋊C4×C53—22no—
159C2×C4⋊C4×C53—22no—
160C2×C4⋊C4×C53—22no—
161C2×C4⋊C4×C53—22no—
162C2×C4⋊C4×C53—41no—
163#95×C53—22no—
164#95×C53—22no—
165#95×C53—22no—
166#95×C53—41no—
167C24×C53C2411yescharacteristic
168C23×D53—21no—
169C23×D53—21no—
170C23×D53—21no—
171C23×D53—21no—
172C23×D53—21no—
173C23×D53—21no—
174C23×D53—21no—
175C23×D53—21no—
176C23×D53C2×D412yes—
177C23×D53C2×D412yes—
178C23×D53C2×D412yes—
179C23×D53C2×Q812yes—
180C23×D53C2×Q812yes—
181C23×D53C2×Q812yes—
182C23×D53#4112yes—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
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×C53C2×D412yes—
224C22×C4×C53C2×D412yes—
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D412yes—
227C22×C4×C53C2×D412yes—
228C22×C4×C53C2×Q812yes—
229C22×C4×C53C2×Q812yes—
230C22×C4×C53C2×Q812yes—
231C22×C4×C53#4112yes—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
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×Dic53C2×D412yes—
271C22×Dic53C2×D412yes—
272C22×Dic53C2×D412yes—
273C22×Dic53C2×D412yes—
274C22×Dic53C2×D412yes—
275C22×Dic53C2×D412yes—
276C22×Dic53C2×D412yes—
277C22×Dic53C2×Q812yes—
278C22×Dic53C2×Q812yes—
279C22×Dic53C2×Q812yes—
280C22×Dic53#4112yes—
281C2×C4×D53—28no—
282C2×C4×D53—28no—
283C2×C4×D53—28no—
284C2×C4×D53—28no—
285C2×C4×D53—28no—
286C2×C4×D53—28no—
287C2×C4×D53—28no—
288C2×C4×D53—28no—
289C2×C4×D53—28no—
290C2×C4×D53—28no—
291C2×C4×D53—44no—
292C2×C4×D53—44no—
293C2×C4×D53—44no—
294C2×C4×D53—44no—
295C2×C4×D53—44no—
296C2×C4×D53—44no—
297C2×C4×D53—44no—
298C2×C4×D53—44no—
299C2×C4×D53—44no—
300C2×C4×D53—44no—
301C2×C4×D53—44no—
302C2×Dic106—28no—
303C2×Dic106—44no—
304C2×Dic106—44no—
305C2×Dic106—44no—
306C2×Dic106—44no—
307C2×Dic106—44no—
308C2×Dic106—44no—
309C4⋊C4×C53—28no—
310C4⋊C4×C53—28no—
311C4⋊C4×C53—44no—
312#11719921—28no—
313#11719921—28no—
314#11719921—28no—
315#11719921—28no—
316C4⋊Dic53—28no—
317C4⋊Dic53—44no—
318#11719919—28no—
319#11719919—28no—
320#11719919—28no—
321#11719919—28no—
322#11719919—44no—
323#11719919—44no—
324C23×C53C22×D411yescharacteristic
325C23×C53C22×D411yescharacteristic
326C23×C53C22×D411yescharacteristic
327C23×C53C22×D411yescharacteristic
328C23×C53C22×D411yescharacteristic
329C23×C53C22×Q811yescharacteristic
330C23×C53C22×Q811yescharacteristic
331C23×C53C22×Q811yescharacteristic
332C23×C53C2×#4111yescharacteristic
333C23×C53C2×#4111yescharacteristic
334C23×C53C2×#4111yescharacteristic
335C23×C53H(5,𝔽2)11yescharacteristic
336C23×C53H(5,𝔽2)11yescharacteristic
337C23×C532−1+411yescharacteristic
338C23×C532−1+411yescharacteristic
339C22×D53—22no—
340C22×D53—22no—
341C22×D53—22no—
342C22×D53—22no—
343C22×D53—22no—
344C22×D53—22no—
345C22×D53—22no—
346C22×D53—22no—
347C22×D53—22no—
348C22×D53—22no—
349C22×D53—22no—
350C22×D53—22no—
351C22×D53—22no—
352C22×D53—22no—
353C22×D53—22no—
354C22×D53—22no—
355C22×D53—22no—
356C22×D53—22no—
357C22×D53—22no—
358C22×D53—22no—
359C22×D53—22no—
360C22×D53—22no—
361C22×D53—22no—
362C22×D53—22no—
363C22×D53—22no—
364C22×D53—22no—
365C22×D53—22no—
366C22×D53—22no—
367C22×D53#12014yes—
368C22×D53C22⋊Q814yes—
369C22×D53C22⋊Q814yes—
370C22×D53C22⋊Q814yes—
371C22×D53C4⋊Q814yes—
372C22×D53C4⋊Q814yes—
373C22×D53C4⋊Q814yes—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—22no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53—22no—
386C2×C4×C53—22no—
387C2×C4×C53—22no—
388C2×C4×C53—22no—
389C2×C4×C53—22no—
390C2×C4×C53—22no—
391C2×C4×C53—22no—
392C2×C4×C53—22no—
393C2×C4×C53—22no—
394C2×C4×C53—22no—
395C2×C4×C53—22no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—41no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53C22⋊Q814yescomplemented
423C2×Dic53—22no—
424C2×Dic53—22no—
425C2×Dic53—22no—
426C2×Dic53—22no—
427C2×Dic53—22no—
428C2×Dic53—22no—
429C2×Dic53—22no—
430C2×Dic53—22no—
431C2×Dic53—22no—
432C2×Dic53—22no—
433C2×Dic53—22no—
434C2×Dic53—22no—
435C2×Dic53—22no—
436C2×Dic53—22no—
437C2×Dic53—22no—
438C2×Dic53—22no—
439C2×Dic53—22no—
440C2×Dic53—22no—
441C2×Dic53—22no—
442C2×Dic53—22no—
443C2×Dic53—22no—
444C2×Dic53—22no—
445C2×Dic53—22no—
446C2×Dic53—22no—
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—22no—
450C2×Dic53—41no—
451C2×Dic53—41no—
452C2×Dic53—41no—
453C2×Dic53—41no—
454C2×Dic53—41no—
455C2×Dic53—41no—
456C2×Dic53—41no—
457C2×Dic53—41no—
458C2×Dic53—41no—
459C2×Dic53—41no—
460C2×Dic53—41no—
461C2×Dic53—41no—
462C2×Dic53—41no—
463C2×Dic53—41no—
464C2×Dic53—41no—
465C2×Dic53—41no—
466C2×Dic53—41no—
467C2×Dic53—41no—
468C2×Dic53—41no—
469C2×Dic53—41no—
470C2×Dic53#12014yes—
471C2×Dic53C22⋊Q814yescomplemented
472C4×D53—232no—
473C4×D53—416no—
474C4×D53—416no—
475Dic106—416no—
476#14720—531nomaximal, Sylow
477C22×C53C2×#12011yescharacteristic
478C22×C53C2×#12011yescharacteristic
479C22×C53C2×C22⋊Q811yescharacteristic
480C22×C53C2×C22⋊Q811yescharacteristic
481C22×C53C2×C22⋊Q811yescharacteristic
482C22×C53C2×C22⋊Q811yescharacteristic
483C22×C53C2×C22⋊Q811yescharacteristic
484C22×C53#52511yescharacteristic
485C22×C53#52511yescharacteristic
486C22×C53#52511yescharacteristic
487C22×C53C2×C4⋊Q811yescharacteristic
488C22×C53C2×C4⋊Q811yescharacteristic
489C22×C53C2×C4⋊Q811yescharacteristic
490C22×C53#53411yescharacteristic
491C22×C53#53611yescharacteristic
492C22×C53#53911yescharacteristic
493C22×C53#53911yescharacteristic
494C22×C53#54411yescharacteristic
495C22×C53#54411yescharacteristic
496C22×C53D4211yescharacteristic
497C22×C53D4211yescharacteristic
498C22×C53D4211yescharacteristic
499C22×C53D4211yescharacteristic
500C22×C53#54711yescharacteristic
501C22×C53#54711yescharacteristic
502C22×C53#54711yescharacteristic
503C22×C53#54711yescharacteristic
504C22×C53D4×Q811yescharacteristic
505C22×C53D4×Q811yescharacteristic
506C22×C53D4×Q811yescharacteristic
507C22×C53D4×Q811yescharacteristic
508C22×C53#55411yescharacteristic
509C22×C53#55411yescharacteristic
510C22×C53#55411yescharacteristic
511C22×C53#55411yescharacteristic
512C2×D53—24no—
513C2×D53—24no—
514C2×D53—24no—
515C2×D53—24no—
516C2×D53—24no—
517C2×D53—24no—
518C2×D53—24no—
519C2×D53—24no—
520C2×D53—24no—
521C2×D53—24no—
522C2×D53—24no—
523C2×D53—24no—
524C2×D53—24no—
525C2×D53—24no—
526C2×D53#39518yescomplemented
527C4×C53—24no—
528C4×C53—42no—
529C4×C53—42no—
530C4×C53—42no—
531C4×C53—42no—
532C4×C53—42no—
533C4×C53—42no—
534Dic53—24no—
535Dic53—24no—
536Dic53—42no—
537Dic53—42no—
538Dic53—42no—
539Dic53—42no—
540Dic53—42no—
541C22×C22⋊Q8—531no—
542C23×C4⋊C4—531no—
543C2×#395—531no—
544C2×#395—531no—
545C2×#385—531no—
546C2×#385—531no—
547#1444—531no—
548#1444—531no—
549#1444—531no—
550#1444D5311yescharacteristic, complemented
551#1441—531no—
552#1441—531no—
553C22⋊#95—531no—
554C22⋊#95—531no—
555C22⋊#95—531no—
556C2×C53C2×#39511yescharacteristic
557C2×C53#240311yescharacteristic
558C2×C53#240611yescharacteristic
559C2×C53#243411yescharacteristic
560C2×C53#244011yescharacteristic
561C2×C53#244011yescharacteristic
562C2×C53#244011yescharacteristic
563C2×C53#244011yescharacteristic
564C2×C53#244911yescharacteristic
565C2×C53#244911yescharacteristic
566C2×C53#244911yescharacteristic
567C2×C53#244911yescharacteristic
568C2×C53#258311yescharacteristic
569C2×C53#262711yescharacteristic
570C2×C53#284811yescharacteristic
571D53—28no—
572C23×Q8—531no—
573C24×C4—531no—
574C24×C4—531no—
575C24×C4—531no—
576C2×C22⋊Q8—1064no—
577C2×C22⋊Q8—1064no—
578C2×C22⋊Q8—1064no—
579C22×C4⋊C4—531no—
580C22×C4⋊C4—531no—
581C22×C4⋊C4—531no—
582C22×C4⋊C4—531no—
583C22×C4⋊C4—531no—
584C22×C4⋊C4—531no—
585C22×C4⋊C4—531no—
586C22×C4⋊C4—531no—
587C22×C4⋊C4—1064no—
588C22×C4⋊C4—1064no—
589C22×C4⋊C4—1064no—
590C22×C4⋊C4C2×D5311yescharacteristic
591C22×C4⋊C4C2×D5311yescharacteristic
592C22×C4⋊C4C2×D5311yescharacteristic
593C22×C22⋊C4—531no—
594C22×C22⋊C4—531no—
595C22×C22⋊C4—531no—
596C22×C22⋊C4—531no—
597#395—1064no—
598#395—1064no—
599#385—1064no—
600#385—1064no—
601C2×#95—531no—
602C2×#95—531no—
603C2×#95—531no—
604C2×#95—531no—
605C2×#95—531no—
606C2×#95—531no—
607C2×#95—531no—
608C2×#95—531no—
609C2×#95—531no—
610C2×#95—531no—
611C2×#95—531no—
612C2×#95—531no—
613C2×#95C2×D5311yescharacteristic
614C2×#95C2×D5311yescharacteristic
615C2×#95C2×D5311yescharacteristic
616C2×#95C2×D5311yescharacteristic
617C53#1472011yescharacteristic, complemented, Sylow
618C25—531no—
619C22×Q8—1062no—
620C22×Q8—1062no—
621C22×Q8—1062no—
622C22×Q8—1062no—
623C22×Q8—1062no—
624C22×Q8—2121no—
625C22×Q8—2121no—
626C23×C4—531no—
627C23×C4—531no—
628C23×C4—531no—
629C23×C4—531no—
630C23×C4—531no—
631C23×C4—531no—
632C23×C4—531no—
633C23×C4—534no—
634C23×C4—534no—
635C23×C4—1062no—
636C23×C4—1062no—
637C23×C4—1062no—
638C23×C4—1062no—
639C23×C4—1062no—
640C23×C4—1062no—
641C23×C4—1062no—
642C23×C4—1062no—
643C23×C4—1062no—
644C23×C4—1062no—
645C23×C4—1062no—
646C23×C4—1062no—
647C23×C4—1062no—
648C23×C4—1062no—
649C23×C4—1062no—
650C23×C4—2121no—
651C23×C4—2121no—
652C23×C4—2121no—
653C23×C4—2121no—
654C23×C4C22×D5311yescharacteristic
655C23×C4C22×D5311yescharacteristic
656C23×C4C22×D5311yescharacteristic
657C23×C4C22×D5311yescharacteristic
658C23×C4C22×D5311yescharacteristic
659C23×C4C22×D5311yescharacteristic
660C23×C4C22×D5311yescharacteristic
661C22⋊Q8—10632no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—534no—
672C2×C4⋊C4—534no—
673C2×C4⋊C4—10632no—
674C2×C4⋊C4—1062no—
675C2×C4⋊C4—1062no—
676C2×C4⋊C4—1062no—
677C2×C4⋊C4—1062no—
678C2×C4⋊C4—1062no—
679C2×C4⋊C4—1062no—
680C2×C4⋊C4—1062no—
681C2×C4⋊C4—1062no—
682C2×C4⋊C4—1062no—
683C2×C4⋊C4—1062no—
684C2×C4⋊C4—1062no—
685C2×C4⋊C4—1062no—
686C2×C4⋊C4—1062no—
687C2×C4⋊C4—1062no—
688C2×C4⋊C4—1062no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—1062no—
691C2×C4⋊C4—1062no—
692C2×C4⋊C4—1062no—
693C2×C4⋊C4—2121no—
694C2×C4⋊C4—2121no—
695C2×C4⋊C4—2121no—
696C2×C22⋊C4—534no—
697C2×C22⋊C4—534no—
698C2×C22⋊C4—534no—
699C2×C22⋊C4—534no—
700C2×C22⋊C4—1062no—
701C2×C22⋊C4—1062no—
702C2×C22⋊C4—1062no—
703C2×C22⋊C4—1062no—
704C2×C22⋊C4—1062no—
705C2×C22⋊C4—1062no—
706C2×C22⋊C4—1062no—
707C2×C22⋊C4—1062no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—41no—
712#95—1062no—
713#95—1062no—
714#95—1062no—
715#95—1062no—
716#95—1062no—
717#95—1062no—
718#95—1062no—
719#95—1062no—
720#95—1062no—
721#95—1062no—
722#95—1062no—
723#95—2121no—
724C24—532no—
725C24—532no—
726C24—532no—
727C24—532no—
728C24—532no—
729C24—532no—
730C24—532no—
731C24—1061no—
732C24—1061no—
733C24—1061no—
734C24—1061no—
735C24—1061no—
736C24—1061no—
737C24—1061no—
738C24—1061no—
739C24C23×D5311yescharacteristic
740C2×Q8—1068no—
741C2×Q8—2124no—
742C2×Q8—2124no—
743C2×Q8—2124no—
744C2×Q8—2124no—
745C2×Q8—2124no—
746C2×Q8—2124no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—532no—
788C22×C4—532no—
789C22×C4—532no—
790C22×C4—532no—
791C22×C4—532no—
792C22×C4—532no—
793C22×C4—532no—
794C22×C4—532no—
795C22×C4—532no—
796C22×C4—532no—
797C22×C4—532no—
798C22×C4—1068no—
799C22×C4—1068no—
800C22×C4—1068no—
801C22×C4—1068no—
802C22×C4—1068no—
803C22×C4—1068no—
804C22×C4—1068no—
805C22×C4—1068no—
806C22×C4—1068no—
807C22×C4—1061no—
808C22×C4—1061no—
809C22×C4—1061no—
810C22×C4—1061no—
811C22×C4—1061no—
812C22×C4—1061no—
813C22×C4—1061no—
814C22×C4—1061no—
815C22×C4—1068no—
816C22×C4—1061no—
817C22×C4—1061no—
818C22×C4—1061no—
819C22×C4—1061no—
820C22×C4—1061no—
821C22×C4—1061no—
822C22×C4—1061no—
823C22×C4—1061no—
824C22×C4—1061no—
825C22×C4—1061no—
826C22×C4—1061no—
827C22×C4—1061no—
828C22×C4—1061no—
829C22×C4—1061no—
830C22×C4—1061no—
831C22×C4—1061no—
832C22×C4—1061no—
833C22×C4—1061no—
834C22×C4—1061no—
835C22×C4—1061no—
836C22×C4—1061no—
837C22×C4—1061no—
838C22×C4—1061no—
839C22×C4—1061no—
840C22×C4—1061no—
841C22×C4—1061no—
842C22×C4—1061no—
843C22×C4—1061no—
844C22×C4—1061no—
845C22×C4—1061no—
846C22×C4—2124no—
847C22×C4—2124no—
848C22×C4—2124no—
849C22×C4—2124no—
850C22×C4—2124no—
851C22×C4—2124no—
852C22×C4—2124no—
853C22×C4—2124no—
854C22×C4—2124no—
855C22×C4—2124no—
856C22×C4—2124no—
857C22×C4#1171994512yes—
858C22×C4D4×D5312yes—
859C22×C4D4×D5312yes—
860C22×C4D4×D5312yes—
861C22×C4D4×D5312yes—
862C22×C4D4×D5312yes—
863C22×C4Q8×D5312yes—
864C22×C4Q8×D5312yes—
865C22×C4Q8×D5312yes—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—44no—
869C4⋊C4—1068no—
870C4⋊C4—1068no—
871C4⋊C4—1068no—
872C4⋊C4—1068no—
873C4⋊C4—1068no—
874C4⋊C4—2124no—
875C4⋊C4—2124no—
876C4⋊C4—2124no—
877C22⋊C4—1068no—
878C22⋊C4—1068no—
879C22⋊C4—1068no—
880C22⋊C4—1068no—
881C23—534no—
882C23—534no—
883C23—534no—
884C23—534no—
885C23—534no—
886C23—534no—
887C23—534no—
888C23—1062no—
889C23—1062no—
890C23—1062no—
891C23—1062no—
892C23—1062no—
893C23—1062no—
894C23—1062no—
895C23—1062no—
896C23—1062no—
897C23—1062no—
898C23—1062no—
899C23—1062no—
900C23—1062no—
901C23—1062no—
902C23—1062no—
903C23—1062no—
904C23—1062no—
905C23—1062no—
906C23—1062no—
907C23—1062no—
908C23—1062no—
909C23—1062no—
910C23—1062no—
911C23—1062no—
912C23—1062no—
913C23—1062no—
914C23—1062no—
915C23—1062no—
916C23C2×D4×D5311yescharacteristic
917C23C2×D4×D5311yescharacteristic
918C23C2×D4×D5311yescharacteristic
919C23C2×D4×D5311yescharacteristic
920C23C2×D4×D5311yescharacteristic
921C23C2×Q8×D5311yescharacteristic
922C23C2×Q8×D5311yescharacteristic
923C23C2×Q8×D5311yescharacteristic
924C23#41×D5311yescharacteristic
925C23#41×D5311yescharacteristic
926C23C2×#1171994511yescharacteristic
927C23#1313326211yescharacteristic
928C23#1313326311yescharacteristic
929C23#1313326411yescharacteristic
930C23#1313326511yescharacteristic
931Q8—21216no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—534no—
981C2×C4—534no—
982C2×C4—10632no—
983C2×C4—1062no—
984C2×C4—1062no—
985C2×C4—1062no—
986C2×C4—1062no—
987C2×C4—1062no—
988C2×C4—1062no—
989C2×C4—1062no—
990C2×C4—1062no—
991C2×C4—1062no—
992C2×C4—1062no—
993C2×C4—1062no—
994C2×C4—1062no—
995C2×C4—1062no—
996C2×C4—1062no—
997C2×C4—1062no—
998C2×C4—1062no—
999C2×C4—1062no—
1000C2×C4—1062no—
1001C2×C4—1062no—
1002C2×C4—1062no—
1003C2×C4—1062no—
1004C2×C4—1062no—
1005C2×C4—1062no—
1006C2×C4—1062no—
1007C2×C4—1062no—
1008C2×C4—1062no—
1009C2×C4—1062no—
1010C2×C4—21216no—
1011C2×C4—21216no—
1012C2×C4—2121no—
1013C2×C4—2121no—
1014C2×C4—2121no—
1015C2×C4—2121no—
1016C2×C4—2121no—
1017C2×C4—2121no—
1018C2×C4—2121no—
1019C2×C4—2121no—
1020C2×C4—2121no—
1021C2×C4—2121no—
1022C2×C4—2121no—
1023C2×C4—2121no—
1024C2×C4—2121no—
1025C2×C4—2121no—
1026C2×C4—2121no—
1027C2×C4—2121no—
1028C2×C4—2121no—
1029C2×C4—2121no—
1030C2×C4—2121no—
1031C2×C4—2121no—
1032C2×C4#1313319514yescomplemented
1033C22—538no—
1034C22—1064no—
1035C22—1064no—
1036C22—1064no—
1037C22—1064no—
1038C22—1064no—
1039C22—1064no—
1040C22—1064no—
1041C22—1064no—
1042C22—1064no—
1043C22—1064no—
1044C22—1064no—
1045C22—1064no—
1046C22—1064no—
1047C22—1064no—
1048C22#120×D5311yescharacteristic
1049C22#120×D5311yescharacteristic
1050C22C22⋊Q8×D5311yescharacteristic
1051C22C22⋊Q8×D5311yescharacteristic
1052C22C22⋊Q8×D5311yescharacteristic
1053C22C22⋊Q8×D5311yescharacteristic
1054C22C2×#1313319511yescharacteristic
1055C22#1681113111yescharacteristic
1056C22#1681113211yescharacteristic
1057C22#1681113211yescharacteristic
1058C22C4⋊Q8×D5311yescharacteristic
1059C22C4⋊Q8×D5311yescharacteristic
1060C22C4⋊Q8×D5311yescharacteristic
1061C22#1681118111yescharacteristic
1062C22#1681119611yescharacteristic
1063C22#1681121611yescharacteristic
1064C22#1681122111yescharacteristic
1065C22#1681125011yescharacteristic
1066C22#1681125311yescharacteristic
1067C22#1681125511yescharacteristic
1068C22#1681125711yescharacteristic
1069C22#1681125711yescharacteristic
1070C22#1681125811yescharacteristic
1071C22#1681127111yescharacteristic
1072C22#1681127411yescharacteristic
1073C22#1681127511yescharacteristic
1074C22#1681127811yescharacteristic
1075C22#1681128611yescharacteristic
1076C22#1681128611yescharacteristic
1077C22#1681128811yescharacteristic
1078C22#1681128811yescharacteristic
1079C22#1681132711yescharacteristic
1080C22#1681132811yescharacteristic
1081C22#1681132911yescharacteristic
1082C22#1681133311yescharacteristic
1083C4—24no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—1064no—
1091C4—1064no—
1092C4—2122no—
1093C4—2122no—
1094C4—2122no—
1095C4—2122no—
1096C4—2122no—
1097C2—1068no—
1098C2#395×D5311yescharacteristic
1099C2#2027802411yescharacteristic
1100C2#2027804811yescharacteristic
1101C2#2027835411yescharacteristic
1102C2#2027841011yescharacteristic
1103C2#2027841211yescharacteristic
1104C2#2027841911yescharacteristic
1105C2#2027842011yescharacteristic
1106C2#2027851911yescharacteristic
1107C2#2027852311yescharacteristic
1108C2#2027852711yescharacteristic
1109C2#2027853111yescharacteristic
1110C2#2028009311yescharacteristic
1111C2#2028053311yescharacteristic
1112C2#2028300111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC53×#1444C2
prime radicalC24×D53C23
hypercenter#1444D53
hypocenterC53#14720
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#16810544C2semidirect
4. C2×#16810543C2semidirect
7. #20272979C2semidirect
8. #20272978C2semidirect
9. #20272978C2semidirect
10. #20272967C2semidirect
11. #20272966C2semidirect
15. C53×#1444C2semidirect
96. C22×C4×D53Q8semidirect
133. C2×#11719921Q8semidirect
134. C2×#11719921Q8semidirect
422. C2×C4×C53C22⋊Q8semidirect
471. C2×Dic53C22⋊Q8semidirect
526. C2×D53#395semidirect
550. #1444D53semidirect
617. C53#14720semidirect
1032. C2×C4#13133195semidirect

Maximal subgroups

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

subgroupindex
C22×#131331952
C22×C4⋊C4×D532
C2×#168105442
C2×#168105432
C2×#168104972
C2×#168104942
#202729792
#202729782
#202729672
#202729662
#202729362
C53×#14442
#1472053